One of the most intuitive and (thus) inexplicable concepts that we have got too used to to wonder about, is time. We ask for the time, ask for more time, manage time, and even kill time! But to define time in all its complexity and depth is much more challenging, if not impossible.
Two related aspects of time come up in everyday life. The first is the concept of duration, which is conveyed by questions like "how much time does it take to complete this activity?" or "how long have you been living here?", and definitions such as "a day is the time taken by earth to rotate once on its own axis". The the other aspect - as implicit in questions like "what time is it?" or "when did that happen?" - is obtained by applying the first one in combination with an arbitrary reference point. While we understand these aspects and use them freely, these are actually points or intervals in the continuum that we know as time. The question of what time is remains as elusive.
According to Srimad Bhagavatam, time is the potency of God that brings about change. It is without beginning or end, undifferentiated, and can only be inferred from its effect, which is change. Not surprising then, that all measures of time are actually measures of change. For example, a day is the measure of change in the angular position of a point on Earth's surface by 360 degrees. However, it looks like we can't use just any change for measuring time. For example, time taken for me to count from 1 to 100 is seldom accepted as a unit. This is because we somehow decide that this time cannot be guaranteed to be the same each time I count. So, in this age, measures of time are defined pretty elaborately, with a second being the duration for a certain number of radiations corresponding to a specified transition of Cesium 133 atom. But how do we know that this time is constant?
If you ask me, it is just defined so as to be made a constant. But at least, it is defined in a way that does not conflict with our inherent, intuitive notion of passage of time; in a way that is consistent with measures based on many other phenomena which we accept as periodic. For example, the time taken for moon to go through a cycle of waxing and waning has a more or less constant relation with the time taken by earth to complete a rotation, or with that for earth to revolve around the Sun. These, again, are in sync with our biological notion of time - heart beat, cycles of sleep or hunger, growth and ageing.
Time, as we generally agree, is uni-dimensional - there is only past, future and an intervening present. Furthermore, our experience of time is unidirectional - it keeps flowing forward, from past to future, and never in the reverse direction. According to thermodynamics, this directionality is a result of the natural tendency of all systems to progress in the direction of increasing randomness (entropy) as laid down in the second law of thermodynamics, famously referred to by Eddington as the Arrow of Time, and follows from the premise that randomness cannot be undone. Take the example of two rooms separated by a closed window, one with hydrogen and the other with oxygen. If the window were to be opened, the gases each diffuse into the other room and gradually reach a state of uniform distribution across the two rooms. The reverse of this change has not been observed, and hence its direction is aligned with the intuitive direction of time which we all accept.
For a moment, let us consider the fascinating possibility that time can, and it actually does, flow backward. Since the forward direction of the time is the direction in which our memory builds up, the backward direction would be the one in which it gets undone. So even if we were shuttling back and forth in time, we would remember only one direction of it since all trace of the other would be erased in our memory! In case we actually do manage to remember, then we would remember it as our past and direction of progression will appear to us as from past to future. Not sure if this is very convincing to others, but I believe that our consciousness of something having happened, or us having undergone an experience is what makes it the past, and gives direction to time. The thermodynamic arrow of time just seems to be aligned to it so far as we have observed in this universe.
My thoughts on time travel, its implications and applicability are based, chiefly, on the consciousness or memory arrow of time. Say, a person experiences a grave tragedy, then goes into the past and undoes its cause (assuming he could do that), will that tragedy remain in his memory even as a dream? If it will, that means one cannot completely remove an experience even by going into the past, because a memory remains of that experience and memory is all that remains of many other past experiences. If not a trace of it remains in his memory, then he wouldn't remember going into the past and applying a correction either - so any learning from that experience is totally lost and he is likely to commit the same mistake again - until he is prepared to accept the tragedy along with the learning that comes with it. It is the ability to undo the results without undoing the learning that makes checkpoints so valuable in video games. This is possible because in a game, memory is held by the player and results are reversed or lost only for the character. In real life, if memory is associated with our undying consciousness (the player) while the consequences for body and mind are reversible through time travel, we may have a similar advantage!
The real paradox of changing the past that led to the present (from the present) is that it would undo the change you made to the past as well, nullifying the course of events that led to the present action of changing the past, bringing everything back to square one. I understand that there are some people who believe this paradox can be circumvent by considering numerous parallel universes, with each decision in present giving rise to a new branch of reality, and a change to the past switching you form one branch to another. That is, having read this article, if you go into the past and kill me before I write this article, you'd actually be killing a me in some other universe, inhabitants of which would be spared the ordeal of reading this article by a miraculous savior who appears out of nowhere (well, a parallel universe, to be precise - but they might not realize it because they didn't get a chance to read this article!). On the other hand, if you had killed the author from your own past, you wouldn't have got a chance to read the article and seek out its author, which means the author will be spared, giving you an opportunity to read this article and seek out the author, and so on, indefinitely (hence the paradox!). The reason I believe the parallel universes hypothesis does not really solve the paradox I mentioned in the first sentence of this paragraph is because in this case you're not altering the past that led to this present, but entering an alternate past that leads to some other present.
Considering the uni-directional flow of time in a single universe, changing the past seems to be a very difficult opiton - at least to explain within the confines our our logic (Personally, I don't believe that the infinite truth has to fit into finite human logic! But due to the limitation of my intellect, I'll stick with a logical analysis for now). Even in a multiverse setting, with a universe for each possible different quantum state, there doesn't seem to be any real option of "changing" the past. The best you can do is end up in another past where the choice you made has already been decided. What is interesting is that in this case you even don't have any control over the future because all futures already exist, and you are simply part of one or the other - a fatalism that many would find scary. Even if we consider the evolution of a single universe with time, if the laws of nature could be applied on the current state of the universe with absolute accuracy to predict a future state, we would end up with a similar degree of fatalism. All that is to happen will already be pre-determined, and would happen as dictated by the flow of time. Is the entire universe subject to this tyranny of time? This will be the subject of our next discussion.