cyclic mechanics
DESCRIPTION
Cyclic mechanics. The principle of cyclicity. Vasil Penchev Associate Professor, Doctor of Science, Bulgarian Academy of Science [email protected] http://www.scribd.com/vasil7penchev http://vsil7penchev.wordpress.com. Notations : Quantities : Q − quantum information S − entropy - PowerPoint PPT PresentationTRANSCRIPT
Cyclic mechanicsThe principle of cyclicity
Vasil PenchevAssociate Professor, Doctor of Science,
Bulgarian Academy of Science
[email protected]://www.scribd.com/vasil7penchev
http://vsil7penchev.wordpress.com
The mutual transformation between mass, energy, time, and quantum information
Notations:Quantities:Q − quantuminformationS − entropyE − energyt − timem − massx − distance
Constants:h − Planck c − light speedG − gravitationalk − Boltzmann
𝒕𝒉↔𝑬𝒄
↔𝒎
G
Skquantuminformation []
Quantum information in terms of quantum temperature and the Bekenstein bound
𝑸𝟐=𝑺𝟐
𝑬𝟐= 𝟏𝑻 𝟐≤𝟐 π𝒌ħ𝒄 𝒙 𝟐
𝑸𝟏=𝑺𝟏 𝒕𝟏ħ
=𝑺𝟏
𝑬𝟏≤𝟐 π𝒌ħ𝒄 𝒙 𝟏=
𝟐 π𝒌ħ𝒕 𝟏
Here are the corresponding radiuses of spheres, which can place (2) the energy-momentum and
(1) the space-time of the system in question
The transformation in terms of quantum measure
Notations:Quantities:Q − quantuminformationE − energyt − timem − massx − distance
Constants:h − Planck c − light speedG − gravitationalk − Boltzmann
𝒉
Q𝑸𝟐𝑸𝟏
quantuminformation
The universe as a single qubit ...and even as a single bit
YIN
“0”“1”YANG
A qubit A bit
?No,
the Kochen-Speckertheorem
the axiom of choice,Yes
QUANTUM INVARIANCE
Quantummechanics
Generalrelativity
The universe as an infinite cocoonof light = one qubit
Space-time
Energy-momentum
Light coneAll the universe can arise trying to divide
one single qubit into two distinctive parts, i.e. by means of quantum invariance
The Kochen-Speckertheorem stars as Yin
The axiom of choicestars as Yang
Minkowski space
Mass at rest as another “Janus” between the forces in nature
Banach spaceEntanglement
GravityPseudo-Riemannianspace
Weakinteraction
Stronginteraction
ElectromagnetismMinkowski
spaceGroupsrepresented in Hilbertspace
Mass atrest
?The “Standard
Model”
The Higgs mechanism? ?
?
How the mass at rest can arise bya mathematical mechanism
The universe as a cocoon of light
Space-time
Energy-momen-tum
The Kochen-Specker theoremEntanglement=
m Quantum invariance
The mass at restis a definite masslocalized in a definite spacedomain
= The mass at rest The axiom of choice
Mass at rest in relativity and wave-particle duality
Minkowski spaceRelativity
Hilbert spaceWave-particle duality
The lightcone
𝒕
𝒎𝒗 𝒑
spacedual space
𝑟 𝑆𝑇
Any qubit in Hilbert space
The qubit corresponding
in its dual space
𝑟 𝑆𝑇
𝑟 𝐸𝑀
𝒎 𝒓 𝑬𝑴𝒓 𝑺𝑻
𝒎 𝒑𝒗
Wave function as gravitational fieldand gravitational field as wave function
Gravitationalfield
Wavefunction
Infinity
Wholeness
+
Actual infinity=
How to compare qubits, or a quantum definition of mass at rest
Hilbert spaceWave-particle duality
spacedual space
𝑟 𝑆𝑇
Any qubit in Hilbert space
The qubit corresponding
in its dual space
𝑟 𝑆𝑇
𝑟 𝐸𝑀
𝒎 𝒓 𝑬𝑴𝒓 𝑺𝑻
𝜶≠𝟏≡𝒆𝒏𝒕𝒂𝒏𝒈𝒍𝒆𝒎𝒆𝒏𝒕Mass at rest means
entanglement
How the mass at rest can arise bya mathematical mechanism
The universe as a cocoon of light
Space-timeEnergy-
momen-tum The Kochen-
Specker theoremEntanglement=
m Quantum invariance
Mass at restarises if a biggerEM qubit (domain)must be insertedin a smaller STqubit (domain)
= The mass at rest The axiom of choice
𝑬𝑴
𝑬𝑴→𝑺𝑻
Mass at rest and quantum uncertainty: a resistless conflict
“At rest” means:
Consequently, the true notions of “rest” and “quantum uncertainty” are inconsistent
probability speed
Generalized
Internal External
Observers
Whole
Mass at rest and quantum uncertainty:a vincible conflict
The quantity is a power. According to generalrelativity this is the power of gravitational energy, and to quantum mechanics an additional degree offreedom or uncertainty:
Quantum mechanics General relativity
Gravitationalfield with the power p(t) in any point:
𝑷 𝒊(𝒕𝒊)𝒕 𝒊𝑷 𝒊
The Bekenstein bound as a thermody-namic law for the upper limit of entropy
The necessary and sufficient condition for the above equivalence: (−frequency). This means that the upper bound is reached for radiation, and any mass at rest decreases the entropy proportionally to the difference to the upper limit:
∴ Mass at rest represents negentropy information
The Bekenstein bound as a function of two conjugate quantities (e.g. t and E)
where
𝑺𝟎=𝟒𝝅𝟐𝒌−𝒎𝟎
:
That is the quantum uncertainty (Я)
as a rest mass ()
The generalized observeras any “point” or any relation (or even ratio) between any internal andany external observer
About the “new” invariance to the generalized observer
Quantum mechanicsSpecial & general relativity
All classical mechanics and science
System An(y) exter-nal observer
relativityspeed
Reference frame
System
An(y) internal observer
probability
Any internal observer
Any external observer
System
Cyclicity from the “generalized observer”
Any internal observer
System
Any external observer
The generalizedobserver
The universe
Any internal observer ¿
Any external observer
The generalized observer
The generalized observer is (or the process of) the cyclic return of any internal observer into itself as an external
observer All physicallaws shouldbe invariantto thatcyclicity, or to “the generalizedobserver”
Also:
General relativity as the superluminal generalization of special relativity
Minkowski space where:“ “ means its imaginary region, and “ “ its real one. The two ones are isomorphic, and as a pair are isomorphic to two dual Hilbert spaces.Gravitational energy by the energy to an externalobserver or to an internal one :
The curvature in “ “ can be represen-red as a second speed in “ “. Then theformer is to the usual, external observer,and the latter is to an internal one
Cyclicity as a condition of gravity
A space-timecycle
Gravity =( ) – ( )S – actionP – powerE – energy
h – homebodyt – travellerg - gravity
Cyclicity as the foundation of conservation of action
𝑺𝒊=𝑺𝒆𝒑𝒆𝒓 𝒂𝒖𝒏𝒊𝒕𝒐𝒇 𝒆𝒏𝒆𝒓𝒈𝒚⇔
𝒕 𝒊=𝒕𝒆
The universe
Simultaneity of all points
The Newtonabsolute time
and space
CIclIcIty
Simultaneity of quantum entities
Apparatus
Entangle-ment
CIclIcIty
Mathematical and physical uncertaintyCertainty Uncertainty Independence
Set theory Any element of any set (the
axiom of choice)
Any set Disjunctive sets
Logic Bound variable
Free variable
Independent variables
Physics (relativity)
Force Degree of freedom
Independent quantities
Quantum mechanics
The measured value of a conjugate
Any two conjugates
Independent quantities
(not conjugates)
General relativity is entirely a thermodynamic theory!
The laws of thermodynamicsThe Bekenstein bound
GeneralRelativity⇒
Since the Bekenstein bound is a thermodynamic law, too, a quantum one for the use of this impliesthat the true general relativity is entirely a thermody-namic theory! However if this is so, then which is the statistic ensemble, to which it refers?
To any quantum whole, and first of all, to the universe, represented as a statistic ensemble!
Cycling and motion
The universe
Mechanical motionof a mass point in it
Cycle 1 = Phase 1
Cycle 3
Cycle 2 = Phase 2
ACTION CONSERVATION
Energy conservation
Time conservation
General relativity is entirely a thermodynamic theory!
The laws of classicalthermodynamics
The Bekenstein bound
GeneralRelativity⇒
A quantum thermodynamic law
A quantum wholeunorderable in
principle ⇒A relevant
well-ordered,statistical ensemble: SPACE-TIME
⇒
The statistic ensemble of general relativity
Quantum information = = Action =
Energy (Mass) ⨂ Space-Time (Wave Length)
A quantumwhole
SPACE-TIMEdifferentenergy –
momentum and rest mass
in any point in general
The axiomof choice
The Kochen-Speckertheorem
Einstein’s emblem:
The question is: What is the common fundament of energy and mass?Energy conservation defines the energy as such: The rest mass of a particle can vanish (e.g. transforming into photons), but its energy never! Any other funda-ment would admit as its violation as another physicalentity equivalent to energy and thus to mass?!
However that entity has offered a long time ago, and that by Einstein himself and another his famous
formula, , Nobel prized
The statistic ensemble of general relativityThe Bekenstein bound
Informationas pure energy
(photons) = max entropy
A domain of space-time asan “ideal gas”of space-time
points
OR A body with nonzero mass as
informational “coagulate”
Informationas a nonzero rest mass
(a body) <max entropy
𝑬=𝒎𝒄𝟐The particular case if
Information -“I”𝒕𝟏𝑬=𝒕𝟐𝒎𝒄𝟐−𝒉𝑰
The general case: or - speed of body time, which is 1 in the particular case above
Reflections on the information equation:
𝒕𝟏𝑬=𝒕𝟐𝒎𝒄𝟐−𝒉𝑰
𝑬𝒗𝟏
=𝒎𝒄𝟐
𝒗𝟐−𝟐𝝅𝒌𝑬𝟎
𝒄
The information equation for the Bekenstein bound:
For action:
For momentum:
For energy:The information equation for the “light time”:
𝑬=𝟏𝜷 𝒎𝒄
𝟐−𝑬𝟎
The distinction between energy and rest mass
If one follows a space-time trajectory (world line),then energy corresponds to any moment of time,
and rest mass means its (either minimal or average)constant component in time
Energy (mass)
Time𝒎𝟎
𝑬𝟎𝑬𝟏
𝑬𝒏𝒕𝟎 𝒕𝟏 𝒕𝒏
... ... ... ...𝒎𝟎 𝒎𝟎
The laws of classical thermodynamics
Gravitational field as a limit, to which tends the statistical ensemble of an ideal gas
Gravitational field
Differential representation
An infinitelysmall volumeof an ideal gas
The Bekenstein bound (a quantum law)
A back transformationto the differen-tials of mecha-nical quantities
The rehabilitated aether, or:Gravitational field as aether
A point under infinitelylarge magnification
A finite volumeof an ideal gas
Space-time ofgeneral relativity
as
aether
The laws of classical thermodynamics
The Bekenstein bound (a quantum law)
The gas into the pointpressuretemperature
momentumenergy
The back transformation
An additional step consistent with the “thermodynamic” general relativity
A finite volumeof ideal field
The universeas a whole
A cyclical structure
The infinity of ideal field ===
===A point in it
=
The cyclicity of the universe by the cyclicality of gravitational field
The universeTwo “successive”
points in it𝒏𝟐𝒏𝟏
𝒕𝒏𝟏𝒕𝒏𝟐
, - two successive cycles
⇔Hilbert
Dual
Hilbert
space As to the universe,
as to any point in itby means of
the axiom of choice andthe Kochen – Specker theorem
“Light” “Light”
The cyclicity of gravitational and of quantum field as the same cyclicity
The universe
A point in it
GeneralrelativityGravity
Quantummechanics
The StandardModelStrong,
electromagne-tic, and weak
interaction
?
?
gravityQuantum??
Gravitational and quantum field as an ideal gas and an ideal “anti-gas” accordingly
Dual
Hilbert
space
Hilbert
The universe
A point in it
All the space-time
Pseudo-Riemannian
space
A volume ofideal gas orideal field
Quantum field
Gravitationalfield
Specific gravity as a ratio of qubits
Conjugate A
Conj
ugat
e B Quantum uncertainty
Gravity as if determines the quantum uncertaintybeing a ratio of conjugates
Quantum mechanics General relativity
An “ideal gas” composed of mass points (
𝒓 𝟏𝒕
𝒓 𝟐𝑬
isuncertain
Qubits
The gas constant R of space-timeThe axiom of choice needs suitable fundamental
constants to act physically:
How much to (or per) how many?
The Boltzmann constant Avogadro’s number ?⇔
Quantum mechanics General relativity
In Paradise: No choice
On earth: Choices, choices ...
⇔𝑲𝑩
𝑵 𝑨
Paradise on earth!An ideal gas (aether) of
space-time points:
𝑹=𝑲 𝑩.𝑵 𝑨
Time as entropy: “relic” radiation as a fundamental constant or as a variable
Seen “inside”:Our immense andexpanding universe
determined bythe fundamental
constants
Seen “outside”:A black hole
among many onesdetermined by
its physical parameterslike mass, energy, etc.
𝑺𝒑𝒆𝒆𝒅𝒕𝒊𝒎𝒆𝟏 𝑺𝒑𝒆𝒆𝒅𝒕𝒊𝒎𝒆𝟐
𝑫𝒆𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏 𝒕𝒊𝒎𝒆𝟏−𝟐+Energy (D) flow(D) +Energy (S) flow(S)
𝑺𝒑𝒆𝒆𝒅𝒕𝒊𝒎𝒆=𝑺𝒕=𝒕𝒕𝟎
= 𝒉𝑪𝑴𝑩 .
𝟏𝒕𝟎
=( 𝒉𝑪𝑴𝑩 )𝒕𝟎=𝟏
Horizon
How much should the deceleration of time be?
The ideal gas equation is:
𝐒=𝒑𝒙=(𝑵𝑲 ¿¿𝑩 /𝑲𝒖)𝑬𝒕 ¿𝑺𝒖=𝑵𝒉𝑲 𝒖=
𝑲 𝑩
𝑵 𝑨𝑵
𝟏𝒕 =𝑲𝑩
𝑪𝑴𝑩𝒉
𝟏𝒕 =𝑲𝑩
𝑪𝑴𝑩𝒉 =𝝂=
𝝎𝟐𝝅
The “Supreme Pole” (the Chinese Taiji 太極 )
The universe
Any separatepoint in it
The Einstein and Schrödinger equation:the new cyclic mechanics
The Einstein equation Schrödinger’s equation
Space & Time= “0” Info
d(Info)=d(Energy)Pseudo-Riemannian
space-time ≠ 0 info
d(Information) = d(Energy of gravity)
Cyclic mechanics: Conservation of information
actIon
The Great Pole
The universeAny and all points in it