Emergent Time and Time Travel in Quantum Physics (2312.05202v2)

Abstract: Entertaining the possibility of time travel will invariably challenge dearly held concepts of fundamental physics. It becomes relatively easy to construct multiple logical contradictions using differing starting points from various well-established fields of physics. Sometimes, the interpretation is that only a full theory of quantum gravity will be able to settle these logical contradictions. Even then, it remains unclear if the multitude of problems could be overcome. Yet as definitive as this seems to the notion of time travel in physics, such a recourse to quantum gravity comes with its own, long-standing challenge to most of these counter-arguments to time travel: These arguments rely on time, while quantum gravity is (in)famously stuck with and dealing with the problem of time. One attempt to answer this problem within the canonical framework resulted in the Page-Wootters formalism, and its recent gauge-theoretic re-interpretation - as an emergent notion of time. Herein, we will begin a programme to study toy models implementing the Hamiltonian constraint in quantum theory, with an aim towards understanding what an emergent notion of time can tell us about the (im)possibility of time travel.

• The paper introduces a toy model using the Page-Wootters framework to demonstrate that emergent time underpins self-consistent time travel scenarios.
• It employs a simplified harmonic oscillator system under a Hamiltonian constraint to illustrate the application of Novikov's self-consistency principle.
• The study implies that viewing time as an emergent property in quantum gravity could bridge conceptual gaps between quantum mechanics and general relativity.

Analyzing the Implications of Emergent Time and Time Travel within Quantum Physics

The paper "Emergent Time and Time Travel in Quantum Physics" addresses a nuanced topic that intersects with several complex domains in theoretical physics, primarily focusing on the relationship between quantum gravity and time travel through concepts of emergent time. This work by Alonso-Serrano, Schuster, and Visser ventures into re-examining one of physics' most enigmatic problems—the emergence and nature of time within the canonical quantum gravity framework.

The authors commence by highlighting the perennial issues surrounding the concept of time travel, presenting both the classical and quantum mechanical objections that have historically challenged its plausibility. Recognizing these challenges, they stress that any discussion regarding time travel is contingent upon solving the "problem of time" within the field of quantum gravity—a field that notoriously struggles with well-defined temporal constructs due to the incompatibility between quantum mechanics and general relativity.

The paper introduces the Page-Wootters (PW) formalism, a framework that provides a possible resolution by suggesting that time is not fundamental but rather an emergent concept arising from quantum correlations between subsystems in a closed universe. This notion allows the authors to approach time travel from a different perspective, postulating that an emergent concept of time could influence the viability of time travel itself.

To operationalize their theoretical discussion, Alonso-Serrano and colleagues develop a toy model involving two non-interacting harmonic oscillators subjected to a Hamiltonian constraint akin to the Wheeler-DeWitt equation. Through this model, they seek to understand the implications of emergent time for potential time-travel scenarios. The choice of harmonic oscillators allows the exploration of a mathematically feasible regime, where complex interactions are sufficiently diminished to enable clarity in the examination of fundamental principles.

One of the model's critical outcomes is its demonstration of Novikov's self-consistency principle, which maintains that in any time travel scenario, the history must be self-consistent, negating any possibility of paradoxes that conventional time travel arguments might suggest. In essence, the time evolution described by their system shows that, even in quantum gravity toy models, a notion of self-consistent time travel can arise without leading to logical contradictions.

The authors' approach utilizes positive operator-valued measures (POVMs) to address the absence of a traditional time operator, an advance that potentially circumvents historical no-go theorems regarding time operators in quantum mechanics. This suggests that novel approaches in quantum theory could harmonize with the unconventional requirements posed by models of time travel.

The implications of this paper are both theoretically significant and practically speculative. If further developed, emergent-time frameworks could provide a robust foundation for understanding time in quantum gravity. The discussion prompts several exciting avenues for future research, including the exploration of more complex systems and interactions, which could further challenge or support the model's implications. Moreover, the intersection with entropic considerations is highlighted as a potential area where emergent time might offer fresh insights into the underlying statistical mechanics of quantum systems involving time travel.

Overall, the paper gives us an innovative perspective on time and time travel by relying on the emergence of these concepts in quantum settings, challenging traditional arguments against time travel by recontextualizing them within novel theoretical paradigms. This work encourages further exploration into how time, as an emergent phenomenon, can reconcile with the quantum aspects of the universe and offers a starting point for the continued interplay between mathematical modeling and conceptual clarity in one of modern physics' most perplexing inquiries.