Are All Electrons Created Equal? The Implications of Quantum Field Theory

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Discussion Overview

The discussion revolves around the nature of electrons in quantum mechanics, specifically whether all electrons are fundamentally identical or if variations could exist. Participants explore implications of quantum field theory, the concept of indistinguishability, and the consequences for quantum mechanics and particle interactions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question the assumption that electrons are identical, proposing hypothetical scenarios where differences in size, strength, or spin could affect quantum mechanics.
  • Others explain that the wave function of identical particles is anti-symmetrized due to their fermionic nature, leading to principles like the Pauli exclusion principle.
  • Wheeler's idea is mentioned, suggesting that electrons are literally the same.
  • The Gibbs paradox is referenced, highlighting the resolution that identical particles must be treated as indistinguishable in statistical mechanics.
  • Some participants assert that electrons cannot be distinguished from one another due to their identical physical characteristics.
  • Questions arise about whether the emitted electron is the same as the detected one, with some arguing that the question lacks meaning without context.
  • Discussions include the implications of measuring properties like momenta and the challenges posed by the definition of indistinguishability in experiments.
  • One participant suggests that while we may perceive an emitted electron as the same, the reality of quantum mechanics complicates this notion.

Areas of Agreement / Disagreement

Participants express a mix of agreement on the indistinguishability of electrons, while also raising questions and hypothetical scenarios that suggest uncertainty about the implications of this concept. The discussion remains unresolved regarding the nature of electrons and the meaning of their identity in various contexts.

Contextual Notes

Limitations include the dependence on definitions of indistinguishability and the unresolved nature of how to experimentally determine if two electrons are the same particle.

  • #31
Except... It might change the momentum?
 
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  • #32
Jilang said:
Except... It might change the momentum?

Except it must be conserved.
 
  • #33
craigi said:
Except it must be conserved.

Mmmm, doesn't the uncertainty in the momentum increase with time or am I getting that bit wrong?
 
  • #34
Jilang said:
Mmmm, doesn't the uncertainty in the momentum increase with time or am I getting that bit wrong?

Are you talking about the Heisenberg uncertainty principle?
 
  • #35
I'm talking about the diffusion type process described by the Schroedinger equation.
 
  • #36
doesn't the uncertainty in the momentum increase with time or am I getting that bit wrong?

Measurements always show a statistical distribution.
 
  • #37
Jilang said:
Do we know if the electron that is emitted is the same one that is detected?
This is a meaningless question for identical particles such as electrons.
 
  • #38
atyy said:
If they were not identical, this anti-symmetrization would not be required. This anti-symmetrization leads to things like the Pauli exclusion principle which has experimental consequences.

What do you think are the most striking experimental consequences?
 
  • #39
ddd123 said:
What do you think are the most striking experimental consequences?
Now that's an open-ended question :)
The Pauli exclusion principle is responsible for the behavior of electrons around the nucleus, and this in turn is responsible for just about all the behavior of matter: chemistry, solidity, density, ... Without the exclusion principle, EVERYTHING would be unimaginably different.
 
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  • #40
Are all electrons equal?

Yes, but some are more equal than others.

Quarks of England, quarks of Ireland,
Quarks of every land and clime,
Hearken to my joyful tidings
Of the Golden future time.
 
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  • #41
The idea of particles as these individual entities is superseded by quantum field theory, in the second quantization. It doesn't really make sense to think of two electrons as separate things, since they are both excitations of an underlying electron field. The only way for two electrons to have different properties is for there to be multiple different electron fields. In which case, we would not call them both electrons. For example, we call an electron-like object with higher mass a muon.

Bad analogy time: if I have two cents in my bank account, I can transfer them one at a time, but there's no way to distinguish one cent from the other cent since they are just numbers in a computer, not physical pennies.
 
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