Black holes and the Chandrasekhar limit

[Nenad]

I had a question, I was reading Stephen Hawhings book on the universe and black holes. I came on to a segment which I could not understand. In the book, it says that when a star runs out of its fuel and starts collapsing: "the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities. This makes them move away from each other and therefore makes the star expand"

I don't understand why the difference in velocities of particles would make then repell each other.

 

[Parth Dave]

Can someone let me know why "the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities" that is true. Pauli's exclusion principle doesn't say anything about the velocity of particles. Maybe that should say Heisenberg uncertainty principle?

 

[selfAdjoint]

Can someone let me know why "the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities" that is true. Pauli's exclusion principle doesn't say anything about the velocity of particles. Maybe that should say Heisenberg uncertainty principle?

Velocity here is a pop sci stand-in for momentum. Momentum is part of the state of the particles, and since the exclusion principle says no two fermions can be in the same state, if all the other observables were equal the momenta would have to be different.

 

[Labguy]

Velocity here is a pop sci stand-in for momentum. Momentum is part of the state of the particles, and since the exclusion principle says no two fermions can be in the same state, if all the other observables were equal the momenta would have to be different.

Stolen quote from an otherwise worthless web site.

Paulis exclusion principal says that 2 fermions(matter particles) can't be at the same place at the same time. When a particle from the fermion family gets cornered, like if you where to trap it in an ever shrinking box(the box is made up by Fermions so the particle and the particles making up the box can't be at the same place at the same time), it would start to move fast and in an unpredictable fashion. This is because the wave length(which corresponds to the energy of the particle, the lower wave length the higher energy and higher energy corresponds to faster motion) has to be a whole number of waves between the two walls of the box(meaning that it can't have a 2.2, 3.3 wave waves, only 2, 3 e.t.c), and when the box shrinks the wave length also has to shrink and the particle gets a higher energy. The pressure form this motion in confined space is called degeneracy pressure. The same thing is true for the core of a star. If the star starts to shrink because of the gravitational pressure, the particles inside it will react similar to the particles in a shrinking box and start to move around furiously thereby creating a degeneracy pressure which can actually hold the star up from collapsing under its gravitational pressure.

This part: "2 fermions(matter particles) can't be at the same place at the same time." ain't exactly the whole truth since the exclusion principal includes four different quantum states that are exclusive in any given atom. These are: Energy Level (n), Angular momentum (l), Magnetic quantum Number (M₁) and Spin (M_s). Some particles (usually electrons here) can have the same spin or other property but no two can have equality in all four states. Again, this is in one, single atom only.

EDIT:
I meant to quote the original poster, not selfAdjoint. However, the atoms under pressure don't have to have different energy / momentum from each other, it is just that the whole conglomerate of atoms will have increased energy = degeneracy pressure.

 

[Nenad]

Thanx guys. That clears up a lot of things.