Continuity/Locality and Discreteness/Nonlocality

[cryptist]

Is there a relationship between Continuity and Locality? or between Discreteness and Nonlocality?

For example can we say that, if space time is continuous then, principle of locality must hold? Similarly, can one say discreteness of spacetime leads to nonlocality?

I don't know why, but I feel like there is a relationship between these. Can anyone inform me about these issues?

 

[bcrowell]

For example can we say that, if space time is continuous then, principle of locality must hold? Similarly, can one say discreteness of spacetime leads to nonlocality?

Nonrelativistic quantum mechanics is nonlocal but takes place on a background of spacetime that is continuous.

Physical models based on cellular automata http://en.wikipedia.org/wiki/Cellular_automaton#CA_as_models_of_the_fundamental_physical_reality have discrete spacetime but are local.