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Spin and the violation of the speed of light

  1. Aug 19, 2012 #1
    this is from Omnes' book Understanding QM

    Has this problem been resolved or is it still outstanding?
     
  2. jcsd
  3. Aug 19, 2012 #2

    CAF123

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    The spin of an electron is not meant in the literal sense (ie like some sort of spinning top or rotating sphere). Instead, it is a vector quantity and we define a spin quantum number.

    I believe a sort of rough calculation goes as follows:
    [tex] \tau = \frac{dL}{dt} = Iα [/tex]
    If we define [itex] L = m_l\hbar = \frac{\hbar}{2}[/itex] and [itex] I = \frac{2}{5}mr^2, [/itex] an electron as a solid sphere with [itex] r ≈ fm[/itex]

    Then, [tex] L = Iω = \frac{Iv}{r} => v = \frac{Lr}{I} = \frac{5Lr}{2mr^2}. [/tex]
    Simplifying and inputting known data gives v ≈ 1011 ms-1, which is 1000 times the speed of light.
     
  4. Aug 19, 2012 #3
    So in other words the problem of the violation of the speed of light has not been resolved, right?
     
  5. Aug 19, 2012 #4

    CAF123

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    The above calculation assumes that the electron is behaving like a rotating sphere and so it is meant to demonstrate why we should not think of spin as a classical concept here.
     
  6. Aug 19, 2012 #5
    well if the electron is not spinning then what is it doing?
     
  7. Aug 19, 2012 #6

    CAF123

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    Just to be a little clear on the question:
    What do you mean by 'what do they do?'
     
  8. Aug 19, 2012 #7

    Bill_K

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    The electron is observed to be pointlike, which means its size, if it has one, is smaller than we have so far been able to detect. (10-16 cm). As a particle, it has a number of properties: mass, charge and angular momentum. Angular momentum comes in two varieties: orbital angular momentum (r x p) and spin angular momentum. There is no motion associated with spin angular momentum, and so the electron does not rotate. The angular momentum it carries (ħ/2) is simply an intrinsic property.
     
  9. Aug 19, 2012 #8

    mfb

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    The model (small, rotating sphere) which produced this prediction was wrong. Therefore, it is not a problem any more.

    Spin is just another particle property, like its mass and charges (not just the electromagnetic charge).
     
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