Thank you for your question. The standard answer is that an instant lasts for no time at all. That is to say, the start of an instant and the end of an instance occur at exactly the same time. An instant is indivisible; it has no separate beginning, middle, or end. You might think of time as like a number line, with (for instance) zero as the time when you started reading this sentence and 1 as the time when you arrived at the end of it. Then each number between zero and 1 corresponds to an instant of time. None of those instants is any length of time at all.

Of course, that an instant of time lasts for no time at all might lead you to wonder how a span of time lasting, say, for an hour could possibly consist of a bunch of instants each lasting for no time at all. This is closely related to some of the paradoxes first proposed by the Greek philosopher Zeno thousands of years ago.

Bear in mind as well that between any two instants of time, there is another instant of time -- and, indeed, infinitely many instants of time, since you can repeat this thought infinitely many times. But that should be no more surprising than that between any two numbers, there is another number -- and, indeed, infinitely many numbers. If an instant of time lasted for any length of time (other than zero) and all instants lasted for the same length of time, then you couldn't fit infinitely many instants between any two instants.

So in thinking about how an hour of time could consist of many instants, each lasting for no time at all, you have to bear in mind that an hour consists not just of many instants, but of infinitely many instants. I hope that this answers your question (a little).

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.

You make a very interesting point. If time travel takes a second, then since a later Earth - say Earth in a year - might be zillions of miles away (i.e. more than 186,000), I must travel faster than light, which is impossible. But how long does my time travel take? How do we know that it takes a second? After all, if on the new or later Earth it is a year later, presumably it took me a year to get "there", the same amount of time as it took the Earth itself, even if it felt instantaneous. So there is a difficulty about the meaning of "How long does my time travel take?" If we move in time, or times moves past us, there is a difficulty about the concept of the speed of the movement. Movement in space is distance divided by time, so movement in time, or the movement of time, it seems, is time divided by time; and it is hard (as D.C. Williams pointed out ages ago in "The Myth of Passage") to attach any sense to this idea. This is the interest of your point for me; how do we attach sense to the speed of time travel? In what reference frame does it take place?

Any "change" in the past is inherently paradoxical (to say the least). In fact, I think it is actually worse than that: Such changes would involve making it both true and false in the history of our world that the changed event did (or did not) take place. That's a contradiction, not a paradox.

On the other hand, one could go back in time and do what one actually did in some time long past (or do what one actually will do, some time long in the future). If it is actually possible to go back in time, for example, and be one's own father, then one would live in a universe in which that is (and always was) precisely what happened. What are called "looping" universes, in which time did not flow linearly, but in a closed loop, would make such apparently strange events possible. And though we have good reasons for supposing that we do not live in a looping universe, it does not seem that logic makes such an idea impossible.

To find out more about this topic, have a look at an article by David Lewis entitled "The Paradoxes of Time Travel" which was published in the American Philosophical Quarterly, vol. 13 (1976), 145-152. Lewis also cites two stories by Robert Heinlein in which the picture of time travel that he develops appear to be assumed.

I already addressed your second concern in response to a previous question on this site. I'd invite you to take a look at my answer there.

As to the first concern, when we speculate about a possible beginning to time, we are doing so from a frame in time. We start at the present, and we conceptually project ourselves backwards through the period that intervened between the present and that supposed first moment. Was there a time one year ago? Yes. Was there a time two years ago? Yes. Was there a time thirteen billion years ago? Yes. Was there a time fourteen billion years ago? No! The supposition of a beginning to time means that there exists a number n, such that there was a moment of time n years back from the present but no moment n+1 years back. The supposition of an infinite past simply means that there is no such number.

Not a silly question at all, absolutely not! But the answer is no.

Suppose you built a time machine last year, 2008. Then it is true now that you built a time machine in 2008, and it always will be true that you built a time machine in 2008. Suppose now that, next year, you decide that it would be amusing to create a paradox by using your machine to go back in time and prevent yourself from building the machine in the first place. But it's still going to be true that you did in fact build it in 2008. Which means that, no matter how determined you might be, it will still be a fact that you didn't succeed in your plan of preventing this. Logic alone can show that something or other must have scuppered your plan: because success would indeed generate a paradox, whereby you both did and did not build the machine, which is a logical impossibility. Now, what logic won't show us is what scuppered your plan. Maybe you had a last-minute fit of conscience and just decided not to go through with it. Maybe you did make an attempt, but your 2008 self managed to overpower your intruding 2010 self. Or maybe something else intervened. If you had CCTV cameras set up around your laboratory last year, you might actually be able to find out what prevented your scheme. Now in 2009, you could go back and watch the images of your 2008 self as you were still tinkering with the machine, and maybe you'll spot your 2010 self, tiptoeing up out of the shadows, about to conk the other one on the head with a spanner... and then slipping on a banana peel, knocking themselves out instead, while the younger one, quite oblivious to what's going on behind them, successfully completes the machine. There will be some perfectly ordinary explanation for why you failed to prevent the building of the machine, and this will be a proper subject for historical research -- because, even if it was initiated by events in 2010, that failure already happened in 2008. But something will have thwarted your plan, because the fact is that you did build the machine.

My own thinking on matters like this has probably been most influenced by the late, great American philosopher, David Lewis, particularly his article 'The Paradoxes of Time Travel'. It first appeared in the American Philosophical Quarterly, 13 (1976) 418-46, and is reprinted in his own Philosophical Papers, vol. II. I recommend it.

'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.

If the alternatives are living in the past and living in the future, we can only live in the present. If the alternatives are thinking about the past and thinking about the future and thinking about the present, we have choices. "Living in the present" is a cognitive psychological technique used, often successfully, by those who brood about the past or fret about the future. Concerns with the past or future may be appropriate (e.g. someone regrets a romantic choice or gets a worrisome medical diagnosis) or inappropriate (due to anxiety, excessive guilt etc); the technique works for all of them. Many people report that it helps them live a fuller and calmer life. For those who suffer from poor impulse control or psychopathy, however, it might be better to focus more on the future and the past and less on the present.

Why does there have to be a reason? Maybe some events occur when they do just by chance. There seems to be nothing incoherent about that idea. Indeed, that's how we think that the world actually works. For example, the law governing the radioactive decay of an unstable atomic nucleus seems to be merely chancy. An atom of polonium-214 has a fifty/fifty chance of decaying in the next 3 minutes or thereabouts. But nothing determines when it actually decays. There is, according to our best scientific theory of the matter, no answer to the question of why the decay happens at the moment that it does rather than a little while before or a little while after. Why should there be?

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.