I get your point about classical gas pressure being just microscopic particle momentum exchange with the wall. And the particles never actually touch the wall, they are are repelled by the EM force.Higgsy wrote:I'm not sure I would look at it like this. Let's start by considering the pressure in a classical gas. Ask yourself which of the three or four (depending on whether you include gravity) fundamental forces is responsible for the pressure? In statistical mechanics, the pressure is derived by the statistics of the particle momentum distributions, and in calculating the equilibrium condition for a main sequence star, none of the fundamental forces is required to derive the balancing condition against the influence of gravity - it all comes from the Maxwellian distribution of the gas particle momenta.querious wrote:

Looks like, quantitatively, the PEP comes down to the HUP . . .

Now, this just moves the mystery to the HUP level, but I feel a little better now. It still doesn't explain why fermions can't occupy the same place, and thus are "pushed apart" by the HUP. But the PEP/HUP should be included on the list of fundamental forces! When looking at a white dwarf, you are literally seeing macroscopic evidence of the HUP! To some degree this is true with ordinary matter, (the filled electron shells), but mostly it is due to electrical repulsion among nuclei.

If you measure pressure by enclosing a classical gas in a closed volume and measuring the force exerted on a wall, then you are measuring the momentum condition of the gas, by the exchange of momentum between the gas particles and the wall, and that is mediated (mainly) by the electromagnetic force - but that doesn't mean that the pressure in a classical gasarises fromthe electromagnetic force.

In the case of a degenerate gas, the PEP forces particles into higher energy states when all low energy states are filled and therefore the particle momentum distribution is different from a classical gas (higher energy at low temperatures, even at absolute zero, and different statistics). If you could enclose a degenerate gas and measure the force it exerts on a wall, the mediating fundamental force would still be (mainly) electromagnetic. In that respect, a degenerate gas is no more mysterious than a classical gas. We don't ask why classical gas pressure isn't included in the fundamental forces, so why should we for a degenerate gas?

I am sure there are many textbooks that cover this, but the one on my shelf is R J Tayler, The stars: their structure and evolution, Cambridge University Press. He derives the equations of stellar structure in Chapter 3, discusses degenerate stars in Chapter 10, and derives the expressions for degenerate pressure in Appendix 3.

But, what is the actual mechanism that degenerate fermions use to avoid each other?

I found an interesting slide show on PEP... http://www.tcm.phy.cam.ac.uk/~mdt26/PWT ... _pauli.pdf

...but I confess to not understanding most of the equations in it.