That sounds similar to the way I've posted about it, for one. I don't think of time as real, not in the truest sense, anyway. In the first sense, there is only space and matter. No past, no future; only now, the present. There is space and there is matter; the universe, existence. There are no increments of time creeping by, or river of time, or moments.

But then there is motion. Matter moves through space regularly, consistently changing positions and states, and that is where time steps in. My definition of time is a measure of a comparison between two or more motions. For instance, the rotation of the Earth we call a day, or the revolution of the Earth around the sun for a year. Those are really just cyclic regular motions we use to compare everything else. We can do this with any motion that is steady and consistent, as with a clock. So in my way of thinking about it, there is really just space, matter, and motion, always in the now in the primary sense, and time comes secondary to that, but only as a measure, a convenient mathematical tool for comparing motions.

My definition of time coincides with astromark's comments rather well. The way I have defined time above, time itself does not and cannot run faster or slower, for it does not run at all. Only the devices that compare motions, such as clocks, along with everything else that exists within the same frame of reference, can run slower or faster, and so a comparison between two frames of reference is really a comparison of the rate of the motion within each frame to the other.

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To run off on a tangent somewhat, you also mentioned time travel, and this would lie on similar ground. In order to reverse time, one must first somehow reverse all of the motions that have taken place. Some things might not run as well forward as back, though, so some of the physics might also need to be altered. To truly be as they were, we must reverse everything, like a video tape, right down to the last particle and photon. But many of the photons would have already travelled far away from the central zone we wish to reverse, perhaps light years away, depending upon how far back we wish to go, and we would have to find some way to retrieve them and send them all back the same way they came.

So as a fun exercise, let's say we build some kind of containment field around the Earth. Nothing can escape and nothing gets in. We are capable of altering the physics within this field in such a way that motion can be run backward and forward at will. Any particles and photons that reach the boundary of the field will just bounce back in, and when the field is reversed, they will just come back and bounce the other way, the way they came. Everything can be run forward or back, just like in a video tape.

But you see, there is a problem with that as well, because when most people talk about going back in time, they mean going back within their own history with the knowledge they have now. Going back wouldn't do much good if they just go back with the same knowledge they had and do the exact same things over again, not even knowing they had already done the same things before. In order to retain that knowledge, they must leave the containment field, reverse all of the motions from the outside, and come back in. But if they do that, then the essentially part of their life's history is missing, themself. While reversing the motion, they would no longer be present, so everything they affected, everyone they had contact with, and every particle and photon that react with them would now pass through where they ordinarily would have been, and play out in a different way, and things would reverse to an entirely different history than they remembered, mostly depending upon how far back everything is reversed.

Now, if one just went back a little bit like that, they might not change too much of their own history, although anyone they had direct contact with at the point that the reversing stops would be surprised to see them suddenly gone, since that's the last thing they remembered. Also, one could probably go back to the day before, knowing the lottery numbers for the next day, as long as they hadn't had any direct contact with anybody on the lottery commision or anything, or anything that might affect how the numbers turn up.

One couldn't go much further back than when the containment field was built, either. If they did, the history would come out differently than it did before the field was in place also, and since many particles and photons and such would already be lost to the rest of the universe, it would probably just make a big mess the further back they tried to go. I'm wondering also, in order to solve that reversing one's own history without them present thing, if one could leave the containment field, record some important knowledge, and then return to within the field and reverse everything then. Maybe they could make a clone and send that back with the same knowledge to be reversed somehow. Well, anyway, that was fun to think about, but it's beginning to sound like a sci-fi novel, and I'm sure you get the idea, so I'll stop here ...

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"Let's define another operator, Sz, which we won't pay any attention to."
"This transformation will automatically make zero equal zero."
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