the natural philosophy of the cosmos (b)

8/14/2019 The Natural Philosophy of the Cosmos (B)

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The atural Philosophy of the Cosmos (B)

Riccardo C. Storti

[email protected] Group Engineering (dgE)

Keywords: CMBR, Cosmological Expansion / Inflation, Dark Energy / Matter, Gravitation, Hubbleconstant.

Abstract

Application of the Electro-Gravi-Magnetic (EGM) Photon radiation method on aCosmological scale suggests the nature of light to be that of propagating matter; facilitating the

derivation of the present values of the Hubble constant H0 and Cosmic Microwave Background

Radiation (CMBR) temperature T0. It is demonstrated that a mathematical relationship exists

between the Hubble constant and CMBR temperature such that T0 is derived from H0. The

values derived are 67.0843(km/s/Mpc) and 2.7248(K) respectively. Consequently, utilising the

experimental value of T0, improved estimates are derived for the solar distance from the Galactic

centre Ro and total Galactic mass MG as being 8.1072(kpc) and 6.3142 x1011(solar-masses)

respectively. The EGM construct implies that the observed accelerated expansion of the Universe

is attributable to the determination of the Zero-Point-Field (ZPF) energy density threshold UZPF

being < -2.52 x10-13(Pa) [i.e. < -0.252(mJ/km3)]. Moreover, it is graphically illustrated that thegradient of the Hubble constant in the time domain is presentlypositive (i.e. dH/dt > 0).


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1 Electro-Gravi-Magnetics (EGM)Pursuant to the synoptic results presented in [1], this manuscript sets forth modelling

propositions for community consideration, directly resulting in the derivation of critical

Cosmological information such as the present values of the Hubble constant H0 and Cosmic-

Microwave-Background-Radiation (CMBR) temperature T0. The key concepts presented herein

are that: (i) Photons possess mass (i.e. a Photon is a propagating piece of matter) andconsequently (ii), Dark Matter / Energy is not required to mathematically articulate and precisely

numerically determine H0 and T0. The accelerated Cosmological expansion phenomenon (i.e.dH/dt > 0) is derived organically from Particle-Physics, in favourable agreement with

experimental evidence. Therefore, it is proposed that the observational suggestion for the existence

of Dark Matter may be explained by halos of ejected Gravitons existing as conjugate

wavefunction pairs of non-zero mass Photons. [2, 3, 4] Moreover, it is demonstrated in [5] that

Dark Energy is analogous to the Zero-Point-Field (ZPF) energy associated with the Casimir

Effect, acting on a Cosmological scale.

i. Quantum Vacuum (QV) is a generalised theoretical Quantum Mechanical reference to thespace-time manifold of General Relativity (GR).ii. ZPF refers to the ground-state of the QV.

iii. Polarisable Vacuum (PV) refers to a polarised form (i.e. non-ground-state) of the ZPF / QV.Table 1: Applied Definitions,

The primary methodology applied to resolve this dilemma and achieve the stated objectives

is termed Electro-Gravi-Magnetics (EGM). The initial premise in the development of the EGM

method is the assumption that gravity and ElectroMagnetism may be unified via Quantum

Mechanics (QM) in terms of the QV, utilising Buckingham Theory (BPT) and DimensionalAnalysis Techniques (DATs). In order to compare a mathematical model to a physical system, it

must possess Dynamic, Kinematic or Geometric similarity to the real-world (any or all of these if

applicable). Dynamic similarity relates forces, Kinematic similarity relates motion andGeometric similarity relates shape (i.e. the topology of space-time curvature within the context of

GR).

An obvious question arising thus far is; how may Gravity be unified with ElectroMagnetism

in (at least) a convenient mathematical sense? This may be achieved as follows;

i. Assume that all matter radiates Gravitons into the QV. Let a Graviton bedefined as a coupled pair of transverse ElectroMagnetic (EM) plane waves,

propagating in the same direction, phased and orientated in such a manner that

the Electric and Magnetic fields sum to zero. The EM energy is not annihilated

by zero summation; it is conserved and may be transformed into an equivalent

representation of space-time manifold stress within General Relativity (GR).

ii. Let the mass of a Photon and Graviton be given by m 3.2 x10-45(eV) andmgg = 2m respectively. [2, 3] Leading to the proposition that the minimumgravitational lifetime of starving matter is given by TL = h/m = 2h/mgg;

where, h = 6.6260693 x10-34(Js). [5]

iii. As a consequence of the definition of a Graviton applied herein, the Electriccharge on all fundamental particles (where applicable), may be usefully

neglected (i.e. rendering them electrically neutral for the purposes of the statedobjectives), without impinging upon the proposed methodology for the quasi-

unification of ElectroMagnetism and Gravity.

ote: within the EGM construct, the Photon is considered to be a massive particle; consequently,

the Weinberg-Witten Theorem is inapplicable.


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Two distinct and practical advantages exist for representing Gravitons in accordance with

the EGM construct, these are;

iv. It avoids (not dismisses) the classical many orders of magnitude problemwhen relating Gravitational and Electrical forces.

v. A single paradigm is applicable to all matter.EGM is an engineering approach, not a theory, it is a tool for mathematically simulating

real-world systems in order to model physical problems in GR and QM utilising standard

engineering techniques. EGM asserts that Gravity is the resultof an interaction between matter and

the space-time manifold; leading to the following precepts,

vi. An object at rest polarises the QV surrounding it (see Figure 1).vii. An object at rest is in equilibrium with the QV surrounding it (see Figure 1).

viii. The Quantum-Vacuum-Energy (QVE) [i.e. the gravitational field energy]surrounding an object at rest is equivalent to E = mc2.

ix. The frequency distribution of the spectral energy density of the QVsurrounding an object at rest is cubic. The cubic form of the Spectral Energy

Density of the QV was determined mathematically in a manuscript

formulating the Quantum-Vacuum-Inertia-Hypothesis (QVIH). [8]

Figure 1: free fundamental particle with classical form factor,

The EGM method commences by mathematically representing mass as an equivalent

localised density of wavefunction energy, contained by the QV surrounding it. Properties of Fourier

harmonics are utilised to mathematically decompile the mass-energy into a spectrum of EM

frequencies. The QV is predicted and required by QM and Quantum-Electro-Dynamics (QED), both

dictating that virtual energy must exist within the fabric of space-time. The EGM construct

represents matter as a precisely defined spectrum of EM energy utilising Fourier techniques and

models its interaction with the QV as a dynamic system. Subsequently, the unique spectral

signatures of matter are superimposed upon the QV demonstrating that a change in Poynting

Vector P results in a gravitational effect.All natural systems seek to find equilibrium; this implies that the energy condensed as

matter exists in a state of equilibrium within the Universe surrounding it. Consequently, EGM

asserts that mass is relativistic because it equilibrates to the ambient energy conditions of its local

environment. The methodology articulated in [4] specifies the mass-energy equilibrium point

between an object and the space-time manifold such that the metaphysical conception of

curvature is re-interpreted as being a local polarisation of the QV, explicable by the superposition

of EM fields. P is analogous to variations in the Refractive Index KPV of the space-timemanifold in an optical model of gravity.

The EGM construct models vacuum polarisation by the superposition of mass-energy and

QV spectra. A key difference distinguishing mass-energy from QVE is that the energy containedwithin matter is highly localised, whereas QVE is distributed homogeneously throughout the vast

regions of free-space.


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Haisch, Rueda and Puthoff (HRP) determined that the QV spectrum obeys a cubic frequency

distribution (i.e. the energy density of QV spectral modes increases to the cube of the frequency).

However, this presents a rather formidable dilemma. This type of distribution implies that the

energy density of empty space is staggering. Calculating the total energy represented by the HRP

interpretation suggests that every cubic centimetre of empty space is so packed full of energy that it

should cause the Universe to collapse in upon itself.

Because of this theoretical result, many Physicists discount the existence of the QV in cubicfrequency form, believing that something must be fundamentally wrong with its formulation,

despite the fact that it is derived utilising standard QM. However, the EGM construct does not

suffer from this ailment and emphatically rejects the assertion that an infinite quantity of energy is

contained within the vanishing volume associated with the QM derivation of the QV.

The physical justification for this emphatic rejection spawns from the derivation of the H0

and T0 utilising the harmonic representation of fundamental particles. The derivation of H0 and

T0 within the EGM construct yields experimentally impressive results, substantially beyond the

abilities of the Standard Model (SM) of Cosmology (SMoC), without the vanishing volume

implications of QM; hence, the emphatic rejection asserted herein is substantiated. Applying

EGM to the energy dynamics of Hubble expansion spectrally, H0 is derived by modelling the QV

spectrum of the Primordial-Universe (i.e. instantaneously prior to the Big-Bang) as a singlehigh-frequency wavefunction representing the energy of the entire Universe.

Instantaneously after the Big-Bang, the single wavefunction rapidly decomposed into a

broad spectrum of lower-frequency wavefunctions, forming localised gradients through the

condensation of mass. Summing the energy associated with all lower-frequency wavefunctions in

the present QV yields the total energy of the Universe, equalling the total energy at an instant prior

to the Big-Bang; hence, energy is conserved and the cubic frequency distribution of the QV

spectrum predicted by HRP is preserved.

Setting the QV spectrum temporarily aside, we shall now define and describe the energy

spectrum associated with matter; termed the EGM spectrum. This is a wavefunction

representation of mass-energy obeying a Fourier distribution such that the number of modes

decreases as energy density increases, implying that the energy density of free-space approaches

zero, avoiding the infinite energy in a vanishing volume problem. This is because each mode is

representative of the possibility of the existence of virtual Photons only, not that virtual Photons

must exist. In other words, free space can accommodate the existence of high energy Photons;

however, the probability of their existence in the absence of mass approaches zero. Similarly, theprobability of low frequency virtual Photons existing in the QV of free space approaches unity.

Consider the action of adding a point mass to an empty Universe. This action superimposes

the EGM spectrum of the point mass onto the QV spectrum of the Universe; doing so forms the PV

spectrum (i.e. a quantised representation of the gravitational field) surrounding the point mass,

inducing a mode population gradient in space-time between the point mass and the edge of the

Universe. The mode population gradient modifies the KPV value of the vacuum such that itchanges at the same rate as gravitational acceleration g from the point mass. Thus, the gradient is

curved in an analogous manner to space-time within GR.

A mass-object pushes the vacuum around it uphill, against the natural flux of expansion.

Mass may be modelled as doing work on the surrounding vacuum by curving it. This occurs

because the nature of the Universe is to expand and upon encountering resistance to its normal flux

from high to low energy, the Universe pushes back as it strives to find balance ( i.e. equilibrium).Thus, the matter-Universe interaction is a dynamic mass-energy-vacuum exchange system rather

than material inertly suspended in a vast expanse of nothingness.

EGM considers the spectral energy of a gravitational field to be equivalent to the mass-

energy of the object generating the field, expressible in terms of a PV spectrum analogous tospace-

time curvature within GR. It models each of the EM frequencies as populations of conjugatePhoton pairs, i.e., each population is 180 out of phase with its conjugate, consistent with aFourier harmonics representation of a constant function in complex form. A conjugate Photon pair


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constitutes the definition of a Graviton within the EGM construct. The mathematical summation of

conjugate wavefunction pairs (typically represented as oscillating about zero) produces a constant

function, analogous to the manifold stress tensor within GR. The summation of opposing sinusoids

of equal amplitude does not result in the non-existence of energy; otherwise the law of conservation

of energy would be violated. That is, a mathematical zero point is an arbitrary assignment and

should not be mistaken for the absence of manifold stress energy.

The density of Gravitons surrounding a mass-object is maximal nearby, graduallydecreasing with radial distance; thus, the greater the population density of Gravitons, the stronger

the gravitational field. These factors are consistent with the manner in which the PV spectrum is

defined via Fourier harmonics, resulting in a spectrum which increases in mode number with radial

distance from a mass-object (i.e. QV mode numberdecreases with Graviton density).The tendency of the space-time manifold is to expand; however, the presence of matter

interrupts this movement, polarising the QV. Energy is required to alter its state to fewer modes of

higher frequency, counteracting the thermodynamic tendency of any system to move towards a state

of lowest energy and greatest stability. Subsequently, an observer held fixed within a QV gradient

senses that the mode energy is asymmetrical (i.e. higher in the direction of the centre of mass of anobject and lower out in space) and based upon the Quantum-Vacuum-Inertia-Hypothesis (QVIH),

vacuum asymmetry results in an apparent acceleration force on the observer, perceived as gravity.Rather than a geometric curvature of nothingness, the manifestation of g is better

represented as back-pressure from the vacuum as mass-energy exerts its influence upon it. EGM

represents this process as the superposition of two spectra, resulting in a mathematical description

of g, utilising Fourier harmonics (enhanced by the PV representation of GR; developed by

Puthoff et. Al.). Thus, it may be stated that the EGM construct yields a quantiseddescription of

gravity as articulated in [4]. Moreover, EGM derives the Casimir Force from first principles,demonstrating that it differs depending on the gravitational field strength of where it is measured.

For example, EGM asserts that the strength of the Casimir Force on Jupiter will be smaller than on

the surface of the Moon. [6]

2 CosmologyEGM represents a single paradigm which may be applied to precisely derive Cosmological

measurements such as H0 and T0 (it is demonstrated that T0 may be derivedfrom H0). The

EGM harmonic representation of fundamental particles serves to validate and substantiate the

evolutionary epochs of our Universe, as science has come to understand them, since the time of the

Big-Bang. EGM models mass-objects as being in equilibrium with the QV such that the energy

state of matter describes the energy state of the vacuum. Hence, H0 and T0 represent

observational evidence of Cosmological mass-energy equilibration.

Invoking principles of similitude, H0 is derived by relating the PV spectrum of a Planck-

Particle (representing the Universe at the instant of the Big-Bang) to the present-day utilising theMilky-Way Galaxy as a basis for comparison. Within the EGM construct, a Planck-Particle

denotes the condition of maximum permissible energy density, representing the Universe

compacted to a point. As mass-energy density increases, the PV modal bandwidth compresses such

that for a particle approaching the Planck Scale, the PV spectrum converges into a single mode

approaching the Planck Frequency.

Galaxies are homogeneously distributed throughout the Universe and are approximately in

the same stage of evolution. Hence, it follows that we may utilise our own Milky-Way Galaxy as

a universal reference to yield an average value of Cosmological gravitational intensity. Utilising

astronomical estimates of total Galactic mass and radius, we may represent the Milky-Way as a

particle at the centre of the galaxy, termed the Galactic Reference Particle (GRP). The radiant

gravitational intensity of the GRP may be calculated from its PV spectral limit.The GRP is representative of the total mass-energy density and vacuum equilibrium state of

the Universe at the present time; as viewed by instrumentation within our solar system. Thus, H0


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is derived by comparing the Planck-Particle Universe at the instant of creation to the GRP;

facilitated by utilisation of the harmonic representation of fundamental particles.

Relating the Cosmological expansion of the primordial Planck-Particle Universe to the

GRP yields an expansive scaling factor KT. Subsequently, Wiens displacement law is applied to

determine a thermodynamic scaling factor TW quantifying the manner in which Photons radiated

at the instant of the Big-Bang have red-shifted to the microwave range after Hubble time. The

microwave frequency is converted to temperature by relating KT and TW, producing a value ofT0 precisely matching physical measurement.

The resulting history of the CMBR temperature corroborates with all epochs of cosmic

evolution as predicted by the SMoC. The theory of early cosmic inflation is reinforced and the

recently measured accelerated expansion is derived. The Cosmological inflation and accelerated

expansion phenomena emerge naturally within the EGM construct and are not presumed a priori

as part of the modeling process. The EGM construct generates the inflationary epoch from first

principles, derived from Particle-Physics. Even though the cosmic inflation epoch is a contrivance

introduced to fit a theory, EGM substantiates its existence because it emerges as a natural

consequence of the derivation of H0 and T0. However, the existence of dark energy / matter

must be questioned due to the fact that the EGM method predicts H0, T0 and Cosmological

inflation / accelerated expansion, without invoking dark matter or energy; producing resultssubstantially more precise than the SMoC. Within the EGM construct, the contribution of dark

matter / energy to the Cosmological model is shown to be < 1(%).

The EGM construct produces H0 and T0 formulations of approximately

67.0843(km/s/Mpc) and 2.7248(K) respectively [T0 experimental tolerance is presently

2.725 0.001(K)]. The derivation of H0 and T0 is possible assuming that, instantaneouslyprior to the Big-Bang, the Primordial Universe was analogous to a homogeneous Planck scale

particle of maximum permissible energy density, characterised by a single EGM wavefunction.

Simultaneously, the Milky-Way is represented as a Planck scale object of equivalent total

Galactic mass MG, acting as a GRP characterised by a large number of EGM wavefunctions with

respect to the solar distance from the Galactic centre Ro.

This facilitates a comparative analysis between the Primordial and Galactic particle

representations yielding H0 in terms of Ro and MG. Moreover, the analysis is extended by

determining the theoretical frequency shift of a fictitious Graviton radiated from the Primordial

particle, yielding T0 in terms of H0. Consequently, by utilising the experimental value of T0,

improved estimates for Ro and MG are derived as being approximately 8.1072(kpc) and

6.3142 x1011(solar-masses) respectively. The key mathematical facts derived and subsequently

analysed in [5, 6, 7] are as follows,

Key Mathematical Fact SMoC EGM

Dark Matter / Energy required Yes No

Maximum Cosmological Temperature 1031(K) Yes YesBig Bang Temperature = 0(K) No Yes

Unification with Particle-Physics No Yes

Relationship between H0 and T0 No Yes

Precise determination of distinct Cosmological evolutionary phases No Yes

Sign of the Deceleration Parameter is in agreement with expectation No Yes

Prediction of Accelerated Cosmological Expansion No Yes

Table 2: SMoC vs. EGM,


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3 ConclusionThe EGM construct implies that Accelerated Cosmological Expansion is attributable to

the determination of the ZPF energy density threshold UZPF being < -2.52 x10-13 (Pa) [i.e. < -

0.252 (mJ/km3)]. Moreover, it is graphically illustrated that the gradient of the Hubble constant in

the time domain is presently positive (i.e. dH/dt > 0). Subsequently, it is mathematically

demonstrated that the magnitude of the impact of Dark Matter / Energy upon the value of theHubble constant and CMBR temperature is < 1 (%) such that the Universe is composed of:

> 94.4 (%) Gravitons, < 1 (%) Dark (i.e. inexplicable) Matter / Energy, 4.6 (%)Atoms.

Refer to Appendix A for simulation results produced utilising the MathCad computational

environment.

Bibliography

[1] The natural philosophy of the cosmos (A); Riccardo C. Storti, Proc. of the 18th National

Congress [Australian Institute of Physics (AIP)], 2008, Pg. 231-234, ISBN 1-876346-57-4.{Available for download: http://www.lulu.com/content/4852726}

[2] Derivation of the photon mass-energy threshold; Riccardo C. Storti and Todd J. Desiato, Proc.SPIE 5866, 207 (2005), DOI:10.1117/12.614634.

[3] Derivation of the photon and graviton mass-energies and radii; Riccardo C. Storti and Todd J.

Desiato, Proc. SPIE 5866, 214 (2005), DOI:10.1117/12.633511.

[4] The natural philosophy of fundamental particles; Riccardo C. Storti, Proc. SPIE 6664, 66640J(2007), DOI:10.1117/12.725545.

[5] Quinta Essentia: A Practical Guide to Space-Time Engineering Part 4; Riccardo C. Storti,

ISBN-13: 978-1847533548, LuLu Press.

{Available for download: http://www.lulu.com/content/795547}

[6] Quinta Essentia: A Practical Guide to Space-Time Engineering Part 3; Riccardo C. Storti,ISBN-13: 978-1847539427, LuLu Press.


[7] Quinta Essentia: A Practical Guide to Space-Time Engineering Part 2; Riccardo C. Storti, &G. S. Diemer, ISBN-13: 978-1847993618, LuLu Press.


[8] B. Haisch & A. Rueda, On the relation between a Zero-Point-Field-Induced inertial effect and

the Einstein-de Broglie formula Physics Letters A, 268, 224, (2000).


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Appendix A

Figure A1: Average Cosmological Temperature vs. Hubble Constant

{http://www.lulu.com/content/2588584}. Note: The Mag. of Hubble Constant (i.e. |H| in Fig.A1 and the graph title of Fig. A2) is an abbreviated reference to the square-root of the

magnitude of the rate of change of the Hubble Constant in the time domain (required due to text

field character limitations). The value of the Hubble Constant at t1 is graphically stated in Fig.A1; |H| = |dH/dt| = 0 denotes the instant when dH/dt = 0 (as represented by the equations inFig. A2).


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Figure A2: (i) Magnitude of the Hubble Constant vs. Cosmological Age, (ii) 1st

Derivative of

the Hubble Constant in the Time Domain vs. Cosmological Age

{http://www.lulu.com/content/2486994}. Note: the graph title is an abbreviated reference to the

square-root of the magnitude of the rate of change of the Hubble Constant in the time domain(required due to text field character limitations). The logic for the specified abbreviation arises

twofold; (i) from two distinct numerically coincident derivations of H0 within the EGM constructsuch that, for the present day, |dH/dt| = H0 (see [4] for details) and (ii), to visually accentuatecurve characteristics at t4.


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Figure A3: (i) 1st

Derivative of the Hubble Constant in the Time Domain vs. Cosmological Age,

(ii) 2nd

Derivative of the Hubble Constant in the Time Domain

{http://www.lulu.com/content/2526284}.

the natural philosophy of the cosmos (b)

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