Is Impulse a Discrete Observable in Physics?

[the_pulp]

Hi there, I have a short thought that I want to share with all of you and see if there has been something written about it and, if not, why not?:

A free particle spin is something that can take a discrete range of values, as it happens with electromagnetic or colour charge. However the other important observable, impulse, can take a continum range of values. This seems suspicious to me since nature seems to be formed by a finite (inmense, but finite) number of mathematical objects. Isnt out there any model or research where it is supposed that impulse is also a discrete observable? perhaps lattice quantum mechanics or something like that?

Thanks!

 

[Jano L.]

The problem with discrete view of physics is that most of laws and equation are formulated using differential equations and these refer to continuous and smooth functions. If we try naively to discretize equations, they lead to wrong conclusions. For example, Euler forward scheme is a discretized version of continuous description. But it gives incorrect description and prediction of events, while differential equation is confirmed with fantastic accuracy.