Time travel and the Laws of Physics
As the “Twin Paradox” and Einstein’s Theory of Relativity implied, time travel to the future is possible if enough energy is available. As for time travel to the past, while it seems to be the most envied hypothetical time-travel capability, it also seems to be the only one that is impossible (in my opinion). I will discuss why I believe this to be the case, specifically how it pertains to certain physical laws and theories including: Einstein’s Theory of Relativity, The Law of Conservation of Mass and Energy, and The Law of Causality.
One method proposed by some, in order to be able to travel back in time, is to utilize Einstein’s theory of relativity to take time dilation “one step further”, that is, by traveling faster than the speed of light the time dilation may theoretically reverse the arrow of time. To better picture this, recall that traveling closer to the speed of light slowed down the passage of time, and reaching the speed of light appeared to stop it. If time dilation or the deceleration of time were to continue in the direction implied (slowing down to a stop), then continuing this deceleration by traveling faster than light would cause the arrow of time to reverse, thus making time travel to the past possible. Unfortunately this “faster than light-speed” travel would violate Einstein’s Theory of Relativity, as one of the primary elements of the theory is the assertion that the speed of light is the fastest speed that can be attained by anything moving in space. Furthermore, Relativity asserts mathematically that it would take an infinite amount of energy to accelerate a mass (e.g. a time traveler) to the speed of light, which implies that it would take even more energy to accelerate a mass to a speed higher than that of light. Since you can’t have an infinite amount of energy, let alone more than an infinite amount of energy, traveling at or faster than the speed of light is impossible.
Relativity aside, if we found some other way to travel back in time and were to able to exist in a previous “version” of the universe, I think that we would violate the Law of Conservation of Mass and Energy, because we as the time traveler would be adding our own mass to a previous version of the universe which should have a fixed amount of mass and energy over time. The only way around this would be to somehow sacrifice matter in the previous version of the universe that one travels to, that is, the time traveler’s body would have to be assembled out of matter already located in the past version of the universe. If this occurred however, we would no longer exist in a previous version of the universe and would by definition have failed to time travel to “the past”. It would appear to be close to matching the past, but it would be a moment in time that had never existed, and the causal chain would be altered beyond what we can possibly comprehend. So time travel to the past appears to be impossible even if this particular law of physics was upheld, as we would be forced to alter the past (in order to satisfy the law) thus preventing us from traveling to a real moment of the past.
Finally, if we were to find a way to travel back in time and somehow solve the aforementioned issues, we’d still have a problem with causality. If a time traveler were to go back to the past, and actually exist in that causal chain, the “Butterfly Effect” would immediately change the course of history such that the “present” time from which the time traveler came from would no longer exist. If this was the case, then it seems unreasonable to assume that the time traveler would still have time traveled in the first place. Let’s take a look at a simple causal diagram to appreciate this scenario.
From this diagram, we can see that time traveling to the past would create a new causal chain up to and including a new “present”. This new causal chain would no longer be causally connected to the old “present”. This would mean that the time from which the time traveler initially left (i.e. the old present) would no longer exist. Wouldn’t this imply that the time traveler (their sense of self, the “I”, the “me”, etc.) as well as the trip itself never would have been? I see no way around this dilemma.
So it appears that time travel to the past is physically impossible for a number of reasons. At least time travel to the future has some promise as it doesn’t appear to violate any of these physical laws and is implied as a possibility due to consequences of Relativity. This type of time travel seems to only be limited by the energy requirements needed to accelerate the time traveling matter to a high enough velocity for a long enough period of time, and return the time traveler back to the previous frame of reference (e.g. Earth). Or if the time traveler utilized the effect of gravitational time dilation, their time travel would be limited by the gravitational field of the celestial body they chose to travel to as well as the time it would take them to get back to the previous frame of reference (e.g. Earth). Either way, time travel to the future is possible simply by moving through space in a particular way.
Final thoughts
Regarding temporal experiences, it appears to me that memory is the most important of the mental requirements in order to have a mental frame of reference, that is, to make an experience of the past and present possible (as well as a concept of the future). I think that how this memory is stored and retrieved in the brain, the amount or types of memory available as well as the psycho-pharmacological substance-induced or otherwise caused physiological changes to this memory no doubt affect our temporal experiences in profound ways. Memory also appears to transcend physical time by providing a means for experiencing an ever-changing temporal rate.
The Theory of Relativity suggests that physical time does not exist for entities moving at the speed of light because entities moving at the speed of light (which is a constant in all frames of reference) have no physical frame of reference, and have an infinite time dilation between themselves and all inertial frames of reference. All physical time for entities that are not moving at the speed of light would be relative to one another based on relative velocity, acceleration, and gravity. Time also appears to pop in and out of existence due to Einstein’s mass-energy equivalence, as matter is converted into energy and vice versa.
Thus, both mental and physical frames of reference are needed in order for a temporal experience to exist.
As for time travel, it appears to be possible but only if traveling into the future, if we are to uphold the Law of Conservation of Mass and Energy, Einstein’s Theory of Relativity and the Law of Causality.
The Open Mind 
All three parts to this essay were very interesting! It makes me think. I wonder about your assertion that a ‘new causal chain’ would be formed by going back in time. I believe I saw a comment of yours on another post that mentioned how the universe could simply be a deterministic system with only the illusion of choice. If we take the universe to be as such, would causality be an issue with going back in time? Wouldn’t the act of going back in time be accounted for in the deterministic system?
In other words, if I went back in time, I could end up becoming a part of the same causal chain that led to me going back in time, and I wouldn’t be able to help it, because all my actions would already be accounted for in the system. This is a common theme in time-traveling stories: the ‘circle’ of cause and effect that goes on and on and on e.g Harry Potter and the Prisoner of Azkaban, to name a popular book. If free will is truly just an illusion of the human brain, then causality doesn’t seem like it would be an issue with traveling back in time. Sure, let’s consider the strange hypothetical scenarios.
Let’s say I wanted to escape this ‘infinite’ loop by traveling back in time and changing my actions from 10 minutes ago. First of all, this is a deterministic system, so would that thought even occur? It couldn’t possibly occur because if that train of thought were followed, then the very train of thought that produced those actions would never exist. So, that thought could never occur. It would be impossible. And in this fashion, there would be no way to escape the ‘loop’, and traveling back in time would be possible, and the flow of time would follow a perfect ‘destined’ path.
Of course, if ‘choice’ exists, it would introduce an unexpected ‘metaphysical’ component into the otherwise deterministic system, rendering backwards time travel impossible for the reasons you stated. So I guess while the implications of ‘free will’ normally don’t make a difference, when hypothesizing about traveling back in time, they might. Very interesting. This is just something I’m writing straight from the top, so I could definitely have flaws in my logic. What are your thoughts?
Thanks again for the intriguing blog posts!
Blue
Blue,
Yes, causality would still be an issue in my opinion regardless of any determinism that exists. This is but one of the many reasons I believe that time travel to the past is impossible. If time travel to the past is not possible, then reconciling a new causal chain with determinism isn’t necessary, because the situation could never occur (in my opinion based on certain laws of physics, etc.). See what I’m saying?
As I wrote in my essay, if you went back in time, you would now exist in addition to what was in that past, which means you could no longer be in the same state temporally — because your unprecedented existence in that past time (as a time traveler) would inevitably change the causal chain. The only way around this would be if you as a time traveler were somehow a “ghost” whereby you could not be detected or affect anything around you in any way. This however, is even less realizable than time traveling itself.
Causality is an issue of time travel (only to the past mind you) regardless of free will because of the aforementioned issues regarding violated laws of physics. Remember, free will can be an illusion whether the universe is deterministic or not. If the universe is ontologically random (take the Copenhagen interpretation of Quantum Mechanics for example), we still have no free will because everything is ultimately governed by fundamentally random processes. Free will is an illusion based on certain properties of what is conscious, what is not, and a feeling of being in control based on how our consciousness operates. It is true that this illusion depends in part on some level of determinism (let’s call this adequate determinism), that is, the ability to say that X caused Y, and thus if I do X than I am causing Y. However, if you “causing” X is really just a matter of A causing B causing C causing D….causing X, and A, B, C, D, etc., are factors that lie outside of your consciousness or lie outside of one’s direct involvement, then we have a circumstance where determinism (some level of causality that we believe exists for all rational thought to exist) exists, and yet free will does not (because I had no control over factors A, B, C, D, etc.).
Let me know if you want any further explanation. I think I addressed the main points you mentioned, but let me know if I missed something.