CoffmanPhDIs space-time discrete or continuous?

[Universe_Man]

I think zeno's paradox tells us something about the nature of what we think reality is. Reality, or the construct of time and space that we presently see around us is only a part of something much larger. I personally believe that the fact that there exists a paradox indicates that there is a larger category of reality which encompasses or is somehow associated with our universe. I like to think of this "realm" if you will, that is infinite; it's a place of pure thought. Of course this will most likely be regarded as speculative, but I once read that Plato or some other greek philosopher held a similar idea.

 

[DeaconJohn]

If I understand correctly, the question discussed here is related to the question of whether or not space and/or time are continuous or discrete in their underlying nature.

I don't think modern physics has a definite answer to that question. Mainline physics uses continuous models, but, discrete models have been seriously investigated off and on for at least the last 50 years (I heard Pere Lax say he had spent a lot of time looking at them at a lecture he gave in 1968).

The place in physics that I have personally seen discrete models discussed the most is in various attempts attempts to unify the gravitational force with the other forces in a single coherent theory. (String theory is one of many attempts to unify gravity with the other fundamental forces of nature.)

So far, the discrete models have not produced any interesting descriptions or predictions or whatever, as far as I know. People make that complaint about string theory, but, string theory is far better in that area than the discrete models are. At least string theory has a place for the graviton (that must be a spin two particle (a boson?) if the Einstein field equations for general relativity are correct) without the divergent integrals of "the standard model" (quantum field theory, QFT) to compute the possible values of its observables.

However, string theory (according to vol 2 of Joe Polinski's book "String Theory," still the baisc graduate level text in the field) implies that the Heisenberg uncertainity principle applies to the underlying space-time continum. If this suggestion matches reality, it amounts to a perturbation of our normal concepts of space and time that is far greater than the question of whether or not space-time is discrete or continuous. It is saying that the underlying structure of space time is properly described by Noncommutative Geometry - a field dominated by the name of Allain Connes.

Not to worry, it is likely we will never know for sure. Polchinski points out that if the basic space-time vaiables of reality in fact do not commute, the lack of commutativity is only observable (i.e., measureable by experient) if you have access to enough energy to get you within two orders of magnitude of the Plank length (10**(-33) meters). That means 1% of all the energy in the visible universe. That much energy never existed in one place in the entire universe except for a very short time after the big bang.

Yours,

DJ