I'm fairly new to this topic, so please excuse any amateurism.
I'm confused about how a boson (i.e a particle that does not obey Pauli's exclusion principle) can have mass. For example, W and Z bosons have mass, as does a helium nucleus.
How can two particles that have mass be in the same place at the same time?
You clarify in a comment:
If something has 'mass', it has physical presence. Obviously two light waves can overlap each other. However, I cannot, for example, overlap my hands together, because each has a mass and cannot exist in the same position at the same time.
The correspondence between mass and physical presence is a good one in the macroscopic world. However, one of the repeated lessons of quantum mechanics is that your macroscopic intuitions are related to the microscopic world in surprisingly complicated ways.
Here your macroscopic intuition is just failing you completely. It’s fermions that can’t overlap; we just happen to live in a world where room-temperature electrons (which happen to be fermions) are major constituent of matter. Multiple bosons, even composite bosons which are constructed from pairs of fermions, can occupy the same state. This ability to overlap gives rise to several counterintuitive properties of Bose-Einstein condensates, to some surprising phenomena in the flow of superfluid helium, to many important properties about superconductivity, and more examples.
As for why bosons can overlap and fermions can’t: it’s complicated. A good introductory textbook on quantum mechanics will have an inadequate explanation near the middle; a good graduate-level course on quantum field theory will have a better explanation near the end. I lack the talent to squeeze such an explanation into this answer.
At the quantum mechanical level of particle interactions one does not have trajectories , one has probability loci: i.e. when measuring a particle how probable it is to be found at x,y,z, at time t. For interacting particles and particularly for bound states where in the Bohr model were orbits in the quantum mechanical solutions they are orbitals, with very specific quantum numbers . The Pauli principle applies to these orbitals and given quantum numbers for defining the state.
How can two particles that have mass be in the same place at the same time?
If you look at the hydrogen orbitals you will see that even the electrons can have a probability to be on the proton space, for S=0, without any interaction happening, because there is not enough energy. This probability for nuclei leads to beta decay by capturing the S=0 electron to turn a neutron into a proton when there is enough energy .
It is hard to think of a possibility of getting two Z in an interaction, due to the large masses involved, the quantum number constraints, and the weak coupling constant. The same for pions kaons etc which decay very fast to experiment with (make a pionic atom with two pions in the same state, for example). From what I know the concept is useful in quantum models of solid state for example.
You can bring two massive particles as close together as you want. The "force" introduced by the exclusion principle can be broken in the case of fermions (collapsing neutron star, where all particles are spin half neutrons). Electrons can get as close together as you want. Just shoot two of them head-on towards each other. The exclusion principle can't hold them from being on top of each other. If the exclusion principle can't do this for massive fermions, it certainly cannot do that for massive bosons. Though exactly at the same place they will never be.
Regarding your hands. Luckily they don't fuse if you clap them. But if you smash them together at an enormous speed they do fuse. Just don't try this when your mother is present...
