- #1

LostConjugate

- 850

- 3

How is this physically logical?

If one electron on Earth gains some momentum, some other electron in another galaxy must change it's momentum?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

In summary: So the principle would not allow you to predict which electron in another galaxy has gained momentum.

- #1

LostConjugate

- 850

- 3

How is this physically logical?

If one electron on Earth gains some momentum, some other electron in another galaxy must change it's momentum?

Physics news on Phys.org

- #2

SpectraCat

Science Advisor

- 1,402

- 3

LostConjugate said:

How is this physically logical?

If one electron on Earth gains some momentum, some other electron in another galaxy must change it's momentum?

I think the key point is that the Pauli exclusion principle is only concerned with electrons that are part of the same coherent wavefunction. In other words, if you have two H-atoms, A & B, separated by a distance of 1 meter, they can effectively be considered to have separate and independent wavefunctions. So it is no problem if the 1s electron in atom A has precisely the same quantum numbers as the 1s electron in atom B. However, if we move the two atoms close enough together so they start to interact, all of that changes. The interaction splits the energy levels that were degenerate at large distance, and you have to talk about the overall wavefunction of the system, and now the Pauli exclusion principle applies to the molecular states.

If you want to get into the more philosophical aspects of this, I think the answers probably lie in decoherence. The reason that two widely separated H-atoms can be considered as independent systems is that, even if they start out as part of the same system, as the separation between them increases, the amount of energy it takes to perturb the system and induce decoherence decreases until it is negligibly small. At that point, even vacuum fluctuations can break the coherence of the two-atom state. One that happens, the two atoms are independent systems and the PEP is no longer relevant.

- #3

LostConjugate

- 850

- 3

SpectraCat said:I think the key point is that the Pauli exclusion principle is only concerned with electrons that are part of the same coherent wavefunction. In other words, if you have two H-atoms, A & B, separated by a distance of 1 meter, they can effectively be considered to have separate and independent wavefunctions. So it is no problem if the 1s electron in atom A has precisely the same quantum numbers as the 1s electron in atom B. However, if we move the two atoms close enough together so they start to interact, all of that changes. The interaction splits the energy levels that were degenerate at large distance, and you have to talk about the overall wavefunction of the system, and now the Pauli exclusion principle applies to the molecular states.

If you want to get into the more philosophical aspects of this, I think the answers probably lie in decoherence. The reason that two widely separated H-atoms can be considered as independent systems is that, even if they start out as part of the same system, as the separation between them increases, the amount of energy it takes to perturb the system and induce decoherence decreases until it is negligibly small. At that point, even vacuum fluctuations can break the coherence of the two-atom state. One that happens, the two atoms are independent systems and the PEP is no longer relevant.

Point noted. Although the electrostatic force never reaches 0 over any distance. So in all fact, nothing is isolated by distance, there is still a contribution from the protons and electrons to the Hamiltonian. A single state can be constructed.

- #4

SpectraCat

Science Advisor

- 1,402

- 3

LostConjugate said:Point noted. Although the electrostatic force never reaches 0 over any distance. So in all fact, nothing is isolated by distance, there is still a contribution from the protons and electrons to the Hamiltonian. A single state can be constructed.

The state can be constructed, you are correct .. however see my point about decoherence.

- #5

Vanadium 50

Staff Emeritus

Science Advisor

Education Advisor

2023 Award

- 34,518

- 21,272

LostConjugate said:the Pauli Exclusion principle also concludes that no state exists with more than two electrons having the same momentum. Even the state of the entire universe.

This is not true.

Tha Pauli exclusion principle says that no two electrons can share (all) the exact same quantum numbers. This is a consequence of the spin-statistics theorem, which states that swapping any two electrons will cause the wavefunction to change sign.

- #6

matonski

- 166

- 0

LostConjugate said:If one electron on Earth gains some momentum, some other electron in another galaxy must change it's momentum?

By the uncertainty principle, if you know the momentum of an electron exactly, then you can't simultaneously say that its on earth.

On the other hand, if you know that one electron is on Earth and one electron is in another galaxy, then they are obviously in different states.

- #7

LostConjugate

- 850

- 3

Vanadium 50 said:This is not true.

Tha Pauli exclusion principle says that no two electrons can share (all) the exact same quantum numbers. This is a consequence of the spin-statistics theorem, which states that swapping any two electrons will cause the wavefunction to change sign.

If you put 2 electrons in a state, both with the same spin [polarity] and momentum, the wave equation is symmetric, therefore cannot exist in nature.

There is no other option than to have one electron spin up and one spin down which leaves no room for any other electrons.

That is profound!matonski said:By the uncertainty principle, if you know the momentum of an electron exactly, then you can't simultaneously say that its on earth.

On the other hand, if you know that one electron is on Earth and one electron is in another galaxy, then they are obviously in different states.

- #8

Vanadium 50

Staff Emeritus

Science Advisor

Education Advisor

2023 Award

- 34,518

- 21,272

LostConjugate said:If you put 2 electrons in a state, both with the same spin [polarity] and momentum, the wave equation is symmetric, therefore cannot exist in nature.

No, that's false. Position matters as well.

- #9

LostConjugate

- 850

- 3

Plug any position in you would like for x_1 and x_2, the equation is still symmetric.Vanadium 50 said:No, that's false. Position matters as well.

[tex] e^(\frac{ipx_1}{\hbar})e^(\frac{ipx_2}{\hbar})X_+X_+ [\tex]

- #10

matonski

- 166

- 0

I don't know if you are being sarcastic, but I do think this answers the question. If you know one electron is on Earth and the other electron is in another galaxy, then their position-space wavefunctions are obviously different. Therefore, their Fourier transforms (aka momentum-space wavefunctions) will also be different.LostConjugate said:That is profound!

- #11

LostConjugate

- 850

- 3

matonski said:I don't know if you are being sarcastic, but I do think this answers the question. If you know one electron is on Earth and the other electron is in another galaxy, then their position-space wavefunctions are obviously different. Therefore, their Fourier transforms (aka momentum-space wavefunctions) will also be different.

Opps I did not mean to sound sarcastic, what I mean't was that it was a great answer and made me think. I don't think it disproves that no more than two electrons can have the same momentum in the entire universe though.

- #12

matonski

- 166

- 0

- #13

LostConjugate

- 850

- 3

matonski said:

Another good point.

According to the Pauli exclusion principle, no two electrons can have the same set of quantum numbers, which includes momentum. This is due to the fact that electrons are fermions, particles that follow the Fermi-Dirac statistics and are subject to the exclusion principle.

Yes, the Pauli exclusion principle states that no more than two electrons can have the same momentum. This is a fundamental principle in quantum mechanics and has been experimentally verified.

If more than two electrons were to have the same momentum, it would violate the Pauli exclusion principle and the laws of quantum mechanics. This would not be observed in nature.

The Pauli exclusion principle applies to all fermions, including protons, neutrons, and other subatomic particles. It is a fundamental principle in quantum mechanics that governs the behavior of particles with half-integer spin.

Yes, the momentum of an electron can be changed through various interactions, such as collisions or interactions with electromagnetic fields. However, the Pauli exclusion principle still applies, and the electron's new momentum must be different from any other electron's momentum in the universe.

- Replies
- 19

- Views
- 919

- Replies
- 2

- Views
- 1K

- Replies
- 3

- Views
- 854

- Replies
- 10

- Views
- 2K

- Replies
- 17

- Views
- 2K

- Replies
- 1

- Views
- 1K

- Replies
- 3

- Views
- 2K

- Replies
- 3

- Views
- 1K

- Replies
- 12

- Views
- 1K

- Replies
- 4

- Views
- 896

Share: