We divide time logically into three segments: past, present and future. It is fairly straightforward to conclude that past and future do not really exist but as notions in our minds. After all, the past is but a memory, while the future is but an expectation. Only the present stands a chance of being really 'out there.' This much is pretty clear, isn't it? So only through the present can time be said to be real. But where precisely is the present?
We could say that the present is today, while the past is yesterday and the future is tomorrow. Yesterday is a memory and tomorrow is an expectation, so both exist only in mind. But today is really there, isn't it? Well, if you come to think of it, today is quite a long period of time. Within today there is last hour, this hour, and next hour. Last hour and next hour only exist in mind. Only this hour is really there. Or is it? After all, within this hour there is last minute, this minute and next minute. Well, you know where I am going with this.
You could say that the present is a very short moment squeezed in between a growing past and an approaching future. But even that would be too generous to the present: it isn't merely very short; it is shorter than anything you could state it to be, because any period of time, of any length whatsoever, would still contain past and future. The present is infinitely short, so it isn't really there. If you try to pin down the present moment by saying 'Now!', by the time your mouth begins to move to say it, it's already gone into the past and exists merely as a memory. The conclusion is inescapable: the present doesn't exist but as an idea in our minds.
So we find ourselves arriving at an interesting conclusion: the past is a memory; the present is an idea; the future is an expectation. They all exist merely in mind. None of them is real in the sense of really being 'out there.' And since there is nothing to time but past, present and future, clearly time doesn't exist 'out there,' but is merely a mental construct. Mind invents time.
No, really, time is merely an invention of mind. What else could it be?