Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Gold Member

    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


    User Avatar
    Gold Member

    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


    User Avatar
    Gold Member

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


    User Avatar
    Science Advisor

    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


    User Avatar
    2017 Award

    Staff: Mentor

    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).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook