[techno_modus]

> David Hilbert famously argued that infinity cannot exist in physical reality.

This statement reduces the problem to the definitions of "existence" and "physical reality" which of course may have quite different interpretations. For example, the existence of particles (with finite mass and finite coordinates which can be "touched") and the existence of waves are rather different notions.

[jamesrcole]

It seems to me that something can only have existence for us if it can have a transitive causal influence upon us, and surely both particles and waves exist in that same sense.

[whatshisface]

If by existence you also mean, "something that continues to exist upon closer inspection," then neither particles nor waves exist, you can always design an experiment to refract something around a corner and meausre individual quanta of it when it gets to the detector.

[openfuture]

Then this is easy, we are discussing the concept infinity, hence it is having a causal influence on our actions and so by your definition it exists.

[subroutine]

What aspect of waves as they exist in our universe is infinite?

[whatshisface]

If waves are continuous then they are over the real numbers, and there are an infinite number of reals between any two points.