Re: A question of discrete space-time.
- From: a student <of_1001_nights@xxxxxxxxxxx>
- Date: Sat, 28 May 2005 05:39:20 +0000 (UTC)
Ed Hanna wrote:
>
> A unit particle in constant motion within a discrete space-time lattice
> would have a maximum speed limit of one position per moment, and this
> should be a testable prediction -- a piece of evidence that space-time
> may be discrete?
>
Mike Helland has pointed out a velocity addition problem.
There is also an isotropy problem when you move to two or more space
dimensions - and perhaps hexagonal tiling is better than rectangular
tiling for one space dimension:
In particular, tiling with space with cubes (and spacetime with
hypercubes), there are now different 'unique' maximum velocities in
different directions - eg, moving from (000) in the (111) direction is
different than moving in either of the (100) and (110) directions.
This doesn't agree with present physical evidence.
Even with one space dimension, it seems that your rectangular tiling of
spacetime allows TWO natural non-zero speeds - corresponding to
horizontal motion (instantaneous speed) and to diagonal motion (unit
speed). Hence, unless you want to reserve an instantaneous motion for
quantum collapse :) , it might be better to use a hexagonal tiling
(with flat tops parallel to the space axis), and only permit motion
across edges, as this will give a single non-zero speed.
Unfortunately, this doesn't overcome the isotropy problem in higher
dimensions.
.
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