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There can be never two fermions in exactly the same state, which is known as Pauli’s exclusion principle, but infinitely many bosons.

I read in the book saying that if Pauli's exclusion principle does not exist (that means not valid), matter will not exist. But I don't get that point why? Can someone explain this fact?

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  • $\begingroup$ Related/possible duplicates physics.stackexchange.com/q/1077/50583, physics.stackexchange.com/q/121522/50583 $\endgroup$ – ACuriousMind Oct 23 '20 at 15:09
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    $\begingroup$ Does this answer your question? Pauli's Exclusion Principle $\endgroup$ – John Rennie Oct 23 '20 at 15:15
  • $\begingroup$ I already get my answers from @Dr JH. $\endgroup$ – Young Kindaichi Oct 23 '20 at 15:57
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    $\begingroup$ Voting to reopen. I like questions like this because they often lead to a better understanding of connectivity between different physical phenomena and mechanisms. $\endgroup$ – ProfRob Oct 24 '20 at 8:15
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    $\begingroup$ I agree with Rob J. This isn't non-mainstream, it's attempting to understand the implications of the Pauli exclusion principle. $\endgroup$ – PM 2Ring Oct 24 '20 at 14:34
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The simplest form of this principle states that two (or more) electrons (fermions, spin $\frac{1}{2}$ particles) cannot occupy the same quantum state in an atom. If an arbitrary amount of electrons could occupy say the first energy level in an atom, then all of these atom's higher energy level electrons would also fit into this state. Matter would collapse into a much smaller volume*.

Another consequence would be that, like for bosons, any number of fermions could occupy the same quantum state for any system. So everywhere, all systems that once had restricted particle number due to the Pauli exclusion principle, would allow for unlimited particle numbers in the same state. Stars, planets, everything will begin to collapse.

“Infinite" numbers of particles throughout space will begin to combine into the same state at which point there would be many points or regions with energy density approaching infinity. Eventually regions everywhere would collapse into black holes as explained in the general theory of relativity.

For more about infinite bosons (photons) in a finite region, see this post here.

Virtually “infinitely” many regions of space will have these black holes and these black holes everywhere may begin to merge and eventually the universe itself would collapse into an infinitely dense singularity. I think that is what is meant by in that book stating matter would not exist.

  • It is important to note that physicists considered repulsive forces between electrons and between nuclei and attractive forces between the nucleus and electrons and showed that matter will still collapse into a smaller volume if the Pauli exclusion principle did not hold.
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    $\begingroup$ Why would stars collapse? Yes, they would at the ends of their lives, rather than forming white dwarfs and neutron stars. $\endgroup$ – ProfRob Oct 23 '20 at 8:20
  • $\begingroup$ They’d collapse for the reasons explained above. Note that when a black hole forms the exclusion principle is violated (as is all of quantum physics) due to gravitational collapse. The exclusion principle is what keeps stars from collapsing but if you remove this principle a similar thing will happen but because of a different reason. $\endgroup$ – joseph h Oct 23 '20 at 8:36
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    $\begingroup$ @Drjh: Average stars like the Sun don't rely on electron degeneracy pressure to keep from collapsing; they rely on the energy generated from fusion reactions to maintain sufficient temperature (and therefore pressure) to maintain equilibrium. It's only once their fusion fuel "runs out" (roughly speaking) that electron degeneracy becomes important. $\endgroup$ – Michael Seifert Oct 23 '20 at 12:01
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    $\begingroup$ The exclusion principle is not what keeps stars like the Sun collapsing. The formation of a black hole does not violate the exclusion principle. $\endgroup$ – ProfRob Oct 24 '20 at 8:12
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Also, there would be no chemistry. All electrons would just be in the lowest orbitals around nuclei.

As already mentioned, there would be no Fermi gas; not in stars, not in metals.

Atomic nuclei would also be totally different: no even-odd alternation in binding energies, no magic numbers.

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You would die, and you would have Fermionic condensate, which is pretty cool. Also some stars will collapse. Guess quantum computers will be harder to make, and you won't even have a computer to begin with. It would truly be a sad universe, imagine all the HBOs you'd miss.

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I like Dr jh’s answer:

The simplest form of this principle states that two (or more) electrons (fermions, spin 1/2 particles) cannot occupy the same quantum state in an atom.

This is what Pauli (1925) found. One year earlier - in 1924 - repeated examination of the emission spectrum of alkali metals showed that electrons should have a two-valuedness. This was - suggested by Ralph Kronig - as a consequence of the self-rotation of the electron. Indeed, the experiments were carried out with strong external magnetic fields and showed a hyper-fine structure of electron emission with pairs of emission lines.

The explanation was given in the following cause-effect sequence: All particles with charge and angular momentum have a magnetic dipole moment (like a tiny bar magnet).Now imagine - just for the moment you follow these explanations - that the cause-effect sequence would have been different: Charges not only have an intrinsic (permanent) electric field, but also an intrinsic magnetic field by nature.

The pairs of emission lines are the result of the emission from electrons with identical quantum states but opposite orientation of their magnetic dipoles. Full periods in the table of elements are 2 and 8 and 8 (never an odd number). 2 and 8 bar magnets can be arranged in perfect equilibrium around a nucleus.

Now imagine - just for the moment you follow these explanations - that the cause-effect sequence would have been different: Charges not only have an intrinsic (permanent) electric field, but also an intrinsic magnetic field by nature. The pairs of emission lines are the result of the emission from electrons with identical quantum states but opposite orientation of their magnetic dipoles.

Full periods in the table of elements are 2 and 8 and 8 (never an odd number). 2- and 8-bar magnets can be arranged in perfect equilibrium around a nucleus.And the deflection of moving electrons in an external magnetic field is also the result of magnetic interactions (together with the photon emission that occurs during sideways acceleration).

To your question in another formulation: What would happen if electrons did not have a magnetic dipole?:

  • First at all technical electric currents will not exist. Remember, that a generator is based on magnetic windings and in fact the current is the result of the deflection of electrons in their interaction with external magnetic fields.
  • Snow flakes will not have their perfect symmetries
  • Lat not least molecules will have another shapes respectively will be less stable. And methane CH4 is the best example for 8 electrons in an perfect spatial symmetry.

Anyway the question is highly speculative because (with or without the found by Pauli principle; with magnetic dipole moment as the primary or highly rotating electrons), the world is as it is.

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    $\begingroup$ Electrons in a circuit interact with the magnetic field because of their charge, not their dipole moment. I don't remember the electron's dipole moment coming up once in any of the EE classes I took. $\endgroup$ – eyeballfrog Oct 23 '20 at 20:38

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