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In this paper we resolve the grandfather paradox in non-quantum and quantum gravitation theories for time travelling in a time wormhole. For macroscopic bodies, the main solution is alignment of the thermodynamic time arrows, resulting in the time traveller destroying. For microscopic bodies and for small probability cases of macroscopic bodies, the main solution is fracture of the time wormhole. As a result, multi-world system appears. These explanations are similar in non-quantum and quantum gravity. On the contrary, we can clarify some problems of quantum gravity by this consideration. “Indestructible finite gravitation interaction of an observer with an observable system (resulting in the time arrows alignment)” and “instability with respect to even infinitesimally small interaction in the gravitation theory” can resolve the wave function reduction paradox of quantum mechanics.

In Einstein’s general relativity theory, motion is reversible, similar to classical mechanics. Nevertheless, two important topological differences exist between general relativity and classical mechanics.

The first difference is the ambiguity in general relativity in theory. In general relativity, two various initial states can give infinitesimally close states after a finite time interval. This phenomenon occurs, for example, during the formation of a black hole (

the white hole. As a result of this property, the law of increasing entropy turns out to be an exact law, not an FAPP law. Therefore, the entropy becomes a fundamental concept. There actually is a fundamental concept, such as the entropy of a black hole. Additionally, it is possible to explain the existence of this entropy using the perturbation created by the observer. Even now, this perturbation may be infinitesimally weak, unlike in classical mechanics. During the formation of a black hole, the entropy increases. Time reversion leads to the appearance of a white hole and to a decrease in entropy. The white hole cannot exist in reality because of the decrease in entropy. Decreases in entropy are prohibited in general relativity for the same reasons that they are prohibited in classical mechanics: the instability of the decreasing-entropy processes, which is much stronger in general relativity than that in classical mechanics. This instability results in the synchronisation of the time arrows of the white hole and of the observer/environment. The direction of the time arrow of the white hole changes to the opposite direction, coinciding with the time arrow of the observer/environment. The white hole transforms into a black hole. Note that a small interaction between the observer/environment and the observed system always exists in gravity theory, which is the gravity interaction. This interaction along with the above-described finite time instability produces unpredictability. This unpredictability cannot be prevented even theoretically. In contrast, in typical classical mechanics and quantum mechanics, unpredictability can be prevented in principle except for in some degenerated singular cases.

The second topological difference between classical mechanics and general relativity is the additional feedback between the final and initial states through a time-wise wormhole. Let us consider a wormhole [

fly to Vega taking one of the mouths with her. Moving (almost) at the speed of light she will reach Vega (almost) instantaneously by her clocks. In doing so she rests with respect to the Earth insofar as the distance is measured through the wormhole. Therefore, her clocks remain synchronous with those on the Earth as far as this fact is checked by experiments confined to the wormhole. So, if she returns through the wormhole she will arrive back to the Earth almost immediately after she will have left it”. A wormhole can be used for human evacuation to another universe in the case of the destruction of our universe due to its accelerated expansion or shrinkage. Microscopic wormholes exist everywhere as fluctuations of the quantum vacuum. Nevertheless, to create real macroscopic wormholes from such small fluctuations, we need a significant amount of energy. Creating real macroscopic wormholes is a challenging problem for future technology.

We consider the Morris-Thorne wormhole [

This part considers the analysis of general relativity theory (the theory of gravitation) from the perspective of the

thermodynamic time arrow. Within this framework, the “paradox with the grandfather” for time travel “wormholes” is resolved.

We consider a thermodynamic time arrow [

Let us consider the paradoxical object of general relativity theory the time “wormhole” from the perspective of entropy [

From the physical perspective, the paradox of the grandfather means that not all of the initial states that exist before time machine formation are realisable. The introduction of additional feedback between the future and past, the time wormhole, makes these states impossible. Thus, we should either explain the non-reliability of such initial states ( [

Curiously enough, both of these explanations are true. However, for macroscopic wormholes, the first explanation has the highest priority. It would be very desirable to have a stable macroscopic topology of the space. The constraints on the initial states arise from the law of increasing entropy and the corresponding alignment of the thermodynamic time arrows that is related to the instability of states with opposite directions of time arrows [

A space wormhole does not lead to a paradox. The objects immersed by its one extremity will go out the other extremity at later time. Thus, the objects from a more normalised low-entropy past occur in a less normalised high-entropy future. During the motion through the wormhole, the entropy of the travelling objects also increases: they transfer from a more normalised state into a less normalised state. Thus, the time arrows of the object travelling inside the wormhole and the time arrow of the world around the wormhole have the same directions. This situation is also true for travelling through the time wormhole from the past to the future.

However, for travelling from the future to the past, the time arrow directions of the traveller in the wormhole and of the world around the wormhole will be opposite [

Which mechanism for travelling in the wormhole ensures the alignment of the thermodynamic time arrows of the traveller and of the Universe? Both extremities of a “wormhole” are large bodies with a finite temperature. Both extremities under the second law of thermodynamics should inevitably radiate light, which partially penetrates into the wormhole. At the moment of the formation of a “time machine” (the transformation of a space wormhole into a time one), a closed light ray already appears between its extremities. Every time the ray spins in a circle, it becomes increasingly biased towards the violet part of the spectrum. Passing circle after circle, the rays lose their focal point; therefore, the energy does not get amplified and does not become infinite. The violet bias means that the history of a particle of light is finite and is defined by its coordinate time, despite the infinite number of circles [

Let us describe possible mechanism of the alignment of the thermodynamic time arrows and destroying a time traveller in a wormhole (see

“Free will” allows us to freely initiate only irreversible processes with an increase in entropy but not with a decrease in entropy. Thus, we cannot send an object from the future into the past. The process of the alignment of thermodynamic time arrows and the corresponding law of increasing entropy forbids the initial conditions that are necessary for the travelling of a macroscopic object into the past and the resulting “paradox of the

grandfather”.

In paper [

The macroscopic laws of thermodynamics are probabilistic. For a very small number of cases, these laws do not work (large-scale fluctuations). For both these situations and microscopic systems, where thermodynamics laws are not applicable, the other explanation of the grandfather paradox will have priority. In this case, the time wormhole, like a white hole, appears unstable even with respect to infinitesimally weak perturbations from the gravitation of the travelling object. This instability can result in the wormhole’s fracture and the prevention of the paradox, as is strictly proven in [

“As we argue… non-uniqueness does not let the time travel paradoxes into general relativity—whatever happens in a causal region, a space-time always can evolve so that to avoid any paradoxes (at the sacrifice of the time machine at a pinch). The resulting space-times sometimes… curiously remind one of the many-world pictures”.

Let us formulate the following conclusion: for macroscopic processes, the instability of the processes with a decrease in entropy and the corresponding alignment of the thermodynamic time arrows make the existence of the initial conditions that allow travel to the past almost impossible. Thus, this instability prevents both wormhole fracture and the travelling of macroscopic bodies into the past that leads to the “paradox of the grandfather”.

For the very improbable situations of macroscopic wormholes and for microscopic wormholes, wormhole fracture must occur. This fracture is the result of a remarkable property of general relativity theory—extreme instability: an infinitesimal external action (e.g., gravitation from a traveller) can produce a wormhole fracture for a finite time!

This chapter considers the analysis of quantum gravitation theory from the perspective of the thermodynamic time arrow. Within this framework, the “paradox with the grandfather” for time travel “wormholes” is considered. This paper includes an analysis of quantum gravitation theory from the perspective of the thermodynamic time arrow [

Let us consider the paradoxical object of general relativity theory the time “wormhole” from the perspective of entropy [

Let us consider the fact that the answer to this problem is given by the semi-classical theory of gravitation. Suppose that the macroscopic topology of the space that is related to the time machine is unchanged. At the moment of time machine formation (the transformation of the space wormhole into the time one), there is a closed light ray between its extremities. The energy of the light ray does not reach infinity, despite the infinite number of passes, because of the defocusing of the light [

However, the situation in quantum gravitation is different. Quantum fluctuations contain large energies when they arise over short distances. Therefore, it is possible to find a distance so small that the energy of the fluctuation will be sufficiently large to form a tiny black hole, and the horizon of this tiny black hole will have the same size as this small distance. Space-time is not capable of remaining homogeneous over such short distances. This mechanism ensures the natural “blocking” of singular fluctuation formation, restricting the fluctuations in their sizes: the “maximum energy in minimal sizes” [

The detailed calculations of quantum gravitation show [

We see that the informational paradox and the paradox of the grandfather are resolved in quantum gravitational theory similarly to in non-quantum general relativity theory. This resolution is realized through the consideration of the weak interaction of the systems with the real non-equilibrium macroscopic observer. Moreover, this approach (similar to in conventional quantum theory) enables the resolution of the wave packet reduction problem [

1) Indestructible finite gravitation interaction of an observer with an observable system;

2) Instability with respect to even infinitesimally small interaction in the gravitation theory.

I thank the painter Gukov Yury Yurjevich for his help in drawing the figures.