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Are all electrons equal?

  1. Nov 11, 2013 #1
    Were electrons to be slightly different sizes, or have different strengths, or slightly different spin moments, then what effect might this have on the fundamentals of quantum mechanics? So fart, we "assume" an electron has certain characteristics, but are they all the same??
     
  2. jcsd
  3. Nov 11, 2013 #2

    atyy

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    For a system of identical particles, the wave function is symmetrized or anti-symmetrized. Because electrons are fermions, their wave function is anti-symmetrized. 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.

    http://farside.ph.utexas.edu/teaching/qmech/lectures/node59.html
    http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html
    http://chemwiki.ucdavis.edu/Inorganic_Chemistry/Electronic_Configurations/Pauli_Exclusion_Principle
     
  4. Nov 11, 2013 #3

    kith

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    There's also Wheeler's idea that they are literally the same. ;-)
     
  5. Nov 11, 2013 #4
    You might also be interested in reading about the Gibbs paradox. That's a paradox that appears in the calculation of the entropy of a system within classical statistical mechanics. This paradox is resolved by assuming that identical particles are exactly identical, to the point that if you interchange two of them you get exactly the same physical state. That has important measurable consequences.
     
  6. Nov 11, 2013 #5

    Meir Achuz

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    They are all identical.
     
  7. Nov 15, 2013 #6
    According to the modern physics, system of electrons as well as other particles are an identical system. It means that we cannot distinguish electrons in the system because they have the same physical characteristics
     
  8. Nov 15, 2013 #7
    Do we know if the electron that is emitted is the same one that is detected?
     
  9. Nov 15, 2013 #8
    It's hard to answer a general question without a context :smile:. Emitted from what? Detected how? Anyway, there are cloud chambers, and other detection technologies.
     
  10. Nov 15, 2013 #9

    OCR

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    Here's some context... :smile:

    https://en.wikipedia.org/wiki/Electron#Quantum_properties

    https://en.wikipedia.org/wiki/Identical_particles#Distinguishing_between_particles

    So...


    OCR
     
  11. Nov 15, 2013 #10
    OCR, is your post above a reply to Jilang, a reply to me, an interpretation of what Jilang meant or a completely new question? With all respect, I do not understand your post :wink:.
     
  12. Nov 15, 2013 #11

    TumblingDice

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    Posts 4, 5, and 6 have something in common. They all use the word 'identical', explaining one cannot be distinguished from another. My interpretation of OCR's post was to logically substantiate the earlier responses, and maybe subtle sarcasm around why the question didn't require context? As in, "What part of 'identical' don't you understand?" :)

    I could be wrong, that's how I read it...
     
    Last edited: Nov 15, 2013
  13. Nov 15, 2013 #12
    Ok, thanks. If so, no problem - then it was probably me who did not understand the context :smile:.
     
  14. Nov 16, 2013 #13

    Meir Achuz

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    If electrons were not all the same, there would be no atoms as we know them.
     
  15. Nov 16, 2013 #14
    I could have phrased by question better. I understand they are indistinguishable on exchange, but If one electron is emitted and one electron is detected is it the same particle?
     
  16. Nov 16, 2013 #15

    Vanadium 50

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    If they are identical, what experiment could you possibly do to tell if they were the same particle or not?
     
  17. Nov 17, 2013 #16
    Could you measure the momenta and see if they were the same?
     
  18. Nov 17, 2013 #17

    OCR

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    That's exactly how it was meant...

    Lol... although, I wasn't really attempting to be sarcastic...

    I can, however, understand how that might be construed, but...

    It was merely an unintended consequence, that happened to lead to an emergent property... :cool:


    So, in summation...

    You aren't... :approve:



    OCR
     
  19. Nov 17, 2013 #18

    OCR

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    It would seem not...

    www.cond-mat.de/events/correl13/manuscripts/koch.pdf




    OCR
     
  20. Nov 17, 2013 #19
    I think at the fundamental level, this is actually turns out to be a meaningless question. Though we'd often percieve that it is the same one to help us visualise what's going on.

    Conceptually, if a closed system contains only one electron and nothing else and we ignore decay and spontaneous particle creation, then we would call it the same electron. In reality there is no such condition, though the probabiltiy of finding an electron can often be very predicticable along a path. We would still call this the same electron.

    If we have 2 electrons in a closed system, the wave function is combined and non-zero everywhere. They are indistinguishable and no process can give us perfect certainty which is found at a certain location. However, in many arrangements the probabilties will be such that we can meaningfully talk about which is which.

    We get into interpretational issues when we talk about the location of an electron between measurements. Many interpretations assign no meaning to ascribing a position to a particle between measurements, however, some do. I'd be interested in understanding what their take on the Pauli exclusion principle is.

    Perhaps a fair analogy would be, if you created a surface wave in a lake and watched as it interacted with the other surface waves, under what conditions would you say that a point on the surface is or isn't your wave?
     
    Last edited: Nov 17, 2013
  21. Nov 17, 2013 #20

    Vanadium 50

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    To tell if they are the same particle is to distinguish. Indistinguishable means "not able to be distinguished". So this question can be restarted "Can you distinguish particles that cannot be distinguished?" The answer is no.
     
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