Rob,
The uncertainty principle is a quantum mechanical
result. It has nothing to do with relativity.
It holds equally well for Schrödinger's equation
(which is nonrelativistic) and for Dirac's later
relativistic version.
> If the speed of light were infinite would this still
> result in an Uncertainty Principle?
Yes.
In any case, I believe that the analogy with QM is
about as useful as most analogies: it might suggest
some new ideas, but if you push it too hard, it tends
to break down in the details.
John
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