Infinity is not physics’ most pressing problem. The real problems are related to our perception of reality. First, they have to get it fixed in their minds there is a difference between ‘zero’ and ‘nothing’. Zero is a mathematical placeholder representing an absence of anything within a given context while ‘nothing’ signifies there is no context at all.
The second problem, is neither the Wave or Particle models work. Wave theory implies a there is always something but with no gaps between whatever makes up the waves, how do you get movement. Particle theory says there is emptiness between particles but then how do you get those last smallest particles to bound or do anything but collide. And if there is nothing between particles, then they should be able to transverse any distance instantaneously.
Any defined volume is not ‘nothing’. There maybe a lack of known components or context within the volume, which establishes it as having zero contents, but zero is more than nothing.
Thus we come to the third problem. We define space as X, Y, Z axis and anything that changes position is defined as movement. But how big is big? How far does existance go?
In looking at the equation E=MC², what many fail to realize is there is only one real value C². Effectively what it says is M (Mass) and (E) Energy, are just states of (C²) or velocity. In other words they are just states of motion. If everything is either energy or matter, then it’s all motion and thus any X, Y, Y coordinates are established by that motion not the other way around.
With this realization, you no longer have the zero/nothing conflict, there are no gaps required to get motion and big is only as big as it needs to be.
So I only have a year of formal physics training under my belt, but I can see a couple of problems with these problems you laid out.
The zero/nothing conflict is not something physicists worry about. That is more philosophical.
The particle/wave duality is also a resolved issue. Heisenberg’s uncertainty principle states that it is impossible to know both the position and velocity of a particle. Yet this is not just a statement about experimental limitations, it is an assertion about a physical reality. More generally, the principle states that particles do not have a fixed velocity and/or position. Therefore, to describe a particle, you have to sum up all the potential states of the particle (the “eigenstates” as far as I know), which ends up being a wave. Because that summation is just a description of physical reality, that wave-like quality is an actual quality of the particle. That is my understanding. There isn’t really a problem there.
As for your third problem, both velocity and size are relative, meaning big is whatever you experience it to be. Also energy and mass are not movement, C^2 is just the conversion factor between mass and energy (the speed of light is a frequently occurring constant in physical equations).