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Time Travel and General Relativity

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Introduction 3

Relativity and Time Travel 3

Closed Time-Like Curves 4

Conclusion 6

References 7

Time Travel and General Relativity

# Introduction

The dominant historical paradigm in philosophy and physics is that systems evolve over time, modelled by dynamic laws, with past states determining future states. However, Epstein theories of general relativity challenge the paradigm. The theory of general relativity describes the relationship between mass-energy and space-time geometry that contains closed time curves (CTC) that are counterintuitive to such conclusions (Tobar & Costa, 2020). While these CTC could potentially allow time travel to the past, they raise the question of paradoxes, of which the grandfather paradox is one of the most important. The existence of these paradoxes, raising the question of whether time travel is possible and presents challenges for physicians on how to approach the problem (Deutsch & Lockwood, 2016). The goal of the paper is to discuss whether time travel is possible, with a particular focus on CTCs, and potential paradoxes, and whether such travel would raise those paradoxes.

# Relativity and Time Travel

The majority of scholarly work on time travel relies on Epstein theory of general and special relativity. The theory of general relativity suggests that space-time has four dimensions, where the three-dimension space combines with time to form a fourth-dimension worm (Deutsch & Lockwood, 2016). Unlike space, which consists of spatial points, space-time contains events or spatiotemporal points, which represent a specific time and place. For example, the time of birth of a person is the tip of the worm, which corresponds with that specific time, while the time of death is the head of the worm. Any object observed on this worm, when viewed from a three-dimension cross-section, will manifest as a thin long line (Deutsch & Lockwood, 2016). The worldline is the line whether this worm lies. When time connects two temporal spaces, then it is possible to transverse those two spatial times through a wormhole.

From the theory of relativity, it is possible to travel through space-time through a wormhole or a tunnel connecting two different regions of space-time. A key characteristic of the wormhole is that it is possible to transverse it from point A to point B (Miritescu, 2020). A particle entering one point of the wormhole will exit at the end of the wormhole. In regular space-time, a wormhole can either be short or long, depending on the time it takes to move from one point to another. When moving through a wormhole, it is possible to reach the destination using less time compared to if the particle travelled using spatial points (Miritescu, 2020). If physical objects within space-time are time-like, then hypothetically, they could form corridors, which connect a person to the past, allowing them to travel to the past. Generating wormholes in the space-time continuum would hypothetically allow a person to travel from one time to another, either to the future or to the past. While there is no observable evidence of wormholes, Einstein mathematical solutions and field equation suggests that such a phenomenon could exist (Miritescu, 2020; Rahman, 2019).

# Closed Time-Like Curves

CTCs are causal loops in space-time that return to the same place in time and space. It has been hypothesized it is possible to follow these loops to the past and allow a person to participate in past events (Liberati, 2016). Particles often follow time-like trajectories, where time must pass for them to follow a given trajectory. However, in CTCs, the space-time curve is closed, meaning that the particle will return to the temporal and spatial coordinate that originated (Deutsch & Lockwood, 2016). As such, if one was to move through a CTC, one would return to a temporal and spatial coordinate in the past, allowing one to interact with themselves. The only possibility of travelling to the past using a CTC is to tear the space-time fabric or use naturally occurring CTCs.

Existing empirical evidence suggests that CTCs are theoretical conjectures. Although they could actually exist, our technological advancements do not allow us to exploit them to travel either forward or back in time (Rahman, 2019). The Deutsch CTC model suggests it is possible to simulate CTCs using photonic systems (Ringbauer et al., 2014). On the other hand, Kurt Gödel’s solutions to Einstein equations shows that CTCs could exist. The solution suggests that the universe rotates, although the idea has been refuted (Luminet, 2020). However, Epstein theory of relativity does provide some evidence of the existence of CTCs. However, for one to access the CTCs, one would have to travel across the Cauchy horizon, where there is little understanding of physical laws (Rahman, 2019). It would be difficult when using the theory of relativity to determine the point of entry and the trajectory of travel, which further makes travelling in time difficult.

There are a number of paradoxes that would arise when a person travels back in time. The first paradox is logical inconsistency if the person who travels changes events, which could produce a butterfly event. For example, in the grandfather paradox, one could potentially murder their ancestors and change future events (Tobar & Costa, 2020). Recent evidence suggests that such paradoxes may not occur in case we are able to find CTCs or wormholes and travel back in time. In their seminal work, Ringbauer et al. (2014) used quantum simulation to test the theory of such possible paradoxes. They studied the effects of incoherencies in space-time after time travel. They found that such incoherencies only contribute to nonlinear effects only in some scenarios. On the other hand, Tobar and Costa (2020) reported that CTCs create multiple pathways through space-time that loop back to the original position, which means that it could be difficult to alter time, as it has the potential to self-correct. The existence of multiple CTCs that point to the same spatial and temporal point would eliminate the grandfather paradox, meaning that the person using a CTC would return to the same position, regardless of whether they disrupt events when they travel back in time.

# Conclusion

Historically, time was thought to be linear, with past events determining future events, and people could not travel back in time. However, the theory of general relativity suggests that time travel is both to the future and to the past. One way is through a wormhole between two spatial-temporal points in space-time. The second way is through CTCs, which connect two points in space and time, both present and past. However, observation or experimental data on the existence of both is lacking, either suggesting that such postulations are largely hypothetical or our technology is not sufficiently advanced to exploit wormholes or CTCs.

# References

Deutsch, D., & Lockwood, M. (2016). The quantum physics of time travel. In S. Schneider, Science Fiction and Philosophy: From Time Travel to Superintelligence (pp. 372-383). New York: John Wiley & Sons.Liberati, S. (2016). Do not mess with time: Probing faster than light travel and chronology protection with superluminal warp drives. The Fourteenth Marcel Grossmann Meeting on General Relativity (pp. 1407-1414). Roma, Italy: University of Rome “La Sapienza”.Luminet, J. (2020). Closed time-like curves, singularities, and causality: A survey from Godel to chronological protection. Universe, 7(12), 1-11.Miritescu, C. (2020). Tranversable wormhole constructions. London, UK: Imperial College London.Rahman, O. (2019). The mystery of time travel. Dhaka, Bangladesh: A Sleek Publication.Ringbauer, M., Broome, M., Myers, C., & White, A. R. (2014). Experimental simulation of closed timeline curves. Nature Communications, 5(4145), 1-6.Tobar, G., & Costa, F. (2020). Reversible dynamics with closed time-like curves and freedom of choice. Classical and Quantum Gravity, 37(205011), 1-18.