Cyclic mechanics

1. Cyclic mechanics The principle of cyclicity

2. VasilPenchevAssociate Professor, Doctor of Science,Bulgarian Academy of Sciencevasildinev@gmail.comhttp://www.scribd.com/vasil7penchevhttp://vsil7penchev.wordpress.com

3. Notations: Quantities: Q −quantum information S − entropy E − energy t − time m − mass x − distance quantum information [] S The mutual transformation between mass, energy, time, and quantum information k Constants: h − Planck c − light speed G − gravitational k − Boltzmann G

4. Quantum information in terms of quantum temperature and the Bekenstein bound Here are the corresponding radiuses of spheres, which can place (2) the energy-momentum and (1) the space-time of the system in question

5. quantum information Q Notations: Quantities: Q −quantum information E − energy t − time m − mass x − distance The transformation in terms of quantum measure Constants: h − Planck c − light speed G − gravitational k − Boltzmann

6. The universe as a single qubit ...and even as a single bit the axiom of choice, Yes “1” “0” Y A N G Y I N ? No, the Kochen-Specker theorem Abit Aqubit Quantum mechanics General relativity QUANTUM INVARIANCE

7. The universe as an infinite cocoonof light = one qubit Minkowski space Energy- momentum The Kochen-Specker theorem stars as Yin The axiom of choice stars as Yang Space -time Light cone All the universe can arise trying to divide one single qubit into two distinctive parts, i.e. by means of quantum invariance

8. Mass at rest as another “Janus” between the forces in nature ? ? The Higgs mechanism Gravity Pseudo- Riemannian space Weak interaction Electromagnetism Minkowski space ? ? Groups represented in Hilbert space Strong interaction Banach space Entanglement Mass at rest The “Standard Model”

9. How the mass at rest can arise bya mathematical mechanism The mass at rest is a definite mass localized in a definite space domain Space- time The Kochen- Specker theorem Entanglement= Energy- momen- tum Quantum invariance m = The mass at rest The axiom of choice The universe as a cocoon of light

10. Mass at rest in relativity and wave-particle duality The qubit corresponding in its dual space Any qubit in Hilbert space The light cone space dual space Minkowski space Relativity Hilbert space Wave-particle duality

11. Wave function as gravitational fieldand gravitational field as wave function Infinity + Wave function Gravitational field Wholeness = Actual infinity

12. How to compare qubits, or a quantum definition of mass at rest The qubit corresponding in its dual space Any qubit in Hilbert space space dual space Mass at rest means entanglement Hilbert space Wave-particle duality

13. How the mass at rest can arise bya mathematical mechanism Space- time Mass at rest arises if a bigger EM qubit (domain) must be inserted in a smaller ST qubit (domain) Energy- momen- tum The Kochen- Specker theorem Entanglement= Quantum invariance m = The mass at rest The axiom of choice The universe as a cocoon of light

14. Mass at rest and quantum uncertainty: a resistless conflict “At rest” means: Consequently, the true notions of “rest” and “quantum uncertainty” are inconsistent Observers Whole Generalized Internal External probability speed

15. Mass at rest and quantum uncertainty:a vincible conflict The quantity 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

16. 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

17. The Bekenstein bound as a function of two conjugate quantities(e.g. t and E) where : That is the quantum uncertainty (Я) as a rest mass ()

18. About the “new” invariance to the generalized observer Any external observer Any internal observer The generalized observer as any “point” or any relation (or even ratio) between any internal and any external observer System System relativity speed probability An(y) exter- nalobserver System An(y) internal observer Reference frame Special & general relativity All classical mechanics and science Quantum mechanics

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

20. General relativity as the superluminal generalization of special relativity The curvature in “ “ can be represen- red as a second speed in “ “.Then the former is to the usual, external observer, and the latter is to an internal one Minkowskispace 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 external observer or to an internal one :

21. Cyclicity as a condition of gravity A space-time cycle h – homebody t – traveller g - gravity S – action P – power E – energy Gravity =( ) – ( )

22. Cyclicity as the foundation of conservation of action C I c l I c I t y C I c l I c I t y Apparatus The universe Entangle- ment The Newton absolute time and space Simultaneity of all points Simultaneity of quantum entities

23. Mathematical and physical uncertainty

24. 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 ofthis implies that 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!

25. Cycling and motion Cycle 1 = Phase 1 The universe Cycle 3 Mechanical motion of a mass point in it Cycle 2 = Phase 2 Action conservation Energy conservation Time conservation

26. General relativity is entirely a thermodynamic theory! The laws of classical thermodynamics The Bekenstein bound General Relativity A quantum thermodynamic law A quantum whole unorderable in principle A relevant well-ordered, statistical ensemble: SPACE-TIME

27. The statistic ensemble of general relativity SPACE-TIME different energy – momentum and rest mass in any point in general A quantum whole The Kochen- Specker theorem The axiom of choice Quantum information = =Action= Energy (Mass)⨂Space-Time (Wave Length)

28. 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 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,,Nobel prized

29. The statistic ensemble of general relativity The Bekenstein bound OR A body with nonzero mass as informational “coagulate” A domain of space-time as an “ideal gas” of space-time points The particular case if Information as a nonzero rest mass (a body) < max entropy Information as pure energy (photons) = max entropy Information -“I” The general case: or - speed of body time, which is 1 in the particular case above

30. Reflections on the information equation: For action: The information equation for the Bekenstein bound: For momentum: The information equation for the “light time”: For energy:

31. The distinction between energy and rest mass If one follows a space-time trajectory (world line), then energycorresponds to any moment of time, and rest mass means its (either minimal or average) constant component in time Energy (mass) ... ... ... ... Time

32. Gravitational field as a limit, to which tends the statistical ensemble of an ideal gas Gravitational field Differential representation The laws of classical thermodynamics A back transformation to the differen- tials of mecha- nical quantities An infinitely small volume of an ideal gas The Bekenstein bound (a quantum law)

33. The rehabilitated aether, or:Gravitational field as aether The laws of classical thermodynamics Space-time of general relativity as A finite volume of an ideal gas A point under infinitely large magnification momentum energy pressure temperature The gas into the point The back transformation aether The Bekenstein bound (a quantum law)

34. An additional step consistent with the “thermodynamic” general relativity The infinity of ideal field = The universe as a whole = = = = = A finite volume of ideal field = A point in it A cyclical structure

35. The cyclicity of the universe by the cyclicality of gravitational field ,- two successive cycles D u a l H i l b e r t “Light” “Light” The universe H i l b e r t s p a c e Two “successive” points in it As to the universe, as to any point in it by means of the axiom of choice and the Kochen – Specker theorem

36. The cyclicity of gravitational and of quantum field as the same cyclicity ? Quantum mechanics The Standard Model Strong, electromagne- tic, and weak interaction • The universe ? General relativity Gravity Quantum gravity ? ? • A point in it

37. Gravitational and quantum field as an ideal gas and an ideal “anti-gas” accordingly • The universe D u a l H i l b e r t H i l b e r t s p a c e All the space-time A volume of ideal gas or ideal field Pseudo- Riemannian space Gravitational field • A point in it Quantum field

38. Specific gravity as a ratio of qubits Quantum uncertainty Conjugate B Gravity as if determines the quantum uncertainty being a ratio of conjugates Conjugate A is uncertain An “ideal gas” composed of mass points ( Qubits Quantum mechanics General relativity

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

40. Time as entropy: “relic” radiation as a fundamental constant or as a variable +Energy (S) flow(S) +Energy (D) flow(D) Seen “inside”: Our immense and expanding universe Seen “outside”: A black hole among many ones determined by the fundamental constants determined by its physical parameters like mass, energy, etc. Horizon

41. How much should the deceleration of time be? The ideal gas equation is: The universe Any separate point in it The “Supreme Pole” (the Chinese Taiji太極)

42. 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 a c t I o n d(Information) = d(Energy of gravity) Space & Time = “0” Info d(Info)= d(Energy) Pseudo-Riemannian space-time ≠ 0 info The Einstein equation Schrödinger’s equation