Life on a closed timelike curve (2405.18640v2)

Abstract: We study the internal dynamics of a hypothetical spaceship traveling on a close timelike curve in an axially symmetric universe. We choose the curve so that the generator of evolution in proper time is the angular momentum. Using Wigner's theorem, we prove that the energy levels internal to the spaceship must undergo spontaneous discretization. The level separation turns out to be finely tuned so that, after completing a roundtrip of the curve, all systems are back to their initial state. This implies, for example, that the memories of an observer inside the spaceship are necessarily erased by the end of the journey. More in general, if there is an increase in entropy, a Poincar\'{e} cycle will eventually reverse it by the end of the loop, forcing entropy to decrease back to its initial value. We show that such decrease in entropy is in agreement with the eigenstate thermalization hypothesis. The non-existence of time-travel paradoxes follows as a rigorous corollary of our analysis.

• The paper demonstrates how quantum mechanics and entropy dynamics within an isolated system on a closed timelike curve ensure self-consistent timelines free from paradoxes.
• It shows that entropy in a thermally isolated system traversing a CTC ultimately reverts to its initial state, leading to memory erasure and supporting self-consistent histories.
• The findings suggest that conventional time travel paradoxes are circumvented in theories incorporating CTCs when considering these quantum mechanical and thermodynamic constraints.

Analysis of "Life on a Closed Timelike Curve"

The paper by L. Gavassino offers an examination of the implications of a closed timelike curve (CTC) on the dynamics within an isolated system, exemplified by a spaceship. This paper is placed in the context of an axially symmetric, rotating universe like that described by Godel's solutions to Einstein's field equations. The CTC discussed in this setting permits the exploration of profound questions related to time travel, entropy, and quantum mechanics.

Quantum Mechanics on a Closed Timelike Curve

The author applies Wigner’s theorem to demonstrate the spontaneous discretization of energy levels within a system traversing a CTC. Essentially, the evolution of the system is defined such that the time operator corresponds to the angular momentum. This setup naturally leads to a quantization condition analogous to the Bohr-Sommerfeld quantization rule known from quantum mechanics. Such discretization leads to strong claims regarding the behavior of entropy in a CTC.

Entropy Reversal and Memory Erasure

A critical aspect of this paper is the theoretical demonstration that entropy within a thermally isolated system on a CTC will ultimately revert to its initial state. This finding aligns with the eigenstate thermalization hypothesis and is further supported by statistical mechanics via Poincare recurrence theorems. In an isolated system, the thermodynamic arrow of time, which is generally governed by the unidirectional increase in entropy, experiences a reversal. This conclusion extends to processes such as aging and memory retention, with significant implications: by the journey's end, any observer's memories are effectively erased, supporting traditional self-consistent histories free from paradoxes such as grandfather paradoxes.

Implications for Time Travel and Self-Consistency

The findings discussed in this paper suggest that conventional time travel paradoxes do not arise in theories accommodating CTCs, as long as the proper quantum mechanical and thermodynamic constraints are applied. The spontaneous discretization of energy levels ensures that any fluctuations bringing the system out of equilibrium will inevitably bring it back to its original state, thereby maintaining self-consistency of events. This conclusion posits that if time travel within such a universe were possible, it would not allow for retro-causal contradictions, as all observable histories would remain consistent.

Speculative Outcomes and Theoretical Extensions

For physicists considering the broader implications of this research, Gavassino's results imply that memories and physical histories along CTCs are inherently self-consistent due to their quantum mechanical underpinnings. This effectively eliminates unpredictable outcomes associated with simultaneous self-interaction, such as meeting a future self. Additionally, the paper suggests a need for further exploration into the intersection of quantum and classical thermodynamics within extreme relativistic contexts and exotic geometries, particularly how these results might translate to more complex spacetimes like those involving Kerr black holes.

Conclusion

The paper rigorously presents a quantum mechanical framework that supports the consistency of timelines on CTCs, circumventing paradoxes previously thought to challenge the fabric of causal history. This research opens the pathway for further theoretical exploration into the nuanced relationship between quantum mechanics and general relativity, while maintaining robust adherence to standard principles. As such, the findings have profound implications for both theoretical physics and our understanding of potential models of time travel.