What would happen if I put two identical particles close enough?

Is there a repulsive force between these two particles to prevent them from being in the same point? I mean, in order to obey Pauli exclusion principle?

• Yes, it's called Pauli repulsion. – lemon Mar 20 at 8:28
• @lemon So is that means these two particles will repulse each other, but there is no real force there? Is it a force we don't know yet or it just doesn't exist? – alst Mar 20 at 8:43

No, there is no repulsive force in the way that you would describe coulomb repulsion as a force. It is sometimes interpreted as an effective force, but it isn't and there is no exchange of virtual particles as there are in fundamental forces.

The PEP does not prevent ideal, pointlike fermions from being squeezed arbitrarily close together. Indeed, they can occupy the same position if they have different spin. What it prevents is those fermions occupying the same quantum state or for more than two (spin-up/down for half integer spin) to occupy the same location in phase space (momentum $$\times$$ position)$$^3$$.

To get fermions very close together means they must occupy different spin/momentum states. It is this spread of momentum that is responsible for degeneracy pressure in a dense, degenerate fermion gas.

• The origin of the PEP is not understood. For example, in Bohmian mechanics it is formulated as the gradient of a potential. – lemon Mar 20 at 9:23
• @lemon What is the force carrier? – Rob Jeffries Mar 20 at 9:28
• @RobJeffries So we haven't find the force carrier, but we can't say that it doesn't exist, right? – alst Mar 20 at 9:37
• @alst there is no need for one, since exchange interactions (as they are called) can be understood without appealing to a force. – Rob Jeffries Mar 20 at 9:40
• @alst We can say that since it is not a force, there is no carrier. Correlations are not forces, they are different objects. – GiorgioP Mar 20 at 9:41

The effect you drafted exists in reality. For a gas of electrons, effects of quantum theory are noticeable. In simple terms, it is forbidden to have two electrons (or other particles) in the same place - as you mentioned. Any attempt to bunch electrons together in a small volume causes a pressure, the degenerating pressure. If you take only two particles, you get a force instead. This degeneracy pressure of the electron gas prevents a white dwarf star from collapsing further.

• This is a misleading answer. The PEP forbids occupation of the same phase space. Fermions can be squeezed arbitrarily close together (as long as they are pointlike and non-interacting). – Rob Jeffries Mar 20 at 9:23