[Physicist]

On the other hand, if many different particles can arise from the same point, I would expect something to "always" occupy the point.

That's literally how I envision it. At every point in space, there is an infinite number of things going on.

[AndrewC]

At every point in space, there is an infinite number of things going on.

But, infinities are paradoxical, something along the lines of --- an infinite number of non-zero weight particles would weigh an infinite amount. That implies to me a minimum division of time and a maximum weight particle.