# What Causes Degeneracy Pressure?

• loom91
In my opinion, it is more accurate to say that degeneracy pressure is a result of the fundamental principle of the Pauli exclusion principle. Essentially, the fermions are trying to occupy the same state, but cannot due to this principle, so they exert a pressure to resist compression.
loom91
I was wondering something, a collection of fermions can resist compressing forces due to what is termed degeneracy pressure. I was wondering, which of the four fundamental interactions is this due to? Thanks.

Molu

To my knowledge, this is due to the Pauli exclusion principle, and not to force interaction between the electrons.

as gendou2 said it's to do with Pauli exclusion, since

$$\Delta{x}\Delta{p}\geq\frac{\hbar}{2}$$

when a material is compressed (such as the interior of a star under the effect of gravity) the uncertainty in x gets smaller, leading to less uncertainty in momentum. The fermions are called degenerate when the pressure due to this momentum equals or exceeds(?) the pressure due to the fermions thermal motion. So in a sense it's due to whatever of the fundamental forces is causing the compression, mainly gravity in a stellar core - which is what this problem is usually used for I think, although I'm sure it must be quite important in studying fusion.

jbunten said:
as gendou2 said it's to do with Pauli exclusion, since

$$\Delta{x}\Delta{p}\geq\frac{\hbar}{2}$$

when a material is compressed (such as the interior of a star under the effect of gravity) the uncertainty in x gets smaller, leading to less uncertainty in momentum. The fermions are called degenerate when the pressure due to this momentum equals or exceeds(?) the pressure due to the fermions thermal motion. So in a sense it's due to whatever of the fundamental forces is causing the compression, mainly gravity in a stellar core - which is what this problem is usually used for I think, although I'm sure it must be quite important in studying fusion.

I understand that it's due to Pauli's exclusion principle. But how does that fit in with the Standard Model, where all forces can be classified as due to one of the four fundamental interactions? I mean, if a star is resisting a compressive force, that means an opposite force is acting. To which interaction can we attribute that force?

Molu

The 'force' is called 'degeneracy pressure'. As you probably know the fermions are excluded from occupying the same state, so they need a fixed number of states to exist in. As the star contracts the energy gap between those states increases, so the energy of the fermion population has to grow. And that increase is just due to the shrinking geometry they are confined to (as in the square well). So even if you could find a type of fermion that experienced no standard model interactions whatsoever and managed to confine them somehow, they would still exert this same 'pressure'.

loom91 said:
I was wondering something, a collection of fermions can resist compressing forces due to what is termed degeneracy pressure. I was wondering, which of the four fundamental interactions is this due to? Thanks.

Molu

The actual pressure is due to the usual forces of the Standard Model (In actuality, it will be mostly the electromagnetic force). If you put the fermions in a container at near zero temperature and you compress the container, the actual pressure exerted by the fermions on the box is simply the electromagnetic force between the fermions and the particles in the box. The reason resist compression is the degeneracy pressure but the actual force they exter on the container is electromagnetic (electric for the most part).

It's not much different from heat pressure. The pressure is due to thermal agitation but thermal agitation is not a force. The actual pressure is due to the "collision" between the particles in the box and the container. But the collision occurs because of the electromagnetic force between the particles.

At least, that's the way I think about it.

You may think about it that way, but I don't think that's correct. Neutral fermions (like neutrinos) would exhibit the same degeneracy pressure. Are you going to say that's because of the weak force? Really, there is no interaction term necessary to compute it. You are right in that you need a force to confine them to begin with, but in this case that's gravity. And degeneracy pressure opposes gravity.

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So the degeneracy pressure is to be considered a characteristic of the interaction that is causing the compression?

Molu

As it is independent of the nature of the force causing the compression, I'd have a hard time think of it like that.

## 1. What is degeneracy pressure?

Degeneracy pressure is a quantum mechanical effect that arises in a system of particles, such as atoms, when they are packed tightly together. This pressure prevents the particles from collapsing under their own gravity.

## 2. How does degeneracy pressure differ from thermal pressure?

Thermal pressure is a result of the motion and collisions of particles, while degeneracy pressure is caused by the quantum mechanical properties of particles. Thermal pressure increases with temperature, while degeneracy pressure remains constant regardless of temperature.

## 3. What are the different types of degeneracy pressure?

There are two main types of degeneracy pressure: electron degeneracy pressure and neutron degeneracy pressure. Electron degeneracy pressure occurs in systems where electrons are closely packed together, such as in white dwarfs. Neutron degeneracy pressure occurs in systems where neutrons are tightly packed together, such as in neutron stars.

## 4. What is the significance of degeneracy pressure in astrophysics?

Degeneracy pressure plays a crucial role in the formation and structure of stars. It is responsible for preventing the collapse of stars and maintaining their stability. It also determines the maximum mass that a white dwarf or neutron star can have.

## 5. Can degeneracy pressure be overcome?

Yes, degeneracy pressure can be overcome by increasing the temperature and density of a system beyond a certain point. This can lead to collapse and the formation of a black hole, where the gravity is strong enough to overcome the degeneracy pressure of even the most extreme systems.

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