The Problem of Temporal Paradox in Time Travel
On a Monday morning, you found a mysterious blueprint behind your bookshelf that includes every detail on how to build an actual biplane. You were bewildered but inspired by this surprise, so it made sense to you to surprise someone else by traveling back in time, arriving somewhere in the 1890s. You happened to wander into one of the Wright Cycle Company shops to share your biplane blueprint, hoping to make an impression on the owners. Fair enough, the two shop owners — Orville and Wilbur — developed a deep passion for flight. After their successful test flight in 1903, you “stole” a copy of their blueprint and left it behind the bookshelf at your old home, leaving it for your younger self to discover years later.
So who originally came up with the biplane design?
Or imagine there are two close friends in 2021: John and Sophie. Only John travels back in time to 2016 and gives an automatic watch to Sophie from 2016. John then tells her to give that exact watch to himself from her current time period. 5 years later, John still has the automatic watch that Sophie gave to him.
So where did the automatic watch originally come from?
The Causal Loop
These are examples of the ontological paradox (one of the causal loops), where the linear cause & effect relationship fails to exist. Our common intuition is that for B to happen, A must occur ahead of time to cause B. To stop at a traffic light, I must see the traffic signal first before I can decide to stop — not the other way around. We would logically believe that the latter event is contingent on the earlier one.
In a causal loop, however, there is no clear starting point because everything is looped endlessly. It creates an infinite causal sequence where each event is caused by the previous, resulting in the absence of an origin. If today you suddenly comprehend Einstein’s Theory of Special Relativity and travel back in time to tell Einstein before he published his paper, then who really discovered the theory? Was it Einstein, who wouldn’t have done it differently regardless of your intervention, or is it you, who would’ve stepped in anyways and warped the inevitability of time?
Either way, the discovery has to be made at some point for the timeline to progress. Otherwise, neither event would exist.
All three of the examples above are very similar — they are classic bootstrap paradoxes that violate the Law of Causality. But the first two examples encounter an extra problem. They also violate the Second Law of Thermodynamics, which states “as one goes forward in time, the net entropy (the degree of disorder) of any isolated or closed system will always increase or remain the same.” Because the blueprint would wrinkle and the automatic watch would eventually wear out, an item cannot be the same each time it is brought back in time — it would look different at some point during the loop. Unless energy outside of the closed-loop can somehow repair the item and cancel out the increase in entropy, the paradox remains only inexplicable — but not necessarily impossible.
Solutions? A multiverse could explain the ontological paradox. In this case, each universe would have its unique copy of the same timeline, meaning that the chrononaut could travel to a specific moment in time within an alternative universe of his past. Although there are 10 dimensions in a universe — 3 that we know, 6 other spatial dimensions, and time — living in parallel universes could mean accessing higher dimensions up to 11, where the multiverse of the universe could be that 11th dimension. However, any action made in second universe cannot affect or contradict the person’s own events in life. More of this later in the grandfather paradox.
Nevertheless, the concept of the multiverse must be proven before we can think about time travel.
The Grandfather Paradox
The presented problem should be clear — the HOW of time travel. If we exclude the fact that we are time traveling at one second per second, the faster mode of time travel really is possible — at least a one-way ticket to the future is. Einstein’s Theory of Special Relativity states that time is relative to the observer, and that an object in motion experiences time dilation compared to stationary one. If you come back to Earth after being near a strong source of gravity, such as a black hole or a neutron star, everyone else would appear older than you are. At this point, you are technically in the future from their point of view, but not yours. You are still here in your present.
What about traveling to the past, such as through a traversal wormhole or a closed timelike curve (CTC)?
Besides the problem of finding one first, it is theoretically possible for one to travel into the past through a CTC. Essentially, if a person enters the traversable loop tomorrow, he or she could end up at today — effectively achieving the purpose of time traveling to the past. Hawking, however, was very critical of this idea. In 1992, he stated: “What would happen if you killed your parents before you were born? It might be that one could avoid such paradoxes by some modification of the concept of free will.” (S. W. Hawking 1992)
So the real question is, would it still be possible to retain our free will and change the past as if we have the option of not doing so?
That is why, in addition to Hawking’s theory, Novikov’s self-consistency principle also claims that it’s impossible for intelligent beings to change the past — simply because physics restricts free will, thus invalidating any time paradoxes. Whether or not CTCs are physically possible, they cannot allow the initial conditions to evolve into causality-violating outcomes. Philosopher David Lewis even states “If a time traveler visiting the past both could and couldn’t do something that would change it, then there cannot possibly be such a time traveler”. It simply defeats the purpose of time traveling.
Perhaps there are no paradoxes after all. Perhaps our incorrect concepts of how space and time behave led us to believe that paradoxes do exist, where in reality, none of them are actually true. Or perhaps it’s the other way around — that paradoxes are possible, but they remain inexplicable.
In a causal loop, the origin fails to exist. In a grandfather paradox, attempting to change the past create inconsistencies. And time travel largely remains a mystery.
Perhaps a time traveler can only repeat the past, but is unable to warp anything that didn’t happen.
If so, what is the purpose of time traveling?
References
Kim, G. (2017, November 21). There are 2 types of time travel and physicists agree that one of them is possible. Retrieved from https://www.businessinsider.in/there-are-2-types-of-time-travel-and-physicists-agree-that-one-of-them-is-possible/articleshow/61742986.cms
Borealis, S. (2020, November 23). Time travel is possible, but it’s a one-way ticket. Retrieved from https://blog.scienceborealis.ca/time-travel-is-possible-but-its-a-one-way-ticket/
Abbruzzese, J. (2001, January 01). On using the multiverse to avoid the paradoxes of time travel. Retrieved from https://academic.oup.com/analysis/article-abstract/61/1/36/352190?redirectedFrom=PDF
Billings, L. (2014, September 02). Time Travel Simulation Resolves “Grandfather Paradox”. Retrieved from https://www.scientificamerican.com/article/time-travel-simulation-resolves-grandfather-paradox/
Hawking, S W. Chronology protection conjecture. United States. https://doi.org/10.1103/PhysRevD.46.603
Lewis, D. K. (1976, January 01). David K. Lewis, The Paradoxes of Time Travel — PhilPapers. Retrieved from https://philpapers.org/rec/LEWTPO-8
Peter Millington Research Fellow in the Particle Cosmology Group. (2019, March 26). Stephen Hawking’s final book suggests time travel may one day be possible — here’s what to make of it. Retrieved from https://theconversation.com/stephen-hawkings-final-book-suggests-time-travel-may-one-day-be-possible-heres-what-to-make-of-it-106566
