Cyclic mechanicsThe principle of cyclicity

Vasil PenchevAssociate Professor, Doctor of Science,

Bulgarian Academy of Science

vasildinev@gmail.comhttp://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