Re: A question of discrete space-time.

Mike Helland wrote:

[..]

> This is called "Zeno's Stadium Puzzle" or paradox, whatever.
>
> So the conclusion of this puzzle is:
>
> 1. space-time is not discrete
> or
> 2. space-time is not a dimensional medium
>
> Since 1 is alot easier to understand than 2, conclusion 1 is what most
> people automatically assume must be true.
>
> I'm personally a fan of conclusion 2.
>

I don't agree with this. All that has been demonstrated is that
certain discrete models do not exhibit explicit Lorentz or Galilean
symmetry in a way that we might like them to do. In the case discussed,
we demanded that a "Lorentz transformation", consisting of shifting
then N_th rows N columns to the left or right, leaves the system
unchanged, which as you show, it does not. But
you could also define a Lorentz
transformation on this system that leaves the cell structure
unchanged, but changes the variables defined on these cells.
In that case we would not be looking at "particles" in the
cells anymore, but at "fields".

Another remark on this discussion is that continuous systems
also have speed limits. For example, wave equations such as
the Klein Gordon equation do not allow waves to travel
faster than the speed of light.

I've got some stuff on the discrete klein gordon equation at
http://www.xs4all.nl/~westy31/Electric.html


Gerard

.