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Do Electrons gain mass in an electrostatic potential?

  1. Aug 23, 2010 #1

    I have been looking into the phenomenon of Zitterbewegung which is a high frequency oscillatory motion of the electron that is predicted by the Dirac Equation for a free electron.

    One way of looking at this motion is that it is the interference of plane waves with positive and negative energies that appear to produce a fluctuation of the electron wavefunction at the speed of light with a frequency of w radians where w:

    w = 2 * m *c^2 / hbar (1)

    I was wondering if one could "model" the electron at rest as a massless particle that is travelling at the speed of light around a circular path.

    Let us assume that it's mass/energy is largely given by its rotational energy:

    Rotational energy = Angular momentum * angular velocity

    For an electron we know that the angular momentum = spin = hbar / 2

    If the total energy of the electron, m c^2, is its rotational energy we have:

    m * c^ 2 = hbar/2 * w


    w = 2 * m * c^2 / hbar, which is equation (1) above.

    Now if the mass of the electron is just the rotational energy of a massless particle going round in a loop, could we increase this rotational energy artificially and thus increase the rest mass of the electron?

    How about simply subjecting the electron at rest to a high electrostatic potential?

    I think this will increase the Zitterbewegung frequency and thus artificially increase the mass of the electron.

    If we could do this maybe we could change the mass of an electron orbiting a deuterium nucleus. If the electron was made 200 times heavier it would orbit the nucleus closer and would thus allow two deuterium atoms to get closer. Maybe we could initiate "cold fusion" this way as in the muonic fusion concept without the short-lived muons?

    Or maybe not? ;)
  2. jcsd
  3. Aug 24, 2010 #2


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    Apparently "looking into" means reading the first paragraph of the Wikipedia article. Because based on the rest of what you wrote, I don't believe you're studying relativistic QM.
    No. But I'll give you audacity points for trying to 'model' a relativistic effect by violating special relativity.
    Why? And why would it remain in a circular path for that matter? The equation for rotational energy is classical, but electrons in an atom don't move classically. Also, spin and angular momentum aren't the same thing.
    Ever heard of the Stark effect?
    On what grounds?

    I know I probably sound pretty harsh here, so here's some encouragement: It's good that you're interested and enthusiastic about physics. But you've got to learn to walk before you can run. Try to focus that energy and enthusiasm on learning the basics (even if you find them boring compared to advanced concepts), because it's the only way you're going to be able to do the advanced stuff eventually. Every physicist ever took that route. It works. But reading piecemeal bits on various advanced topics and cobbling together an ad-hoc 'model' doesn't work, and it isn't a good way to learn.
  4. Aug 24, 2010 #3

    Thanks very much for the response.

    You are absolutely right of course - I need to learn to walk before I can run. I find it hard to study on my own though. I need to find some like-minded amateur physics enthusiasts around Hampshire, England who want to study some basic quantum mechanics.

  5. Aug 24, 2010 #4
    The composite system of charged particles and the electromagnetic field will gain mass if its energy increases. It has not become clear to me where the mass increase happens precisely. It could be that this is related to the self-interaction problem.

    Actually I don't think, that a composite system of two massless particles bound together, would yet violate relativity.
  6. Aug 26, 2010 #5
    I've come across an experiment that claims to have measured a change of electron mass in a static electric potential:

    http://www.ensmp.fr/aflb/AFLB-264/aflb264p633.pdf [Broken]
    Last edited by a moderator: May 4, 2017
  7. Aug 26, 2010 #6


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    Staff: Mentor

    Frankly, I would be very skeptical of anything published in that journal (the Annales de la Fondation Louis de Broglie) that has not been followed up by other people, especially after nine years. It publishes a lot of "fringe" material that can't get published elsewhere.
  8. Aug 26, 2010 #7


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    Zitterbewegung is related to motion of free electron and not "motion" of electron in atom.

    About how a wave moving at speed of light can acquire inertia and can stop moving straight ahead is of course interesting question. But I will withhold any speculations from my side as I sense that this was devised as rhetorical question. :rolleyes:
  9. Sep 1, 2010 #8

    I asked a physics professor whether the Zitterbewegung frequency of the electron changes in the presence of a constant electrostatic potential.

    He said:

    Interesting question. I ran an undergraduate project on Zitterbewegung once, a long time ago. For a constant electrostatic potential the frequency does not change. The easiest way to see this is to note that a constant electrostatic potential maps a wavefunction to exp (-i V t/hbar) times the wavefunction. The extra phase factor drops out of expectation values.
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