Pauli Exclusion Principle in Black Holes.

[CarlosLara]

Good evening. I have been reading that the repulsion generated by the Pauli exclusion principle barely prevents neutrons in neutron stars from occupying the same quantum states (after all, they are fermions). However, the principle seems to be violated in a black hole, given that fermions are compressed to the point where everything is in the same place (the singularity). For example, what happens to a proton as it approaches the singularity? I am wondering if the exclusion principle is violated in black holes. The alternative would be that at some point, matter gets turned back into energy (given that matter and energy are equivalent, it seems plausible); the Pauli exclusion principle would no longer apply because the fermions would have turned into energy, thus the principle would not be violated. What are your thoughts on this?

Thank you in advance.

 

[chill_factor]

everything is energy (and particles). every particle obeys either bose-einstein or fermi-dirac statistics. i think you mean that it turns into a boson.

 

[Chronos]

It is not known if another barrier exists past the neutron degeneracy limit. Some scientists suspect there is also a quark degenercy limit. A black hole may represent a special case bounded only by Planck scale physics.

 

[Drakkith]

However, the principle seems to be violated in a black hole, given that fermions are compressed to the point where everything is in the same place (the singularity).

It is unknown what happens behind the event horizon of a black hole. Given that our knowledge of such objects is missing key components, it is possible that there is no singularity and something else happens instead.

For example, what happens to a proton as it approaches the singularity? I am wondering if the exclusion principle is violated in black holes.

Well, consider the neutron star. Before it was a neutron star it was a normal stellar core composed of nickel and iron and such. During the supernova process the core collapses as the electrons combine with protons to form neutrons. Perhaps the neutrons all combine into a quark fluid or something more exotic. Our knowledge of physics at these kinds of pressures and densities is extremely limited.

The alternative would be that at some point, matter gets turned back into energy (given that matter and energy are equivalent, it seems plausible); the Pauli exclusion principle would no longer apply because the fermions would have turned into energy, thus the principle would not be violated. What are your thoughts on this?

Thank you in advance.

Matter and energy are not equivalent. The equation e=mc^2 merely tells us that energy and mass are related. Moving mass around requires energy and energy moves mass around.

 

[Chimps]

There is no violation.

Time dilation, as predicted by Einstein's theory of general relativity, has prevented any such violation from occurring.

 

[Drakkith]

There is no violation.

Time dilation, as predicted by Einstein's theory of general relativity, has prevented any such violation from occurring.

Maybe. I have heard that from the frame of infalling objects that they cross the event horizon and continue on in finite time, even while the rest of the universe evolves around them. But I feel we need more information on black holes to really say anything.

 

[Chimps]

Maybe. I have heard that from the frame of infalling objects that they cross the event horizon and continue on in finite time, even while the rest of the universe evolves around them. But I feel we need more information on black holes to really say anything.

The frame of infalling objects must become irrelevant. All infalling objects do so from a finite reference.

 

[castro94]

how can electrons and protons combine to form a neutron ?
when beta minus decay occurs then a neutron interacts with a w-boson which has the ability to change the quarks " flavor" , making the neutron`s two down quarks to two up quarks and the one up quark to a down quark, and then the W boson "deacays" to an electron and an antineutrino , how can this go the other way around ?

 

[Steely Dan]

how can electrons and protons combine to form a neutron ?
when beta minus decay occurs then a neutron interacts with a w-boson which has the ability to change the quarks " flavor" , making the neutron`s two down quarks to two up quarks and the one up quark to a down quark, and then the W boson "deacays" to an electron and an antineutrino , how can this go the other way around ?

You are correct, $n \rightarrow p + e + \bar{\nu}$ is beta decay, so $p + e \rightarrow n + \nu$ is inverse beta decay (I have neglected the neutrinos here), or electron capture. You can think of this, if you want, as

$$u \rightarrow d + W^+$$

where the $W^+$ and electron can then "decay" into the neutrino. Clearly the up -> down decay is not energetically favored and therefore normally suppressed, but if your electron, say, has a lot of kinetic energy then that can be used up.

 

[lpetrich]

The Pauli exclusion principle is not violated. Instead, the material's mass density increases and increases and increases.

To a first approximation, that principle states that there is only one particle inside a box with its size being the particle's de Broglie wavelength. Strictly speaking, there are as many as there are spin states, but electrons and nucleons both have 2 spin states. A particle's de Broglie wavelength is related to its momentum by wl = h/p.

 

[castro94]

$$u \rightarrow d + W^+$$

where the $W^+$ and electron can then "decay" into the neutrino. Clearly the up -> down decay is not energetically favored and therefore normally suppressed, but if your electron, say, has a lot of kinetic energy then that can be used up.

but the w boson is supposed to have a mass 100 times greater than the proton ? , how can this amount of mass be created , is this why the electron needs to have a lot of kinectic energy ?
and how can the change of the "flavor" of the quark occur ? do you need to have a w boson to do so to begin with ?

 

[twofish-quant]

However, the principle seems to be violated in a black hole, given that fermions are compressed to the point where everything is in the same place (the singularity).

The rule for Pauli is that no two fermions can be at the same energy state.

What happens as you increase gravitational force is that the number of energy states increases so that the degeneracy is lifted.

The alternative would be that at some point, matter gets turned back into energy (given that matter and energy are equivalent, it seems plausible); the Pauli exclusion principle would no longer apply because the fermions would have turned into energy, thus the principle would not be violated. What are your thoughts on this?

The difference is not "matter" and "energy". It's "fermion" and "boson".