Can theories which say space-time is fundamentally discrete be compatible with Lorentz invariance? And if the answer is yes, in what sense is space-time no longer continuous?
I'm sure this has been asked in various forms before, but I wanted to ask in the context of this:
"Quantized Space-Time"
Hartland S. Snyder
Phys. Rev. 71, 38 – Published 1 January 1947
http://journals.aps.org/pr/abstract/10.1103/PhysRev.71.38
Abstract:
It is usually assumed that space-time is a continuum. This assumption is not required by Lorentz invariance. In this paper we give an example of a Lorentz invariant discrete space-time.
Searching for Synder on physics stackexchange didn't bring up anything relevant to this.
Unfortunately the paper is behind a paywall, so I've only seen the abstract. Searching around I can't find much on Synder spaces except in discussions of non-commutative space-time. Which I wouldn't really call discrete. Discrete brings to mind a lattice, or possibly irregular graph of spacetime events as nodes. So it is possible the technical meaning of the word discrete as used here may mean something other than "non-continuous" (but I'm hoping not since the abstract uses the word continuum), or maybe I don't understand the implication of non-commutative geometry. In other words, explanation of terminology would be much appreciated, and unfortunately may even be the only depth this possibly misguided question needs to be discussed to give an adequate answer.
