hotson dirac's equation and the sea of negative energy, 44p

I S S U E 4 3 , 2 0 0 2 • I n f i n i t e E n e r g y 1

PrefaceDirac’s Equation has profound implications both for sci-ence and for the search for new energy. If we continue touse the wrong model (and the Standard Model is pro-foundly wrong) we will continue to get confusing resultsthat are difficult to replicate.

The enclosure shows the nature of the energetic, non-stationary aether that Einstein missed, that Dirac’s equa-tion demonstrates, and that Heisenberg and othersdestroyed when they dismantled this equation. It furthersuggests that special conditions, catalysis, and energyavailable to a plasma may cause the synthesis, rather thanthe release, of free neutrons, causing transmutations andthe release of energy via beta decay.

The treatment of Dirac’s equation is a lesson in the waymodern science works (or rather doesn’t). This treatment hasmore recently been paralleled by the treatment of Reich,Pons and Fleischmann, Halton Arp, and others. But I thinkif one had to point to a single place where science went pro-foundly and permanently off the track, it would be 1934 andthe emasculation of Dirac’s equation. This crisis at the heartof science caused a chronic “hardening of the paradigm” andscience thereby lost the ability to self-correct.

AbstractDirac’s wave equation is a relativistic generalization of theSchrödinger wave equation. In 1934 this brilliantly success-ful equation was shorn of half of its solutions by a question-able bit of mathematical slight-of-hand. Because it was“politically correct,” this bit of juggling became the accept-ed interpretation. However, recent developments haveshown the very basis of this mathematical trick to be invalid,in that it would involve massive violations of conservation.A reevaluation is therefore warranted.

The Schrödinger wave equation has been said to “containmost of physics and all of chemistry.” Since Dirac’s equationis a relativistic generalization of this already generally appli-cable wave equation, in formulating it Dirac expected thatits solutions would describe “everything that waves.” Sinceall matter and energy evolve as waves, Dirac thought hisequation would be a unitary “theory of everything.”However, the discovery of several new particles and peer crit-icism resulting in the truncation of the equation frustratedthis expectation, and it is generally known at present as“Dirac’s equation of the electron.”

Dirac’s complete equation, however, describes a quan-tum spinor field, which has as solutions four differentkinds of electron: electrons and positrons of positiveenergy, and electrons and positrons of negative energy.Such supposedly “fundamental” entities as quarks andgluons have no comparable wave equations; yet theywave. Therefore they cannot be truly fundamental. Sincein principle the Dirac field comprises “everything that

waves,” the equation therefore predicts that the entirephysical universe can be made from these four kinds ofelectron. This study validates this prediction: all matterand all forces are shown to be necessary combinationsand applications of just these four kinds of electron, ful-filling Dirac’s unitary expectation.

In addition, direct applications of Dirac’s equation pro-vide simple, logical, and natural models of the electromag-

Dirac’s Equation and the Sea of Negative Energy _____________________________ PART 1 _____________________________

D.L. Hotson*

About the AuthorThe Hotson “family business” is English literature. Mr. Hotson’sfather and uncle had Harvard Ph.D.s in the subject, and his lateuncle was a famous Shakespeare scholar. Mr. Hotson, however,always intended a career in physics. Unfortunately, he could notresist asking awkward questions. His professors taught that con-servation of mass-energy is the never-violated, rock-solid founda-tion of all physics. In “pair production” a photon of at least 1.022MeV “creates” an electron-positron pair, each with 0.511 MeV ofrest energy, with any excess being the momentum of the “creat-ed” pair. So supposedly the conservation books balance.

But the “created” electron and positron both have spin (angu-lar momentum) energy of h/4π. By any assumption as to the sizeof electron or positron, this is far more energy than that suppliedby the photon at “creation.”

“Isn’t angular momentum energy?” he asked a professor.“Of course it is. This half-integer spin angular momentum is

the energy needed by the electron to set up a stable standing wavearound the proton. Thus it is responsible for the Pauli exclusionprinciple, hence for the extension and stability of all matter. Youcould say it is the sole cause of the periodic table of elements.”

“Then where does all this energy come from? How can the ‘cre-ated’ electron have something like sixteen times more energy thanthe photon that supposedly ‘created’ it? Isn’t this a huge violation ofyour never-violated rock-solid foundation of all physics?”

“We regard spin angular momentum as an ‘inherent property’of electron and positron, not as a violation of conservation.”

“But if it’s real energy, where does it come from? Does theEnergy Fairy step in and proclaim a miracle every time ‘creation’is invoked, billions of times a second? How does this fit yournever-violated conservation?”

“‘Inherent property’ means we don’t talk about it, and youwon’t either if you want to pass this course.”

Well, this answer sounded to him like the Stephen Leacockaphorism: “‘Shut up,’ he explained.” Later Mr. Hotson was takenaside and told that his “attitude” was disrupting the class, andthat further, with his “attitude,” there was no chance in hell of hiscompleting a graduate program in physics, so “save your money.”He ended up at the Sorbonne studying French literature, and laterbecame a professional land surveyor.

However, he has retained a lifelong interest in the “awkwardquestions” of physics, and with Dirac’s Equation has foundsome answers.

* P.O. Box 789, Green Mountain Falls, CO 80819Email: [email protected]

2 I S S U E 4 3 , 2 0 0 2 • I n f i n i t e E n e r g y

addition to these there was Anderson’s newly discoveredpositron, the photon which was now widely considered tobe a particle, and the gravitational and electromagneticfields. Thus in 1932 the number of entities recognized by sci-ence totaled no more than seven. The unifying progress ofscience had over time reduced the number of entities frominfinity to less than one hundred to a mere seven. (The actu-al low water mark had been reached a decade or so earlier,before the discovery of the positron and the neutron. Theneutron was then supposed to be an electron/proton fusion,and the photon wasn’t yet considered a particle, so the enti-ties then recognized by science totaled merely four.)

So far so good. It seemed obvious that this process of uni-fication would continue, and reduce the number of entitiesstill further. Great scientists such as Einstein dedicated theirentire lives to unification. Nonetheless around that time thesimplifying trend reversed, and by the end of the century,the accepted Standard Model (SM) of particle physics calledfor around thirty-six “fundamental” particles, most with anantiparticle, and each with its very own “field”: again almostone hundred separate entities. What happened? William ofOckham’s test would seem to indicate that science took avery wrong turn sometime around 1932.

Well, perhaps the universe doesn’t shave with Ockham’srazor—maybe it really is that complicated. But the evidencepoints the other way. The universe exhibits very conspicuouseconomy, even parsimony, of means. The DNA molecule, thebasis of life, is arguably the most complex entity known. Yet itscode is written using just four components, the four baseswhose combinations comprise the genetic code. It can beshown by complexity theory that three bases would not pro-vide sufficient complexity for this code, and five would beredundant. Yet any number of components could have beenused. However, only four are necessary, only four are used.Further, all stable matter, including all of the chemical ele-ments and their compounds such as DNA, is built of just threecomponents—electron, proton, and neutron. Again only threecomponents are necessary, only three are used. Consider thisas a sequence, from more complex to less complex: four com-ponents are both necessary and sufficient to build DNA, threecomponents are both necessary and sufficient to build all sta-ble matter. Does this suggest that to build these three compo-nents would require thirty-six “fundamental” components, andnearly one hundred entities? Surely not.

Going by the above sequence, we should instead considerhow many components are necessary to build electron, pro-ton, and neutron. And here the computer shows the way.

Computer science shows that operations of unlimited com-plexity can be built up from just two binary components,yes/no, on/off, plus/minus. Since two binary components areall that is necessary, by Ockham’s razor and the universe’sdemonstrated parsimony, two binary components should besufficient. This is not to suggest that the universe “is” a com-puter (although several respected scientists, such as David

netic field, the “photon,” the “strong nuclear” force, the Ψwave, inertia, and gravitation. It provides direct-contactphysical models that agree with experiment, as opposed tothe purely mathematical (and unworkable) models so muchin vogue. The phase-entanglement feature of quantummechanics, demonstrated by Bell’s Inequality and the proofsthereof, requires that our reality be non-local. This seems tobanish causality. However, Dirac’s equation provides causal,direct contact models which are nonetheless non-local.

Great theorists from Bohr to Feynman have asserted that“no one understands quantum mechanics.” The student iswarned for the sake of her sanity not to try to understand“how it can be like that,” but to take all its strangeness onfaith (Feynman, 1985). Like the White Queen in Alice, quan-tum physicists must “believe six impossible things beforebreakfast.” However, merely with the single assumption thatthe Dirac equation means what it says, these features are intu-itively, understandably resolved: all the “strange” or “odd”features of quantum mechanics follow simply, logically, nat-urally, and necessarily.

IntroductionThe principle criteria for a successful scientific theory wouldseem to be the following:

Criterion 1. Simplicity. It should embody as few “entities” aspossible, preferably only one. (This is William of Ockham’stest, known as “Ockham’s Razor”: “Multiplicity ought not tobe posited without necessity.”)

Criterion 2. It should have few, preferably no, adjustableparameters. (Also known as fudge factors.)

Criterion 3. It should be mathematically consistent.

Criterion 4. It should satisfy all of the known data, includingdata unexplained, anomalous, or dismissed as “coincidence”according to previous theories.

Criterion 5. It should obey causality: every effect should havea proximate cause, with no “action at a distance.”

Criterion 6. It should be falsifiable, making testable predic-tions.

The first of these, Ockham’s razor, can be used as a generaltest of the soundness of a theory, as the general trend of suc-cessful science is from disorder and complexity toward orderand simplicity. Before the advent of modern chemistry,although matter was thought to consist of the four “elements”earth, air, fire, and water, these could combine in unlimitedways. Thus contemporary thought allowed for an infinitenumber of “entities” with no valid rules for their combinations.

By 1890 science had shown that all matter consists ofordered combinations of ninety-two “irreducible” elements,or atoms. The “gravitational field” was another entity, andMaxwell had unified electricity and magnetism, so the “elec-tromagnetic field” was another. Therefore, by this time theprogress of science had reduced this infinite number of enti-ties to less than one hundred.

The discovery of radioactivity showed that these “ele-ments” were not irreducible after all, and by 1932 afterChadwick’s discovery of the neutron it was found that allstable matter consists of ordered and understood combina-tions of just three entities—electron, proton, and neutron. In

William of Ockham’s test would seem

to indicate that science took a very

wrong turn sometime around 1932.


result, “renormalization” is invoked: the positive infinity is,in effect, divided by a negative infinity. Since the result ofthis mathematically forbidden procedure is indeterminate,the desired value of 0.511 MeV is then simply entered byhand. This admitted fudge would not work if we didn’talready know the answers.

Feynman, who originated the “renormalization” process(with Schwinger and Tomonaga), himself called it a “. . .shellgame. . .Having to resort to such hocus-pocus has preventedus from proving that the theory of quantum electrodynam-ics is mathematically self-consistent. . .[renormalization] iswhat I would call a dippy process!” (Feynman, 1985) Askedfor what he had won the Nobel Prize, Feynman replied, “Forsweeping them [the infinities] under the rug.” (Gleick, 1992)

On the face of it, if the results of calculations of ordinaryvalues come out to be infinite, in case after case, shouldn’twe take this as a gentle hint that something basic must bewrong, and start looking for a better model? Instead, like thefreshman that looks up the correct values in the back of thebook, we fudge the answers. A student who pulled such astunt would flunk. The three famous professors who pulledit shared a Nobel Prize.

This grant of a Nobel Prize for what is, after all, nothingbut an elaborate fudge, testifies to the malaise of current the-ory. This incredible award legitimized the fudge, which as aresult is now an accepted, even rewarded scientific proce-dure. With this, physics lost the ability to self-correct, as afudge can always be concocted to bring any datum, howev-er discordant, into at least apparent accord with the currentparadigm. As a direct consequence, most of the nearly onehundred entities required by the SM are unobserved. Theproblem with the medieval debate over how many angelscould dance on the head of a pin was that angels were unob-served entities, and so could have any desired properties.Each of these classes of unobserved entities in the SMamounts to a fudge or patch applied to save a failing theory.So long as these fudged entities are made unobservable inprinciple, like the angel or the quark, they are safe fromexperimental falsification.

The SM also has a major problem with mass. GordonKane (1995) argues that the Standard Model should reallybe called the “Standard Theory” because it is nearly per-fect—just a few minor flaws. He then goes on to mentionone of them (p. 117):

In its basic form, the Standard Theory is a theory formassless particles. All the leptons, quarks, and bosonsmust be particles without mass, or the mathematicalconsistency of the theory is destroyed. The photonand the gluons indeed have no mass, but the othersdo. Why not just insert a mass for them in the equa-tions? Unfortunately, in a quantum theory all aspectsof physics are so highly interconnected that if themasses are just put in, then calculations start to giveinfinite values for many ordinary measurements. (Inthe language of the last section of Chapter 4, the the-ory is then not renormalizable.)

In other words, the Standard Theory is a beautiful theo-ry—but it applies to some other universe, one in which all par-ticles oblige the theorists by being massless. Unfortunately,in our universe, the stubborn particles perversely persist inhaving mass, while stubborn theorists persist in clinging to

Deutsch [1997] think it is), merely that computer logic and thelogic of building a universe appear, necessarily, to be parallel.

As an exercise, consider for a moment in broad terms howa computer of unlimited capacity might go about modelingthe physical universe, using merely its two entities. The ulti-mate aim must be the unlimited complexity and flexibilityof the unlimited numbers of chemical compounds. But thefirst thing a binary computer must do is construct the three. Threeis the builder. A triangle is the simplest figure to enclosespace, a stool needs three legs, a universe needs three dimen-sions. And all stable matter requires just three entities.

Let’s suppose that the computer, constrained by the uni-verse’s physical laws, manages to model the electron, pro-ton, and neutron using just its two entities, which is cer-tainly possible, as we will later show. Then, again con-strained by physical laws, the only physically possible com-binations of these three entities result in ninety-two “natu-ral elements,” most of them stable. (Note that all possiblecombinations are actually used.) And the possible (chemical)combinations of these ninety-two “elements” are unlimited.So the numbers of entities in the computer modelingsequence would be 2, 3, 92, unlimited.

This is the fastest physically possible route to unlimited complex-ity. It is faster than any arithmetic or geometric progression.These are the necessary numbers of entities; they should be suf-ficient. It is totally absurd to suppose that the sequence wouldgo 36, 3, 92, unlimited, as the Standard Model (SM) insists.

By William of Ockham’s test, therefore, the SM is far offtrack. How does it fare judged by the other above criteria?Even worse.

In contrast to the ideal of no adjustable parameters(Criterion 2), the SM requires at least nineteen adjustableparameters, values which have to be entered by hand. Sinceit can be proven that 2 + 2 = 3 with just one adjustableparameter, this would seem to be a major defect.

Further, the SM is not mathematically consistent(Criterion 3). The SM calculations of many ordinary values,such as the rest mass of the electron, come out to be infi-nite. However, from experiment we know the electron’srest mass to be 0.511 MeV. To get rid of this “impossible”

The problem with the medieval debate

over how many angels could dance on

the head of a pin was that angels were

unobserved entities, and so could have

any desired properties. Each of these

classes of unobserved entities in the

SM amounts to a fudge or patch

applied to save a failing theory. So long

as these fudged entities are made

unobservable in principle, like the angel

or the quark, they are safe from exper-

imental falsification.


are made. In each case, suppose that the rejected alterna-tive has only one chance in three of being right. In eachcase, clearly science will choose the more probable out-come. Nonetheless, over the ten cases, the probabilities areover three to one that at least one of the ten rejected alter-natives is correct, and that the adopted paradigm will bepartially or completely wrong as a result.

Moreover, if the choice involves a paradigm change, theodds may be totally the other way, as it seems we will choosethe alternative that defends the paradigm if that alternativehas any plausible chance whatever of being right (Arp, 1998).

Many such choices were made in the early 1930s. Of course,in real cases the actual odds are difficult or impossible to assess.One choice in particular stands out, however, because of the pas-sion aroused by the controversy, and because of its far-reachingeffect on the shape of subsequent theory. This controversyinvolved the Dirac relativistic wave equation (Dirac, 1928a,1928b), a relativistic generalization of the Schrödinger equation:

Pais (1994) ranks this spectacularly successful equation“. . .among the highest achievements of twentieth-century sci-ence.” It was the first to be Lorentz-invariant, it had electronspin as a necessary consequence, it gave the right magneticmoment, the Thomas factor appeared automatically, and theSommerfeld fine structure formula was derived with the cor-rect Goudsmit/Uhlenbeck quantum numbers. At low energies,the results of the ordinary Schrödinger wave equation arerecovered. It predicted the positron, which was discovered byAnderson soon after. It has since become the very basis ofQuantum Electrodynamics (QED) (Pais, 1994).

Despite these successes, the physics community greeted itwith alarm and outrage. This was because the equation gavetwice as many states as they thought it should have. Theyexpected a Ψ with two components; but this equation gavefour. After the discovery of the positron, it was realized that itsfour solutions call for electrons and positrons of positive ener-gy, and electrons and positrons of negative energy (Pais, 1994).

As Dirac pointed out, this is because the energy-momen-tum-mass relation E2 = c2p2 + m2c4, always associated withEinstein and Special Relativity has two roots; it calls for bothpositive and negative energy:

± E = (c2p2 + m2c4)1/2

[The mass-energy relationship E = mc2 was first derived andpublished by Oliver Heaviside (1890) and further refined byPoincare (1900), but Einstein (1905) first furnished the com-plete expression including momentum.] Dirac wondered whatto do with the negative energy solutions. “One gets over thedifficulty on the classical theory by arbitrarily excluding thosesolutions that have a negative E. One cannot do this in thequantum theory, since in general a perturbation will causetransitions from states with E positive to states with E nega-tive.” (Dirac, 1928a)

Since all negative-energy states have lower energy thanany positive-energy state, Dirac wondered why there wereany filled positive states, since according to Hamilton’s law allentities tend to seek the lowest-energy state. He suggested

a theory that treats them as if they didn’t. The current hopeis that two more fudged entities, the (unobserved) Higgsfield and its supposed quantum, the (unobserved) Higgsboson, will somehow solve this dilemma.

The remaining above criteria (4-6) are also violated by theSM, as will be shown in what follows. The roots of most ofthese violations go back to the early 1930s as well. The infini-ties that so plague the model, as we will demonstrate, also havetheir origin in the early 1930s, in an apparently wrong turntaken by science.

The Fork in the Road By the above criteria, then, the SM would appear to fail innearly every possible way, and all of its failures seem to stemfrom the early 1930s. By all indications science seems tohave taken a wrong turn about this time. After three hun-dred years of progressively simplifying the description of theuniverse, with fewer entities and simpler laws, it suddenlyturned the other way, with complexity and entities multi-plying like rabbits. (Quantum Field Theory [QFT] in the SMis now so mathematically complex with its thirty-six or so[unobserved] fields that, as Treiman [2000] puts it, “Thereare no remotely realistic theories that are exactly soluble.”)

Science frequently makes choices between alternatives. Oncethe choice is made, however, scientists tend to unify behind theaccepted alternative to the extent of denying and eventuallyforgetting that there was any “real” choice made. Subsequenttextbooks gloss over any possible alternatives, depicting scienceas a straightforward march up the one correct path towardtruth. Since it is forgotten and denied that such choices existed,the results of these choices are rarely reviewed. Not only is thereno provision, or incentive, for such a review, there is positive,and powerful, peer pressure against any such questioning ofbasic premises. (The inexcusable treatment of the astronomerHalton Arp [1998] is just one example.)

However, it is an axiom of sciencethat no theory will remain valid forev-er. That being so, the “current para-digm” is by definition invalid!“Defense of the paradigm” is thereforeindefensible. Each new datum shouldbe cause for a review, not just of thecurrent paradigm, but of every choicethat led up to it. Let’s suppose that,over the course of the history of sci-ence, ten paradigm-affecting choices

It is an axiom of science that no theory

will remain valid forever. That being so,

the “current paradigm” is by definition

invalid! “Defense of the paradigm” is

therefore indefensible. Each new datum

should be cause for a review, not just of

the current paradigm, but of every

choice that led up to it.

P.A.M. Dirac (1902-1984)


He made use of one of Dirac’s own suggestions. Afterabsorbing extended criticism from the Machians, Dirac hadconcluded that, contrary to his earlier “hole” theory, all thenegative-energy states must be filled with negative-energyelectrons and positrons. He reasoned that if all the negativestates and none of the positive states were filled, the twocould have no effect on each other. Thus Dirac made whatcame to be called the “zeroth order subtraction,” removingthose parts of the theory which referred to the negative-energy “sea.” (The subtraction utilizes a mathematical trick,the Grassman elements, to remove two of the states calledfor in the Dirac equation, the two negative energy solutions.The Grassman elements are generalizations of Hamilton’s“quaternions,” elements that satisfy such strange-lookingequations as a x b = -b x a. Grassman’s elements look evenstranger. In them, a x a = 0. They can be used mathemati-cally to express the exclusion principle, but at the cost ofeliminating negative energies. There is no justification forsupposing they apply to Dirac’s oscillators. Their use isequivalent to saying, “Let black equal white. Now, blackdoesn’t exist!”) While Dirac intended the step merely tosimplify calculations, Heisenberg seized on it, using it todeny any existence to such states.

The problem was that such states seemed necessary, both tothe theory and to the experimental evidence. Using the theo-ry, Dirac (1930a), Oppenheimer (1930), and Heisenberg (1931)had all shown that every charged particle can give rise tounlimited numbers of electron-positron pairs and their associ-ated photons, pulled up from the “sea” by the charge, makingevery interaction an infinite-body problem. Moreover, this“polarization of the vacuum,” apparent in measurements eventhen, has since been rigorously verified (Pais, 1994). The Diractheory (1934) required every charge to be surrounded byunlimited numbers of the opposite charged ends of electron-positron pairs (henceforth “epos”). Experiment verified thatthe epos were both present and necessary.

This “polarization of the vacuum” has since become QED’smost celebrated success. Using difficult perturbation calcula-tions involving the charges of an unlimited number of eposand their associated photons surrounding a charged particle,the theory computes the electron’s magnetic “g” factor to anagreement with experiment of ten significant figures or more.

Along with the other Machians, Heisenberg had for sixyears been trying to find the “obvious” mistake in Dirac’s“learned trash.” He failed utterly: the equation was mathe-matically flawless, it was Lorentz invariant, it accounted forvirtually everything concerning the electron and positron,and it was becoming increasingly useful. But it called for theunthinkable, the politically incorrect “sea” of negative-ener-gy epos. So Heisenberg looked for and finally found whatseemed to be an escape hatch. (Furry and Oppenheimer[1934] independently made similar suggestions.)

Since Dirac’s “zeroth order subtraction” removes all traceof the negative-energy “sea” from the equations, Heisenberg(1934b) found that he could skirt around the “sea” (mathe-matically) as if it doesn’t exist. The equations call for elec-tron-positron pairs. But since the negative-energy “sea”removed from the equations now doesn’t exist, they can’tcome from there. Therefore the operator that previouslycalled for unlimited numbers of negative energy electron-positron pairs to be raised in state (from negative to positiveenergy), now magically became a “creation operator” of

that all of the negative energystates must be filled, like the filledelectron shells in the Pauli exclu-sion scheme. Then, unless a“vacancy” occurred, positiveenergy particles would “float” onthe surface of the negative-energy“sea” and stay positive.

Dirac’s “sea” of filled negativeenergy states, while it satisfied theequation, didn’t at all satisfy thephysicists. Heisenberg (1928a)

wrote to Pauli: “In order not to be forever irritated with DiracI have done something else for a change.” A little later hewrote, “The saddest chapter of modern physics is andremains the Dirac theory.” He further added that Dirac’s“magnetic electron had made Jordan melancholic.”(Heisenberg, 1928b)

Later, after the discovery of the positron, again in a letterto Pauli, who had reported himself “Your (drowned inDirac’s formulae) W. Pauli,” Heisenberg remarked, “I regardthe Dirac theory. . .as learned trash which no one can takeseriously.” (Heisenberg, 1934a)

These emotional responses were not limited toHeisenberg, Pauli, and Jordan. They were general among thephysics community. Their objection was not to the success-ful equation, but to its requirement of a sea of negative-ener-gy states. They were all good Machians, insisting that theo-ry should be based on observables alone. They were not at allopen to a suggestion that they might have been missing halfof reality all these centuries, as Mach had missed the atom.(Mach insisted to his death in 1916 that the atomic hypoth-esis “went beyond the data.”) Heisenberg had developed thefirst successful version of quantum mechanics on a Machianbasis, and an unobserved, ubiquitous “sea” was anathema.

Worse, it harked back to an old war, the “aether” conflict.On largely Machian grounds, Einstein in 1905 had declaredthe “luminiferous aether,” the supposed carrier of light, to beunobserved, hence nonexistent. [Lorentz’s electromagneticaether (Lorentz, 1904, 1909) answered all of the other objec-tions to a carrier of light, including the results of theMichelson-Morley experiment, so the only remaining objec-tion was the Machian one.] For a generation, the “AetherWar” had raged in every faculty. By 1930 the tide was defi-nitely running with the Relativists, and most remainingaether enthusiasts were dying out. (Lorentz, their doyen,died in 1928.) They were far from forgotten, however. Anyreference to a universal substance that undetectably filledspace sounded too much like an aether.

The final argument was always that negative energy isimpossible, with no imaginable physical meaning. Of course,pronouncements that something is impossible have a long his-tory of looking foolish in retrospect, but this one seemed per-suasive at the time, and is still heard. (We will later suggest avery possible physical meaning for negative energy.)

Heisenberg’s “Window”Heisenberg was the most upset by this theory, which out-raged his Machian belief system, so it is no surprise that hewas the first to work out a way to squirm out of the Diracequation’s and the energy equation’s requirements of nega-tive energy states (Heisenberg, 1934b).

Werner Heisenberg (1901-1976)


the respective latitudes in energy and time of observation,then ∆E • ∆ t ≥ h/2π. He took this to mean that if oneobserved for a sufficiently brief interval of time, (∆tapproaches 0), then the energy available would be effective-ly unlimited (∆E approaches infinity).

He therefore decided that these “created” epos must be“virtual” rather than “actual” (though the equations suggestno such thing), coming into being (in unlimited numbers)for a brief instant of time using energy “borrowed” (inunlimited amounts) from this relation. And when they“annihilate,” he argued, they merely “pay back the loan” tothe uncertainty relation.

Operationally, of course, “virtual” here means “havingwhatever properties we chose.” One of the handy propertieschosen for these unlimited numbers of “virtual” epos is that,although formed of unlimited amounts of energy, theysomehow don’t gravitate. Thus they violate GeneralRelativity, which states that such unlimited energy shouldcurl the universe into a little ball. Every electron, surround-ed by unlimited numbers of epos, should be a “black hole.”

So stood the question in 1934. The Dirac equation was adirect threat to the reigning paradigm. As Dirac noted,physicists had always arbitrarily ignored the negative energysolutions. If they were real in some sense, as Dirac’s “learnedtrash” insisted, they had all been mortifyingly, catastrophi-cally wrong all these years, ignoring exactly half of reality.And that other half of reality, alarmingly, seemed to resem-ble the anathematized aether. Though his interpretationseemed to violate either conservation or General Relativity,or both, Heisenberg’s mathematical conjuring trick offeredan escape route, a window, however tiny and iffy. Perhapsthe paradigm could yet be saved.

As we know, science took this escape route and neverlooked back. They saved the paradigm. But were they rightto do so? Let’s try to set up some kind of balance sheet.

At What Cost?On one side we have perhaps the two most used and respect-ed relations in modern physics, the energy equation andDirac’s relativistic wave equation. The energy equation callsfor negative energy, and Dirac’s equation specifically calls fornegative-energy electrons and positrons in unlimited num-bers. Experiment confirms that electron-positron pairs(epos) in unlimited numbers actually exist, surrounding andbeing polarized by every charged particle.

As noted above, the Dirac equation was spectacularlysuccessful. Not only did it explain everything Dirac hopedit would, the above listed accomplishments include sever-al complete surprises, as were the totally unanticipatedpredictions.

But if we follow Heisenberg, we are expected to believethat this colossus of equations has feet, or roots, of clay.We are told that it is completely wrong only in this onething, the sign of the electron-positron pairs verified byexperiment. They are not merely “raised in state” from anegative energy “sea” of such pairs. That, we are assured, isimpossible: it must be “an accident of the formalism.”Instead, these necessary epos must be created on the spot inan operation that violates either conservation or GeneralRelativity or both.

Arthur C. Clarke pointed out that if a man in a longwhite coat tells you that something is possible, he is prob-

unlimited numbers of positive energy electron-positron pairs.(Magically because they apparently appear from nowhere.)Since they come from nowhere, yet must be present, thisoperator creates them on the spot. Similarly, when they dis-appear again at this same sea level, they can’t be returning tothe non-existent “sea,” they must be annihilating, so thestate-lowering operator magically becomes an “annihilationoperator.” (See Pais [1994] for the details.)

In effect, Heisenberg merely put “horse blinders” on theequations, so they could no longer “see” the negative ener-gy solutions. He reset his gauge to zero at “sea level.” Usingthe “zeroth order subtraction,” which forces all results to bepositive, an “ocean” no longer exists: there are no negativesolutions, so nothing is below “sea level.” Those waves outthere? Oh, they’re just vacuum fluctuations around the zerobaseline. We call them “Zero-Point Fluctuations.” When adolphin is ill-mannered enough to jump out of this non-existent ocean, we merely utilize the “creation” operator,and voilà, a dolphin appears. When it dives back into thenon-existent ocean, quick, Henry, the “annihilation” opera-tor, and presto! It’s gone.

In defense of Heisenberg, the experimental evidence hadindeed begun to look as if “creation” and “annihilation”were actually happening. In cloud chamber studies of cos-mic rays, high-energy gamma rays (photons) suddenly gavebirth to electron-positron pairs (epos), which separated athigh velocity. The positron then would approach anotherelectron, and the two would disappear, being replaced byhigh-energy (0.511 MeV) photons.

There was, however, one immense difference:Heisenberg’s “creation operator” required the creation ofunlimited numbers of electron-positron pairs (epos) withoutany high-energy photons, or, indeed, any measurable energyinput at all. And when they are “annihilated” by the otheroperator, the epos vanish without a trace, producing nohigh-energy photons or any other detectable energy.

This massive violation of conservation botheredHeisenberg only momentarily, because there was a seeming“energy window” in the uncertainty relations that he him-self had famously developed. These limited what one couldknow (measure) about a quantum state: if one measured theposition of a particle exactly, then its momentum was max-imally uncertain, and vice versa. He developed a similarexpression for energy and time, namely that if ∆E and ∆t are

As Dirac noted, physicists had always

arbitrarily ignored the negative energy

solutions. If they were real in some

sense, as Dirac’s “learned trash” insist-

ed, they had all been mortifyingly, cata-

strophically wrong all these years,

ignoring exactly half of reality. And that

other half of reality, alarmingly, seemed

to resemble the anathematized aether.


sic attribute.” All that says is, “This energy is there; we don’tknow where it comes from, so let’s not talk about it.” Callingit an “intrinsic attribute” is supposed to close the subject,like the Stephen Leacock aphorism: “‘Shut up,’ heexplained.” Naming and agreeing to ignore it makes this1600% violation of conservation go away. In effect, currenttheory proclaims a miracle every time “creation” or “annihi-lation” is invoked—perhaps 10100 or more times a second.This demonstrates that conservation is merely paid lip serv-ice in the present practice of physics—something to berespected if it agrees with the current paradigm, but thrownto the winds if it proves inconvenient.

Even ignoring these massive violations of conservation, itseems hopelessly naïve to suppose that complex entitiessuch as electrons and positrons, with spin, charge, and anumber of other properties, could be “created out of noth-ing” but “pure energy.” This is like supposing that if we puta bunch of electronic components in a box, and shake themhard enough (i.e. add “pure energy”) the result will be a com-puter. “Pure energy” can never supply the exact and specificinformation necessary to make the highly complex little enti-ties that we call electron and positron. After all, we don’tknow how to make either electron or positron. What is“electric charge”? We haven’t a clue. Why are their spinsquantized in half-integer values? No idea. Where do they gettheir immense, anomalous angular momentum? Beats us.And how on earth do they manage to pack all this into azero or near zero radius? Yet we baldly suppose that “pureenergy” knows how to do all these things we can’t do!

Given all these problems with Heisenberg’s “window,”wouldn’t it have made sense to at least look at what two ofthe most successful equations in recent scientific historymandate? They say that electron-positron pairs already exist,everywhere. Instead of being “created” in pair production oraround every ion, which as we have seen involves massiveviolations of conservation, they are merely raised in statefrom negative to positive energies.

We will later look at this question more closely, and showwhy this “raising in state” requires no additional energy,resulting merely from the ion’s unbalanced charge. First weneed to look at more problems with “annihilation.”

When an electron approaches a positron, they don’t justrush together and disappear. Instead, they approach untilthey are a distance apart that is the width of the electronicground state of hydrogen. At this relatively large distance(some 56,000 times the diameter of a proton) they start toorbit around each other in the configuration called“positronium.” (This in itself should have told us thatsomething other than “annihilation” was going on.) Theynever get closer to each other than atomic distances. Afterorbiting each other in this pseudoatom for a time thatdepends on whether their spins are parallel or opposed,they emit two or more photons that total all of their posi-tive energy. After that they are no longer detectable, andconventional wisdom says that their charges and spinshave “cancelled” and that they have “annihilated” and areno more. But since they never get closer to each other than56,000 times the diameter of a proton, how can they pos-sibly “cancel and annihilate”? They never get anywherenear each other, and nothing passes between them. Forthem to “annihilate” would be action at a distance, a directviolation of causality. Doesn’t it make more sense to sup-

ably right. But if he tells you something is impossible, heis almost certainly wrong. Yet here we are told that some-thing called for by both of these most respected of rela-tions is impossible. There are about eight different thingsthat the Dirac equation got exactly right, but this one thingit got wrong? Surely, if it is completely wrong on some-thing so basic, it would have given wrong answers or feweranswers elsewhere as well. To be so certain it is wrong sci-ence, we must have direct evidence that negative energydoesn’t exist, right?

Well, that’s a problem—you can’t prove a negative. Thereis no way to prove that negative energy won’t someday beshown to be real, with a physical meaning. For the moment,let’s leave the question hanging.

The Miracle of “Creation”However, for Heisenberg to put physics into the “creation”business is something else entirely. In what form does a“relation” loan out “pure energy”? Cash, check, or moneyorder? And since there are unlimited numbers of epos aroundevery charge at all times, it doesn’t matter how briefly eachindividual epo exists, this amounts to a permanent loan ofinfinite energy. “Creation” is the proper term for it: only Godcould have that much energy to loan.

There are further conservation problems with any “cre-ation” process, even one where the mass-equivalent energyis supplied by real, 0.511 MeV photons. For both electronand positron have spin (angular momentum) energy equalto \/2. By any assumption as to the size of electron andpositron, this is much more energy than that supplied byphotons at “creation,” or taken away by photons at “anni-hilation.” Somehow the “created” electron has something likesixteen times more energy than the photon that “created” it.

This spin energy is real energy. It is the angular momen-tum needed by the electron to set up a stable standing wavearound the proton. Thus, it alone is directly responsible forthe extension and stability of all matter. Ultimately, it sup-plies the hν energy acquired by a photon when an electronjumps from one orbit to another. This half-integer energy isthe cause of Fermi-Dirac statistics, of the Pauli exclusionprinciple, and ultimately of the periodic table of elements.

In mathematics, if you set two things spinning in oppo-site directions, and take the average, the spins average tozero. But in the physical world, giving two real objects largeamounts of angular momentum takes real energy. Instead ofhonestly facing this gross abandonment of conservation,current theory dubs particle angular momentum an “intrin-

Since there are unlimited numbers of

epos around every charge at all times, it

doesn’t matter how briefly each individ-

ual epo exists, this amounts to a perma-

nent loan of infinite energy. “Creation” is

the proper term for it: only God could

have that much energy to loan.


which is forbidden to conventional science,” Arp, 1998.] Yetin this case, the odds that they made the wrong choicewould seem almost incalculably high. Surely they were highenough that someone, in the time this question was beingdebated, would at least have suggested examining the ramifi-cations of the other choice: of the negative energy electron-positron “sea.” At the least someone might have suggested thatthe choice be held in abeyance until more evidence was in.

But neither of these appear to have been suggested; if theywere suggested, they were certainly not done. [H. Bondi(1957) appears to be an exception. Much later, he examinednegative energy within General Relativity. Also, T.E. Phipps,Jr. (1976, 1986) explores both negative energy (the “holetheory”) and negative (or “imaginary”) momentum in his“Beta Structure Hypothesis.”] The case seems to have beendecided with apparent unanimity soon after Heisenberg’s“window” became widely known. (That Furry andOppenheimer [1934] independently made similar sugges-tions of course would seem to strengthen Heisenberg’s case.)Even Dirac appears not to have pursued negative energymuch farther. His objections to QED were on the grounds ofinfinities (Pais, 1994).

Would the decision have changed, had the question beenheld in abeyance? To consider this, we have to look at theresults of this choice, immediate and longer-ranged.

The first result was highly questionable by William ofOckham’s test. Heisenberg introduced four new (unobserved)entities, bringing the total number of entities instantly fromseven to eleven. (The virtual electron, the virtual positron, thevirtual photon, and a “relation” gone into the loan business,with infinite energy to loan out.) This was a considerable aban-donment of his Machian principles. And as we know, entitieshave proliferated without limit ever since.

Furthermore, almost immediately the theory wasengulfed in infinities. For, of course, if these epos are “creat-ed” by the electron’s charge, its mass must include them—aninfinite-body problem, making the mass of the electron, asTreiman (2000) puts it, “slightly infinite.” Moreover, sur-rounded by this infinity of positive charges, its “bare” chargehad to be infinite also, or no charge would “leak out” to bemeasured. And virtually any electromagnetic process onecould name turned out to be infinitely probable.

These infinities continued to plague the theory, turning upin endless additional cases and making life miserable for every-one until, in exasperation, we fudged the answers we wanted.This only swept under the rug certain classes of infinities, butat least it allowed us to do the theory and extract additionalinformation after some of the infinities were wished away.

After the Nobel Committee had dignified this fudge witha prize, there was no longer any need to consider changingthe paradigm when conflicting data threatened it. FollowingHeisenberg’s lead, one merely crafted unobservable entitieswith suitably designed properties that made it all right again.

“But wait,” the defenders of the paradigm exclaim. “Theelectron’s magnetic ‘g’ factor agrees with experiment to bet-ter than ten significant figures. This proves that we made theright choice!” Sorry, it doesn’t. The Dirac theory also calls forpositive-energy epos to surround every charge. (Moreover, asDirac pointed out, a perturbation such as this will cause tran-sitions from states with E positive to states with E negative.)So this one calculation would be exactly the same, whichev-er choice was made. But seemingly all of the other calcula-

pose that they still exist, as the Dirac equation requires,merely lowered in state to negative energies?

Another problem: to say that something has charge meansthat it has potential energy with respect to every othercharged particle in the universe, and vice versa. For an elec-tron and positron to “annihilate” while they are a large dis-tance apart means that, according to Maxwell’s equations,the potential energies of every charged particle in the uni-verse must change instantaneously, except for those that areexactly equidistant from both of them. This violates conser-vation not only locally, but universally. It is real action at adistance, violating causality as well. But again the problemwould seem to be solved merely by taking seriously what theDirac equation says: that the spins and charges still exist,merely lowered in state to negative energies.

What the equations call for validates the conservation ofcharge, which is violated by “creation” and “annihilation.”Just as conservation of mass-energy means that mass-energycan neither be created nor destroyed, so conservation of chargemeans that charge can neither be created nor destroyed. (Wewill later look at other supposed creations of charge, such asbeta decay, and show that in each case the supposed creationwas merely the separation of an existing epo.)

Arp’s AxiomSo we see the choice that scientists of the time had to make:whether to believe what these fabulously successful equa-tions say about negative energy, and try to figure out whatnegative energy might mean, or to escape throughHeisenberg’s “window” and save the paradigm. As we know,they saved the paradigm, even though this required whole-sale miracles that put science into the “creation” business ona scale rivaling the God of religion. Almost incidentally, itrequired immense violations of causality, of conservation ofcharge, and of conservation of angular momentum, as wellas the mind-numbing violation of conservation ofmass/energy. Thus it violated four of science’s most basic“laws.” One wonders if there are any lengths to which sci-entists will not go in order to save the paradigm. In this case,saving the paradigm would seem to involve the virtual aban-donment of science itself.

In this, they obeyed what we might call “Arp’s Axiom.”The astronomer Halton Arp (1998) noted that when facedwith a choice involving a paradigm change, scientists willalmost invariably choose the alternative that will save theparadigm, regardless of the evidence. [“Can we count onconventional science always choosing the incorrect alterna-tive between two possibilities? I would vote yes, because theimportant problems usually require a change in paradigm

The astronomer Halton Arp noted that

when faced with a choice involving a

paradigm change, scientists will almost

invariably choose the alternative that

will save the paradigm, regardless of

the evidence.


action. If that is not the case, as the above “smoking gun”emphatically shows, then Heisenberg’s window doesn’t exist.

But the paradigm escaped through that nonexistent window.

Negative EnergyIt seems we need to go back to 1934 and take another look atDirac’s negative energy solutions. As mentioned above, simplytaking these equations at their word eliminates most of theseinfinities and gross violations of conservation. The equationssay that unlimited numbers of epos already exist, everywhere,and that they are merely raised in state, not “created.” It is pos-sible, perhaps, that there exists another “window.” Certainlydefenders of the paradigm will search for one. However,Heisenberg (and other brilliant theorists, such as Pauli, Jordan,Furry, and Oppenheimer) searched for six years, then came upwith a window that wasn’t. In any case, the above difficultieswith the present paradigm indicate very clearly that there wereimmense problems with the choice they made.

What might we expect to find down the “road nottaken”? As noted in the opening argument, Ockham’s razormeasures the progress of science in terms of simplicity. If“negative energy” is a correct road, we would expect thenumber of entities recognized by science, seven in 1932, todecrease further rather than to increase to nearly one hun-dred, as they have done since then. We would expect a con-sequent simplification of the mathematics involved. Wewould certainly expect to clear up the gross violations ofconservation implicit in Heisenberg’s “creation” window.And this would, as we will show, clear up the infinities thatplague current theory without recourse to fudging.

This is such an ambitious project that we cannot hope toprove all of this in the present work. We merely hope to indi-cate the directions that future theory might take in follow-ing the clear leads of the energy equation and, most particu-larly, of the complete Dirac equation in the light of subse-quent discoveries. And above all we should remain flexible.Clearly, this crisis at the heart of science was the result of achronic “hardening of the paradigm.” With new discoveriesbeing made almost daily, no theory can be expected to bethe final answer. In all probability, there is no “final answer.”

Therefore, while we may present a number of probableconsequences of following this new road, keep in mind thatthey are all tentative, subject to revision as well as analyticaland experimental falsification. In view of this, the first stepis to take a long look at the rejected alternative, the negativeenergy sea that this most successful of equations calls for. Inparticular, what could “negative energy” represent?

SymmetryThese two equations call for symmetry between positive andnegative energy. This only matches the symmetry betweenthe forces recognized by physics. There are two kinds offorces in nature, those that bind matter together, and thosethat free it, that blast it apart. The binding forces, such asgravitation, the “strong nuclear” force, and the Coulombforce between unlike charges, all have negative signs. Thefreeing forces, such as the repulsive Coulomb force betweenlike charges, have positive signs. The positive-sign forces actto increase the amount of positive energy; the negative-signforces all act to decrease it. Logic would indicate that “posi-tive energy” would be the result of positive forces, and “neg-ative energy” the result of negative forces. However, because

tions come up either infinite, or so imprecise as to call intoquestion the validity of the theory. An example is the mag-netic moment of the proton, in which the measured value is10,000 times more accurate than the theoretical value(Feynman, 1985). Obviously, this is why we hear only aboutthis measurement of the “g” factor, the one total success, notabout the numerous total failures and near misses.

Therefore it would seem that the accepted paradigm’s onlyinstance in which near-perfect agreement is reachedbetween theory and experiment is the one instance in whichboth choices would give the same result.

It is increasingly clear that we made a choice to save theexisting paradigm despite the basic laws of physics, the evi-dence, and the clear meaning of the equations. As a directresult, violations of conservation, entities, infinities, and evermore mathematically intractable theories proliferated withoutlimit, right up to the present. But there is one recent develop-ment that calls into question the very basis of that choice.

The Smoking GunIt turns out that, in effect, the equations of QM act as if timeis quantized. As Prof. Treiman (2000) explains, “There isanother inequality relation in quantum mechanics that isoften cited, one involving energy and time. It has the look ofan uncertainty principle but it stands on a different footingthan the Heisenberg uncertainty relations discussed above.”He goes on to show that there is a minimum time, τ, whichmust elapse before the wave function “changes appreciably.”[This minimum time appears to be 2e2/3mc3, or 6.26 x 10-24

seconds. We will discuss this later.] This means that the wavefunction changes only in increments of the constant τ. Fromthe time t = 0 to t = τ there is no change in the function;then at t = τ, all the change happens at once. He then showsthat the modern version of what Heisenberg assumed to bethe uncertainty relation ∆t • ∆E ≥ \ is really the inequalityτ • ∆ E ≥ \. (We will examine this apparent quantization oftime in more detail later.)

If time is a constant that can only come in increments ofτ, as this inequality relation shows, then obviously it can notbe taken in increments approaching zero. Furthermore, in a“perfect quantum measurement” situation (such as the Airypattern) (Herbert, 1986) the root mean square energy devia-tion would equal \/τ. At most it would be a random amountover this, depending on the measurement situation.Therefore Heisenberg’s “relation” is a poor “relation”: it doesnot have infinite amounts of energy to lend on every occa-sion. In a good measurement situation all the energy avail-able is \/τ. There certainly is none to spare to “create” infi-nite numbers of electron-positron pairs.

This means that Heisenberg’s window never existed.To recap: Heisenberg’s window was not outrageously in vio-

lation of conservation only because Heisenberg’s relation wassupposed to supply infinite amounts of energy to every inter-

With new discoveries being made

almost daily, no theory can be expected

to be the final answer. In all probabili-

ty, there is no “final answer


up places where the “single-entry” system has problems,such as near absolute zero. Just as an exercise, try to think of“positive energy” as the result of positive forces, and “nega-tive energy” as the result of negative forces. Then, in the“lowering in state” called for by Dirac’s equation, when allpositive energy is removed from an electron and positronand they drop into the “sea,” the only force between themis the negative Coulomb force, and they clearly would haveonly “negative energy.” And since they are then apparentlyundetectable, it would seem that “negative energy” doesn’tgravitate or have inertia. (“Mass” is only the result of positiveenergy.) We will discuss the reason for this in what follows.

There are other clear indications that negative energy doesexist, but has merely been mislabeled. According to Feynman’s“parton” model, the nucleon consists of a swarm of chargedparticles which are held together by the “strong nuclear force,”which is negative in sign. As many of these partons have likecharges, these are strong positive energy forces trying to blast thenucleon apart, which must be balanced by the even strongernegative strong nuclear force. To avoid calling the results of thisforce “negative energy” is a purely semantic prejudice. To bestable, the nucleon must be a balance of negative and positiveforces, hence negative and positive energies.

The measured mass of an alpha particle is substantially lessthan the sum of the mass-energies of the two neutrons and twoprotons that make it up. To avoid the proscribed term “nega-tive energy,” this difference is called the “mass deficit” or the“binding energy” or “negative potential energy.” (“Potentialenergy,” in general, is a euphemism for the dirty term “nega-tive energy,” used when the energy supplied by a negativeforce such as gravitation is unavoidable.) But each nucleon stillhas its like “parton” charges, so when you add the two protons,the “bound” nucleus must have more (positive) energy than its“unbound” constituents. (The positive Coulomb repulsionbetween the two protons in these close quarters is enormous.)

The only way in which a “bound” nucleus with more totalenergy can have less positive energy is if this “binding energy”is negative energy. (Its sign of course is negative, as is the signof the strong nuclear force that binds the nucleus together.)Since the strong nuclear force is negative in sign, and since the“binding energy” that results from it is negative in sign, it seemsclearly doubletalk to say that negative energy doesn’t exist.

When two additional positive charges are added in theformation of an alpha particle, all of the parton charges arestill there. Thus, the particle has more blasting-apart (posi-tive) energy, and by conventional thinking should massmore. However, to be stable, the negative energy-positiveenergy balance must change. So the alpha particle as it formsdivests itself of some positive energy, the energy that powersthe sun, thus giving the particle a higher percentage of (non-gravitating) binding negative energy, and making it stableagain in spite of the additional two positive charges.

Negative RootsScience has ignored the negative energy solutions to theseequations as “imaginary,” like the square root of a negativenumber. However, the square root of minus one is not “imagi-nary”—that is perhaps an unfortunate name. Mathematically,represented as i, it simply designates a number field, or dimen-sion, at right angles to the everyday three. It is necessary tomany disciplines, especially electronics. In the Einstein-Minkowski interpretation of special relativity this “imaginary”

matter (mass) is positive energy,our reality has a large positive-energy balance. It never seems toventure into negative territory, sowe get by with an illogical “single-entry” bookkeeping that treatspositive energy as the only kind.

The blame for this appears tofall on Ben Franklin, who flippeda coin and chose to designatestatic electricity with a deficiencyof electrons “positive” and that

with a surplus of electrons “negative.” He assumed correctlythat there was a “unit of electricity,” that electricity was thetransfer, the flow of some charged entity; but he guessedexactly wrong as to which one. By this mischance the elec-tron, the very unit of electricity, was saddled with a minussign. But this mistake had far reaching consequences. Hadhe guessed correctly as to what was flowing, both the electronand what we now call “negative energy” would have had apositive sign. In this much more logical case, would we havebeen so certain that something called “negative energy” isthe only kind, and that something we would have to call“positive energy” doesn’t exist? Would we have been so quickto say that “positive energy” is impossible?

All through science, we observe almost total symmetrybetween positive and negative. Charges come in positive andnegative, forces come in positive and negative, particles aresymmetric between matter and antimatter. This last came as agreat shock to physicists in the 1930s, but after it was accept-ed, symmetry became the justification for many of our theo-retical structures. Only in energy do we deny that such a sym-metry exists. This prejudice would seem to have its roots in thepast, in a time when most scientists were profoundly religious.To them, “negative energy” perhaps sounded like somethinginvoked by someone calling on Powers of Darkness, and theywere only too glad to ignore it and deny its existence. But sure-ly it is time to rise above such superstition, especially when werealize that, but for Franklin’s mistake, “negative energy”would be “positive energy.”

Surely the forces that combine, that draw things together,that build, in all propriety should be considered positiveforces. Yet Ben’s mistake saddles them with a minus sign.And just as surely, the forces that force apart, that breakdown, that explode, we would normally call negative forces.Had Franklin made the right choice, this illogic would becured. But mark the sequel: our reality then would have beenseen to have a large negative energy balance.

In this case, since both the energy equation and Dirac’sequation are symmetric with respect to positive and negativeenergy, surely someone would have postulated a symmetricalreality somewhere with a balancing positive energy surplus. Thesolutions to Dirac’s equation amount to a matter field contain-ing unlimited, symmetrical amounts of negative and positiveenergy. This implies that there exists a symmetrical “sea” witha surplus of energy opposite in sign to that of our matter/ener-gy. This would restore the symmetry between negative andpositive energy called for by these successful equations.

This will require a change of focus, especially for physi-cists who have worked with the “single-entry” bookkeepingfor so long. However, a more logical “double-entry” systemworks equally well with everyday energy issues, and it clears

Benjamin Franklin (1706-1790)


of mass in the Lorentz relationships (Huang, 1952).According to Haisch, Rueda, and Puthoff (1994), mass iscaused by an action of the Zero-Point Fluctuations (ZPF) ofthe vacuum electromagnetic field that resists the accelera-tion of a harmonically vibrating charge. “Mass is the mani-festation of energy in the ZPF acting upon [vibrating]charged particles to create forces.” (Haisch and Rueda, 1997)

By this kinetic definition, an electron-positron pair vibrat-ing in a direction at right angles to our ordinary four, an“imaginary” direction, would have negative energy, the nega-tive root of the Dirac equation. Just as the square root of a neg-ative number merely refers the result to a direction at right anglesto our ordinary directions, so the negative root of the energy equa-tion refers to an energy (a vibration of charges) in one of these“imaginary” directions.

All of the groundbreaking equations of quantum mechan-ics contain i either explicitly or implicitly. The meaning ofthis has been staring us in the face for seventy years. These“complex” functions involve vibrations partly in “real” partly in“imaginary” directions. (And some that are “pure imaginary,”such as the ±c velocity eigenvalue of the electron/positron.)We have been like Mr. A. Square from Flatland witnessingthe intrusion of a three-dimensional creature into his two-dimensional domain, puzzled over such seemingly impossi-ble events, but unable to comprehend “how it can be likethat.” Clearly, in both his case and ours, reality comprisesmore dimensions than those we can directly sense.

And most conclusively, a perturbation, as Dirac pointed out,must cause transitions from states of positive energy to thoseof negative energy. Quantum mechanics must be symmetricwith respect to energy. Since our reality has a large positiveenergy balance, symmetry requires another reality with a largenegative-energy balance. Vibrations of epos in these “imagi-nary” directions, as called for by the energy equation andDirac’s equation, would seem to meet this requirement.

This would also seem to explain the relative unobserv-ability of this negative-energy domain. It has no inertia,hence no “mass,” for reasons we will examine later. This, ofcourse, will explain why “binding energy,” above, has noinertial or gravitational mass.

Since these equations call for negative energy solutions,and since there is in fact a physically possible explanationfor negative energy, there seems to be no further excusefor doubting that all four of the Dirac equation’s rootshave physical meaning.

The Electron-Positron PairThe negative-energy electrons and positrons called for, how-ever, appear to be permanently associated in pairs—epos.What can this mean? In our experience, an electron and apositron form “positronium,” then lose all their positiveenergy and become undetectable. According to Dirac’s equa-tion, they drop into the negative energy sea. What configu-ration do they assume there? For a possible answer, we needto consider what Dirac’s equation says about the electron.

Dirac’s equation describes a “spinor field.” In such a field,rotation of the wave function through 360˚ does not get itback to its original state, but to its opposite: the electron hasto “turn around twice” to get back to where it was. At 360˚,its wave function Ψ becomes -Ψ and it becomes, in effect, apositron travelling backwards, to arrive at 0˚ and switch backto an electron. (In QED, a positron is considered to be an

dimension is time. According to Minkowski (1909), there is “nodifference” between x, y, z, and ict, where t is time and c is thevelocity of light. Everyone who takes relativity seriously, there-fore, believes in the reality of at least one direction in whichone cannot point: a definitely non-Machian belief. However,mathematically there is no limit to the number of dimensions.In electronics, for instance, this “imaginary” dimension is nottime. So it would seem that we need at least five dimensions.

Many of the popular string and superstring theoriesrequire, for symmetry, a space of ten dimensions (Sirag,2000). General Relativity as well calls for ten tensors, or“dimensions of curvature” (Sirag, 1977a). To quote Dirac,(1963), commenting on the ten tensors of curvature ofGeneral Relativity, “The gravitational field is a tensor fieldwith ten components. One finds that six of the componentsare adequate for describing everything of physical impor-tance and the other four can be dropped out of the equation.One cannot, however, pick out the six important compo-nents from the complete set of ten in a way that does notdestroy the four-dimensional symmetry.” Recent studies inastronomy have shown that space on a large scale is notcurved, but appears to be Euclidean to the limits of meas-urement (Arp 1998, Van Flandern 1998). In this case,General Relativity’s ten tensors of curvature become merelylinear degrees of freedom, or dimensions.

Dirac (1928a, b) laid the foundations of QED with his rela-tivistic wave equation. In doing so, though, Dirac found thathaving three dimensions “real” and the fourth “imaginary”didn’t work—it violated the symmetry. He took the first deriv-atives of all four dimensions by introducing i as well into x, y,and z, making them symmetrical by making them all “imagi-nary.” Most physicists have considered this a trick, an “acci-dent of the formalism,” and disregarded it. However, whenadded to Dirac’s above statement about the six “necessary”(dimensional) components and the four “unnecessary” ones,this might imply that our entire reality is “imaginary,” as east-ern mystics have insisted for thousands of years.

All it need mean, though, is that there exist six otherdimensions that are in “imaginary” (orthogonal) directionswith respect to our four, while our four are similarly “imagi-nary” with respect to the other six. This gives us a place toput Dirac’s negative-energy “sea.” As we will demonstrate, italso gives us a physical explanation of “negative energy.”

The Kinetic Theory of Mass/EnergyWhat is mass? Recent thought suggests that the energy equa-tion, instead of saying that two different things can some-how be converted into each other, really means that mass isjust another form of energy (Haisch and Rueda, 1997). At afundamental level, all matter consists of charged particles inharmonic motion (Cf. Feynman’s “parton” model of the pro-ton/neutron). Mass appears to be the harmonic motion ofcharged particles “trapped” within an energy well of somekind. This is why the most convenient and most often usedunit expresses mass in terms of energy: the eV.

What then is this stuff, energy? As mentioned above, theSM has no idea what mass is. But as just another form ofenergy, it appears to be firmly associated with motion: theharmonic vibration of a charge, or linear motion (momen-tum). Many of the recent theories in StochasticElectrodynamics (SED) use this kinetic definition (Puthoff,1989) which is of a piece with the general kinetic definition


tiples of this “quantum of time.” Since they travel at c aselectromagnetic waves, this would make the “length” ofan epo (a one-dimensional string, with a “point particle”at each end) equal to τc, 2e2/3mc2, or 1.87 x 10-15 meters.This is the measured diameter of the proton, which, as wewill see, is not a “mere coincidence.”

“Pair Production”We can now consider the interaction miscalled “creation.” Ahigh-energy photon collides with something, say a leadnucleus, and produces a “pair”—a “real” electron and positron,which separate at high velocity. Using the “complete” Diractheory, we would regard this as the capture by a (negative ener-gy) epo of sufficient positive energy to split the epo in half, andto give each half 0.511 MeV of “positive” energy plus sufficientmomentum to escape their mutual Coulomb attraction. Theyeach now have a positive energy of mec2 plus momentumenergy, pc, in a “real” direction.

However, the electron, as part of a negative-energy epo,has a one-dimensional oscillation at ±c in an “imaginary”direction. It retains this oscillation as a “real” electron—hence its velocity eigenvalue of ±c (Huang, 1952). (Since thisone-dimensional oscillation has no “mass” or inertia, it can’tbe affected by the capture, and the electron, obeying conser-vation of angular momentum, retains it.) Therefore the“real” electron’s wave function has a circular vibration at c intwo “real” directions (giving it mc2 of positive energy) plusa vibration at ±c in an “imaginary” direction, which adds nopositive energy. This makes its total (spherical) vibrationcomplex—part “real” and part “imaginary.” However, a com-ponent of the angular momentum of its “imaginary” spin car-ries over, giving the “real” electron its immense angularmomentum of \/2. Note that if all three vibrations were allpositive energy, the electron’s energy would have been mc3,around 1.5 x 108 MeV. As it is, because of our four “real”dimensions, the component of this complex spin energy inany “real” direction appears to be 42(mc2) or around 16times the electron’s positive rest energy.

This also accounts for the fact that this quantum numberis two-valued—”spin up” or “spin down,” as any “real”direction can only be at right angles to three “imaginary”directions at a time. And it of course accounts for the factthat the electron’s wave function is a complex variable, with“real” and “imaginary” parts.

This further accounts for the hitherto mysterious fact thatthe electron’s angular momentum is also complex, as the elec-tron’s angular momentum vector can not point in any “real”direction. Consequently, neither can the electron’s orbitalangular momentum vector in an atom (Treiman, 2000).

With this understanding, we have at a stroke eliminated themassive violation of energy and angular momentum conserva-tion involved in “creation. The \/2 angular momentum of theelectron is compounded from the epo’s vibration at ±c in an“imaginary” direction in the negative energy sea, and returnsto that sea when it meets a matching positron. This under-standing also eliminates the violation of conservation ofcharge, as well as the violation of energy conservation involvedin the “creation” of two charges, as a charge is energy—poten-tial energy with respect to every other charged particle in theuniverse. The “creation” and “annihilation” of charges alsoviolates, as we have seen, causality.

We can further see reasons for some of the properties of

electron travelling backwards in time [Feynman, 1985].) So apositron is really only a totally out-of-phase electron.

However, the equation also says (Huang, 1952) that the elec-tron always travels at velocity c: its velocity eigenvalue is ±c.Thus, in addition to whatever overall (macrocosmic) motionthe electron has, which we could call its momentum, the elec-tron has an internal vibration at velocity ±c. Doesn’t this meanthat this internal vibration is as an electromagnetic wave? That’sthe only momentum-carrying entity allowed to travel at c.Furthermore, this internal vibration must be in an “imaginary”direction, or, combined with its “momentum” velocity, itwould at times exceed c, which is not allowed in “real” direc-tions for a “positive energy” particle. (This is the first explana-tion ever given for this eigenvalue vibration that doesn’t violatethe Lorentz relationship.)

The only way it could travel at c and not at any othervelocity would be for the electron’s wave (Ψ) to be reflected at360 degrees by the spinor “phase change” (positive to nega-tive), thus changing electron to positron. (Since in this statethey have no “mass” or inertia, this reflection takes no timeor energy.) The analog would be a vibration traveling alonga string fixed at each end, therefore reflected at each end. Aspin 1/2 particle is out of phase with this phase change, andso is reflected. A spin 1 particle merely gets sent on its way,this being the fundamental difference between fermion andboson. This accounts for the fact that the fermion’s wavedoesn’t spread. (The Fourier sums of waves that have ampli-tude only in a small area [“wave packets”] show that a non-spreading wave is possible, but don’t explain why this shouldhappen. Moreover, they do spread with time, as required bythe uncertainty relationship. Also, the waves are still presenteven in areas where they add to 0 amplitude.)

This gives a possible model for a non-annihilating, non-spreading electron-positron pair. For one thing, they are bothfermions, so the probability of them being in the same place atthe same time is exactly zero. (Another reason they can’t“annihilate.”) Therefore they must establish some stable rela-tionship at a non-zero distance from each other. However,according to the above reciprocation, an electron and apositron could share a very stable relationship, vibrating in animaginary direction while turning into each other every 360˚.On this model, they would be “particles” only at 0˚, 360˚, and720˚, turning into waves in between (“wave-particle duality”).And if they traveled as electromagnetic waves, they would notinterfere with each other as they passed. Since in the least-ener-gy arrangement their spins and charges would cancel, the epowould appear to all the universe (and to the equations) as aneutral spin-zero boson, vibrating in an “imaginary” direction.(According to the kinetic theory, only charged entities canhave energy, so any neutral spin-zero boson would have to bean association of entities whose spins and charges cancelled.)

Moreover, the period of this reciprocation would have tobe the “quantum of time,” τ, equal to 2e2/3mc3, or 6.26 x10-24 seconds. As shown above, this is the time requiredfor an “appreciable change” in the wave equation, whichtherefore only changes in increments of τ. This is Γe, theLorentz-Abraham damping constant of the electron, andin classical electrodynamics, it is called the “damping con-stant” (Jackson, 1975) or the “characteristic time”(Jackson, 1993) of the electron. In particle physics, this isthe minimum time taken by any interaction, and interac-tions that take longer than this seem to require exact mul-


of energy and time, the units of angular momentum, as inthe above inequality. It has always simply been assumed thatenergy is the quantized entity, and you will find this stated asfact in textbooks. But a photon can have any energy (witnessthe results of a Doppler shift) and the equations of QMwould work exactly the same if it is assumed that time, notenergy, is the quantized entity.

It is perhaps unfortunate that QM came to maturity at thesame time as Relativity. Einstein convinced everyone that abastard unit, space-time, was a more accurate designationthan either space or time separately. Thus physicists came toaccept another bastard unit, the energy-time of Planck’s con-stant, which is not even a true constant, but a constant of pro-portionality. Heisenberg (1938a, 1938b, 1944) always consid-ered Planck’s constant to be shadow or projection of some trueconstant in some other dimension, a constant that wouldexplain the “size” of the uncertainty principle. The constanthe arrived at was τc, 2e2/3mc2, or 1.87 x 10-15 m. He attempt-ed to cut the universe into tiny cubes τc3 in size. This, ofcourse, was a failure. However, one wonders why he neversuggested the more natural unit τ as his “pure” constant.Could it be that he realized that if time were quantized, his“window” through which the paradigm had escaped wouldbe nonexistent?

If we take Dirac’s equation seriously, moreover, time must bequantized. As everyone from von Neuman (1928) to Pais (1993)recognizes, the equation describes a spinor field in which elec-tron changes to positron and vice versa every 360°, which as wehave seen is the time τ. If this change happened at randomtimes, no charge could ever be measured, as our measuringdevices don’t work that fast. The result would be zero averagecharge. So every electron in the universe must change polarityat the exact same instant. In this case, at every phase angle oppo-site charges still attract, and like charges repel, no matterwhether the lepton is nominally electron or positron at thatinstant. And since, as we will show, all matter is compoundedof electrons and positrons, this means that all matter mustchange polarity in this same rhythm, the “quantum of time,”which is the “clock speed” of “least count” of the universe.

In any case, Heisenberg clearly agreed with the aboveassessment of the “size” of the uncertainty principle.Moreover, our understanding that this “size” is the inescapableuncertainty involved in an analog-to-digital conversion clearsup several further problems with the electron, particularly withthe infinities involved in the “point-electron” model.

The Quantum FieldAssuming the reality of this negative energy epo sea, we canaccount for many of the hitherto mysterious properties ofthe electron. But how can we account mathematically forthe sea itself? Here quantum field theory comes to the res-cue. In his book The Odd Quantum, Sam Treiman (2000)introduces “only for pedagogical purposes” a very simple“model field”: a single, scalar field φ (x,y,z,t) which classical-ly obeys the linear differential equation

Treiman then goes on to quantize the field, and solve forthe eigenvalues. The results, as he states, are “quite remark-

the electron, properties totally inexplicable by conventionaltheory, properties that are just brushed aside with remarkslike “Quantum mechanics is odd!” (Treiman, 2000)

This is only the beginning of the riches to be mined from tak-ing these equations seriously. For as is well known, everyunmeasured quantum entity evolves as a wave, yet every meas-urement reveals it to be a particle—as accurately as we canmeasure, a point-particle. (The latest measurements show theelectron to be smaller than 10-18 m [Lederman, 1993], which is2000 times smaller than the proton. And these measurementsare consistent with a true point-electron.) However, there aresevere difficulties with the point-electron model. A true point-electron, for instance, would have infinite density and infinitegravitational and Coulomb self-energy. Current theory is wild-ly divergent on this issue. The followers of Feynman and QEDinsist that everything behaves as particles, and QED treats themas point-particles (Feynman, 1985). Quantum field theoristsinsist that everything is wave or field, that particles are mereepiphenomena (Weinberg, 1977).

There is, however, a logical way of resolving these views. Inorder to negotiate the “two slit” experiment and its variants,the quantum object must have total knowledge of “the entiremeasurement situation”—in theory, the entire physical uni-verse. That a single electron or photon should have suchomniscience is of course absurd. However, if the unmeasuredquantum object exists as a non-local, multidimensional,phase-entangled analog wave or set of interference patterns, asthe equations and experiments insist, then any interaction ormeasurement would represent a digital slice of this analogwave. Our “quantum of time” τ would then represent the“reporting cycle” of this process, the minimum time between“reports.” As Gribben (1998a) says, the universe seems to“make the computation and present us with the result.” Thus,when a measurement or interaction happens, the analog waveis converted to a digital solution with the result reported to aspecific set of coordinates—thus a “mathematical point.”

Thus, every measurement or interaction involves an analog-to-digital conversion—and this involves a minimum quantiz-ing error proportionate to the “quantum of time.” This is theminimum time between digital “slices” of the analog wave,and so fixes the minimum “uncertainty” of the conjugate vari-ables. This is the first explanation ever given for the uncertain-ty principle—it represents merely the minimum quantizingerror. We can now see that the fundamental relation is that oftime and energy,

τ • ∆ E ≥\.

The other conjugate (complementary) properties derivefrom this.

Of course, the units of Planck’s constant are the products

It is perhaps unfortunate that QM

came to maturity at the same time as

Relativity. Einstein convinced every-

one that a bastard unit, space-time,

was a more accurate designation than

either space or time separately.


terms in the differential equations that describe them in orderfor there to be interactions, and this is why none of the theo-ries are exactly soluble.) But as we noted above, this “free fieldtheory” exactly describes our strictly identical, negative-energyboson sea, in which electron and positron approach as if for acollision, but in fact they don’t collide, as they are both wavesat the time. (We will later show that this lack of interactionsbetween fields is a non-problem, because there is only onefield, this simplest Dirac field.)

The form that this negative-energy boson sea must takecan be seen as we approach the absolute zero state of the zeropoint. In laboratory ultra-cold studies, we remove “positive”energy and achieve lower temperatures to come closer andcloser to “zero absolute,” which is a state of no positive ener-gy. That there is still immense energy (hν/2) at this zeropoint of no positive energy should immediately have informedus that positive energy is not the only kind of energy. Sowhat is the alternative to positive energy?

As we approach the zero-point, some curious things hap-pen. First, centered at about 2.73˚K, we find an immensenumber of photons. Then, at 0˚K, the equations of QM tellus that there is unlimited energy. Let’s say you are approach-ing a wall. As you approach, you detect a large amount ofenergy. And at the wall, you find it is glowing white hot. Youask what is behind the wall, and someone tells you, “Oh,there is nothing behind the wall. The universe ends there.”Would you be inclined to believe it? Yet that’s what we aretold about the zero-point. Energy and activity decline rapid-ly with temperature, then near the wall, suddenly there areimmense numbers of photons, and at the wall, unlimitedenergy. But nothing is behind it. Believe that, and there aresome bridges you might be interested in buying.

The matter that registers in our measuring devices is pos-itive energy. But all matter except the electron is composite,and positive energy is pushing-apart or explosive energy. Ittakes immense negative energy to bind matter together. Ifpositive energy were the only energy, one would think thatat temperatures near absolute zero matter would lose itscohesion and fall apart. Nothing of the kind—in fact matterbinds closer and closer together until it becomes all onething. It takes energy to bind matter together, yet all positiveenergy has been removed. What is left? Only the negative ener-gy that is the result of negative forces.

The Bose-Einstein CondensateVarious typical changes occur in the physical characteristics ofmaterial substances near 0˚K. In a conductor, some of the elec-trons change their phase so that they become, in effect,positrons. An electron and this pseudo-positron then formwhat are called “Cooper pairs,” bosons formed of two fermi-ons, in which the two 1/2 spins add up to spin 1, and bothmust be in the same state governed by the same wave function.(The members of a Cooper pair are separated by about 10-6 m,thousands of times the distance between the ions in the con-ductor’s lattice.) At even lower temperatures a true Bose-Einstein Condensate (BEC) may be formed, which acts as a sin-gle unit rather than as a collection of molecules. This permitsthe special states in which superconductivity and superfluidityoccur. These are very energetic states, as their behavior demon-strates. They are states in which negative (binding) energy hasovercome the tiny residual positive (freeing) energy, so thatthey are all governed by the same wave function.

able.” Notably:

. . .The allowed momentum eigenvalues p form a con-tinuum, all magnitudes and directions being allowed.For any given momentum p there is a particular statewith energy

E = [(cp)2 + (mc2)2]1/2, where m = \p/c.

This is just exactly the relativistic energy-momentumrelation that holds for a material particle of mass m.It is natural to interpret this state as in fact describingjust that; we may speak of this as a one-particle state.A particle has somehow emerged out of the quantumfield. The parameter p that we started with fixes itsmass. [Emphasis his]

It is important to note that, to be accurate, the aboveexpression should read “plus or minus E.” The one-particlestate can have either positive or negative energy. (Typically,as Dirac noted, the negative root is suppressed: if we pretendit isn’t there, maybe it will go away.)

The remarkable thing is that, starting with a simple field,particles emerge as quanta of the field. Treiman further notesthat there are families of one, two, or all possible numbers ofparticles. More, in multiparticle states all the particles must beexactly identical. And finally, this particular “model field,” delib-erately chosen for its simplicity, describes as its quanta neutral,spin-zero bosons. According to Treiman, “. . .it is easy to con-struct analogous linear theories for charged as well as neutralparticles of various spins. Theories involving charge yield bothparticles and antiparticles as their quanta.” (We have previous-ly noted that the quantum spinor field governed by the Diracequation has just such properties.)

We are looking for simplicity here, applying Ockham’sRazor. And it turns out that the simplest possible quantumfield would necessarily be populated with all possible num-bers of strictly identical, neutral, spin-zero bosons. Such parti-cles, as noted above, can have either positive or negativeenergy. To quote Gribbin (1998b), “In the quantum world afield must give rise to particles.” (Emphasis his.) However, nosuch field of unlimited numbers of neutral, spin-zero posi-tive-energy bosons exists. Why not, if a field must give rise toparticles? However, as we have argued above, a “sea” of neg-ative-energy, neutral, spin-zero bosons is a requirement ofquantum mechanics itself: of the energy equation, and ofthe Dirac equation of the electron. Two of its solutions callfor negative-energy electron-positron pairs, which wouldnecessarily associate as neutral spin-zero bosons. Thus thesimplest possible form that the Vacuum Electromagnetic Fieldcould take would have as its unique solution exactly thesame result as the Dirac spinor field: a “sea” of unlimitednumbers of negative-energy electron-positron pairs. Wehave now approached this from three different directions,and they all point to the same result.

Treiman complains that, in the “model field” describedabove, there are no interactions. It is what is called a “free fieldtheory,” a theory free of interactions. Start with a state inwhich two particles approach as for a collision, and in fact theywon’t collide, because the classical field equation on which itis based is linear: the sum of any set of solutions is also a solu-tion. (For this reason, quantum field theory, with its multiplefields, one for each “fundamental” particle, requires non-linear


has no “left-behind potential hill.” Thus, changes in electro-magnetic potential must propagate apparently instanta-neously over any distance.

The same is true of gravitation, as was shown in the clas-sical Laplace demonstration based on the absence of anychange in the angular momentum of the earth’s orbit(Laplace, 1966), and as has been repeatedly demonstrated byVan Flandern (1993, 1996, 1998). He shows that even in astatic field, if gravitation propagated merely at light speed, itwould result in a “couple,” which would measurablyincrease the earth’s angular momentum. This, of course,does not happen. He further shows that General Relativity,supposed to be a local theory, nonetheless assumes andrequires instantaneous changes in the “curvature of emptyspace,” and so is non-local.

Therefore, both electromagnetism and gravitation actnon-locally. They also must be representative of the non-localreality that Bell’s proof shows must contain the local effectswe normally experience.

However, there is one and apparently only one extendedstructure that exhibits non-locality: the BEC. If you insert anelectron into one end of a BEC, however large, an electronemerges from the other end faster than light can travel thatdistance—this is the phenomenon of superconductivity. Thisnon-local action results from the fact that every constituent ofa BEC must be governed by the same wave function and everypart must be in the same state and therefore act as one.

Bell’s proof and the experimental facts of electromagnet-ism and gravitation require a non-local reality. Dirac’s equa-tion, in requiring a universal BEC, provides just that.Therefore all these proofs of non-locality amount to proofsof a universal BEC, our one non-local extended structure. Wewill later demonstrate that these non-local actions are notliterally instantaneous, but take the finite time τ. This resultsin clear, intuitive non-local models of electromagnetism andgravitation which nonetheless act by direct contact, and thusdemonstrate causality.

We will show that this ends the centuries-long debatebetween those who accept the evident action-at-a-distanceof gravitation and electromagnetism as unmediated andacausal and those who insist on causality despite the appear-ances. Accepting that we are imbedded in a universal BECgives the best possible answer to both. As we will see, it pro-vides physical but non-local models which nonethelessdemonstrate direct contact causality.

From what we know of BECs from those we have man-aged to create in the laboratory, this BEC would be thedaddy of them all. It is composed all of negative-energy,one-dimensional epos, all with identical negative energy(but no “mass”). Each epo is charge condensed so thateach charge “sees” only its oppositely charged “pair” (as inthe Cooper pair). No unbalanced charges allowed, no pos-itive energy allowed, and the entire BEC described by a sin-gle wave function.

How many times must nature describe this to us, beforewe get the picture? We have looked at three equations, theenergy equation, Dirac’s equation, and this very simplestquantum field, which we might call the “Zeroth QuantumField” (ZQF). Each of them seem to be describing this sameobject, a universal BEC composed of unlimited numbers ofspin 0 neutral negative-energy bosons, which have to beone-dimensional electron-positron pairs.

All this happens as we approach the zero-point. Orderincreases, everything is bound closer together. Negative(binding) energy becomes predominant. Everything seemsto settle in toward a BEC. (Here we might note a further dif-ficulty with the Standard Model and its Grand UnifiedTheories [GUTs]. These assume that at higher and higherenergies the forces and particles lose their identity and unify.However, the experimental evidence points exactly the otherway. Higher positive energies allow entities more degrees offreedom to resonate in more and different modes, whereas atlower energies they approach the BEC, in which the binding(negative) energy is so strong that the parts lose every bit ofidentity and must all be in the same state. This is empha-sized by the failure of the prediction made by every GUTthat the proton must be unstable. So far, no proton has everbeen observed to decay. Result: no GUTs.)

A BEC can only result from the total dominance of nega-tive (binding) energy over positive. Looked at that way, theinterface between negative and positive is not 0˚K, but a fewdegrees higher, perhaps around 2.7˚K. In any case it is differ-ent for different substances, and certain BEC characteristicsmanifest themselves at much higher temperatures.

And at the zero-point, instead of no energy, there is sudden-ly a flood of it. (Zero-Point [ZP] energy—hν/2 for each mode ofthe vacuum electromagnetic field.) Why would this be, if thereis “nothing” beyond it? What generates this energy, where doesit come from, if it isn’t another “miracle”? [Big Bang theoryinsists that the microwave background comes from the exactother end of the energy spectrum, from a state of infinitelyhigh energy and temperature, created out of nothing: by a“miracle.” We suggest that this is a violation of causality: infi-nite temperatures can not be a “proximate cause” of an energyfield near 0˚K. We suggest that the source of this energy shouldbe sought nearer at hand, at the adjacent “zero-point” with itsunlimited energy, and beyond, in negative territory. We willlater look at this in more detail.] Again, this is real energy, withmany measurable effects.

What becomes clear from all this is that the negative ener-gy sea of bosons (epos) called for by the equations must existin the form of a BEC. According to the equations and everythingwe know, our reality is surrounded by and immersed in a vast, allpervasive Bose-Einstein Condensate.

This is a rather startling conclusion. However, it is support-ed not only by the equations of quantum mechanics, but by alarge and growing body of clear experimental evidence.

Bell’s Inequality and the now numerous proofs thereof(Clauser and Shimony, 1978, Aspect et al., 1982) demon-strate that our reality must be non-local, connected fasterthan light. As Nick Herbert (1985) puts it, “A universe thatdisplays local phenomena built upon a non-local reality is theonly sort of world consistent with known facts and Bell’sproof.” (Emphasis his.) Phase-entangled quantum objectsshare information apparently instantaneously, no matter howgreat their spatial separation.

Non-local or faster than light action also must be a prop-erty of the electromagnetic field, according to a whole seriesof experimental results starting with the Sherwin-Rawcliffeexperiment (1960) and continuing with those of theGraneaus (1982, 1983, 1985, 1987, 1993) and Pappas (1983,1990A, 1990B). These experiments all show that changes inthe electromagnetic field must propagate much faster thanlight, apparently instantaneously, so that a moving charge


“half a boson.” In terms of energy, “half a boson” is hν/2.This is exactly the zero-point energy called for by the equa-tions. The electron and positron in the BEC have no positiveenergy, only charge. But together they make a neutral spin-zero boson whose energy is hν. In this case ν = 1/τ, around1.6 x 1023 Hz. This would give the epo an energy (E = hν) ofaround 660 MeV, and give each “mode” of the vacuum elec-tromagnetic field an energy of half that, 330 MeV. Thus the“Zero-Point Energy” (ZPE) and the jitter-motion(Zitterbewegung) caused by it both emerge as direct conse-quences of Dirac’s equation. As we will see later, “half anepo” is also “half a photon.”

The Electromagnetic FieldWe have seen above that Dirac, Oppenheimer, and Heisenbergall proved that every ion must immediately be surrounded byunlimited numbers of the opposite charged ends of epos.Experiment has since confirmed this to better than ten signif-icant figures. However, if these are “real” epos “created” by thecharge, this makes the mass of the ion “slightly infinite.”

There is a further problem with the conventional view.Unlimited numbers of epos means that in every directionfrom an electron, for instance, there would be the positronend of an epo. This would completely neutralize the chargeof the electron, so that it could not be felt or measured out-side of this surrounding sphere of positrons. Recognizingthis, conventional theory supposes that the “bare” charge ofthe electron must be some unknown higher value, probablyinfinite, which the sphere of positrons reduces to the“dressed” charge that we measure (Pais, 1994). But this sup-position ignores one little matter: if the “bare” charge of theelectron were infinite, so would be the charges of thepositron ends of the epos. Whatever “bare” charge onechooses to assign to the electron, it would be completelyneutralized by this sphere of epos. Moreover, if the “bare”charge of the electron were infinite, the “bare” charge of theproton would also have to be infinite.

We have shown above that electron and positron must setup a stable relationship at a distance of τc, 1.87 x 10-15 m.However, this is the measured diameter of the proton, and ina nucleus the nucleons are packed closer together than this.Therefore, there is no way that the two protons in an alphaparticle, for instance, could be shielded from each other, soif the proton had an infinite charge the alpha particle wouldinstantly explode. What is true of the alpha particle is a for-tiori true of nuclei with even more protons packed closelytogether. From this one must conclude that the proton can

Of course, the BEC wasn’t well described in 1934, so itis no mystery why Dirac didn’t see that this is what hisequation calls for. Only in the light of more recent find-ings is it evident that Dirac’s “sea” must be a BEC. For, ofcourse, it fills the crucial needs of Dirac’s sea—it is “full,”so that no positive energy particle can “fall in” unless itfirst loses all its positive energy, and then only if a balanc-ing antiparticle similarly divests itself. Further, it has no“mass,” hence no inertia or gravitational interaction, so itis virtually undetectable. [Haisch and Rueda (1997) insistthat negative “mass” is impossible, since “mass” is a resultof the action of the ZPF on polarizable entities. Since thiswould not include negative-energy epos in a BEC, they arequite correct. They don’t have “mass.” Negative energy isquite a different thing.] And as we will see, it is the sourceof the unlimited polarized electron-positron pairs that theDirac equation requires, and experiment shows, to be sur-rounding every “bare” charge.

Physics Through the Looking-glassLet’s step back a moment and look at what the full Diracequation and the simplest quantum field, the ZQF, seem tocall for. As Gribbin (1998a) remarks, “In the quantum worlda field must give rise to particles.” Unlimited numbers ofthem, the quanta of the field. This is the famous “secondquantization.” According to QFT, there is nothing in the uni-verse but quantized fields. We here invoke the simplest possi-ble quantum field which “must” supply the unlimited num-bers of epos called for by the full Dirac equation. The ques-tion might then be “Why would this ZQF supply negativeenergy epos? One would think that the first ‘category’ to befilled would have positive energy.” Here we might recall thatwe call positive energy “positive” only because of BenFranklin’s mistaken choice. It would be much more logicalto call the electron, the very unit of electricity, positive insign, in which case what we call “negative energy” would bepositive energy, and would be the first “category.”

That there is a negative-energy “sea” balancing the positiveenergy of our reality restores the symmetry between negativeand positive energy called for by the energy equation andDirac’s equation. Moreover, there are indications that negativeenergy is primary. This has profound implications.

For one thing, we can now follow the process miscalled“creation,” and see where the energies come from. If thenegative energy BEC is a completely filled sea of epos, underevery mode of the vacuum electromagnetic field would beeither an electron or a positron, one end of an epo—hence

Figure 1. “Vacuum polarization” around unlike charges. Figure 2. “Vacuum polarization” around like charges.


they are. So this pattern is a direct solution to the equation.)Note that this result is only possible if the total number ofpositive and negative charges in the universe, whether in the“positive energy” realm or the “negative energy” realm orboth, is exactly equal. And this means that the numbers ineach can only change in pairs—epos.

Furthermore, however many epos the BEC “sacrifices” toaccomplish this neutralization, the number of epos in the BECremains exactly the same. Infinity minus infinity is still infinity.

According to the Zeroth Quantum Field and the “unex-purgated” Dirac equation, verified by experiment, this pat-tern must happen. Moreover, since this complete sphere ofpositrons would neutralize any charge of the “bare” electron,this induction pattern is the only way any charge on the electroncould be felt or measured outside this sphere. Charge is carriedby proxy by these chains of epos. The strength of the chargemeasured anywhere would vary as the inverse square of thedistance, as the Coulomb gauge requires. (This strengthwould be measured in “epo chains per unit area,” just asFaraday would have us measure “lines of force per unitarea.”) Since this pattern must happen, and since it duplicatesevery aspect of the electromagnetic field, as is easily verified,we submit that this is the electromagnetic field, much asFaraday or Maxwell would have drawn it, with Faraday’s“lines of force” exactly duplicated by chains of epos.

The model exactly combines the properties Maxwellexpected his mechanical ether to exhibit, embodied in hisequations. This ether must, he argued, be in a condition ofmechanical stress:

The nature of this stress is, as Faraday pointed out, atension along the lines of force combined with anequal pressure in all directions at right angles to theselines. . .From the hypothesis that electric action is nota direct action between bodies at a distance, but isexerted by means of the medium between the bodies,we have deduced that this medium must be in a stateof stress. (Maxwell, 1873)

In this “epo model,” the “tension along the lines of force”is supplied by the attraction between the aligned unlikecharges in the epo chains. The pressure in all directions atright angles to the epo chains is supplied by repulsionbetween the like charges in different chains lined up rough-ly parallel to each other. This also accounts for the repulsionbetween like charges of “real” ions, as seen in Figure 2.(These features are recognized in plasma physics, where theyare called “MHD” or “Alfven” waves. No satisfactory expla-nation has hitherto been given for them. It is, moreover, aneffect that can not possibly be explained by the photonmodel.) And as Rosser (1971) showed, the magnetic forcecan be derived from the Coulomb force for charged particlesin relative motion. A charged particle, negotiating this“field,” would follow a curved trajectory exactly in accor-dance with Maxwell’s equations.

Note that, in SED, the quantized electromagnetic field is suc-cessfully modeled as a collection of one-dimensional oscilla-tors, each a vector whose direction and force are determined byits place in the “field.” Our “epo model” of a vector field ofone-dimensional (massless) oscillators is an exact analog of thismodel, “already quantized.” The same is true of conventionalquantum theory. As Taylor (2001) remarks:

only have a charge of exactly +e. However, a proton ion, asshown by experiment, must instantly be surrounded by asphere of unlimited numbers of the electron ends of epos.Since its charge must be exactly +e, this charge would becompletely neutralized, which we know is not the case. Sosomething is terribly wrong with the “conventional” view.

However, all of these difficulties disappear when regard-ed from the new viewpoint of an infinite sea of negativeenergy epos. An ionic electron must instantly be surround-ed by a sphere of the positron ends of polarized epos, as hasbeen verified by experiment. The positrons must form asphere of diameter τc. But this takes no energy, since in theinfinite sea there is already a positron and an electron atthe exact points necessary to make that sphere of polarizedepos, each radial to the ion. The only difference is thatthese are now positive energy epos, as their vectors point inreal directions. So far this is the same as the conventionalview, except that it does not violate conservation.

The story is not over, though, as each positron in theinner sphere has a potential induced by the ionic electron.(At that tiny distance, the force between electron andpositron is enormous.) This would unbalance the epo,inducing a potential between the positron and its electron,which would again force the electron end to polarize anoth-er epo, and so on indefinitely, forming chains of polarizedepos. These chains would continue into space until they ter-minated at a charge of opposite polarity. (See Figures 1 and2.) Again, this in a way is the same as the conventional view:the equations call for unlimited numbers of epos. They donot, however, say where they are, and the conventional viewdoes not carry the process to its logical conclusion, which isshown in Figures 1 and 2.

The equations call for a negative-energy BEC that fills allspace, but nearly undetectably, since it vibrates in “imagi-nary” directions. It is full of equal numbers of positive andnegative charges, but they are “charge condensed,” so thateach charge only “sees” its paired antiparticle charge, mak-ing a one-dimensional vibrating object similar to the“strings” in many of the popular string and superstring the-ories. This one dimensional string-epo can vibrate in any“imaginary” direction, but it must average τc in distancefrom its antiparticle.

However, a BEC cannot tolerate an unbalanced charge.Therefore, an unbalanced charge, an ionized electron forinstance, must immediately be neutralized. As we have seenabove, the equations call for it to be instantly surrounded bythe positive ends of an unlimited number of polarized epos.

We can now see that this “neutralization of a barecharge” called for by the equations is a requirement of theBEC, which can’t tolerate an unbalanced charge; however,it has unlimited (infinite) numbers of epos that it canthrow at it, to neutralize it.

Therefore, each “bare” electron is immediately surround-ed by unlimited numbers of epos. However, once again thiswould not solve the BEC’s problem. Only when every unbal-anced charge is neutralized by chains of epos connecting it to andneutralizing every opposite unbalanced charge is the BEC againstable. So the very stability of the BEC requires chains of eposin the patterns shown in these two figures. (And of courseDirac’s equation calls for unlimited numbers of polarizedepos—as is verified by experiment—but it doesn’t state where


energy carried by lines of epos pointing in the vector direction.An epo carrying “real” angular momentum would

change from a spin-0 boson to a spin-1 intermediate vec-tor boson—vector because any amount of energy less than2mec2 is unstable, and can only be carried for one-halfcycle. Since it is unstable, it must dump the energy, polar-izing the next epo in line. And since it is an “epo carryinga photon,” we suggest the name “epho.”

At this point the “photon” amounts to a wavefront trav-eling at c, a coherent bunch of intermediate vector bosons,each carrying a portion of the angular momentum. They takeall possible paths, following the Feynman “path integral” or“sum-over-histories” version of QM, with most of the pathsbeing cancelled by destructive interference. The remainingpaths, summed, make up the amplitude, the Ψ wave. (Again, a“mathematical abstraction” takes on a certain physical form.)

Note how exactly the Feynman sum-over-histories methodmirrors the actual process. Like Feynman’s version, the“ephos” take all possible paths. Feynman breaks down eachpath into a series of short arrows or vectors, the directions ofwhich, summed, keep track of the path’s phase. We have seenthat each epho is a vector, rather shorter than Feynman’s, eachepho being only 1.87 x 10-15 m long. Feynman could notexplain why a “path” should have phase, he merely assertedthat it did. We can now see that it has phase because each ephoon each “path” is itself an electromagnetic wave with phase.Together they form a coherent wavefront. Ephos on the “leastaction” path will reinforce each other, and any epho that takesa “wild” path gets out of phase with the wavefront, suffersdestructive interference, its angular momentum is cancelled,and it drops back into the epo “sea.” Thus the only ephos thatcontinue to carry energy are those that are close to the (leastaction) “classical” trajectory.

In the famous “two slit” experiment, many of the pathscomprising the epho “wave” which represents the “single pho-ton” go through each slit, and interfere with each other, form-ing the well-known Ψ wave “interference pattern.” At thescreen, one of them is randomly selected from this densité deprésence according to |Ψ|2, the probability, to deliver all of thewave’s angular momentum to a single electron in the screen.

Again, the “collapse of the wave function” into a singleresult has never been given a satisfactory explanation.However, it seems likely that the first epho positron to select a“real” electron as its “other end” causes the collapse. Thosewho favor the “many universes” version of QM might say thatall of the vector bosons deliver the full amount of angularmomentum to different electrons, but in different universes. Itis a good thing that angular momentum is conserved in thismanner, one electron’s discarded spin all being delivered to

In quantum theory, the electromagnetic field behavesexactly as an assembly of arbitrarily many masslessparticles. The number of particles of a given momen-tum and energy just corresponds to the energy levelof the corresponding electromagnetic oscillator.

Further, we note that what had been taken to be a math-ematical abstraction, the “electromagnetic field,” now has adefinite physical reality.

So, merely by considering what Dirac’s negative energy“sea” must represent, we are presented with an unexpectedbonus: the first direct contact, causal, workable model of analready quantized electromagnetic field.

Conservation of Angular Momentum(a.k.a. “The Photon”)If the epo is the quantum of the electromagnetic field, asshown above, this would seem to leave the “photon” inlimbo. Let’s look at a single electron of hydrogen, orbitingthe proton at some energy level above its ground state. Aftera few thousandths of a second, it will jump to its groundstate. To do so, it must lose angular momentum—spin—in theamount of hν. In the conventional view, the electron“emits”—instantly creates—a “particle” called the “photon,”which is an electromagnetic “wavicle” traveling at velocity cand which delivers the angular momentum intact to someother electron, whereupon it is no more. Since Einstein ban-ished the aether, however, the question has been “what iswaving?” The photon has no rest mass, and contains nocharges—so it violates our kinetic definition of energy.

However, in every situation in the macrocosm (andaccording to Newton’s laws) in order for a “real” object to getrid of spin angular momentum, that real object must setsome other real object spinning. Can the photon be the onlyexception? As we will see, it isn’t. For while an electron in itsground state is “charge condensed,” in that it only “sees” itsproton, and its proton only “sees” it, an electron in a higherorbit has a slight unbalanced charge which must cause theBEC to surround it with epos, as above. And if an electronneeds to lose spin, what more natural than that it set spin-ning those objects closest to it, the polarized epos that sur-round it? They have charges, and are pointing in “real”directions, so they can absorb the “real” (positive) spin ener-gy that the electron has to get rid of.

So the electron gives a tiny sidewise “push” to certainpositrons in the sphere surrounding it, and then it is “gone”—it is in its ground state. The epos are left “holding the spin,”some more than others, because the lost spin is a vector quan-tity, and its energy will go primarily to epos that are pointing inthe vector direction. Since the electron is gone, the epos are nolonger in chains, and the spin energy will travel up the epo“string” (at velocity c) exactly the way a sidewise impulse willtravel up a plucked guitar string. (Note that a sidewise impulsegiven to a charged particle [an “electric wave”] will, byMaxwell’s equations, generate a magnetic wave at right angles.)

By the time the energy has reached the electron end, theelectron has become a positron, again with a sidewise impulse,so to conserve angular momentum it must select and polarizesome electron in exactly the right direction at the right dis-tance. It thus initiates a vector line of epos, each carrying thespin energy “bucket-brigade” style at velocity c. Therefore the“photon” at this point would be a wave, carried by epos,spreading at velocity c in every direction, but with most of the

One of the tragedies of science is

Lorentz’s death in 1928, just as Dirac’s

equation was formulated, as Lorentz

surely would have recognized the nega-

tive-energy sea as responsible for his

electromagnetic aether.


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Deutsch, D. 1997. The Fabric of Reality, London, Allen Lane.Dirac, P.A.M. 1928a. Proceedings of the Royal Society A, 117, 610.Dirac, P.A.M. 1928b. Proceedings of the Royal Society A,

118, 351.Dirac, P.A.M. 1930a. Proceedings of the Royal Society, 126, 360.Dirac, P.A.M. 1934. Proceedings of the Cambridge Phil. Soc.,

30, 150.Dirac, P.A.M. 1963. Scientific American, May, p. 86.Feynman, R.P. 1985. QED: The Strange Theory of Light and

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45, 245, 343. Gleick, J. 1992. Genius: The Life and Science of Richard

Feynman, New York.Graneau, P. 1982. “Electromagnetic Jet-propulsion in the

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Solid Electric Conductors,” Physics Letters 97A, 253-255. Graneau, P. 1987. “Amperian Recoil and the Efficiency of

Railguns,” Journal of Applied Physics, 3006-3009.Graneau, P. and Graneau, N. 1985. “Electrodynamic

Explosions in Liquids,” Applied Physics Letters, 46, 468-470.Graneau, P. and Graneau, N. 1993. Newton versus Einstein,

Carlton Press, New York. Gribbin, J. 1998a. Q is for Quantum, The Free Press, New York.Gribbin, J. 1998b. The Search for Superstrings, Symmetry, and

the Theory of Everything, London, Little Brown & Co.Haisch, B., Rueda, A., and Puthoff, H.E. 1994. “Inertia as a

Zero-point Lorentz Field,” Phys. Rev. A, 49, 678. Haisch, B. and Rueda, A. 1997. “The Zero-point Field and

the NASA Challenge to Create the Space Drive,” Jour. Sci.Explor., 11, 4, 473.

Heaviside, O. 1890. Electromagnetic Theory, London.Heisenberg, W. 1928a. Letter to W. Pauli, PC, May 3, 1928,

Vol. 1, p. 443.Heisenberg, W. 1928b. Letter to W. Pauli, PC, July 31,

1928, Vol. 1, p. 466. Heisenberg, W. 1931. Annalen der Physik, 9, 338.Heisenberg, W. 1934a. Letter to W. Pauli, PC, February 8,

1934, Vol. 2, p. 279.Heisenberg, W. 1934b. Zeitschr. f. Phys., 90, 209.Heisenberg, W. 1936. “Die selbstenergie des Electrons,”

Zeitschr. f. Phys., 65, 4-13.Heisenberg, W. 1938a. “Uber die in der Theorie der

Elementarteilchen auftretende universelle Länge,” Annalender Physik Lpz., 32, 20-33.

Heisenberg, W. 1938b. “Die Grenzen der Anwendbarkeitder bisherigen Quantentheorie,” Z. Phys., 110, 3-4, 251.

Heisenberg, W. 1944. “Observable Magnitudes in theTheory of Elementary Particles,” Z. Phys., 123, 1-2, 93.

Heisenberg, W. 1951. “On the Question of Causality inthe Quantum Theory of Elementary Particles,” Z.Naturforsch, 6a, 281.

Herbert, N. 1985. Quantum Reality, Doubleday, New York.Huang, K. 1952. Am. J. Phys., 20, 479.Ives, H. 1945. “Derivation of the Lorentz

Transformations,” Philosophical Magazine, 36, 392-403.Ives, H. 1949. “Lorentz-type Transformations as Derived

from Performable Rod and Clock Operations,” Journal of the

another single electron, as other-wise we would never see the stars.(The wavefront of a single “photon”from a distant star can be biggerthan a continent—if this energy wasnot delivered to a single electron,the energy would be so diffuse thatwe probably would never havebecome aware that stars other thanour own sun existed.)

Considering the properties of theBEC, however, we can make a cer-tain amount of sense of the process.

The “rules of the game” seem to be that if the “photon” isgenerated by the jump of a single electron, the BEC mustfind a single electron, somewhere, to accept that angularmomentum. (We may assume that the spreading Ψ wave car-ries as information a certain “memory” of how it was gener-ated.) This amounts to an analog-to-digital conversion, withthe sum of the angular momentum of the entire wave beingdelivered to a single electron, a “point event.” As Gribbinnoted, above, the universe “makes the computation” andpresents us with the result. If, however, the signal was gener-ated by the movement of many electrons as in a plasma orconductor, the resulting radio wave’s angular momentumcan set multiple electrons moving, as in an antenna.

So, again, another unexpected bonus: a model of the“photon” that doesn’t violate the kinetic theory of energy.Note that the model gives physical meaning both toFeynman’s path integral version of QM and to the Ψ wave.

Further, it should be noted that since each epho wave indi-vidually travels at c, the velocity of light would be independ-ent of the velocity of the source, and the same in any frame ofreference. It would in fact be Lorentz’s electromagnetic aether(Lorentz, 1909). The transmission of light would agree withLorentzian relativity, which meets all the tests devised forSpecial Relativity (Ives, 1946, 1949, 1950, 1951), includingthose that SR fails, such as the Sagnac effect (Sagnac, 1913) andthe Silvertooth effect (Silvertooth, 1987, 1989, Silvertooth andWhitney, 1992). One of the tragedies of science is Lorentz’sdeath in 1928, just as Dirac’s equation was formulated, asLorentz surely would have recognized the negative-energy seaas responsible for his electromagnetic aether.

References ________________________________________Arp, H.C. 1987. Quasars, Redshifts and Controversies,

Interstellar Media, Berkeley, CA.Arp, H.C. 1998. Seeing Red: Redshifts, Cosmology, and

Academic Science, Apeiron, Montreal. Aspect, A., Dalibard, J., and Roger, G. 1982. “Experimental

Test of Bell’s Inequalities Using Time-varying Analyzers,”Physical Review Letters, 49, 1804.

In Part 2 (IE #44), the specific implicationsof the negative energy sea will be examined,which include everything from alterednuclear physics to the spacing of the planets.

H. A. Lorentz (1853-1928)


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Sirag, S.-P. 2000. ISSO, October 8 - November 20.Taylor, J.C. 2001. Hidden Unity in Nature’s Laws,

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by Chelsea Pbl., New York.Lederman, L. 1993. The God Particle, Bantam Doubleday

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and Lorentz/Grassmann Force Laws and LongitudinalContact Interactions,” Physics Essays, 3, 15-23.

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Sagnac, G. 1913. “The Luminiferous Ether Demonstratedby the Effect of the Relative Motion of the Ether in anInterferometer in Uniform Rotation,” Comptes rendus del’Academie des Sciences (Paris), 157, 708-710, 1410-1413.

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Summary of Part 1 (Infinite Energy, Issue #43)We show that the Standard Model (SM) of particle physics istotally inadequate by any reasonable criteria, violating thebasic scientific rules of simplicity, mathematical consistency,causality, and conservation. All these violations stem fromthe 1930s, when by a mathematical trick the Dirac waveequation was truncated to eliminate its negative energy solu-tions. Recent developments, however, have shown that timeis quantized (Treiman, 2000), thereby eliminating the verybasis of that mathematical trick, as it would involve massiveviolations of conservation of mass/energy.

The energy equation and Dirac’s equation call for bothpositive and negative energy. Thus they are symmetricalwith respect to energy, as are the forces of physics. Weshow that positive (repulsive) forces increase positive ener-gy, while negative (attractive) forces, such as gravitation,the strong nuclear force, and the Coulomb force betweenunlike charges, all increase negative energy. According tothe modern kinetic theory of mass-energy, negative energywould merely be a vibration of charges at right angles toour ordinary dimensions, in an “imaginary” direction. Theequations of QM, which all include “i”, therefore indicatethat these functions are complex, including vibrations in“imaginary” directions. This understanding explains sever-al anomalies with the electron, such as its velocity eigen-value of ± c, which can only be in an “imaginary” direc-tion. It also explains the electron’s anomalous spin of \/2.

The solutions to Dirac’s equation describe a “spinor” fieldin which electron changes to positron every τ, the quantumof time, (2e2/3mc3, equal to 6.26 x 10-24 seconds). An elec-tron-positron pair (“epo”) therefore must form a neutralspin-zero boson with electron and positron alternating everyτ. A quantum field such as the Dirac spinor field must giverise to particles, unlimited numbers of them (Gribbin,1998b). Therefore, the Dirac field must give rise to a “sea” ofnegative-energy bosons which, since they are “below zero,”must form a universal Bose-Einstein Condensate (BEC).

This universal BEC can not exist in the presence of unbal-anced charges, so every unbalanced charge must instantly besurrounded by epos raised from negative to positive energy.They connect and neutralize every unbalanced charge, form-ing the “electromagnetic field,” which is composed of chainsof one-dimensional epos connecting and balancing everyunbalanced charge. They carry charge “by proxy.”

The universal BEC can’t abide positive energy either.When an electron jumps from a higher energy level to alower one, thereby losing (positive energy) angularmomentum, this momentum is absorbed and carried bythe epos that surround it, forming a wave of epos carryingangular momentum, which carry the “photon” accordingto the Feynman “path integral” version of QM. The pat-tern of these epos form the photon’s Ψ wave.

A “Theory of Everything”?We have seen the power of Dirac’s equation, when all of it istaken seriously. In a sense, though, Dirac took it even moreseriously. It is not an equation of the electron, as it is popu-larly called. It is a relativistic generalization of theSchrödinger wave equation, which is said to “contain mostof physics and all of chemistry.” Dirac thought of it as aTheory of Everything—he thought that its solutions shouldinclude “everything that waves,” i.e. every possible particle. Ashe was deriving it, he hoped it would have only one solu-tion—the one, unitary particle out of which everythingcould be made (Dirac, 1933). Then, when he found that ithad multiple solutions, he thought that one of its solutionsmust be the proton—as at that time, the proton and the elec-tron were the only known particles, and it was ferventlybelieved that they were the only particles. This is why Dirac,in several of his early attempts to use the equation, enteredin as the mass the average mass of electron and proton (Pais,1994). This didn’t work, convincing him that the other“real” particle (the other positive energy one) had to have thesame mass as the electron, but the opposite charge. Thus hepredicted the positron, but gave up his dream that his equa-tion was a “Theory of Everything.” (Of course the discover-ies of the neutron and the positron, and the conviction thatthe photon also was a particle, didn’t help any.)

So, powerful though this equation is, it did not live up toits discoverer’s expectations. It was not unitary, and failingthat, it was not even a Theory of Everything.

The annoying thing is, it should be. It generalizes a verygenerally applicable equation—the Schrödinger wave equa-tion—and makes it covariant. We have seen that every oneof its requirements and predictions, including the negative-energy epo, has withstood every test. It is as valid and widelyapplicable an equation as has ever been discovered. It is as gen-eral as the whole universe. It should describe “everything thatwaves.” Yet as solutions, instead of general ones, it has particu-lar ones: just the positive energy electron and positron, andtheir negative energy counterparts. In a sense, though, that isunitary: two of the four are just different energy states of thesame particles, and electron and positron turn into each other

Dirac’s Equation and the Sea of Negative Energy_____________________________ PART 2 _____________________________

D.L. Hotson*

What if Dirac was right to begin with

about his equation? What if those

four kinds of electron, two negative

and two positive, are all one needs to

build a universe?


ture, instead of increasing all the way down to zero? This isbecause, if the boundary between positive and negative is2.7˚K, photons with less energy than this would randomlydrop back into the condensate and out of “our reality”—theless positive energy, the faster they would drop, forming thelower curve of the black body.

If our positive energy reality is indeed made of “exhaust”from the BEC, then everything must be made of electronsand positrons, as that is all the BEC has to offer. However,“pair production,” one epo at a time splitting into electronand positron, leaves no net positive energy balance, as equalnumbers of them must sink back into the sea. The BEC musthave some other means of permanently expelling the largeamounts of positive energy that make up our reality.

β-decayThere is a major, unnoted anomaly in the relative abundancesof the three entities out of which all stable matter is made. Thenumbers of electrons and protons appear to be exactly equal.(By charge conjugation [C] and charge conservation as out-lined above, they must be exactly equal.) And while the mostcommon element, hydrogen, contains no neutrons, there is anexcess of neutrons in the more complex elements. If you countthe unknown but probably large number of neutron stars,there seem to be nearly as many neutrons as protons. Thusthere appear to be nearly twice as many nucleons as electrons.

However, unlike the simple electron, which seems to haveno parts, there is abundant evidence that nucleons are notfundamental. They do have parts, almost certainly not just afew parts, but swarms of them (Krisch, 1987; Pais, 1994; Rithand Schäfer, 1999). Somehow those parts must have beenassembled to make the nucleon. Modern theory dismissesthis as just another miracle. However, if nucleons cametogether in the same kind of way as the chemical elements,with compound units being compounded of simple ones, wewould expect electrons to be much more numerous thannucleons. How can a compound entity be more abundant thana simple one? Simple hydrogen is about 1012 times more abun-dant than compound uranium, which masses about 238 timesas much. The compound nucleon masses nearly 2000 times asmuch as the simple electron, so by this comparison we wouldexpect electrons to be at least 1013 times more abundant.

every half cycle—they are really the same particle, merely out-of-phase with each other (Huang, 1952). So one could say thatthe four solutions to Dirac’s equation are unitary—they describefour kinds of electron, differentiated by state and phase.

What if Dirac was right to begin with about his equation?What if those four kinds of electron, two negative and two pos-itive, are all one needs to build a universe? There are, after all,no wave equations for quarks, or for gluons, or for any of theother supposedly “fundamental” particles—yet they all wave.Could this mean that they are not fundamental at all? We willleave this question hanging while we consider a related one.

Where Do You Take Out the Garbage?This famous question, invariably asked of architecture stu-dents with regard to their beloved projects, has much widerapplicability. No organism (or energetic machine, for thatmatter) can function indefinitely in an environment of itsown waste products. (A dilemma that increasingly confrontsthe increasing numbers of mankind.)

The BEC, as these equations outline it, is not perhaps anorganism, but it is an energetic machine. Overall, it is com-pletely ordered, covered by a single wave function. But indetail, it is a hive of activity, full of charges going at thespeed of light. Its frantically gyrating epos fill every crannyin every dimension of the negative energy realm. However,the close quarters and random configurations must fre-quently put electron adjacent to electron in positions thatgenerate considerable amounts of positive energy. (Likecharges repel, which is positive energy.) The BEC can’t standpositive energy. It must get rid of it.

The BECs we can generate, at temperatures near 0˚K, needfierce refrigeration to maintain their integrity. The Big BEC issomewhere below zero. How is it refrigerated? Where do itswaste products go? Where does the BEC take out thegarbage, and where is its garbage pile?

I suggest that we are sitting in it. We seem to be, to put itbluntly, BEC excrement.

The BEC must generate positive energy in great quantities.All of its dimensions are full, even if it could accommodatethe stuff. It has to get rid of it. So it is no coincidence that“our reality” has a large positive energy balance. We are theBEC’s dump. (Literally, its “heat dump.”)

We have seen that the effective boundary between the pos-itive and negative energy realms is several degrees aboveabsolute, as BECs, superconductivity, and superfluidity allbegin to happen there. Mercury becomes a superconductor at4.1˚K. An “ideal gas” will form a condensate at 3.1˚K. However,for real substances, because of interactions between the mole-cules, the figure is somewhat lower. (The critical temperaturefor helium liquid is 2.2˚K.) This would seem to put the bound-ary right around 2.7˚K, or at least too close to this figure to becoincidence. We would expect the number of photons“dumped” from the BEC to peak there, falling off randomly oneither side of this peak to form a “black body” spectrum peak-ing at this temperature. This would seem to be the most prob-able explanation for some or all of the “microwave back-ground.” In any case, this vast number of photons seems muchmore likely to come from the negative territory adjacent to it,than from a Bang at the complete other end of the spectrum.(The infinite temperatures of a Bang can not be the “proximatecause” of an energy field near absolute zero.)

Why would the numbers of photons peak at this tempera-

In a total and massive reversal of our

expectations, the compound nucleon

appears to be nearly twice as abundant

as the simple electron. This immense

anomaly cries out for an explanation. It

is the clearest kind of indication that

the production of nucleons themselves

and the process of nucleosynthesis fol-

low entirely different kinds of laws for

some unknown reason.


no other process is/was of any importance. So just from this, we can be almost totally certain that what-

ever else happened, the universe we know began as a wholebunch of neutrons, and nothing but neutrons. (Another indica-tion that no Bang happened.) But there is one other significantfact. Beta decay is a “weak” interaction. As such, it does notobey the symmetry rules obeyed in virtually all other interac-tions. It is “left-handed.” Specifically, it violates both parity (P)and charge conjugation (C) (Pais, 1994), which is the produc-tion of matter and antimatter in equal amounts. Since a mas-sive violation of C is necessary to produce a universe of matterrather than antimatter, beta decay’s violation of C is highly sig-nificant. (We will examine the specifics later.)

Sherlock Holmes was of the opinion that “singularity isalmost always a clue.” And concerning the neutron we havethree singularities, each reinforcing our thesis that the uni-verse began with large numbers of lone neutrons. Each neu-tron was born anomalously left-handed, with the extraordi-narily long mean lifetime of 15 minutes, and with the fur-ther very peculiar property of being completely stable onceinside a nucleus. Without any one of these unique proper-ties, the neutron’s decay would not produce the peculiarabundances of the universe we observe. Each of these pecu-liarities would seem to be evidence for this scenario; togeth-er they virtually exclude any other.

So the big question now is: How does one make a neu-tron? Well, this argument certainly suggests an answer. Wehave seen that according to every experiment ever per-formed, matter and antimatter are always produced in exact-ly equal amounts. The experimental evidence thereforedemands a universe equally of matter and antimatter. Sincethe universe must be composed of equal amounts of matter andantimatter, and since the early universe was composed uniquelyof neutrons, the neutron must be composed of equal amounts ofmatter and antimatter. It’s very simple: the neutron must bemade of electron-positron pairs.

One further indication: we showed earlier that the epo one-dimensional “string” must be τc in length, or 1.87 x 10-15

meters long. If the neutron is made of epos, presumably this“string” length would have to be the diameter of the neutron.Within the limits of the scattering measurements, this is exact-ly the measured diameter of the nucleon.

So it would seem that there are several different approaches,all of which suggest that Dirac was right the first time about hisequation. Perhaps it is a Theory of Everything, and a unitaryone at that. Everything seems to be made of epos: the electro-magnetic field, the Ψ wave, the photon. If the neutron couldbe made of them also, that would be a clean sweep, at least ofthe universe’s stable entities.

Neutrosynthesis

We might say that the Dirac equation, by having only fourroots, predicts that everything else, including the neutron, mustbe made of electrons and positrons. How many epos make aneutron? The question is far from trivial. The answer can notbe 919, the mass ratio between epo and neutron. There wouldbe 919 x 2 like charges packed into a tiny space. The bindingenergy would have to be 80 or 90%, to hold such an aggrega-tion together, even if it were mostly “charge condensed.” So919 epos would mass, at most, about 370 electron masses. Wemight keep in mind the Pauli exclusion principle, which regu-

Instead, in a total and massive reversal of our expectations,the compound nucleon appears to be nearly twice as abundantas the simple electron. This immense anomaly cries out for anexplanation. It is the clearest kind of indication that the pro-duction of nucleons themselves and the process of nucleosyn-thesis follow entirely different kinds of laws for some unknownreason. Nucleosynthesis takes place in stars, and involves anadditive process: individual nucleons, or at most alpha parti-cles, are added one by one to produce the heavier elements.This explains the relative rarity of these heavier elements, asmuch more energy, special conditions, and quite a bit of luck(or “fine tuning”) are necessary to produce them.

However, because of their anomalous abundances, com-pound nucleons must be produced in some entirely differentmanner than the additive process that produces the heavyelements. This is a major indicator of what that processmight be—and what it is not. (It virtually rules out, forinstance, the production of these abundances in a “Bang,”big or little, as production in a “Bang” would mimic theadditive processes of solar nucleosynthesis, and produceorders of magnitude more leptons than nucleons.)

If there were some one known subatomic process whose endproducts were neutrons, protons, and electrons in their veryanomalous observed abundances, with almost equal numbersof each, we could be virtually certain—to a vanishingly smalluncertainty—that this is the process by which the universecame about. Is there such a known process? As it turns out,there is exactly one such known process: it is called β-decay.

Outside a nucleus, the neutron is unstable, but with anextraordinarily long mean lifetime. Whereas all of the otherknown unstable particles decay in nanoseconds or less, oftenmuch less, the neutron hangs around for 14.8 minutes on aver-age. After this uniquely long lifetime, a lone neutron will breakdown, emitting an electron and an antineutrino, and turninginto a proton. The antineutrino is almost never seen again—itcould go through light-years of lead without interacting. Butthis process produces electrons and protons in exactly equalnumbers. (They of course form hydrogen, the most abundantatom.) Moreover, the neutron itself, if it happens to beabsorbed into a nucleus during its 15-minute mean lifetime, isagain completely stable. (Except in certain radioactive nuclei.)And in stars, where nucleons are combined into nuclei, thereis abundant energy available to fuse electrons and protons backinto neutrons, where needed (Conte, 1999). This, of course,happens wholesale, in degenerate stars.

So given enough neutrons, the process of beta decay, alone andunaided, would produce exactly the very strange abundancesof the universe we observe. Moreover, we know of no otherprocess whose end products would be electrons and protons inexactly equal numbers, and neutrons in approximate equality.And since all stable matter in the universe is composed of justthese three products in just these proportions, it follows that

We can be almost totally certain that

whatever else happened, the universe

we know began as a whole bunch of

neutrons, and nothing but neutrons.


proton-electron mass ratio from the two numbers 10and 136, together with the number of unity, 1. . .Eddington’s 1, 10, and 136 are members of a well-known mathematical series that goes 1, 10, 45, 136,325. . .etc. . .The next number in that series is 666.(Sirag, 1977b)

Eddington’s series is (n2)(n2 + 1)/2, n = 1, 2, 3, etc. AsSirag points out, this group-theoretical point of viewaccords with Dirac’s above statement that four-dimension-al symmetry requires ten dimensions of curvature, ordegrees of freedom, in General Relativity (Dirac, 1963).Several of the string and superstring theories also require aspace of ten dimensions (Sirag, 2000), and as we saw, anelectron can vibrate in 136 different ways in ten dimen-sions. If we order these 136 vibrational modes two at atime—one for electron, one for positron (as in the epo)—this would give 136 x 135, or 18,360 different ways for alepton, joined as an epo, to vibrate in 10 dimensions. (Thisis Sirag’s computation, but he lacked the idea of electron-positron pairs. He ordered them two at a time “. . .e.g.,one for proton, one for electron. . .”)

Thus a combination of 9180 electron-positron pairswould be a very stable arrangement, filling all of the possi-ble vibrational modes in ten dimensions. We might imaginethem arrayed in a 10-dimensional vortex or “hypersphere.”(Note that this arrangement would come about in the nega-tive-energy BEC. As is well known, the only way that a BECcan rotate is in a vortex.) Moreover, Krisch (1987) has shownthat colliding protons act like little vortices, shoving eachother around preferentially in their spin directions.

What would be the mass of such an aggregation? Well, inquantum theory, one measures the energy, or mass, by tak-ing the temporal sine attribute of the Ψ wave. Since time isonly one of the 10 dimensions, this would give the aggrega-tion a mass of 18360/10, or 1836 electron-masses. Since it iscomposed of 9180 electron-positron pairs, such an entitywould have 0 charge: it would be neutral.

All symmetries are conserved in this arrangement, withexactly equal amounts of matter and antimatter. There is noreason why such an entity might not be produced, and

lates how many electrons may occupy a given shell in an atomby the possible number of different vibrational modes (differ-ent quantum numbers).

We have seen earlier that for reasons of symmetry the uni-verse must have ten dimensions, six of them (the negativeenergy realm of the BEC) in “imaginary” directions withrespect to our four (Dirac, 1963; Sirag, 1977b, 2000). Howmany different ways can an electron or positron vibrate inten dimensions? We might answer that by an analogy withthe periodic table.

Each electron shell contains the number of electrons thatcan vibrate in different ways. (The electron’s quantum num-bers.) At present, the periodic table consists of 100 elementsin eight complete shells (if you count the rare earth ele-ments) with 16 or so elements in an incomplete ninth shell.(Element 118 was claimed to have been synthesized at theLawrence Livermore National Laboratory in 1999, but theyhave recently retracted that claim [Gorman, 2001].)Completing that shell would give 118 elements, and a tenthcomplete shell would add another 18, for a total of 136. Soif elements were stable to atomic number 136, element 136would be a noble gas with 136 electrons in 10 completeshells. This means that there are 136 different ways for elec-trons to vibrate in 10 shells. Each of these shells amounts toan additional degree of freedom for the vibrating electron. Ifwe substitute 10 degrees of freedom, or dimensions, for these10 shells, it seems inescapable that there again would be 136different ways for electrons to vibrate in 10 dimensions.

These numbers figure prominently in one of the possibledesigns for a neutron made of electron-positron pairs. Thismodel was largely suggested by Saul-Paul Sirag (1977a) as a“combinatorial” model of the proton. He, however, consid-ered it mere number-juggling. The last time I talked to him,he was no longer interested in it, so I “pirate it” withoutscruple. With a few minor additions and changes, it turnsout to be a plausible model of the neutron.

. . . From Eddington’s group-theoretical point of view,creatures to whom space-time has four dimensions willfind algebraic structures having 10 elements and 136elements playing a very fundamental role.

Eddington attempted, unsuccessfully, to derive the

With this single, simple model for the production of neutrons from the unique solu-

tions to Dirac’s equation, we arrive at the extremely anomalous numbers of elec-

trons, protons, and neutrons in our reality. Moreover, this also explains the prepon-

derance of hydrogen over every other atom. Also explained is the oddity that elec-

tron and proton, which are seemingly very different particles, nonetheless have

exactly the same electric charge. A proton is seen to be simply a neutron that has lost

a single electron, leaving it with an extra positron. And the electron is not “created”

as it leaves the neutron; it was there all along. . .Moreover, it would seem to admit

of the possibility that energy, special conditions, and catalysis might synthesize neu-

trons at low temperatures, possibly explaining some or all of the neutrons, trans-

mutations, and excess heat produced in cold fusion.


Moreover, some 90% of the epos that make up the “Siragmodel” have 0 spin, being pure one-dimensional vibrationsin imaginary directions. The remaining 10% share “real”angular momentum, mostly canceling, which must, overall,amount to spin 1/2. But as this is a “real” spin, there is noth-ing to say that a “real” extended neutron with the large“real” mass of some 1838e is not “really” spinning with a“real” angular momentum of 1/2\. In order to obey Fermi-Dirac statistics, it must have this half-integer angularmomentum, but it is not necessary to assign that spin to anindividual electron or epo constituent when it can simply bea property of the extended neutron itself.

The Strong Nuclear ForceHowever, the prime merit of this model has to be its repre-sentation of the strong nuclear force. Here we need to notea strange coincidence: the mass of the proton, in electron-masses, is roughly the same as the strength of the proton’sstrong force, in electron-forces. (Mass of proton: 1836 elec-tron-masses. Strength of the electromagnetic force: the “finestructure constant” α = e2/hc = 1/137; strength of strongforce: g2/hc = ~15. Ratio: ~15 x 137, somewhere around 2000[Shankar, 1994].)

Thus the ratios of the masses and of the forces are rough-ly the same, “around 2000.” This is a major clue to thenature of the “strong force.”

Gravitation and the Coulomb force both have simpleinverse square “shapes” that operate over long distances.Theoretically, at least, they never drop to zero. However, theshape of the strong force between nucleons is radically dif-ferent and very peculiar. Up to a distance of around a fermi(10-15 m.), it is very strongly repulsive, keeping the nucleonsapart. Then, for no apparent good reason, it changes abrupt-ly to very strongly attractive, then drops off very rapidly, sothat at a distance of around three fermis it becomes immeas-urable. This peculiar shape has never been successfully mod-eled by any theory.

Note how current theory, in which the fudge is an accept-ed scientific procedure, “solves” this problem. Since currenttheory can’t model this observed force, it simply ignores it,and instead invents (fudges) an unobserved (fifth!) force car-ried by eight “gluons” (designed to be unobservable) betweeneighteen or thirty-six “quarks” (also designed to be unobserv-able) inside the nucleon. It then “suggests” that this fudgedgluon force in some unspecified way “leaks out” of thenucleon to make up the peculiar shape of the measuredstrong force. However, our “epo model” of the nucleon mod-els this very peculiar shape simply and intuitively.

Because of the uncertainty principle, the nucleon, with itsmeasured diameter of around 1.9 fermis, can not be a perfectsphere, but must be a pulsating spheroid. However, the eposthat make it up have “asymptotic freedom”—they vibrateindividually, and each lepton is free to form a relationship withany available antiparticle. This means that, as two nucleonsapproach each other, at a distance of about three fermis, elec-tron-positron pairs will begin to form, not just within thenucleons, but between them. (Pairs of “internucleon” eposwould have to form at the same time, keeping the total num-ber of paired charges in each nucleon at 9180.) This wouldcause a strong, short-range attraction between the nucleons asmore and more pairs formed. This would increase to a maxi-mum at around 1.5 fermis, after which it would rapidly turn

expelled from the BEC (thrust into “our reality”) wheneverthe random fluctuations of the BEC produced a positiveenergy of 1836 electron-masses, and spin energy in all tendimensions. (The suggestion is that it would be produced ina vorticular “storm” in the BEC, which would have spinenergy in all ten dimensions.) Moreover, since it has only10% positive energy and 90% negative or “binding” energy,such an entity would be stable despite packing 9180 chargesof like polarity into a very small hyperspace. This is the Siragmodel of the nucleon, slightly modified. Note that in ourBEC of unlimited density, there is already an electron and apositron in exactly the positions required for this synthesis(nothing needs to move), so only the positive energy andthe spin is required to produce a neutron.

The mass of a neutron is, of course, 1838.684 electron mass-es, not 1836. However, mass is a tricky business. The “effectivemass” can be quite different from the “bare mass,” as is shownin the conduction atoms of a metal (Pais, 1994). Because oftheir interaction with other electrons and with the positivecore, their effective mass can vary from 0.3e to over 10e. Andin a superconductor, “condensed state” electrons can have aneffective mass that can be 1000 times the “real” electron mass.We will later show that epos in a nucleon are in a semi-con-densed state. Furthermore, there are indications that mass mayvary with time (Narlikar and Das, 1980).

Among the felicities of this model, Sirag points out that ifyou divide the 18360 successively by 9, 8, 7, and 6, you getthe approximate mass-ratios of the other baryons, theLambda, the Xi, the Sigma, and the Omega. Since they havelarger ratios of positive (disrupting) energy to negative (bind-ing) energy, these baryons are progressively less stable.

With this single, simple model for the production of neu-trons from the unique solutions to Dirac’s equation, wearrive at the extremely anomalous numbers of electrons,protons, and neutrons in our reality. Moreover, this alsoexplains the preponderance of hydrogen over every otheratom. Also explained is the oddity that electron and proton,which are seemingly very different particles, nonethelesshave exactly the same electric charge. A proton is seen to besimply a neutron that has lost a single electron, leaving itwith an extra positron. And the electron is not “created” asit leaves the neutron; it was there all along.

Moreover, it would seem to admit of the possibility thatenergy, special conditions, and catalysis might synthesizeneutrons at low temperatures, possibly explaining some orall of the neutrons, transmutations, and excess heat pro-duced in cold fusion.

This model must, however, address the spin of the neu-tron. T.E. Phipps Jr. (1976, 1986) also suggests a model of theneutron made of electron-positrons, but his model runs intodifficulty with the neutron, which has a spin of 1/2\, justlike the electron and positron. But if one has equal numbersof electrons and positrons, each with opposite and cancelingspins, the resulting neutron should have spin 0, whereas itof course has spin 1/2, like all of the fermions.

But this reflects current physics’ tendency to regard thespin of the electron as somehow not a “real” spin, but a“pure quantum effect,” as Bohr liked to call it. But we haveshown above that it can indeed be regarded as a real spin,with real angular momentum, if one regards it as a complexspin, having angular momentum in one or more “imagi-nary” directions as well as its c2 spin in “real” directions.


together” gravitation, similar to LeSage’s “ultramundane cor-puscles,” whereas the other negative-energy forces act by“pulling together.” We suggest a model on the lines of theseother “pulling together” (negative-energy) forces, which alsoutilizes a residual effect of electromagnetism.

MagnetogravitationDirac’s equation predicts that the magnetic moment of theelectron should have a value of e\/2m. This is the magneticmoment balanced by the BEC, attaching every unbalancedcharge to a charge of opposite polarity, thus bringing theBEC back into balance. As shown above, however, the pres-ence of unlimited numbers of epos and their associated pho-tons give Dirac’s value a tiny unbalanced correction, multi-plying Dirac’s value by 1.0011596522, the ‘g’ factor. This fig-ure represents the best agreement between theory and exper-iment in all of science.

As a consequence, every electron has a tiny unbalancedmagnetic moment at the same phase of its cycle. Since timeis quantized, every electron will reach this phase of its cycleat the same instant. For its stability, the BEC must balancethis tiny imbalance as well. It can only do this by initiatingone extra epo chain. This epo chain will have far lessinduced strength than the other, balanced chains, since it isinduced by this feeble unbalanced magnetic moment ratherthan the powerful Coulomb force. However, it cannot connectanywhere, since every electron has the same unbalancedmoment at the same phase angle. (So does every positron, atthe opposite phase angle.) Thus these feeble epo chains willsimply extend into space, connecting at one end to everyelectron and positron (hence to all “real” matter), but beingunconnected at the other end. However, these unconnectedchains, extending into space, will cause a tiny unbalancedattraction between all matter. Since the number of chainsper unit area of space will decrease as 1/r2, it is evident thatthis tiny unbalanced attraction has the form of gravitation.

Moreover, this “magnetogravitation” reacts to changes inmass instantaneously (or at least in time τ.) This explainswhy the Earth and Sun don’t form a “couple,” and why theEarth “feels” gravitation from the Sun at the Sun’s instanta-neous position, rather than its retarded position, as is shownby astronomical observations (Van Flandern, 1998).

This model of gravitation solves many problems withother models, including numerous experiments whichseem to show that gravitation can be shielded, contrary toNewtonian gravitation and General Relativity (Majorana,1930; Allais, 1959; Saxl, 1971; Jeverdan, 1991, and VanFlandern, 1998). In a careful ten-year series of experi-ments, Majorana demonstrated that lead shieldingbetween the Earth and a lead sphere measurably lessenedthe weight of the sphere, while shielding above the spherehad no effect. This would seem to support “pulling togeth-er” gravitation and to disprove “pushing together” modelssuch as LeSage’s, Van Flandern’s, and Puthoff’s. Allais,Saxl, and Jeverdan carefully observed the behavior of var-ious kinds of pendulum during different solar eclipses. Allthree pendulums exhibited major anomalous behavior atthe onset of totality, indicating that the moon stronglyinterfered with the gravitational connection between theEarth and the Sun at that time. This provides major evi-dence for our “epo chain” model of gravitation.

Further analytical work will have to be done to verify that

into a strong repulsion (since the individual epos have tomaintain their average 1.87 fermi separation), keeping thenucleons a stable distance from each other.

Moreover, a maximum of 918 such “internucleon” pairscould form, the number vibrating in the direction joiningthe two nucleons, one-tenth of the total. This would give theinteraction the strength of 1836e, and exactly explain thestrength of the strong force, “about 2000 times as strong asthe Coulomb force” (Shankar, 1994).

Now, what is the chance that a completely wrong model ofthe nucleon would exactly match both the strength and thevery peculiar shape of this most individual of forces? After fiftyor so years of effort, the huge physics establishment admitted-ly has failed utterly to provide a model that comes close tomatching that peculiar shape of the nuclear force. Yet Dirac’sequation provides a model that fits like lock and key.

Dirac’s Theory of EverythingThis model simply, intuitively, and clearly explains the sizeof the nucleon, the mass of the nucleon, the very peculiarshape of the strong nuclear force, the strength of the strongnuclear force, and the strange fact that the very differentproton and electron have charges of exactly the samestrength. No other model explains any of these features, includingthe very cumbersome “Quantum Chromodynamics” of the SM.

The neutron thus constructed is the source of electron,proton, and neutron in their very anomalous abundances,hence of all stable matter in the universe. This makes theamounts of matter and antimatter in the universe exactlyequal, as experiment demands, and as no other model pro-vides. We saw earlier that the “electromagnetic field,” “thephoton,” and the Ψ wave are all epo manifestations neces-sary for the stability of the BEC. So we have complete clo-sure: the BEC “must” be produced by the Dirac “zerothquantum field.” For its stability, it in turn “must” produceour universe, using only the particles called for by the Diracequation, which as we can now see predicts that the entireuniverse is made from just these four kinds of electron.

Einstein spent much of his life trying to unify the “fourforces.” We have shown that the “strong nuclear” force isnothing but electromagnetism. Moreover, the “weak nuclear”force has since been unified with the electromagnetic in the“electroweak” theory (Weinberg, 1967; Salam, 1968). Thisleaves only gravitation. Puthoff (1989, 1993) suggests thatgravitation is a residual effect of the ZPF of the vacuum elec-tromagnetic field, i.e. a residual effect of electromagnetism.Again, however, this paper suggests a different structure andorigin for the ZPF. Moreover, Puthoff’s gravitation is “pushing

After fifty or so years of effort, the

huge physics establishment admitted-

ly has failed utterly to provide a model

that comes close to matching that

peculiar shape of the nuclear force. Yet

Dirac’s equation provides a model that

fits like lock and key.


this tiny unbalance, which must happen, has the force as wellas the characteristics of gravitation. If this hypothesis is cor-rect, all of the matter and all of the forces in the universe areseen to be the result of just these four kinds of electron, ful-filling Dirac’s unitary dream.

InertiaInertia, however, has been a riddle ever since Foucaultshowed that his pendulum responded, not to any localframe of reference, but apparently to the frame of the “fixedstars.” This became the basis of Mach’s principle, whichstates that the “fixed stars,” or (since they aren’t fixed) the“sum total of mass in the universe,” somehow reaches out toaffect pendulums and gyroscopes. (And somehow knocksyou down when the subway starts suddenly). Though this“action at a distance” appears to violate causality, and itsapparently fixed frame of reference violates relativity’s banof any such fixed frame, Einstein set out to incorporateMach’s principle into relativity. In the end, though, he hadto admit he was not successful.

Haisch, Rueda, and Puthoff (1994) made a very plausiblecase that inertia is a residual effect of the ZPE. They were not,however, able to quantify the effect. As this study presents arather different picture of the ZPE, the question is worth anoth-er look. To go along with the “kinetic theory of mass-energy,”we present what might be called the “kinetic theory of inertia.”(Or possibly the “gyroscopic theory of inertia.”)

A gyroscope establishes a vectoral plane of angular momen-tum. Any change in the angle of that vectoral plane is strong-ly resisted. As shown by Dirac’s equation, an electron has a cir-cular vibration in two “real” directions, giving it a “real” ener-gy of mc2. However, it also retains its (negative energy) vibra-tion at ± c in an “imaginary” direction. Thus its oscillation iscircular but complex, having both a “real” and an “imaginary”component, and giving it the anomalously large angularmomentum of \/2 in any “real” direction.

This makes the electron a little gyroscope. However, sincethis vibration is complex, part “real” and part “imaginary,”this angular momentum plane can not point in any “real”direction, as is also the case with the orbital electron’s angu-lar momentum vector, as mentioned above.

This means that acceleration in any “real” direction mustact to change the angle of the electron’s (complex) angularmomentum vectoral plane and thus will be resisted with aforce equal to and in a direction opposite to the acceleration,and proportional to the electron’s “real” mass-energy.

Dirac’s “Operator Theory” or “Transformational” version ofQM represented the wave function as a vector rotating inphase space. This “kinetic theory of inertia” represents a vec-toral plane rotating in a complex space. How this results ininertia can be seen by looking at the wave function Ψ that rep-

resents a particle with definite momentum. The length (value)of the complex number Ψ is the same at all positions, but itsphase angle increases steadily in the direction of the particle’smotion, the x direction, making it a complex helix in shape.

The rate of this complex rotation in its axial (x) direction isthe measure of the momentum. As x increases by a distance ofh/p, this phase angle makes one complete rotation (Taylor,2001). Increasing the momentum (an acceleration in the“real” x direction, increasing p), acts to decrease the distanceh/p, on the exact analogy of a coiled spring being compressed.(QM represents momentum as a spatial sine wave or helix.)However, since Ψ is a complex number, acceleration in the(real) x direction increases the pitch of this complex phaseangle and so is resisted by the electron-gyroscope. This com-pression acts to store the energy added by the accelerationaccording to the Lorentz relationship. Compressing the dis-tance h/p to zero would require (and store) infinite energy.(One might picture this complex helical oscillation as the par-ticle’s flywheel, storing energy as it is accelerated.)

Since the complex gyroscope-electron must resist an accel-eration in any “real” direction, what can this resistance bebut inertia? And since this resistance must be proportionalto its “real” mass-energy (that rotating in “real” directions)it would seem to meet all of the criteria. It is also simpler andmore intuitive than any other, depending solely on theundeniable fact that the electron’s rotation is complex. Wesuggest that any time a QM relationship includes i (andmost of them do) the resulting function will only beexplained by reference to these extra dimensions.

We have shown that all stable matter, and arguably all mat-ter, is compounded of electron-positron pairs with large “imag-inary” components, so that all matter would exhibit this“gyroscopic inertia” in proportion to its “real” mass-energy.

Note that this is a local model of inertia, depending onthe fact that the spins of all “real” particles are complex,extending into extra dimensions. Thus it eliminates themagic action-at-a-distance of Mach’s principle, in which the“fixed stars” somehow reach out across light-years to knockyou down when the subway starts suddenly. It furtherexplains why only “real energy” particles, with complexspins, have inertia, hence mass. Negative energy epos, andalso the positive-energy epos that make up the electromag-netic field, have one-dimensional vibrations, hence no vec-toral plane, hence no mass or inertia. This is why the nega-tive energy “sea” and its effects, which collectively may betermed “the aether,” is virtually undetectable, and offers noresistance to the motion of “real” objects.

The “Neutrino”Several matters remain to be explained, however. The first isanother question of spin. The neutron is a spin 1/2 particle,obeying Fermi statistics. So is the proton, and so is the elec-tron. Therefore, in Beta decay, to conserve angular momentumthe neutron must get rid of this half unit of spin, \/2, as wellas of a random amount of “real” energy. (This energy is the dif-ference between the mass/energy of the neutron and the sumsof the mass/energies of the proton, the electron, and themomentum energy of the ejected electron. It is a randomamount because the electron emerges with a spread of veloci-ties.) Fermi invented a “particle,” the “neutrino,” on themodel of the “photon,” to take away this spin and energy.(Now called the “antineutrino” by modern convention.)

The negative energy “sea” and its

effects, which collectively may be

termed “the aether,” is virtually unde-

tectable, and offers no resistance to the

motion of “real” objects.


find that only “left-handed” vortices are possible. However,there seems to be no way at present of choosing betweenthese possibilities, and there may be more. The importantfact is that, locally at least, we get only left-handed neu-trons from the BEC; otherwise we would have no net pos-itive energy balance.

Other important matters remain unexplained. The 9180pairs of epos in the neutron must perform an elaborate bal-let in the form of a ten-dimensional vortex. Mathematicalanalysis of this elaborate dance is needed, which shouldshow why this structure is slightly unstable, while the pro-ton’s similar dance, performed with one “empty chair,” isapparently completely stable. It should also show why thisstability is extended to the neutron, when it joins in theeven more elaborate dance of the compound nucleus.(Neutron and proton apparently “change places” during thisdance, so that the “empty chair” feature is shared betweenthem, possibly offering a hint to this stability.)

A study of condensation offers further clues to this sta-bility. Ninety percent of the epos in a neutron vibrate inimaginary directions at any one time; therefore the neu-tron has a large negative energy balance, and could be saidto be poised on the verge of condensation.

(The following argument is adapted from Taylor [2001].)Take a sample of liquid helium containing a macroscopicnumber of atoms, N. Cool it until it approaches a state ofminimum energy. It then has a wave function ΨN. Sincethis depends on the individual states of all N atoms, it is avery complicated function. If we now examine a samplecontaining N + 1 atoms, it will have a wave function ΨN +

1, depending on N + 1 states. By comparing ΨN + 1 with ΨN,one can define a function f(x). This depends on just onestate x, the position of the “extra” atom. This f(x) repre-sents the order parameter, and allows the sample to con-dense, as it defines the quantum amplitude for adding oneextra entity. Thus in the condensate this f fixes the orderof the every helium atom, breaking the symmetry to givethe entire condensate the same, arbitrary phase angle,hence the same wave function. The loss of a single elec-tron, in the case of the neutron, would give the resultingproton an extra positron, which might similarly define itsorder parameter, making it a totally stable condensate.

If this model is correct, this analysis should also yieldexact agreement with the experimental values of the mag-netic moment of the neutron and proton, which are lack-ing in the SM. Moreover, analysis of the proton as a con-densate should explain many of the scattering results,which now are obscure. It should also eventually be possi-ble to model all of the unstable particles revealed in cos-mic rays and particle accelerator collisions as fragmentary,temporary associations of epos. (We note that the binary isthe base of all number systems, and suggest that any par-ticle that seems to require combinations of three-basedquarks can also be modeled using binary epos. The quarkis a noble effort at order and simplicity—it simply is notbasic enough.)

However, the model also makes predictions that shouldhave readily measurable effects in the macrocosm. Thoseeffects should manifest themselves wherever there arelarge numbers of ions, which force the BEC to extraordi-nary lengths to balance this instability in its midst. Theselarge numbers of ions are called plasmas.

However, like the “photon,” the neutrino has no charge, andtherefore violates our kinetic definition of energy. But as theelectron emerges from the neutron, it is immediately surround-ed by polarized epos, and these can absorb “real” angularmomentum. However, absorbing this spin makes the epo a“spin 1/2 boson,” which is unstable. It must immediately passon the spin the way the “photon” (epho) passes on the “spin 1”energy, forming a “neutrino wave” on the model of our “pho-ton wave” of polarized epos, which would travel at signal veloc-ity. However, no “real” electron can accept 1/2 unit of spin, sothe (anti)neutrino wave must continue on indefinitely, until itmeets with rare and exceptional conditions such as one inwhich an electron and a proton can combine with it to re-forminto a neutron. (Such conditions are not so rare in a star.) It isthe detection of such rare interactions as this which have beenproclaimed the “discovery” of the “neutrino.” Thus the “neu-trino” is no more a separate particle than is the “photon.”

The Antineutron?We must deal with one further difficulty. We have suggest-ed that a vorticular storm in the BEC seems to be the sourceof the neutrons which, ejected into our four dimensions,have produced the stable matter of “our reality.” However,vortices come in “left-handed” and “right-handed” ver-sions. Presumably, a “left-handed” vortex would produceonly “left-handed” neutrons, and expel them into our real-ity. But what about a “right-handed” vortex? It would pre-sumably produce “right-handed” neutrons (antineutrons)which decay into antiprotons and positrons. (Particleaccelerators produce both kinds.) These would form “anti-hydrogen” and presumably antioxygen, anticarbon, andthe rest. Is it possible that there are places in our realitywhere “right-handed” vortices have produced whole galax-ies of antimatter? At first sight this seems quite possible, asfrom afar an antimatter galaxy would be indistinguishablefrom one made of matter. However, it also seems unlikelythat any nearby galaxies are antimatter, as one would thinkthat sooner or later matter and antimatter must meet and“annihilate,” which would produce floods of easily-detectable 0.511 MeV photons, which are not in evidence.

There are at least two more possibilities. First, the BECmay be separated into a “northern hemisphere” and a“southern hemisphere.” On our planet, the vortices we call“hurricanes” or “typhoons” rotate exclusively counterclock-wise in the northern hemisphere and clockwise in the south-ern. This would place a “great gulf” between the mattergalaxies and the antimatter galaxies, so that they would sel-dom or never meet. (Astronomers have mapped several such“great gulfs” or “voids” around 200 million light years acrossin which few or no galaxies are found. If such a gulf separat-ed matter galaxies from antimatter galaxies, there would beno “annihilation,” hence no means of distinguishing anantimatter galaxy.)

Alternatively, the BEC may in some unknown fashion actas a “sorting device,” sending only “left-handed” neutronsto our reality, while expelling “right-handed” neutrons intoa reality on the “other side” of the BEC. Presumably thiswould be into four more (“imaginary”) dimensions, whichwould also have a positive-energy balance, but would bemade of antimatter. Perhaps in the future we will find thatfor some reason the BEC must act as a sorter to “left-hand-ed” and “right-handed” universes. Or, alternatively, we may


gas-giant planets. All of them have anomalies, mysteries we can’t explain.Regularities in the spacing of the satellites of these planets have long been noted,and ascribed vaguely to “resonances,” though resonances of what has never beenspecified. Celestial mechanics, based solely on gravitation, has never been able toaccount for them. For one thing, resonances are invoked to explain the “Kirkwoodgaps” in the spacing of asteroids in the “belt” between Mars and Jupiter. These areperiods in which no asteroids are found, and which occur at harmonics (1/2, 1/3,etc.) of the period of Jupiter. However, some of these harmonics have a clumpingof satellites, rather than a gap. And the three inner Galilean satellites of Jupiter arelocked into near octave harmonics, with periods within 0.0036 of a 1::2::4 ratio,and there are other octave relationships in the satellites of Saturn. A gravitational“resonance” can’t explain both a gap (an instability) and a stable relationship at thesame harmonic ratio, so some other factor must explain one or the other.

There is a very strange unexplained anomaly in the cases of the gas giantsand their satellites. The semi-major axis of our Moon’s orbit is some 30 Earthdiameters, whereas the innermost satellites of these gas giants orbit no morethan one or two diameters of the primary from these giant dynamos. Withthe Earth and the Moon, tidal forces slow the Earth’s rotation and force theMoon ever further from us.

However, Jupiter’s moon Io orbits only 3.5 Jupiter diameters away. Tidalforces on Io are strong enough to wrack the satellite, making it the most vol-canically active object in the solar system. Why haven’t these fierce tidal forceslong since moved Io far away from its primary? It can not be a new satellite, asIo exhibits profound differences from the other Galilean satellites, indicatingthat these powerful tidal forces have wracked Io for many millions of years. Yetinstead of having been moved away by these tidal forces, as required by celes-tial mechanics, it seems locked immovably in place, a mere three and a half

PlasmasDavid Bohm’s early work at BerkeleyRadiation Laboratory included a land-mark study of plasmas (Bohm, 1980,1987). To his surprise, Bohm found thations in a plasma stopped behaving likeindividuals and started acting as if theywere part of a larger, interconnectedwhole. In large numbers, these collec-tions of ions produced well-organizedeffects. Like some amoeboid creature,the plasma constantly regenerated itselfand enclosed all impurities in a wall ina way similar to the way a biologicalorganism might encase a foreign sub-stance in a cyst. Similar behavior hasbeen observed by Rausher (1968),Melrose (1976), and others, and is nowa commonplace of plasma physics.However, no one has ever explainedhow a collection of ions can act in con-cert. But this is exactly the behavior of oneof our BECs, formed in the laboratory attemperatures near 0˚K and consisting of anaggregation of bosons.

Any BEC must have an exact balanceof positive and negative charges. An ioncan’t be tolerated, and must be expelledby the BEC. It is suggested that theabove behavior of a plasma is notbecause it is self-organizing, butbecause the universal BEC can’t toleratea collection of unbalanced ions, and soorganizes this irritation into a plasma“pocket” of least irritation, tendingtoward a spherical form. This plasmapocket acts, in some ways, as if it wereitself a BEC. The organization exhibitedis because some of its attributes,ordered and controlled by the BEC, aregoverned by a single wave function.

Our hypothesis is that any aggrega-tion of plasma will behave to a certainextent as a single unit, acting as if self-organizing, because, since it is intolera-ble to the Big BEC, it is isolated as abody, organized by the BEC, and thuspartially governed by a single wavefunction. Since the wave function isdetermined by the BEC, whose compo-nents vibrate only at c, the period of thewave function would necessarily be, fora spherical plasma pocket, its light-diameter. This is according toHamilton’s Law of least action also, asin quantum theory the longest-wave-length vibration will have the leastenergy. Thus the light-diameter vibra-tion will be the stable, least energy one.

The largest collections of plasmas inour vicinity have to be the Sun and the

Figure 4. Uranus and satellites.


should orbit at these nodes. This is exactly what is shown in

Figures 4, 5, and 6, for Uranus, Saturn,and Jupiter. Mean distances (semi-majoraxes) of the satellites are from theAstronomical Almanac for 1996. Since therapidly spinning gas giants are notablyoblate, the top of clouds (equatorialradius) is used as the first node.

These systems match the exponentialregression curves with R2 (coefficient ofdetermination) values ranging from0.9978 to 0.9993. (A statistician wouldsay that R2 is a measure of the propor-tion of variation in y that can beexplained by the regression line using x.The remainder is the percentage attrib-utable to chance, “chaos,” or to othervariables.) This indicates that at least99.78% of the value of the semi-majoraxis, the satellite’s orbital position, canbe attributed to the function of the x-value, its (quantum) period number.This leaves rather little (from 0.07% to0.22%) to chance or to other variables.

In nature, such (quantum) periodicityis exhibited only in the normal modes ofwave behavior. Therefore we can saywith some certainty that each of thesethree figures constitutes a wave signature,as clear and definite as the well-knownAiry pattern that they resemble. Andsince the wave clearly originates withthe gas-giant planet, as explained by thesea of charge required by the Dirac equa-tion, the wave’s existence can be consid-ered confirmed. Moreover, it is clearlymore powerful than the powerful tidalforces. (With Jupiter, something else isalso going on. We will discuss this later.)

This would seem to be the clearest kindof evidence for this requirement of theDirac equation. Each of the figuresdemonstrates that a wave of polarization, atleast 99.78% determined by its normalmode period number, originates withthese spinning bodies of plasma. That allthree show the same wave behavior wouldseem to eliminate all further doubt.Moreover, as is to be expected, the innersatellites of each planet, where the wavefunction would have the largest ampli-tude, fit best.

The only selection involved in thesefigures is in the rings, in which smallchunks of matter are evidently disinte-grating under extreme tidal forces andevolving from one node to another.(Neptune, the other gas giant, is notincluded. It shows evidence of somemajor disturbance that stripped it ofPluto and Charon, its former satellites

Jupiter diameters away. It must be held in place by some force even more powerfulthan the powerful tidal force, a force totally unexplained by celestial mechanics.

It has further been noted that the spacing of the satellites of these gas giantsseems to follow a distribution similar to “Bode’s Law” for the planets, thoughthis defies explanation, given these immense tidal forces (Miller, 1938;Richardson, 1945; Ovenden, 1972; Spolter, 1993.) Our new understanding ofDirac’s equation, however, does offer an explanation. These giant spinning bod-ies of plasma are organized by the BEC and therefore have a single wave func-tion. They are charged bodies spinning in an ocean of charge, and must set upstanding waves in that ocean.

For it has never before been remarked that the first term of the “Bode-like” dis-tribution, in each case, is the equatorial radius of the rapidly rotating body ofplasma that makes up the gas giant planet. (See Figures 4, 5, and 6.) The wavefunction governing the spinning body of plasma necessarily has a node at thesurface of the planet. By Schrödinger’s equation, however, that wave functionwould not be limited to the planet itself, but would extend, with greatly atten-uated (1/r2) amplitude out from the planet, forming a (longitudinal) standingwave. Everywhere but at a node, the waveform has amplitude, and would act to“polarize the vacuum.” (It would raise in state epos from negative to positiveenergies, polarizing them to point in “real” directions.) But because the wave-form caused by the spinning plasma “polarizes the vacuum” everywhere but ata node, this “vacuum polarization” would add amounts of energy to any matter(dust, gas, asteroids, etc.) not at a node, nudging the matter towards a node.There it would collect over millions of years, like sand on a tapped drum head,forming rings of material, which eventually would collect into one or moresatellites. These nodes would necessarily be at harmonics of the planet’s radius.Its satellites, unless they are new captures in transition, or disturbed somehow,

Figure 5. The spacing of Saturn and its satellites—exponential regression.


However, by far the largest body ofplasma in our system is the Sun, withover 99.7% of the system’s mass.What of its standing waves?

The SunBy the argument used with the gasgiant planets, the planets of the solarsystem should fall on nodes that areharmonics of the Sun’s radius. (In theSun’s case, we will demonstrate thatthese harmonics are octaves, powers of2.) But the gas giant planets are farfrom the Sun and rotating very rapid-ly, so that their waves of polarizationare the strongest influence on theirsatellites, as shown in Figures 4, 5,and 6. The solar system, however, isdynamic, changing with time. TheSun is an energetic furnace thatexports angular momentum to theplanets, as the Nobelist HannesAlfvén (1981) first demonstrated.

This is the principal, supposedlyconclusive argument that is advancedby conventional astronomers againstsuch attempted correlations as Bode’sLaw. They say the positions of theplanets must change with time, soany correlation at present would nothave been so in the past, and will notbe so in the future, and thereforemust be coincidence.

The Sun exports angular momen-tum by means of the solar wind, theSun’s magnetic field, tidal forces, andradiation pressure. All of these trans-fer angular momentum from the Sunto the planets, both slowing the Sun’srotation and increasing the planets’distances from the Sun. Together, atleast for the inner planets, theseforces are clearly stronger than thepolarization caused by the Sun’s wavefunction. Therefore, all of the planetsout to Jupiter have over billions ofyears been moved from their originaloctave positions. This is one reasonfor the seemingly anomalous distribu-tion of angular momentum in thesolar system, in which the planets,notably Jupiter, have much moreangular momentum than the “par-ent” body. (This may not have beenthe case in the early solar system,when the Sun was rotating muchfaster, as the strength of this wavefunction would seem to be a product,among other factors, of the velocityof rotation of the body of plasma.)

However, Ovenden (1972) with his“least interaction action” calculations,

[Van Flandern, 1993]. Its present clearly disturbed system exhibits only a lim-ited regularity).

The figures show the best fit value in terms of a power of e, base of natural log-arithms. The powers reduce to 1.253 for Saturn, 1.480 for Uranus, and 1.621 forJupiter. That the satellites regularly fall at harmonics of the planet’s diameters isclear. Why nodes fall at those particular harmonics, which are different for eachplanet, seem to be related to the planets’ diameters, hence the periods of theirfundamental wave functions. We will discuss this further at a later time.

That we live in an ocean of charge, of which we are as little aware as a fish in anocean of water, will be difficult for many to accept. Even more difficult to accept isthe above proof that a planet such as Jupiter is the source of a standing wave that hasamplitude millions of kilometers from its surface. Despite our preconceptions,though, waves in this ocean of charge, as required by Dirac’s equation, would seemto be confirmed beyond all reasonable doubt by the above correlations.

Moreover, studies have shown that the planets, particularly Venus and Jupiter,have a pronounced affect on the electron densities in the Earth’s ionosphere, theeffect peaking when these planets are close to the Earth (Harnischmacher andRawer, 1981). The authors had no explanation for this effect, so it took consider-able courage to publish their findings. But the above standing waves of polariza-tion exactly account for this effect. Venus is the planet that comes closest to us,and Jupiter is a powerhouse whose standing wave affects all of the planets. Thismeans that wave functions, harmonics, beats, and interference will ultimately proveto be as important in the macrocosm as they are in the quantum world.

Figure 6. The spacing of Jupiter and its satellites—exponential regression.


(semi-major axis x 2) of Saturn’s orbit is within .0035 of211 times the diameter of the Sun, that of Uranus is with-in .0025 of 212 times that diameter, and that of Pluto iswithin 0.035 of 213 times that diameter. (Since the diame-ter of the Sun is somewhat imprecise and seems to vary byabout 300 kilometers over the course of the 11-year cycle[Gilliland, 1981] these octaves can be considered “exact.”)

Neptune, as Van Flandern (1993) shows, was the victimof some energetic event, probably a collision or “closeencounter” with some major body, which, we propose,caused it to lose sufficient angular momentum so that itdropped into its present (non-octave) position. This freedits satellites Pluto and Charon to continue around the Sunwith the approximate semi-major (octave) axis of the orig-inal Neptune, with their added orbital angular momentum(which was originally around Neptune) throwing theminto their present eccentric orbit. Pluto then capturedCharon as its satellite.

Kepler’s Universal Harmony?Quantum theory treats everything as wave at all times, exceptfor a measurement situation, which no one understands. Boththe Schrödinger and the Dirac equations are wave equations. Wepredicted above that wave functions, harmonics, beats, andinterference will ultimately prove to be as important in themacrocosm as they are in the quantum world. However, sincetime is quantized, the important harmonics should be har-monics of τ, that quantum of time. We live in an ocean of

showed that interactions between the planets serve to keepthem in approximately equal spacing. Thus the planets, asthey evolved from original octave positions, would maintaintheir approximate spacing, so that their present positions showthe roughly regular spacing indicated by Bode’s Law, the limitof which is the original octave relationship. (See Figure 7, a log-arithmic plot of the solar system.)

The principle argument by conventional astronomers isthat, because the solar system is dynamic, Bode’s Law must becoincidence. However, because Ovenden’s “least interactionaction” keeps the spacing regular, at any time during their evo-lution from octave positions, the planets would have formed a“Bode-like” configuration, merely with different coefficients.So this argument fails. (We will later suggest a further factorwhich might act to keep the spacing of the planets regular. Wewill further show that though these inner planets have retreat-ed from their original octave positions, they all now orbit onanother harmonic node.)

Planets inside of Mercury either have been vaporized bythe Sun, or never managed to gather into a planet. Mercuryitself keeps “one foot” in the original octave position, itsperihelion distance falling at the original octave node, andits travels through higher amplitude regions of the wavefunction might, as we will see, account for the excess rota-tion of its perihelion without recourse to “curved emptyspace.” (An oxymoron, as Phipps [1986] pointed out.)

However, Saturn, Uranus, and Pluto remain at the orig-inal octave positions. (See Figure 7.) The mean diameter

Figure 7. Solar system spacing.


charges vibrating at that quantum beat.Therefore the harmonics, particularlythe octaves (powers of 2) of that beatshould, by Hamilton’s law, be the least-energy configurations of energetic bod-ies, particularly bodies of plasma, in themacrocosm. Every energetic body of plas-ma should act, in some ways, as a quan-tum object. And the quantum object itresembles, as we will show, is the BEC,which organizes its wave function.However, the nucleon, which makes upabout 99.97% of the universe’s mass, isa structure that vibrates in ten dimen-sions. Therefore the harmonics of 10τshould be nearly as important.

Moreover, there is a time, h/mec2,equal to 8.09 x 10-21 seconds, thatHeisenberg considered to be the “fun-damental time” (Heisenberg, 1936,1938a, 1944). In 1925, when Einsteinrecommended de Broglie’s theory ofmatter waves to his thesis committee,he suggested that the inverse of thistime, mec2/h, be considered a universalelectromagnetic limit frequency. Andthis time is within 1% of 10τ x 27,another indication that octaves of 10τshould be important.

It has been objected that harmonicsof quantum objects can not be project-ed to macrocosmic dimensions becausesmall errors would be so magnified as tolose all accuracy. However, since time isquantized, and since we live in an oceanoscillating at that frequency, the exactharmonics would be reinforced all alongthe way, with the least-energy configu-rations tending to minimize any sucherrors. An example is the resonancebetween two of the hyperfine levels ofthe cesium atom, used in the atomicclock because of its rock-solid stability.This frequency, which defines the inter-national second, is within 0.005 ofbeing an exact octave of τ (6.26 x 10-24

s. times 244 = 1.101 x 10-10 s. The periodof the cesium resonance, 1/9 129 631770 Hz, is 1.095 x 10-10 s.) This gets usover half way to the macrocosm with-out notable loss of accuracy.

The second thing we note is that themean light-diameter of Jupiter, the sec-ond most energetic body in the solarsystem, is also almost an exact octaveof this quantum of time. (This wouldbe the period of its wave function.)Since Jupiter is notably oblate, themean diameter is based on its volume:D = 2(3V/4π)1/3.(Mean diameter ofJupiter = 139,193 km. Light-diameter =0.46432 s. τ x 276 = 0.47299 s. or less

than 2% different.) Equally remarkably, the diameter of the Sun (1,391,980 km.) is,to 5 significant figures, exactly 10 times the mean diameter of Jupiter. And the diam-eter of just one star has been measured with any accuracy. That star is the blue giantSirius, the brightest star in the sky, which has been repeatedly measured by stellarinterferometer. By the average of its measurements, its diameter is 2.04 times the diame-ter of the Sun, its light-diameter within 0.0013 of 10τ x 277, an almost exact octave bothof 10τ and of the Sun’s light-diameter. Other stars have also been measured, but theprobable errors of these measurements are so large that one can only say at presentthat it looks like their diameters might all be harmonics of τ or of 10τ. Much morerefined measurement techniques are now possible; however, astronomers appear toshy away from such measurements. Could they be afraid of what they will show?We predict that all measurable stars will prove to have light-diameters that are har-monics of τ with octaves of τ and 10τ predominating.

We need to deal here with two objections sure to be raised to these figures. Ithas been objected that the “light-diameter” of a massive body could not beimportant, because the velocity of light in a body such as the Sun would be verydifferent from that in a vacuum: c = 1/(µ0ε0)1/2. Light in a massive body slows,depending on its permittivity and permeability. However, the wave function isdetermined by the BEC, in which the wave always travels exactly at cmax. Theabove wave functions of the gas giant planets support this; and we will presentfurther evidence to this effect in what follows.

Second, it has been objected that figures based on octaves, beats, and harmonics


“sound like numerology.” This is a favorite ploy to discountnumbers we don’t like—as if there were something wrong withnumbers, or as if we could present and collate data other thannumerically. Numbers we like are “data”; numbers we don’tlike are “numerology.” However, as noted above, almost theonly place in physics where whole (quantum) numbers appearis in the normal modes of wave behavior. But we also haveindicated, and will demonstrate in what follows, that allphysics is quantum physics, since all matter is wave, and there-fore all physics devolves ultimately to the (quantum) normalmodes of wave behavior. Ultimately, therefore, all physics is“numerology.”

With this in mind, a quick look through the NauticalAlmanac reveals a host of periods or resonances of macro-scopic objects that are almost exact octaves either of τ or of10τ. Every body of the solar system has a major period that iswithin a few percent of an octave either of τ or of 10τ. (This peri-od is either the light-diameter of the object, the light-diameterof its orbit, or its sidereal period.) Many have more than oneoctave value. The sidereal period of Earth, for instance, fallswithin about half a percent of an octave of τ (6.26 x 10-24 x 2102

= 3.174 x 107 seconds; sidereal period of Earth = 3.156 x 107

seconds. Difference = 0.57%). The farthest from an octave isMars, whose sidereal period falls a fat 6% from an octavevalue. However, Mars, as we will see, falls much closer toanother, stronger harmonic.

This result beggars coincidence. The resulting regressionstatistics (see Table 1 and Figures 8 and 9) for both τ and 10τ

have R2 values of better than 0.999999, meaning that thereis no question that the figures are related, and related totheir (quantum) period numbers, which are octaves, powersof 2. Again, this is the clearest possible wave signature.

With a range of 110 octaves, the exponential regressioncharts are meaningless, so we have shown logarithmic linearregressions both of the entire range (Figures 8 and 9), and of therange covering only the solar system (Figure 10, which showsboth regressions over the range of the solar system). Taken inany detail or combination, the R2 values of better than0.999999 show that the octave relationship is unquestionable,with the possibility that the relationship is chance being lessthan 1 in 1,000,000. Moreover, the “Sun series” and the “Jupiterseries” remain almost exactly parallel, exactly an order of mag-nitude apart, throughout their entire ranges. There is a slightdivergence from a power of 2 in both regressions (on the orderof 1.9995) which is probably not significant, indicating merelythat in the upper reaches of the regression the bodies are faraway from the source of the harmonic wave.

It seems evident that when the inner planets were forcedout of their initial octave positions by the angular momen-tum transferred from the Sun, they moved relatively rapidlyto the next nearby harmonic. (By Kepler’s third law a planetwhose period is an octave of τ or 10τ would have a light-diameter that is also a harmonic, though not an octave.)They could “defend” this harmonic position for a longerperiod, before being forced to the next harmonic. Thiswould seem to be why most of the planets not still at octave

Figure 8. Sun series—log linear regression.


distances have octave periods. However, Jupiter is the powerhouse of the planets. It has

the most angular momentum, both rotational and orbital,and its harmonic is the primary, the τ harmonic. It is note-worthy that the plane of the ecliptic is roughly the plane ofJupiter’s orbit. The Sun rotates a full 7˚ away, and only near-by Mercury orbits over the Sun’s equator, with Venus split-ting the difference with an inclination of 3.4 degrees.

Moreover, the Sun’s export of angular momentum stopsat Jupiter. The outer planets orbit, apparently undisturbed,at their original octave distances. But Jupiter has moved toan apparently unassailable position, the intermodulationharmonic between its τ harmonic and the Sun’s 10τ beat.(Its orbit’s light-diameter is within a percent of (τ + 10τ) x286.) Moreover, there apparently is a “back-eddy” of thisintermodulation beat that affects the next two inner peri-ods, the asteroids and Mars. Those asteroids which remainorbit where Jupiter permits them. The average mean orbitlight-diameter of the ten largest asteroids is exactly at 12τx 285, the intermodulation beat. And Mars, next in, is with-in 2% of 13τ x 284, which apparently also allows it to benear an octave period harmonic. (Jupiter’s τ harmonic. SeeTable 1.) (Yes, this “sounds like numerology” again. Butonce we acknowledge that we live in an ocean of charge,then waves, beats, interference, and harmonics becomedata, not numerology.)

Mercury is a fascinating case. We mentioned that it keeps“one foot” at its original octave position—its perihelion

light-distance is within less than a percent of 10τ x 280, theSun’s octave. Yet its aphelion distance is within a couple ofpercent of τ x 284, Jupiter’s harmonic. Like a good quantumobject, it oscillates between the Sun’s harmonic and Jupiter’sharmonic. Meanwhile its sidereal period is within 1% of yetanother octave, τ x 2100. No wonder all the angular momen-tum exported from the nearby Sun can’t budge it from itsposition—it is locked into three separate harmonics.

This would appear to solve a long-standing problem con-cerning Mercury. The dynamics of a small body orbitingclose to a large body tend to remove the eccentricity fromthe small body’s orbit and place it on a node of its standingwave. The Galilean satellites of Jupiter, for instance, haveeccentricities ranging from 0.002 to 0.009—they are in per-fectly behaved, almost perfectly circular orbits. The innersatellites of Saturn have even less—Tethys has a measuredeccentricity of 0.00000. By contrast, Mercury, closest to theSun, has by far the most eccentric orbit (0.2056) of any plan-et, if you exclude Pluto, which is probably an escaped satel-lite of Neptune. But like the cesium atom’s resonancebetween two hyperfine levels, the Mercury quantum objectresonates between two harmonics while orbiting on a third.

Table 1 requires some further comment. The Sun has twomeasured global resonances—a well-known “5-minute” res-onance, and a “160-minute” resonance measured independ-ently by two different teams of astronomers (Brooks et al.,1976; Severny et al., 1976). Their findings have been repli-cated by Scherrer and Wilcox at Stanford and by a French-

Figure 9. Jupiter series—log linear regression.


American team (van der Ray, 1980) and the “160-minute”solar resonance shown to be stable over more than 1400periods. The Russian group tracked the oscillation for morethan four years. However, this resonance has been discount-ed and ignored because it does not fit the standard solarmodel. Time and again we find scientists saying, in effect,“These are the theories on which I base my facts.” This iswhat the Churchmen told Galileo. Discounting measureddata because it disagrees with a theory is the antithesis of sci-ence. As it turns out, both of these global resonances areexact octaves of each other and of the light-diameter of theSun. (Light diameter of Sun = 4.6432 s. x 26 = 297.2 s.5 m. = 300 s. Diff. = 0.009. 5 x 25 = 160). This has neverbefore been noted, probably because of the above men-

tioned fact that light does not travel at cmax inside the Sun.However, these global resonances are direct evidence for ourhypothesis that a body of plasma’s wave function is set bythe BEC, which always vibrates at cmax.

Moreover, these global solar resonances are interestingfrom another standpoint, one having to do with the Joviansystem. We have noted the power of Jupiter, with all itsangular momentum—that it can reach down and impose itsharmonics even on Mercury. Yet, as shown in Table 1, thethree inner Galilean satellites, mere flies on the face ofJupiter, nonetheless have sidereal periods that are octaves ofthe Sun’s 10τ harmonic! This startling result demands anexplanation, especially as we have earlier seen that thesethree satellites’ semi-major axes fall on an exponentialregression with Jupiter’s radius as the first term.

One answer, of course, is Kepler’s third law. So long as thesatellites maintain ratios of distances that are powers of about1.6, as Jupiter’s satellites do, their periods will have ratios thatare roughly powers of two, as 1.63 ' 22. (The actual ratios withthese three satellites are 1.5913 and 2.0074, which of courseexactly obey Kepler’s law.) The remarkable thing, which we willexamine, is that these ratios are exactly the same between Ioand Europa as between Europa and Ganymede.

The other unanswered question, of course, is how theseperiods “just happen” to fall on exact octaves of the Sun’sharmonic. The period of Io, in particular, is within half a per-cent of 215 times the Sun’s light-diameter.

Figure 10. Solar system ladder of octaves logarithmic linear regression.

Time and again we find scientists say-

ing, in effect, “These are the theories on

which I base my facts.” This is what the

Churchmen told Galileo. Discounting

measured data because it disagrees with

a theory is the antithesis of science.


Io is perhaps the most unique body in the solar system. Itis connected to Jupiter by a “flux tube” of electrons conser-vatively estimated to be 5 million amps at 400,000 volts ormore than 50 times the combined generating capacity of allthe nations of Earth. Yet this immense power still accountsfor less than 1% of the power dissipated by Io! This power isliterally ripping Io apart, making it the most volcanicallyactive object known. Sulfur ions spewed forth by these vol-canoes form a torus in the shape of Io’s orbit. And whenev-er Io, Jupiter, and the Sun form a right triangle, Io emits animmense burst of radio synchrotron energy with a powergreater than 5000 times the combined generating power ofall the nations of Earth (Time-Variable Phenomena in the JovianSystem, 1989). This report in summary concluded that amongthe anomalies they can’t presently account for are “. . .dra-matic short-term changes in the Jovian system, includingchanges in the Galilean satellites’ orbits, geology, and geo-physics, and the planets’ internal structure.” For one thing,they have measured the periods of these satellites accuratelyto nine significant figures, only to find, the next time theymeasure them, that they are different in the sixth or eventhe fifth significant figure.

These short-term changes in the Galilean satellites’ orbitsseem to be connected to Io’s explosive burst of radio noisewhich occurs whenever the three bodies reach a right anglerelationship, the angle between the electric and the magnet-ic fields. This explosion is called, in Table 1, the “Io Shout.”It is synchrotron energy, directed along the tangent of Io’spath as it reaches elongation: thus, once every period of Io,it is directed in a cone more or less exactly at the Sun. Asnoted, this occurs on an exact octave of the Sun’s harmonic.What happens to a resonant body when it is energized by avibration exactly at its resonant frequency? Surprise: it res-onates. Positive feedback, like the public address systemsqueal. This might begin to explain the Sun’s two global res-onances, both octaves of the Sun’s harmonic, both octavesof the “Io Shout,” both largely or totally unexplained byconventional solar theory. (This “Io Shout” takes about 43minutes to reach the Sun. It is a prediction of this theorythat the “Io Shout” and the 160-minute global resonanceshould be in phase, when this 43 minute lag is taken intoaccount. Someone with access to the raw data should checkthis.) Moreover, the 160-minute resonance has been shownto vary greatly in its amplitude (Severny et al., 1966) and thishas led to some of the doubts about its existence. But thisamplitude variation is exactly what we would expect if it isrelated to the strength of the variable “Io Shout.”

Another factor to be taken into account is the inclinationof Jupiter. Io rotates almost exactly above Jupiter’s equator,but Jupiter’s 3.12˚ inclination would cause the effect of the“Io Shout” to vary in intensity throughout the Jovian year,reaching a maximum as the inclination passes the eclipticevery six Earth years or so.

But there is more to the story. Despite these dramaticshort-term changes in the Galilean satellites’ periods, the rela-tionship between the periods remains the same, that found byLaplace. He studied this relationship, calling it a “three-bodyorbital resonance” and showed that the mean orbitalmotions N1, N2, and N3 are connected by the equation

N1 - 3N2 + 2N3 = 0

The net effect is that, when two bodies are in conjunction on

one side of Jupiter, the third is always on the other side. This,however, hardly begins to explain what is going on here.What, exactly, is resonating, in this three-body resonance?How was it set up, how is it maintained, through millions ofyears in the heart of Jupiter’s intensely energetic system? Withthe noted short-term changes in these satellites’ periods, whatmaintains this resonance? No one has ever been able toexplain dynamically how such a system could come intobeing, or connect it to Jupiter’s gravitation or spin.

For the relationship shown in Laplace’s formula to occur,the three inner planets must reach successive conjunctions atelongation (relative to the Sun) in some period of time, keep-ing in mind that one planet will always be on one side ofJupiter, the other two on the other side. Let’s start our timingat one of these conjunctions. For a conjunction to recur at thesame elongation, say between Ganymede and Europa, theremust be some whole (quantum!) number of Ganymede’s peri-ods n such that f(n) = 2n + 2, in other words that Europa musthave made exactly 2n + 2 revolutions while Ganymede made n.Such a relationship, implied by Laplace’s formula, could hard-ly be coincidence; it would mean that they were truly syn-chronous, only on a much longer period than the simple1::2::4 ratio already noted. Is there such a number n? There is

indeed; and it turns out to be the highly interesting number137, the inverse of the electronic Fine Structure Constant α.(This constant is a pure number, not exactly 1/137, but1/137.0359722. Eddington tried to derive it from the numbers1 and 136, used in our “Neutrosynthesis,” but of course thiswas dismissed as numerology.)

What is the ratio of the electronic Fine Structure Constantdoing in the fine structure of the ratios of Jupiter’s satellites?Well, we have shown above that there is only one force, theelectromagnetic. Conventional astronomers claim that theonly force operating between the planets is gravitation, butsince we have shown that gravitation is a residual effect ofelectromagnetism, we can now confidently state that the onlyforce operating between the planets is electromagnetism.Moreover, we have shown above that waves of polarizationwith amplitudes millions of kilometers from the gas giantplanets operate to move their satellites into the normalmode nodes of those waves.

No one knows where the electronic fine structure con-stant comes from anyhow. Feynman (1985) calls it “thegreatest damn mystery in physics.” As the Nobelist Lederman(1993) says, “The fine structure constant. . .[α]. . .can bearrived at by taking the square of the charge of the electron

Conventional astronomers claim that

the only force operating between the

planets is gravitation, but since we have

shown that gravitation is a residual effect

of electromagnetism, we can now confi-

dently state that the only force operating

between the planets is electromagnetism.


divided by the speed of light times Planck’s constant. . .thisone number, 137, contains the crux of electromagnetism(the electron), relativity (the velocity of light), and quantumtheory (Planck’s constant).” He notes that Heisenberg andPauli were obsessed by this “137” mystery, and thatFeynman suggested that all physicists should put up a signin their homes or offices to remind them of how much wedon’t know. The sign would read simply: 137. (Ledermanchose this number as his home address.) However, if “every-thing is electromagnetism,” it is no more (or no less) myste-rious to find the electronic fine structure constant in the finestructure of the ratios of Jupiter’s satellites than it is to findit in the fine structure of the atom, and another indicationthat this unitary thesis is correct.

The Jupiter system appears to be a generator, extractingimmense amounts of energy from the BEC by what seems tobe a three-octave tuned resonance tuned to the Sun’s har-monics. It would seem to hold clear clues as to how wemight extract this energy.

In any case, if n = 137, f(n) = 276; f(276) = 554. It looks like this:

Ganymede: 137 per. x 7.1546631 days/per. = 980.18884 daysEuropa: 276 per. x 3.5511431 days/per. = 980.11550 daysIo: 554 per. x 1.7691614 days/per. = 980.11543 days

After less than three years, all three line up again at elon-gation, although one is on the opposite side of Jupiter fromthe other two. Ganymede trails 3.7 degrees behind, but Ioand Europa arrive at elongation within six seconds of eachother. Six seconds in three years is better timekeeping thanthe original Atom Clock, an error of 1 part in 14 million. (Ofcourse, these periods change almost daily, as noted above,and another set of periods will find Ganymede catching upto the others. These numbers are from the 1976-77 Handbookof Chemistry and Physics, but every edition has different val-ues for these periods. When calculated as above, however, allof them average to 980.14 days.)

There is also an out-of-phase series of elongations, the2n + 1 series, based on 137/2, when Ganymede reaches itselongation at the opposite side of Jupiter:

Ganymede: 137/2 per. x 7.1546631 days/per. = 490.09442 daysEuropa: 138 per. x 3.5511431 days/per. = 490.05775 daysIo: 277 per. x 1.7691614 days/per. = 490.05771 days

Whenever one of the other satellites arrives at elongation atthe same time as Io, the “Io Shout” is orders of magnitudemore powerful. However, as Jupiter orbits around the Sun,these conjunctions at elongation will occur at different anglesrelative to the Sun. Only once in every eight 490-day periodswill the conjunctions of all three planets occur with Io at elon-gation with its synchrotron energy pointing directly at theSun. (Of course, a whole series of near-conjunctions will occurleading up to and trailing away from this time.) And eight490.07 day periods amount to 10.73 years. Could this havesomething to do with the Sun’s 11-year sunspot period? If theSun’s global resonances are caused by the Io Shout, whichpeaks in intensity every 10.73 years, there would indeed seemto be a connection. More study, in conjunction with Jupiter’sinclination, will be necessary to answer this question.

However, we seem to see the outlines of a “harmoniccycle” here, analogous to the terrestrial “oxygen cycle” and“nitrogen cycle,” and so forth. The orbiting planets causetidal and other disturbances in the Sun. The Sun’s export of

angular momentum (necessarily on its 10τ harmonic) seems tobe required for its own stability, to push these disturbing fac-tors further away. Jupiter, with its immense magnetic field,absorbs large amounts of this 10τ energy. However, it hasachieved stability on the intermodulation harmonic betweenits τ energy and the Sun’s 10τ energy, and can’t absorb anymore angular momentum in its orbit, so all of this angularmomentum must go to increase Jupiter’s already enormousrotation, or it must be dissipated somehow. The Jupiter-Io-Europa-Ganymede system seems to act as an enormous gener-ator—and dissipator—of 10τ harmonic energy, much of whichis thrown back at the Sun, completing the cycle.

Earlier we left unanswered the question of why the har-monics of the gas-giant planets were factors of 1.25 for Saturn,1.48 for Uranus, and 1.62 for Jupiter. We have since seen thatthe Jupiter system’s diameters must have a factor of around 1.6for its satellites’ periods to have a factor of 2, and resonate withthe Sun’s octave harmonics. There may be a harmonic reasonas well for the other two factors. Since their light-diameters arenot octaves of τ, they must “beat” with τ. Saturn’s factor is 5/4(1.25). 5/4 times the mean light-diameter of Saturn is within1.5% of the nearest octave harmonic (τ x 276). Uranus’s factoris approximately 3/2 (1.48); similarly, 1.48 times the meanlight-diameter of Uranus comes to within 5% of the nearest τoctave harmonic, τ x 275.

AnomaliesDirac’s equation, followed logically, requires space to be a“plenum” rather than a “vacuum.” It is a BEC full of vibrat-ing charges. Moreover, this universal BEC is sensitive toevery slightest change in ionization, instantly adjusting tomaintain its own integrity. As we have seen, there is clearand overwhelming evidence that rotating bodies of plasmasuch as the Sun and the gas giant planets set up standingwaves in this sea of charge which have physical effects onany matter they encounter. This would indicate that thepresent celestial mechanics, computed using only gravita-tion, could not accurately account for the behavior of bodiesanywhere but at nodes of these standing waves. And thismeans that any body not at a node must have small anom-alies in its celestial mechanics. As we will see in what fol-lows, there do appear to be anomalies that seem qualitative-ly to account for these necessary discrepancies. Since wecan’t yet quantify the standing wave, the anomalies can notbe considered proof of this hypothesis. However, if suchanomalies were not present, this would constitute disproof ofthe hypothesis. Therefore it is important to look at them.

The Solar CoronaSince the planets between Mercury and Jupiter no longerorbit at nodes which are octaves of the Sun’s diameter, wewould expect there to be sizable anomalies near the Sun andwith the inner planets, with their amplitude diminishing atroughly 1/r2 with distance from the Sun. And with the Sunitself we have a major indication that our hypothesis makessense. For while the surface of the Sun is a “cool” 5800˚K orso, the surrounding corona has temperatures that routinelyreach 1,000,000˚K. The corona is expanding from the surface,and by the gas law should cool as it expands. How can theexpanding, cooling exhaust be 170 times hotter than thefurnace? This is regularly called “the greatest problem insolar physics.” All kinds of answers have been proposed,


magnetic “pinching” being the latest, but none comes with-in orders of magnitude of the energies required. However, if,as shown above, the Sun’s surface is the node of a powerfulmacrocosmic polarization wave, it is easy to understand thatthe node would be relatively cool, while anything flowingaway from the node into areas of higher amplitude would beexcited to high temperatures. And of course we would expectthis effect to be strongest closest to the Sun, and to diminishin amplitude at roughly 1/r2 away from the Sun.

The PlanetsThere are minor but persistent anomalies in the celestialmechanics of each of the inner planets, starting with thewell-known one at Mercury. (The Mercury anomaly is rough-ly explained by GR, but none of the others are.)

Newcomb (1897) calculated, and Doolittle (1912) con-firmed, that the celestial mechanics of three planets yieldedanomalous differences with measurements that were verymuch greater than could be attributed to errors. The firstanomaly was the celebrated advance of the perihelion ofMercury, for which Newcomb calculated a differencebetween observed and computed values of 41.24 ± 1.35 sec-onds of arc per century. For this the GR correction is 42.98”,or not quite within the probable error (computations arefrom Spolter, 1993). The second anomaly, the motion of thenode of Venus, Newcomb gives as 10.14 ± 1.86 seconds ofarc per century. GR gives no correction whatever for thisanomaly. The motion of the perihelion of Mars is the thirdanomaly. Newcomb calculates it to be 8.04 ± 2.43 seconds ofarc per century. The GR correction for this is only 1.35”,which is only about 17% of the measured advance.

If GR is the final answer to gravitation, and gravitation is theonly force operating between the planets, GR should provideanswers to all of these anomalies. And there are other reasonsfor suspecting that GR may not be the final answer, primarilybecause space appears to be Euclidean at every scale, and“curved empty space” is a contradiction in terms, as Phipps(1986) observed. Also, the “Magnetogravitation” outlinedherein seems to be a simpler and more elegant answer, but doesnot in itself explain the advance of Mercury’s perihelion.

However, the advance of Mercury’s perihelion, Newcombalso calculated, could be explained by a local modification ofthe force of gravitation from the inverse square to the inverse(2 + ε) power, where ε is a small number of about 10-7 (VanFlandern, 1993). Such a local modification of the force of gravita-tion is exactly what would be required by our hypothesis that the Sunis the source of a macrocosmic vacuum polarization wave. In fact,since Mercury is only on a node of the Sun’s octave wave at itsperihelion position and travels through regions of high activi-ty the rest of the time, it must be said that if Mercury’s perihe-lion did not experience such an advance, it would disprove ourhypothesis. And while we can’t yet quantify it, the above mod-ification is qualitatively in the right direction and seems rea-sonable for such a force at the distance of Mercury.

Furthermore, a large polarization of the vacuum in thevicinity of the Sun would necessarily cause a refraction(bending) of light passing near the limb of the Sun, and somight explain another of the supposed proofs of GR. (Thecorona itself also causes such a refraction, which was nottaken into account in the supposed proofs of GR in 1919.)

Both Venus and Mars would be expected to have measur-able anomalies in their celestial mechanics, as Newcomb

found. These anomalies can not be explained either by GRor by conventional celestial mechanics. Both planets arecaught between the powerful polarization waves of Jupiterand the Sun. However, we noted above that the plane of theecliptic is roughly the plane of Jupiter’s orbit, with onlyMercury orbiting above the Sun’s equator, 7 degrees away.However, Venus, with a 3.4º inclination, is caught half waybetween these influences, and this might explain the other-wise puzzling motion of its node.

This effect, with the Earth, might be expected to reveal itselfin how well the planet observes Kepler’s third law. It shouldnow be possible to measure even tiny discrepancies usingradar, laser, and spacecraft ranging observations. Since theranging observations are considerably more accurate than theold optical data, astronomers now set the size of the Earth’sorbit by these ranging (distance) observations, and then useKepler’s third law to compute the Earth’s period. However,according to Van Flandern (1993) a small but significant dis-crepancy persists with the optical data, which insists that theEarth’s period is about 5 x 10-9 different from that given by theradar data. Astronomers can give no reason for this discrepan-cy; it is currently considered an unsolved mystery. However,the discrepancy is similar to the amount we would expect fromour macrocosmic vacuum polarization wave if the magnitudeof the effect is of the order of 10-7 at Mercury.

The Earth itself has limited amounts of plasma, and rotatesslowly. So it would be expected to be a relatively weak sourceof such vacuum polarization waves. Moreover, we live primari-ly at the surface of the planet, at a node, where they would beat their weakest. It is noteworthy, therefore, that most of theanomalous gravitational measurements which recently led tothe hypothesis of a “fifth force” took place away from the sur-face: deep in mines or high in towers (Stacey, 1981; Holding,1984; Eckhardt, 1988; Zumberge, 1988).

These anomalies were all “explained away” as being “pos-sible” density variations in the Earth. Since such an expla-nation was barely possible, though certainly not proven, itwas instantly accepted as a paradigm-saving explanation,and the anomalies wished away. However, the number andscientific rigor of these experiments must surely create doubtthat all of them “just happened” to be performed in regionsof massive and hitherto unobserved density variations.Moreover, the Holding experiment was performed in anAustralian mine complex, where surrounding densities arewell known; the Zumberge experiment was performed deepin the Greenland ice sheet, whose densities are also wellknown; and the Eckhardt experiment high in a tower, whereearth density variations should have minimal effect. Itwould seem that vacuum polarization might provide thefirst remotely plausible explanation ever given for theseanomalous measurements.

So we see that there are a number of unexplained anomalies,at least one associated with the Sun and each of the innerplanets. The magnitude of these anomalies is very large at theSun itself, where it amounts to “the greatest problem in solarphysics,” large at Mercury, and diminishing in intensity atVenus, Earth, and Mars. And, of course, the powerhouse Jupitersystem contains several immense anomalies.

There is even a tiny anomaly measured with respect to thePioneer 10, 11, and Ulysses spacecraft which have complete-ly exited the solar system. They seem to be experiencing anunexplained “sunward pull” of about 1/10 billionth of g.


Since the anomalies diminish in magnitude with distancefrom the Sun, the source of all of these anomalies is clearlythe Sun itself. All of these anomalies can be explained, qual-itatively at least, by our hypothesis of a macrocosmic polar-ization wave originating in the Sun’s spinning plasma.

Cosmological ConsequencesLet’s step back and take a look at the universe revealed to usby our modern instrumentation. We shall try to look as aphysicist such as Newton or Faraday might have looked,having regard to such eternal verities as conservation andcausality. The mathematicians who have taken over the dis-cipline manage to ignore these verities, or wish them awaywith the wave of a magic tensor. Richard Feynman, one ofthe last real physicists, famously remarked that, “If all ofmathematics disappeared, physics would be set back exactlyone week.” (Of course, M. Kac replied “Yes—precisely theweek in which God created the world.”)

Newton pointed out the absurdity of unmediated action-at-a-distance. His laws of motion state that if somethingphysical changes its state of motion, something physicalmust have pushed or pulled on it to cause such a change.Faraday regarded his “lines of force” as real, physical entities.Maxwell regarded his “field” as a mathematical fiction, aconvenient way of representing the (physical) I-don’t-know-what that causes the observed push or pull.

Dirac’s equation, as shown above, supplies that physical I-don’t-know-what for both electromagnetism and gravita-tion, restoring causality. Faraday’s lines of force are shown tobe real, physical entities, connecting all charges and directlycausing the changes in states of motion referred to as “theelectromagnetic field.” Our “Magnetogravitation” showsgravity to be a similar, though much weaker physical connec-tion. Similarly, “the photon” is shown to be a real wave car-rying real angular momentum in a real, physical medium.

Among the characteristics of real waves in real physicalmedia is friction. However efficient the transmission, someenergy must be lost in the process. This is a characteristic ofall real waves, and is a requirement of the Second Law ofThermodynamics. One way of expressing the Second Law isthat any transformation of energy must entail a loss of ener-gy. A photon from a distant star starts out very small, withatomic dimensions, but because of the uncertainty principleby the time it reaches here it can have a diameter larger thana continent. These immense photons have been measuredby stellar interferometry, where they can be made to inter-fere with themselves over these large distances (Herbert,1985). Such a transformation must, by the Second Law,entail at least some loss of energy.

So natural is this expectation that, in 1921, the Germanphysicist Walther von Nernst predicted that light from distantsources would be found to have lost energy in transmission

(von Nernst, 1921). Then, later in the decade, Edwin Hubble(1929) published a finding showing exactly that. The char-acteristic spectrographic emission lines of light from distantgalaxies, he showed, are shifted into the red end of the spec-trum, indicating a loss of energy apparently proportional tothe distance the signal has traveled, thus exactly fulfillingthe Second Law and von Nernst’s prediction. Further meas-urements only confirmed the relationship between distanceand this redshift loss of energy, and seven months afterHubble published his findings, the Cal Tech physicist Zwicky(1929) renewed the interpretation that red shift is a friction-al loss of energy.

Nothing could be more normal and natural, and consistentwith the laws and eternal verities of physics, than that light,like every other real signal, should lose energy in transmissionover long distances. That the measured loss of energy is pro-portional to the distance traveled is direct evidence that lightis a real signal in a real medium that obeys the Second Law.This interpretation is further supported by von Nernst’s valid,a priori scientific prediction, which was fulfilled by Hubble’sfindings. But will you find this logical chain of events, includ-ing this fulfilled scientific prediction, mentioned in any main-stream treatment of the red shift? Not a chance. This is becausethis natural frictional loss of energy was somehow interpretedas a Doppler shift, supposedly indicating that everything in theuniverse is rushing madly away from us in every direction atvelocities approaching light speed. How this came about, andcame to be enforced as the official and only permitted interpre-tation, must surely be one of the strangest aberrations in all thehistory of science.

Suppose, when you were a child, your mother called out thewindow to you, and you couldn’t hear her clearly. Did youassume 1) that she was far away, and the signal had attenuat-ed with distance, or 2) that she was moving away from you ata large fraction of the speed of sound, and accelerating as shegoes? Surely, in the case of light, the natural presumption mustbe that the signal has attenuated with distance.

How, then, were we saddled with this bizarre Doppler inter-pretation? Well, Einstein in SR had rejected the aether onMachian grounds. He called it “superfluous,” because therewas no measured evidence of an aether, such as a frictional lossof light’s energy. Therefore, when exactly such a frictional lossof energy was later predicted by Von Nernst and measured byHubble, to save the paradigm (and prevent a lot of red faces) ithad to be explained away as something else. Thus was born,out of desperation, the Doppler explanation—an explanationthat Hubble himself rejected, calling it “a forced interpretationof the observational results” (Hubble, 1936). It is therefore agratuitous insult to his memory to call the supposed rate ofexpansion of the universe the “Hubble Constant.”

Unfortunately, at this time Einstein’s GR was looked on asthe “shape” of the universe—and it was unstable, rushingtoward collapse without the “cosmological constant” that headded as a fudge factor. But if the universe was expanding at asufficient rate, the stability problem was solved, as Friedmannshowed. So the Doppler interpretation of the measured redshift was seized upon to solve both problems—to evade thespecter of the aether, and to prevent the collapse of GR.

But there are major problems with the Doppler interpre-tation, as Hubble knew. The observed red shift is of coursesymmetrical, increasing with distance in every direction withus at the center, exactly as a frictional loss of energy would

Richard Feynman, one of the last real

physicists, famously remarked that, “If

all of mathematics disappeared, physics

would be set back exactly one week.”


require. But this is a disaster for the Doppler interpretation.It is pre-Copernican, as it would put us once more at the cen-ter of the universe. To evade this objection, the Bangers addan epicycle. Though there is no evidence for such a bizarreassumption, we are told that this is not an expansion intoempty space, but an expansion of empty space itself, so thatthe expansion is uniform everywhere.

But this doesn’t work either. If space itself is uniformlyexpanding, then the space between proton and electronshould expand; the space between the Earth and the Sunshould expand, the space between the Sun and Pluto shouldexpand. Such an expansion at the Hubble rate would easilybe measurable, and simply does not happen (Van Flandern,1993). So yet another epicycle must be added: the TensorFairy is invoked, to wave a magic equation and decree thatspace expands only where we can’t directly measure it, butmagically avoids expanding anywhere we can measure it.

Further, with millions of galaxies accelerating to inferredvelocities approaching light speed, there is no known sourceof energy that could possibly fuel such expansion. Therefore,the Doppler interpretation flagrantly violates conservation.

Just on the basis of the argument thus far, the frictionalloss of energy explanation would be vastly preferred to theDoppler one on the basis of physical law and of Ockham’srazor. The Doppler interpretation violates conservation, itviolates the Second Law, and it requires two epicycles sounlikely that they tower into fantasy.

There is worse. “Expanding empty space” is another oxy-moron, like “curved empty space.” Let empty space expandas much as it jolly well pleases, the expansion still can’tmove so much as an electron. As Newton pointed out, tomove anything physical takes something physical pushingor pulling on it. How then did such an unphysical conceptas “expanding empty space,” with its gross violation ofcausality, come to be accepted dogma?

It would seem that Einstein created this monster in SR whenhe argued that a “field,” i.e. empty space powered only bymathematical equations, could move things about.(Mathematical physicists seem to believe that their equationsactually have this mystic power.) He compounded this when,in GR, he invented the concept that empty space could some-how curve and magically waft planets about. Once one admitsinto science this gross violation of causality and conservation,the door is open for empty space to perform any miracle youplease, such as to accelerate whole superclusters of galaxies to99% of light speed, without the ghost of a force to move them.Or, if you believe the “Inflation” magicians, it can acceleratethem to 1048 times faster than light.

Moreover, the expanding universe and the static universewhich results from a frictional loss of energy make differentpredictions for a number of matters we can now measurewith modern instruments. Van Flandern (2000) lists sevensuch tests, the results of which overwhelmingly favor thestatic universe. He concludes: “If the field of astronomy werenot presently over-invested in the expanding universe con-cept, it is clear that modern observations would now compelus to adopt a static universe model as the basis of any soundcosmological theory.”

There have, of course, been objections raised to the fric-tional loss of energy concept. The first has always been, “Butspace is a vacuum—where would the energy go?” Dirac’sequation, of course, provides the answer to that. The second

is the problem of scattering—that anything which absorbsand re-emits light would scatter it. Our epho model answersthis. The third has been that light-energy is quantized: thatlight presumably could lose energy only in discrete quanta.However, a long series of observations by Tifft (1977, 1990,1991), Arp and Sulentic (1985), Arp (1987, 1998), andGuthrie and Napier (1988) have all shown that redshiftsfrom stars, galaxies, and clusters are quantized. The redshiftsstep up in small, discrete, consistent amounts, indicatingthat photon energies step down in small, regular quanta.Though the details are not clear at this time, we will showthat this can only be a BEC characteristic, indicating thatlight loses energy to the BEC only in discrete quanta.

In our laboratories, a superfluid such as 4He confined to acircular ring exhibits the same behavior, which is character-istic of the BEC, in which every part must have the samewave function. If angular momentum is applied to the ringof superfluid, it will not move at all, storing the energysomehow, until every boson component has a whole quan-tum of angular momentum. Then instantly the entire ringwill be in uniform motion.

The same behavior has recently been observed with coldneutrons falling in response to a gravitational field (VanFlandern, 2002). The neutrons don’t accelerate smoothly,but in velocity steps of 1.7 cm/second. For instance, a neu-tron falling at 10 cm/sec in a gravitational field has that con-stant velocity for an increment of time, then instantaneous-ly is moving at 11.7 cm/sec, then an increment of time laterit is moving at 13.4 cm/sec, and so forth. This has beencalled “Possible Detection of a Gravitational Quantum,” butif gravitation itself were quantized as crudely as that, theeffect would have been detected long ago.

However, we have shown that neutrons are 90% negativeenergy, and so are in a semi-condensed state. And like thesuperfluid above, the neutron as a whole cannot accelerateuntil every one of its 918 “real” boson components hasacquired a quantum of momentum. Therefore, like thesuperfluid, the neutron accelerates in quantum steps, just asthe photon, which is also a BEC phenomenon, loses energyin quantum steps.

We see that two incredibly bad choices

were made, both at about the same time,

both for the same bad reason: to save the

paradigm, to evade the increasing evi-

dence for the anathematized aether, to

keep some “experts” from being wrong

and looking foolish. The first bad choice

resulted in the truncation of Dirac’s

equation, and ultimately in the enormi-

ty that is the Standard Model. The sec-

ond bad choice resulted in the enormity

that is the Big Bang.


Quasars exhibit the same behavior. They behave likesuperfluids, and their redshifts repeatedly have been meas-ured to step down in regular quantum steps (Arp, 1998). Butbecause neither of these repeated, confirmed observations ofredshift quantization can possibly be explained as a Dopplerphenomenon, both have been ignored, denied, and sup-pressed by Big Bang theorists. Again, the Bang is the theoryon which they base their facts.

No other remotely plausible explanation has been given for anyof these three classes of observed phenomena. Together, theyamount to additional proof both that the nucleon is in asemi-condensed state, and that we are immersed in a uni-versal Bose-Einstein Condensate.

We have seen that without extreme prejudice on the part ofscientists in the early 1930s the Bang would never so much ashave been suggested. Therefore we will not attempt a detailedcritique of the hodge-podge of mutually incompatible theoriescollectively known as the Big Bang, as that has been done else-where (Arp, 1987, 1998; Lerner, 1991, 1992; Van Flandern,1993, 1996, 1998, 2000; LaViolette, 1995, 1996). All versions ofthe Bang massively violate conservation and causality, all out-rage common sense and the eternal verities of physics, all havefailed every observational test. They currently survive only bymeans of ever-proliferating patches and fudges, epicyclestacked on to save the incredibly cumbersome failed concept.As the astronomer R.B. Tully famously observed, “It’s disturb-ing to see that there is a new theory every time there’s a newobservation.” (Lerner, 1991)

So we see that two incredibly bad choices were made,both at about the same time, both for the same bad reason:to save the paradigm, to evade the increasing evidence forthe anathematized aether, to keep some “experts” from beingwrong and looking foolish. The first bad choice resulted inthe truncation of Dirac’s equation, and ultimately in theenormity that is the Standard Model. The second bad choiceresulted in the enormity that is the Big Bang.

Earlier, Dirac’s Equation had shown that the “microwavebackground” is much more likely to be exhaust from the neg-ative-energy BEC than a residuum from a Bang at infinite tem-peratures. Moreover, this energy is uniform, isotropic to betterthan one part in 100,000, as would be required of exhaust fromthe BEC. However, such a hot, uniform gas as the fireball that,on the Bang supposition, would have caused it could nevercondense into anything, much less the vast structures of super-clusters and gaps that we observe. And even if this uniformfireball of hot gas could somehow condense, it could not formthese huge observed structures. At the maximum observedintergalactic velocities, these huge structures would take atleast 100 billion years to form, seven times the maximum timefrom the initial Bang (Lerner, 1991). So the microwave back-ground actually disproves any Bang.

With the above argument, showing that light is a real wavein a real medium which loses energy in discrete quanta to thatmedium, we have removed the last vestige of experimental evi-dence for the unlikely supposition that the universe arose“from nothing” in a magical explosion. Instead, creation isseen to be a continuing, natural process, without a necessarybeginning or end, depending merely on the properties of a sin-gle quantized field. Thus it obeys the “perfect cosmologicalprinciple” that the Bang disobeys, namely that we occupy nospecial place, either in space or in time.

There is one further consequence of magnetogravitation

as outlined above. If gravitation is to be recognized as a“real” electromagnetic force, rather than some magical,unmediated action-at-a-distance, by the Second Law ofThermodynamics the electromagnetic medium that “car-ries” the force must “charge” a tiny amount for that con-veyance. Thus the epo chains would gradually lose theirinduced attraction, hence their coherence. When the epos ina chain fell below the critical “temperature” of 2.7˚K, theywould drop back into the big BEC, and cease to attract at1/r2. Thus gravitation, like any other real force, would havea limited range, rather than magically extending to infinity.

If our magnetogravitation is a correct model, this rangeshould be calculable. We predict that this range will befound to be approximately 2 kiloparsecs. As Van Flandern(1993) shows, if the range of gravitation were about this dis-tance, it would explain the “flat” velocity curves of stars inthe spiral arms of galaxies without the need for any (unob-served) “missing dark matter.” This “missing dark matter”must, to explain the observed velocities, amount in someregions to thousands of times the amount of matter presentin stars. This limited range would also, as Van Flandernobserves, explain a large number of other unexplained phe-nomena, such as the sizes of galaxies.

Conventional cosmology has never been able to explainwhy matter clumps together into galaxies of a certain charac-teristic range of sizes, rather than either dispersing completelyor massing into a single superclump. Using gravitation ofunlimited range, Einstein’s GR equations are unstable, requir-ing a “cosmological constant” (i.e. fudge) to explain observa-tions. But a limited range to gravitation would explain a stable,static universe, and many other astronomical mysteries.

Ockham’s Razor—A SummaryMerely the assumption that all of the solutions of Dirac’sequation are both real and meaningful has brought us a longway toward Dirac’s unitary dream. We have seen that thereare several different reasons for supposing that everything ismade of just the four entities that are really two that couldbe considered only one. The first, of course, is that these arethe only solutions to this very general equation thatdescribes “everything that waves.” Since two of these solu-tions are “above 0,” the other two must be “below 0.” Thisleads to the necessity of a universal BEC completely fillingnegative-energy space. The refrigeration requirements ofsuch a BEC automatically require an adjacent positive-ener-gy space for it to dump its waste products. And if our posi-tive energy balance comes from the BEC, as seems necessary,then everything must ultimately be built of epos, as that isall the BEC has to offer. The “electromagnetic field” and theΨ wave are seen to be epo structures the BEC must form tomaintain its integrity. And the “photon” is very successfullymodeled, not as a “particle,” but as positive energy carriedby successive waves of epos to conserve angular momentum.The measured frictional loss of energy over large distances isevidence that light is a real wave in a real medium.

This model explains things about the electron neverbefore understood, particularly its immense angularmomentum and its “complex” structure, its spin being part-ly “real” and partly a vibration in an “imaginary” direction.And this complex vibration gives us the “gyroscopic” modelof inertia, in which inertia is seen to be a local phenomenon,not depending on unmediated action-at-a-distance by the


“fixed stars.” And the unbalanced magnetic moment exhib-ited at the same phase by all matter gives us a natural modelof gravitation as one more necessary function of the BEC.

So merely with the one assumption that the Dirac equationmeans what it says, we are within sight of a truly unitary view,not only of our present reality, but of its origin as well. If a fieldmust give rise to unlimited numbers of particles, as QFT insists,then the Dirac spinor field or, alternately, Treiman’s “ZerothOrder Field” must fill some space with epos, forming a BECwhich, as we have seen, must energize an adjacent space withits exhaust. So “creation” is seen not as a miraculous one-timeoccurrence, but as a continuing, necessary process dependingmerely on the properties of a quantized field.

We can see that QFT is exactly and completely right—how-ever, just one field is all that is necessary, therefore all that isused. We see this economy of means all through nature. Onlytwo particles are necessary, therefore only two are used. Fromthese can be made the three entities that are both necessaryand sufficient to build 92 atoms, which suffice for maximumcomplexity. Four entities are both necessary and sufficient tocode DNA, the most complex known compound.

This same parsimony of means is seen in the positive-energy states of epos. The sea of negative-energy one-dimen-sional epos, vibrating in imaginary directions, forms a virtu-ally undetectable background, like “off” pixels in a perfectcomputer screen. And like a three-way light switch, they“turn on” in three stages, each stage vital to our reality. Eposvibrating in one “real” dimension form the electromagneticfield. Vibrating in two “real” dimensions, they carry angularmomentum around at the speed of light: the “photon.” Andvibrating in three “real” dimensions, they form matter.

As shown above, changes both in gravitation and in theelectromagnetic field must propagate much faster than light.Bell’s theorem and the proofs thereof show that phase-entan-gled quantum objects also share information much faster thanlight. As Nick Herbert says, “A universe that displays local phe-nomena built on a non-local reality is the only sort of world con-sistent with known facts and Bell’s proof.” In requiring ourreality to be imbedded in a BEC, the one extended structureshown, in the laboratory, to demonstrate non-locality, Dirac’sequation provides exactly that non-local reality in which ourlocal universe is imbedded. These demonstrations of non-local-ity therefore constitute evidence for the BEC.

Not all of this is original, of course, even to Dirac’s equation.The French physicist Le Bon suggested in 1907 that the etherconsists of “weightless combinations of positive and negativeelectrons,” which, considering the date, is positively clairvoy-ant. Others (Phipps, 1976, 1986; Simhony, 1994; Rothe, 2000)have suggested models based on electron-positron pairs, butnone has approached the simplicity, elegance, and range ofproblems solved by the complete Dirac equation.

However, at all times we must keep in mind that this is onlya model. The map is not the territory, the menu is not themeal. We must remain flexible. This model must fail to matchthe terrain in major and unexpected ways, as all of our theo-ries are by definition invalid. Our epo model of the nucleonexplains the size of the nucleon, the mass of the nucleon, thevery individual and peculiar shape of the strong nuclear force,the strength of the strong nuclear force, and several other fea-tures that no other model has begun to explain. However, it isperhaps at a stage similar to the original Bohr model of thehydrogen atom. It explains many hitherto unexplained fea-

tures, but it is perhaps oversimplified and wrong in details,and lacking in quantitative analysis.

We can say with some finality, however, that the Big Bangand the Standard Model are to the physics of the future asPhlogiston is to modern chemistry.

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