Really, it's not perplexing. The connection between causation and time is that causation implies time. A cause has to precede its effect. Now why is that? Some philosophers have thought that the proposition 'A cause precedes its effect' is synthetic a priori. Others have thought, more plausibly, that it tells us part of what a cause is, so it's analytic. (A cause might be a certain juxtaposition of conditions, for example. In that case the cause and the effect could be almost simultaneous.) Still others have thought that a cause can occur after its effect. Even then, though, causation has a relationship to time. And there is the so-called "bilking" argument. If a cause can occur after its effect, all we have to do is wait for the effect to occur, and then prevent its cause from occurring. The fact that this is possible shows that there cannot be reverse causation, i.e. causation in which the effect comes before the cause. As to other dimensions - is there an analogue to causation in them? (1) Are there beagles in these other dimensions? I have just discovered that the most popular dog in Rome is the beagle, but it was a discovery, not something I could have produced an argument for. (Also the plural of "beagles" in Italian is "beagles". I thought it would have to be "beagli" - no such luck.) (2) What is our definition or understanding of causation according to which it has analogues in other dimensions?
Is the idea of backwards causation coherent? It seems not, as you could, for example, cause earlier events, such as your own birth, not to have happened. There is also the famous "bilking" (cheating) argument due to Max Black, according to which you can prevent the future cause of something that has already happened from occurring. All the same, philosophers, particularly Michael Dummett, have taken the idea perfectly seriously, and defended it. You write that you doubt that a scientist would take the idea seriously, but plenty of physicists, including Richard Feynman, have indeed used the idea for a variety of purposes, including the remarkable idea of positrons running backwards in time.
Here are some questions about time that are not scientific but are philosophical. Does time flow? Does it pass? What does it pass? Does it move? If so, how fast? If speed (s) = d/t, what is d/t when s is the speed of time? What temporal distance does time travel in a unit time? Surely the unity distance. But then the speed of time is 1 sec. per sec. How can time be measured, as the past does not exist and the future does not exist and the present is merely a point - nothing to measure there! - dividing the past and future? Does time exist? What (if anything) is it made of? Is time travel possible? In a completely unchanging universe, would time pass anyway? If every true statement corresponds to a fact, how can statements about the future be true now, in the present, as there are no facts about the future now, in the present? If there were, they wouldn't be future. Does it mean anything to say that time has a direction? What does it mean? If omelets came first and then eggs afterwards, time would surely still be going forwards, whatever that means; it's just that omelets would come first and eggs afterwards. And (as Andrew points out) how - in what way - do we experience time? This last question, though, might be thought to have a wholly psychological sense. Perhaps there is no such thing as the experience of time itself, but only of things changing. Would there be any difference in our experience of the world if we did not experience time as such? In fact the conceptual problems of time are interesting partly because so little in the way of answers can be extracted from science. In "Time and Physical Geometry" (1967) Hilary Putnam took the view that science gives the answer to problems about time. Science tells us that the death of Mr. A. is earlier in your reference frame than the death of Mr. A in my reference frame. That leaves a huge philosophical problem about the place of Mr. A's death in reality. One can see how simultaneity is relative to a reference frame, but it is much harder, if not impossible, for philosophical reasons, to see how the reality of something like Mr. A's death could be taken relative to a reference frame. But this is implied by its position in the temporal order.
I agree with everything that Allen writes in his last comment. Some time travel scenarios are ruled out a priori : these are the inconsistent ones, and there may be others, for all I know. Are the consistent ones ruled out by anything? I can't see that they are, as the only reason I am clear about for thinking time travel is possible is the grandfather paradox. But it may only rule out the inconsistent cases. So I am in agreement with Allen here too, and in the dark as to whether anything in physics allows or rules out non-contradictory time travel. Time is a dimension, and dimensions are things that allow you to scale. A direction in the structure of the dimension itself seems a slightly incoherent idea to me, as opposed to the direction of the thing moving in the dimension, e.g. a place moving through colour space, such as the sky going from blue to red, or a bullet moving from there to here.
Nice conundrum. Here is a stab at it. If, in the example, time travel is traveling back one year of time in an instant of another time dimension--call it metatime--then Einstein has not been contradicted. He is silent about how much space can be covered in an instant of metatime. So time travel, conceived this way could be possible even given our actual laws of nature, if there is metatime. If, however, there is no metatime, then traveling back in time would be a case in which what would normally be a later stage of one's life occurs before what would normally be an earlier stage (see David Lewis, "The Paradoxes of Time Travel"). For this to be possible, the laws of nature would already have to be different than ours in such a way as to also allow that what would normally be the very next stage in ones' life occur far away from the current stage. If it is conceivable that the laws of nature be different than what they actually are then time travel would be conceptually possible. And this is the sense of 'possible' most philosophers appeal to in saying that time travel is possible. In other words, it is conceptually possible that something happen that contradicts Einstein.
'We can only live in this "here and now" moment . . . in fact , there is no way we can ever live out of it . . . is it not?'
I am not sure what is supposed to meant by living in the present instant ("moment" I think has more to do with action). Living at an instant seems as impossible as living at some other time, because there isn't even time to draw breath in an instant. In any case I do not believe that there is something called "the present instant", so I don't see how we could live in it (at it?)
It (the present instant) is an abstraction, and it is not, in reality! I do believe there are present times, though, such as the present day or hour. The trouble with the instant is that it is not a time.
Our knowledge of the past derives from perception, memory and inference, in the sense that these are answers to the question, 'How or by what means do you know?' (There are other ways, for example report or testimony). But our knowledge of the future has in it no elements of memory or perception. So as one might therefore expect it is harder to come by knowledge of the future, and we have less of it per hour, if you want. We typically can know more about a past hour than about a future hour, though by no means all of the past hours, for example those in past centuries. If I know p, and p is a proposition about the future, I cannot know it by memory, special cases apart. (A special case would be that I come to know that I am going to Africa next summer - a piece of knowledge about the future - by remembering that I am going to Africa next summer. 'How do you know?' 'I just remembered it . . .' makes sense as a conversation.)
It seems to me, in spite of the assumption you make, however, that in some cases there may not be an element of uncertainty in either knowledge of the past or the future. There is no uncertainty that the cat will be roughly where it is on the sofa in one attosecond - cats don't move that fast - and there is no uncertainty that the cat has been sitting there for the last five minutes, as I have been watching it for the whole time. There is an interesting mistake (I myself think it's a mistake, anyway) to be avoided in this area. Why are there asymmetries in time with respect to knowledge? I am not sure the question put just like that makes sense. Why can we remember the past but not the future, for example? The simple answer is that if I remember something, then it must already have happened, so memory of the future is a contradiction. My own view is that even the alleged logical asymmetries between past and future are much more slippery than they seem at first glance, and we must be careful to get our tenses right. It is certainly true, for example, that the past exists, in the sense that past events have occurred - and what other sense are we considering? But then so does the future exist, in just the same sense: future events will occur.
One answer to your question is that there may be multiple "orders of time" and, in particular, there may exist an order of time that is separate from the one we normally experience and within which events can occur.
Thus, for example, in Western Europe around and in the centuries before 1500 certain religious rituals, ecstatic experiences, moments in liturgical calendars, may have been experienced as occurring in a special "sacred time" that constitutes a different temporal order from commonplace "secular time." In his A Secular Age (and a book I've mentioned before on this site),Charles Taylor argues that our ancestors in Western Europe possessed this bifurcated experience of two orders of time and he provides a rich account of why it is that almost everyone alive today in Western Europe and North America experiences secular time only.