(Originally published on October 22, 2010)

Let’s assume that what we all secretly hope for is true: that backwards time travel is possible (with a fast enough rocket you can travel forward in time already, thanks to Einstein). It’s unclear what such time travel would look like — there are many different theories and, consequently, interesting implications on the Universe, causality (why hasn't anyone visited us from the future?) the existence of paradoxes, and the existence and the nature of time loops. Some include interesting design constraints: my favorite is the theory of time travel put forth in Primer.

Note that to help myself think through this, I have a human being travel in time; this may lead to inaccuracies and further questions — in most of the cases below, we can probably replace me with a photon, or even a quark, and get more precise results (“memory” becomes “momentum” or “spin”, etc.). But it’s more fun to think about people traveling in time.

Possibility one: there is only one version of the Universe

If the links between causes and effects are not maintained, we have a consistent (paradox-free) time travel: moving backwards in time rewrites history and the previous version is lost. The I that travels back in time (call it I1) is not the same as the I that I1 meets in the past (I2). Whether I2 enters the time machine or not is irrelevant to I1. If I1 kills I2′s grandfather, I2 will not be born but I1 will not be affected in any way. It’s a very safe theory of time travel.
If the links between cause and effect are maintained (but their temporal relationship isn’t, necessarily), the Universe has to decide how to handle duplicates of matter/energy: it may choose to allow them, or not, or have an opinion somewhere in between.
- If duplicates are allowed, I1 is identical to I2 but they are allowed to co-exist. If I1 prevents I2 from entering the time machine, I1 will cease to exist. What if I1 kill’s I2′s grandfather (who is also I1′s grandfather)?
- It’s possible that I1 will simply not be able to do this — this is the theory where the Universe maintains its consistency (by making it prohibitively expensive — either by requiring you to put a lot of energy into your action or outright generating laws that locally forbid you to perform it), somewhat akin to what the writers of Lost did in the show. This energy-effect constrained time travel — the Universe not letting me kill my grandfather — is interesting. In order to maintain its consistency, the Universe would need to propagate all actions forward (“play them out”). If there is a sequence of actions that cause an inconsistency, the energy required to continue along this sequence would increase, proportionally to the probability of an inconsistency. It would be like an invisible magnetic field that steers actions in a particular direction. This could be implemented by a biased averaging out of quantum effects: let’s take light for example. We know that according to quantum theory, the movement of photons from A to B is realized through an infinite number of different paths which average out to a straight line. However, if the probabilities of the paths are different (due to the fact that some paths may cause an inconsistency in the future), the paths could actually average to something that’s not a straight line. To us it would seem that light travels in curved paths (without the presence of any “real” field, such a gravitational one)! Of course, these probabilities change gradually so no obviously apparent deviations from the norm would occur at first. For example, if I’m intending to kill my grandfather, the Universe will start steering me away from my intention through a small sequence of very likely events. If I persist in my intentions, the events increase in magnitude, but it’s possible (because there are just so many possible events that can influence me) that I will never realize my intention without even seeing anything strange with the Universe.
- Otherwise, we have a phenomenon known as the Grandfather Paradox. I1 may create an unstable point in the spacetime: I1 (and thus I2, and the grandfather) will both exist and not exist at the same time, in a kind of macro-Shrödinger effect. What’s worse, anything that either was caused by I2 or the grandfather or would have been caused by I1 will also both exist and not exist. It’s unclear what effect this will have on the rest of the Universe — as these effects ripple through time, they expand their scope (the events that the grandfather caused themselves caused other events) but decrease their magnitude (think of it as a sound wave propagating through space, maybe bouncing off objects).
- It’s possible that over time, as soon as they become small enough to be captured by quantum uncertainty, they stabilize so the ripple has a finite size (I can’t visualize what the ripple would actually look like, maybe a really fast-flashing grandfather).
- Or the Universe could cease to exist.
- If duplicates of matter/energy are not allowed, I1 would need to replace I2 (for this to work, the Universe would somehow need to have a unique identifier for everything in it). It’s difficult to think about replacing something complex like a human being because he or she is made of many building blocks, each having a different identifier, so let’s simplify and think of something that consists of a single block (say, a photon). The photon would replace its version from the past. Does this photon have “memory”, that is, its future state?
- If so, the photon will likely change its course (behave differently than I1 did). This may mean that I2 may never end up traveling in time, but that’s fine because there is only version of it. This is equivalent to the theory of rewritten history.
- If not, I1 simply merges into I2 — I2 enters a time loop which it will never be able to leave. It’s not aware of that, however, so to I1, the time travel ends its consciousness.
- If somehow we can maintain this option at a macro scale, it’s possible that an individual may travel back in time and maintain his or her memory, provided that the interval of time travel is small (for example, if I1 travels back to before I2 was born, I1–an individual–would have to replace a bunch of particles which aren’t even part of a human being. That will very likely result either in the destruction of I2–I2 will not be possible given the new state that all of its particles will have assumed before they created it–or in the destruction of I1–the “memory” that each particle has will be insignificant and so I1′s consciousness will end as soon as he travels in time)
- Another way not to allow duplicates would be for I1 and I2 to “swap” places: as soon as I1 travels backwards in time, it takes I2′s place and I2 takes I1′s place in the future. When I1 gets to the time when it first traveled in time, he ceases to exist. There is no paradox because time travel transfers both I1 and I2. It doesn’t matter whether I1 actually enters the time machine the second time around or not, because his existence ceases past that point anyway.
- Finally, the Universe may choose some option in between, for example, I1 and I2 will be entangled in a way that doesn’t increase entropy. This may look like a kind of constrained time travel, where paradoxes are not possible because they are prevented by the entanglement of I1 and I2 (in other words, I1′s and I2′s actions will either make both of them survive the interval of their co-existence, or make them both self-destruct. At the event of time travel, I2 goes back and I1 is the only entity remaining. ** This brings me to an interesting idea: what if time travel and quantum theory are actually one and the same? What if the time interval where I1 exists in the past (and influences outcomes) is equivalent to the cat being both alive and dead: it cannot be inspected, and nothing can be said about what happened or what any of the outcome that I1 could have influenced was. The instant at which I1 entered the time machine would then correspond to the box being open — we find out what all those outcomes were.

Possibility two: there are many versions of the Universe

This is similar to the first case (rewriting history) but if the Universe bifurcates with every time travel, an awful lot of energy is needed to do time travel. Alternatively, the Universe may already exist in its virtually infinite forms, each form corresponding to a different possible unfolding of an event. We know from Newton that at a high level the world seems deterministic, but at a quantum level it’s not — this randomness I see as a basis for the different unfolding of the events (hence, once and for all answering the problem of free will: there is no free will, but there is also no determinism — what we perceive as “choosing” is just a particular folding up of all the quantum uncertainties). So every time we put a cat in a box, there are Universes in which the cat is dead and Universes in which it’s alive. We know which path we’re on as soon as we open the box. Time travel would then simply be an opportunity to follow a different path.

There is one problem with many of the sub-theories above, and that is a problem of the sudden injection of matter/energy: if I appeared from the future, the mass/energy of the universe wouldn’t be conserved (I could build a kind of automated time travel machine that continuously adds energy or mass to the universe, or–even better–reduce the entropy of the entire universe). So my arrival needs to be coupled with disappearance of energy or mass. Or maybe some other matter/energy is transferred into the future (where the travel originated). Possibly an arrangement such as one in Primer is needed where travel is only possible to a limited point in time, where all the prep work has been done, for example enough energy has been set aside to be “displaced” by the newly arriving energy. It may also be that the time travel portal has a standby energy consumption — it consumes energy at some rate, like a leaking pipe, all the time — this would allow energy of at most that rate to be transferred from the future.

Another way to solve the sudden injection problem is to borrow me for the duration of the time travel episode from the time chronologically after the event of time travel. That is, if in the year 2010 I go back to the year 2005, my extra existence for five years between 2005 and 2010 will be borrowed from what would have been my existence between 2010 and 2015. In other words, as soon as I reach the year 2010 the second time around, I jump to the year 2015. This is a kind of quantum entanglement, but not of I1 and I2, but rather of I1 and the future version of I1.