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Re: Whence Degeneracy Pressure?



Robert Cohen wrote:

I don't have any expertise in the area but it seems like the answer is
"convention".

Well, the meaning of words (all words) is established by
convention. But the laws of physics are not established
by convention. Suppose we all decide that henceforth
pi=3 "by convention" ... that wouldn't make it true,
unless we rob pi of all useful meaning.

We have a fairly conventional understanding of what it
means to be a "fundamental force". We can play word
game à la Tweedledee and Tweedledum, and redefine what
it means to be a "fundamental" force, but I don't recommend
it. We could declare friction to be a "fundamental"
force. We could declare the Coriolis effect to be a
"fundamental" force. But I don't recommend it; it
would just rob the word of all useful meaning.

There are profound similarities between gravitation and
electrostatics, which are obvious even at the high-school
physics level. There are profound connections between
electrostatics, magnetism, and the weak interactions. And
there are profound similarities between the weak interaction
and the strong interaction.

The pressure in a degenerate does _not_ share this pattern
of similarities. Pressure in a degenerate gas is just
pressure, just like the pressure in a nondegenerate
gas, and I see _nothing_ about it that makes it "fundamental"
or even raises a serious question about whether it ought
to be considered "fundamental".

This reminds me of primitive religion: If we don't
understand it, blame it on God. The ancients didn't
know where lightning came from, so they invented a
god for it. They didn't understand celestial mechanics,
so they invented a god for each planet. And fertility
goddesses and all the rest.

So in this case the argument seems to be "degeneracy
pressure is a concept I've heard about but haven't
been able to explain in terms of high-school physics,
therefore it must be some really deep fundamental force".
That's not a very sophisticated argument.


I have two questions:

1. What force keeps a neutron star from collapsing?
Is the answer "nothing - it just isn't allowed to"?

The question assumes facts not in evidence.
It turns out that sometimes neutron stars _do_ collapse.

So let's try a modified question: Why don't neutron
stars collapse, except when they do? To give the
answer "They're not allowed to, except when they are"
wouldn't be very informative.

The answer, of course, can be found by doing a first-
order stability analysis. Principle of virtual work
and all that. Standard physics techniques. Same
procedure works for non-degenerate stars. Start with
a ball of gas (or neutrons) of size X and see what
happens to the energy when the size is decrease to
X minus dX. If the energy goes up, pressure is dominant
and the star is stable. If the energy goes down,
gravity dominates, and you might not want to be too
near that star for a while.....

The only slightly tricky bit is to realize that a
gas of fermions (e.g. neutrons) at high density and
low temperature will have a higher pressure than a
19th-century physicist would have predicted, but
there is _nothing_ about this that deviates from
what we would expect based on the conventional list
of fundamental forces, and therefore _nothing_ that
would motivate lengthening the list.

2. What makes gravity reflective of a force but degeneracy pressure not
reflective of a force?

The gravitational field is a force per unit mass.
Pressure is also a field. Dimensionally it is
a force per unit area, or (equivalently) an energy
per unit volume. The question is not whether there's
a force due to pressure; the question is whether it's
fundamental. It's not. It's a simple, direct consequence
of the known fundamental laws.

Skin-friction drag on an airplane is also a force.
No doubt about it. But it's not fundamental. It's
a simple, direct consequence of the known fundamental
laws. Why would anybody think otherwise?

Does it have something to do with gravity being
attractive?

No. Why do you ask? What is the motivation for
such a hypothesis?

People seem to have this idée fixe that pressure
in a degenerate gas is somehow different from
pressure in any other gas. Why?

Just because something is unfamiliar doesn't make
it fundamentally new. If I hear an unfamiliar noise
outside my window, I don't assume it's space aliens
arriving in their UFOs. Until I have reason to
believe otherwise, I will assume it is just some
new combination of ordinary phenomena.