The presentation of cyclic mechanics

Page 1

Cyclic mechanics The principle of cyclicity

Vasil Penchev Associate Professor, Doctor of Science, Bulgarian Academy of Science vasildinev@gmail.com http://www.scribd.com/vasil7penchev http://vsil7penchev.wordpress.com

The mutual transformation between mass, energy, time, and quantum information Notations: Quantities: Q − quantum information S − entropy E − energy t − time m − mass x − distance

quantum information −đ?&#x;? [°đ?‘˛ ]

đ?’•

S k đ?’‰

đ?‘Ź

đ?’„

đ?’Ž

Constants: h − Planck G c − light speed đ?&#x;‘ đ?‘¸ = đ?’™ = đ?’„đ?’?đ?’?đ?’”đ?’• = G − gravitational = đ?&#x;? đ?’’đ?’–đ?’ƒđ?’Šđ?’• k − Boltzmann

Quantum information in terms of quantum temperature and the Bekenstein bound đ?‘şđ?&#x;? đ?&#x;? đ?&#x;?Ď€đ?’Œ đ?‘¸đ?&#x;? = = ≤ đ?’™đ?&#x;? đ?‘Źđ?&#x;? đ?‘ťđ?&#x;? ħđ?’„ đ?‘şđ?&#x;? đ?’•đ?&#x;? đ?‘şđ?&#x;? đ?&#x;?Ď€đ?’Œ đ?&#x;?Ď€đ?’Œ đ?‘¸đ?&#x;? = = ≤ đ?’™đ?&#x;? = đ?’•đ?&#x;? ħ đ?‘Źđ?&#x;? ħđ?’„ ħ Here đ?‘Ľ1 , đ?‘Ľ2 are the corresponding radiuses of spheres, which can place (2) the energy-momentum and (1) the space-time of the system in question

đ?‘¸ = đ?‘¸đ?&#x;? + đ?’Šđ?‘¸đ?&#x;? ; đ?‘¸ =

(đ?‘¸đ?&#x;? )đ?&#x;? +(đ?‘¸đ?&#x;? )đ?&#x;?

The transformation in terms of quantum measure Notations: Quantities: Q − quantum information E − energy t − time m − mass x − distance

quantum information

Q đ?‘¸đ?&#x;? đ?‘¸ đ?&#x;? đ?’„

G

Constants: đ?‘Ź đ?’Ž đ?’• h − Planck đ?’‰ c − light speed đ?&#x;‘ đ?‘¸ = đ?’™ = đ?’„đ?’?đ?’?đ?’”đ?’• = G − gravitational = đ?&#x;? đ?’’đ?’–đ?’ƒđ?’Šđ?’• k − Boltzmann

The Kochen-Specker theorem stars as Yin The axiom of choice stars as Yang

Light cone

Energymomentum

Space -time

All the universe can arise trying to divide one single qubit into two distinctive parts, i.e. by means of quantum invariance

Mass at rest as another “Janus” between the forces in nature Gravity PseudoRiemannian space

?

Banach space Entanglement

? The Higgs mechanism Weak interaction

Electromagnetism Minkowski space Groups represented in Hilbert space

?

Mass at rest

Strong interaction The “Standard Model”

The mass at rest Spaceis a definite mass localized in time The Kochena definite space EnergySpecker theorem momendomain Entanglement= tum Quantum m invariance = The mass at rest The axiom of choice

The universe as a cocoon of light

Mass at rest in relativity and wave-particle duality đ?’•

The qubit

đ?’—

đ?’‘

Any qubit in corresponding Hilbert space in its dual space đ?‘&#x;đ??¸đ?‘€

đ?’‘ đ?’Ž~ đ?’— The light cone Minkowski space Relativity

đ?‘&#x;đ?‘†đ?‘‡

đ?‘&#x;đ?‘†đ?‘‡ đ?’“đ?‘Źđ?‘´ đ?’Ž~ đ?’“đ?‘şđ?‘ť

dual space

space

Hilbert space Wave-particle duality

Wave function as gravitational field and gravitational field as wave function

Infinity Wave function

Gravitational field

Wholeness

How to compare qubits, or a quantum definition of mass at rest The qubit Any qubit in đ?’“đ?’‚đ?’?đ?’š đ?’’đ?’–đ?’ƒđ?’Šđ?’• = đ?&#x;? ⇒ corresponding ⇒ đ?’“đ?‘Źđ?‘´ = đ?’“đ?‘şđ?‘ť ⇔ đ?’Žđ?&#x;Ž = đ?&#x;Ž in its dual Hilbert space space đ?’“ > đ?’“ ⇔ (đ?’“ = đ?&#x;?) & đ?‘Źđ?‘´

đ?‘şđ?‘ť

đ?‘şđ?‘ť

& (đ?’“đ?‘Źđ?‘´ > đ?&#x;?) ⇒ đ?’Žđ?&#x;Ž > đ?&#x;Ž đ?’“đ?‘¸â‰Ąđ?’‚đ?’?đ?’š đ?’’đ?’–đ?’ƒđ?’Šđ?’• ≠đ?&#x;? ⇒ ⇒ đ?‘¸ ⊏ đ?‘¸đ?&#x;Ž (đ?’“đ?‘¸đ?&#x;Ž = đ?&#x;?)

đ?‘¸đ?&#x;Ž ≥ đ?‘¨đ?’†đ?’Šđ?’?đ??Žđ?&#x;Ž +đ??‹đ?&#x;Ž ⇒ ⇒ đ?‘¸ = đ?‘¨đ?’†đ?’Šđ?’?đ?œśđ??Žđ?&#x;Ž +đ??‹đ?&#x;Ž đ?œś ≠đ?&#x;? ≥ đ?’†đ?’?đ?’•đ?’‚đ?’?đ?’ˆđ?’?đ?’†đ?’Žđ?’†đ?’?đ?’•

Mass at rest means entanglement

đ?‘&#x;đ??¸đ?‘€

đ?‘&#x;đ?‘†đ?‘‡

đ?‘&#x;đ?‘†đ?‘‡ đ?’“đ?‘Źđ?‘´ đ?’Ž~ đ?’“đ?‘şđ?‘ť

dual space

space

Hilbert space Wave-particle duality

Mass at rest SpaceEnergyarises if a bigger time EM qubit (domain) momentum The Kochenmust be inserted Specker theorem in a smaller ST Entanglement= qubit (domain) Quantum m đ?‘Źđ?‘´ invariance = The mass at rest The axiom of choice

The universe as a cocoon of light

Mass at rest and quantum uncertainty: a resistless conflict “At restâ€? means: (∆đ?’™ ≥ đ?&#x;Ž) & (∆đ?’— ≥ đ?&#x;Ž) ⇒ ⇒ (∆đ?’‘ = đ?&#x;Ž) & (∆đ?’™. ∆đ?’‘ = đ?&#x;Ž < đ?’‰) Consequently, the true notions of “restâ€? and “quantum uncertaintyâ€? are inconsistent

Observers Generalized Internal

External probability

speed

Mass at rest and quantum uncertainty: a surmountable conflict đ?’Ž quantity đ?’•

đ?‘ˇ đ?’„đ?&#x;?

The = is a power. According to general relativity this is the power of gravitational energy, and to quantum mechanics an additional degree of freedom or uncertainty: Gravitational field with the power p(t) in any point: �� �� �� (�� ) Quantum mechanics

General relativity

The Bekenstein bound as a thermodynamic law for the upper limit of entropy �≤

đ?&#x;?đ??…đ?’Œđ?‘šđ?‘Ź ħđ?’„

⇔�≤

đ?&#x;?đ??…đ?’Œđ?’„đ?’•đ?‘Ź ħđ?’„

đ?&#x;?

⇔ đ?‘ş ≤ đ?&#x;’đ??…

đ?‘Ź đ?’Œ đ?‘Ź

⇔

đ?&#x;?

⇔ đ?‘ş ≤ đ?&#x;’đ??… đ?’Œ The necessary and sufficient condition for the above equivalence: đ?‘š = đ?’„đ?’• & đ?‘Ź = đ?’‰ν (ν−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: đ?’Žđ?&#x;Ž ~∆đ?‘ş = đ?&#x;’đ??…đ?&#x;? đ?’Œ − đ?‘şđ?&#x;Ž

∴ Mass at rest represents negentropy ≥ information

The Bekenstein bound as a function of two conjugate quantities (e.g. t and E) đ?&#x;?đ??…đ?’Œđ?’•đ?‘Ź đ?‘şâ‰¤ = đ?&#x;’đ??…đ?&#x;? đ?’Œđ?’? = đ?&#x;’đ??…đ?&#x;? đ?’Œ đ?&#x;? + ĐŻ , ħ where đ?’? ≼ đ?&#x;?, đ?’‚đ?’?đ?’… ĐŻ ≼ đ?&#x;Ž đ?‘şđ?&#x;Ž = đ?&#x;’đ??…đ?&#x;? đ?’Œ − đ?’Žđ?&#x;Ž đ?‘°đ?’‡ đ?‘ş = đ?‘ş đ?&#x;Ž , đ?’•đ?’‰đ?’†đ?’?: đ?’Žđ?&#x;Ž = −đ?&#x;’đ??…đ?&#x;? đ?’ŒĐŻ That is the quantum uncertainty (ĐŻ) as a rest mass (đ?’Žđ?&#x;Ž )

About the “new” invariance to the generalized observer Any internal observer System System

Any external observer The generalized observer as any “point” or any relation (or even ratio) between any internal and any external observer

An(y) external observer An(y) internal Reference frame observer Special & general relativity Quantum mechanics All classical mechanics and science System

Cyclicity from the “generalized observer” The generalized observer Any external Any internal observer : observer The generalized observer System is (or the process of) the cyclic return of any internal observer into itself as an external observer All physical Any internal Any external laws should be invariant observer observer to that cyclicity, The generalized observer or to “the The universe generalized observer”

=

General relativity as the superluminal generalization of special relativity

The curvature in “ “ can be represenred as a second speed in “ “. Then the former is to the usual, external observer, and the latter is to an internal one 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 đ?‘Źđ?’ˆ by the energy to an external observer đ?‘Źđ?’† or to an internal one đ?‘Źđ?’Š : đ?‘şđ?’† = đ?‘şđ?’Š ⇒ đ?‘Źđ?’ˆ = đ?‘Źđ?’Š đ?&#x;? − đ?œˇ ⇔ đ?‘Źđ?’ˆ =

đ?&#x;?−đ?œˇ đ?‘Źđ?’† đ?œˇ

Cyclicity as a condition of gravity A space-time cycle

đ?‘şđ?’‰ = đ?‘şđ?’• ⇒ đ?‘ˇđ?’‰ + đ?‘ˇđ?’ˆ = đ?‘ˇđ?’• ⇒ đ?‘Źđ?’ˆ =

đ?‘ˇđ?’• − đ?‘ˇđ?’‰ đ?’…đ?’•

h – homebody t – traveller S – action g - gravity P – power E – energy

Cyclicity as the foundation of conservation of action The universe The Newton absolute time and space Simultaneity of all points

đ?‘şđ?’Š = đ?‘şđ?’†

đ?’‘đ?’†đ?’“ đ?’‚ đ?’–đ?’?đ?’Šđ?’• đ?’?đ?’‡ đ?’†đ?’?đ?’†đ?’“đ?’ˆđ?’š

Apparatus

Entanglement Simultaneity of quantum entities

đ?’•đ?’Š = đ?’•đ?’†

Mathematical and physical uncertainty Certainty Uncertainty Independence Any Set theory Any set Disjunctive element of sets any set (the axiom of choice) Bound Free Independent Logic variable variable variables Physics (relativity) Quantum mechanics

Force

Degree of freedom

Independent quantities

The measured value of a conjugate

Any two conjugates

Independent quantities (not conjugates)

General relativity is entirely a thermodynamic theory! The laws of thermodynamics The Bekenstein bound

⇒

General Relativity

Since the Bekenstein bound is a thermodynamic law, too, a quantum one for the use of đ?‘Ź = đ?’‰ν, this implies that the true general relativity is entirely a thermodynamic 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 Cycle 1 = Phase 1

The universe

Cycle 3 Mechanical motion of a mass point in it Cycle 2 = Phase 2

General relativity is entirely a thermodynamic theory!

A quantum thermodynamic law A quantum whole unorderable in principle

⇒

⇒

General Relativity

⇒

The laws of classical thermodynamics The Bekenstein bound

A relevant well-ordered, statistical ensemble: SPACE-TIME

The statistic ensemble of general relativity

A quantum whole

The KochenSpecker theorem The axiom of choice

Quantum information = = Action =

SPACE-TIME different energy – momentum and rest mass in any point in general

Energy (Mass) ⨂ Space-Time (Wave Length)

Einstein’s emblem: � =

đ?&#x;? đ?’Žđ?’„

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 fundament would admit as its violation as another physical entity 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, đ?‘Ź = đ?’‰đ??‚, Nobel prized

The statistic ensemble of general relativity The Bekenstein bound A body with A domain of nonzero mass as space-time as an “ideal gasâ€? The particular informational of space-time case if đ?’• = đ?’„đ?’?đ?’?đ?’”đ?’• “coagulateâ€? points đ?&#x;? đ?‘Ź = đ?’Žđ?’„ Information Information as a nonzero as pure rest mass energy (photons) = đ?’• đ?‘Ź = đ?’• đ?’Žđ?’„đ?&#x;? − đ?’‰đ?‘° (a body) < đ?&#x;? max entropy max entropy đ?&#x;? đ?&#x;? đ?’•đ?&#x;? đ?’…đ?’•đ?&#x;? The general case: = or - speed of body time, đ?œˇ

đ?’•đ?&#x;?

đ?’…đ?’•đ?&#x;?

which is 1 in the particular case above

Reflections on the information equation: đ?&#x;?

đ?’•đ?&#x;? đ?‘Ź = đ?’•đ?&#x;? đ?’Žđ?’„ − đ?’‰đ?‘° The information equation for the Bekenstein bound: đ?&#x;?

đ?‘Ź đ?’Žđ?’„ đ?&#x;?đ??…đ?’Œđ?‘Źđ?&#x;Ž = − đ?’—đ?&#x;? đ?’—đ?&#x;? đ?’„ The information equation for the “light timeâ€?:

đ?&#x;? đ?&#x;? đ?‘Ź = đ?’Žđ?’„ − đ?‘Źđ?&#x;Ž đ?œˇ

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)

đ?’Žđ?&#x;Ž

đ?‘Źđ?&#x;Ž đ?’•đ?&#x;Ž

đ?’Žđ?&#x;Ž

đ?‘Źđ?&#x;? đ?’•đ?&#x;?

đ?‘Źđ?’? ... ... ... ...

đ?’•đ?’?

đ?’Žđ?&#x;Ž Time

Gravitational field as a limit, to which the statistical ensemble of an ideal gas converges

Gravitational field

Differential

representation

The laws of classical thermodynamics

An infinitely A back small volume transformation of an ideal gas to the differenThe Bekenstein bound (a quantum law)

tials of mechanical quantities

The rehabilitated aether, or: Gravitational field as aether The laws of classical thermodynamics

Space-time of general relativity

A finite volume of an ideal gas

A point under infinitely large magnification momentum pressure The gas into the point energy temperature The back transformation The Bekenstein bound (a quantum law)

An additional step consistent with the “thermodynamic� general relativity

The infinity of ideal field A finite volume of ideal field

The universe as a whole A point in it

A cyclical structure

The cyclicity of the universe by the cyclicality of gravitational field D u a l H i l b e r t

s p a c e

H i l b e r t

đ?’•đ?’?đ?&#x;? , đ?’•đ?’?đ?&#x;? two successive cycles “Lightâ€? “Lightâ€? đ?’•đ?’?đ?&#x;? The universe đ?’•đ?’?đ?&#x;? Two “successiveâ€? points in it đ?’?đ?&#x;? đ?’?đ?&#x;? As to the universe, as to any point in it by means of the axiom of choice and the Kochen – Specker theorem

⇔

The cyclicity of gravitational and of quantum field as the same cyclicity Quantum mechanics The universe The Standard General Model relativity Strong, Gravity electromagnetic, and weak A point in it interaction

Gravitational and quantum field as an ideal gas and an ideal “anti-gas� accordingly D u a l s H p i a l c b e e r t

The universe H i l b e r t

All the space-time A volume of ideal gas or ideal field

PseudoRiemannian space

Gravitational A point in it field Quantum field

Conjugate B

Specific gravity as a ratio of qubits

đ?’“đ?&#x;?

is uncertain đ?’“đ?&#x;?

Quantum uncertainty Gravity as if determines the quantum uncertainty being a ratio of conjugates Conjugate A An “ideal gasâ€? composed of đ?’“ mass points ( đ?&#x;? đ?’“đ?&#x;? ~ đ?‘Ź đ?’•)

Qubits Quantum mechanics

General relativity

The gas constant R of space-time The axiom of choice needs suitable fundamental constants to act physically: The Boltzmann Avogadro’s number �� constant ��

?

⇔

How much to (or per) how many?

⇔

In Paradise: No choice Paradise on earth! An ideal gas (aether) of �� space-time points: �� � = � � . �� On earth: Choices, choices ... Quantum mechanics General relativity

Time as entropy: “relicâ€? radiation as a fundamental constant or as a variable +Energy (S) flow(S) +Energy (D) flow(D) đ?‘Ťđ?’†đ?’„đ?’†đ?’?đ?’†đ?’“đ?’‚đ?’•đ?’Šđ?’?đ?’?đ?’•đ?’Šđ?’Žđ?’†đ?&#x;?−đ?&#x;? đ?‘şđ?’‘đ?’†đ?’†đ?’…đ?’•đ?’Šđ?’Žđ?’†đ?&#x;?

đ?‘şđ?’‘đ?’†đ?’†đ?’…đ?’•đ?’Šđ?’Žđ?’†đ?&#x;?

đ?’• đ?’‰ đ?&#x;? đ?’‰ đ?‘şđ?’‘đ?’†đ?’†đ?’…đ?’•đ?’Šđ?’Žđ?’† = đ?‘şđ?’• = = . = đ?’•đ?&#x;Ž đ?‘Şđ?‘´đ?‘Š đ?’•đ?&#x;Ž đ?‘Şđ?‘´đ?‘Š đ?’• =đ?&#x;? đ?&#x;Ž Seen “insideâ€?: Seen “outsideâ€?: Our immense and A black hole expanding universe among many ones determined by determined by the fundamental its physical parameters constants like mass, energy, etc. Horizon

How much should the deceleration of time be? The ideal gas equation is: đ?’‘đ?‘˝ = đ?’?đ?‘šđ?‘ť The universe Any separate point in it

The “Supreme Poleâ€? (the Chinese Taiji 太漾)

đ??’ = đ?’‘đ?’™ = (đ?‘ľđ?‘˛đ?‘Š /đ?‘˛đ?’– )đ?‘Źđ?’• đ?‘şđ?’– = đ?‘ľđ?’‰ đ?‘˛đ?‘Š đ?‘˛đ?’– = đ?‘ľ đ?‘ľđ?‘¨ đ?&#x;? đ?‘Şđ?‘´đ?‘Š = đ?‘˛đ?‘Š đ?’• đ?’‰ đ?&#x;? đ?‘Şđ?‘´đ?‘Š đ??Ž = đ?‘˛đ?‘Š =đ??‚= đ?’• đ?’‰ đ?&#x;?đ??…

The Einstein and Schrödinger equation: the new cyclic mechanics The universe Any and all points in it The Great Pole Cyclic mechanics: Conservation of information d(Information) = d(Energy of gravity) Pseudo-Riemannian space-time ≠ 0 info The Einstein equation

Space d(Info)= & Time d(Energy) = “0” Info

Schrödinger’s equation

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