[Eric A. Taylor (OP)]

If I take any chunk of matter and start cutting it apart I'll eventually get to a chunk I can't cut in half. Are space and time the same? If I take a meter and start cutting it apart will I eventually get to a distance that can't be divided? What about time? Is there a fraction  of a second that can't be split? If so what is between the chunks of space and time?

[Soul Surfer]

This is currently being considered by the fundamental thinkers. It is assumed by many that they are both in effect quantised in some way and this is linked up with the quantisation of gravity. however some people are starting to think that space and time may be emergent properties of the universe.

[LeeE]

If I take any chunk of matter and start cutting it apart I'll eventually get to a chunk I can't cut in half. Are space and time the same? If I take a meter and start cutting it apart will I eventually get to a distance that can't be divided? What about time? Is there a fraction  of a second that can't be split? If so what is between the chunks of space and time?

The phenomenon of relativistic time dilation suggests that space-time is not quantised, or at least, that any quantisation is relative.

The relationship between speed through space and speed through time (being based on Pythagoras's right-angled triangle solution) means that, at the extremes, a small difference in one results in a relatively big difference in the other, but in this solution the two are essentially the same, which is why the solution works, so their quantisation size should be the same, but they're not.

This is most easily seen by normalising the ranges of speed through space and time, and then plotting the relationship, according to the Lorentz/Pythagoras solution, and when you do you end up with a quadrant of a circle.  From this, you can see that for very low spatial speeds, the reduction of the temporal speed is tiny.  But if you then use the size of the reduction of the temporal speed (as the size of the reduction must be greater than the quantisation size) as the new value for your spatial speed then you get an even smaller reduction in temporal speed, which you can then use as your new spatial speed, and so on.  Now, if space-time was quantised, we'd reach a point where we couldn't keep doing this because, at some point, the resulting temporal speed would end up below the quantisation size.  This would mean though, that the spatial quantisation size was much greater than the temporal quantisation size.

However, when we look at the same plot at the other extreme, at high spatial speeds, then exactly the opposite occurs, and the spatial quantisation size would have to be much smaller than the temporal quantisation size.

You can imagine two objects then, on close parallel courses, but travelling at different spatial speeds: the quantisation sizes would appear to different to each of them, even though they're travelling through the same region of space.

[Geezer]

I sometimes wonder if, on subatomic scales, time itself might be a bit "jittery". If it was, it might help to explain why quantum effects can only be explained in terms of probabilities. However, I really have not the faintest clue how to take this idea any further.

[wolfekeeper]

No, that's quite right, time is essentially quantum mechanical at the smallest scales. Particles can move forwards and backwards in time a little bit, particles of light can go faster than the speed of light, or slower than the speed of light for short distances and times. (These are called virtual particles).

However, at the end of the day, it all has to even out, you don't get any large objects going faster than the speed of light.