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Nonlinear vacuum permittivity?

  1. Oct 12, 2009 #1


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    I've been told recently that the vacuum permittivity, given a sufficiently strong electric field, is not a constant, as it can cause positron-electron pair to split out of the vacuum.

    1) is this true?
    2) if so, where do such pairs as the positron-electron come from in a vacuum?

    I did try to research this myself, but I wasn't able to find it. If there's a name for the phenomena, it would be helpful in searching.
  2. jcsd
  3. Oct 12, 2009 #2

    Vanadium 50

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    There is a phenomenon called "vacuum sparking", where the field energy density becomes high enough to excite electron/positron degrees of freedom. I confess I haven't thought about it in terms of permittivity.
  4. Oct 12, 2009 #3

    In QED its usually referred to as vacuum polarization (of the virtual particle pairs).

    In materials non-linear permittivity is well known....in the vacuum it is not as commonly appreciated.
    As the field gets high enough or as one gets close enough to a charge source the vacuum begins to polarize (in effect changing the 'permittivity'), and necessitating what is called "radiative corrections" . If the field is high enough (say from colliding two high Z nucleii) then a "critical vacuum" can be reached whereby the energy of the field gets up to 2 mc^2 and the virtual particle-antiparticle pair becomes real.

    Last edited: Oct 13, 2009
  5. Oct 12, 2009 #4
  6. Oct 12, 2009 #5
    I think there is a paper by Uehling (Phys Rev, 1935) on the vacuum polarization renormalization of Coulomb charge at short distances. See
    Sorry, this is pay per view.
    Also look up Uehling integral in Google.
    Bob S
  7. Oct 13, 2009 #6

    Furthermore, to add to my previous post,...
    ...Because the vacuum acts as a polarizable medium QED predicts vacuum birefringence, (refractive index change in othogonal directions), at sufficiently high electric fields. Detection of vacuum birefringement in the vacinity of highly intense laser fields is currently an active area of research.
    see :http://www.slac.stanford.edu/xorg/ilcac/talks/heinzl.pdf

    Magnetic vacuum birefringence is also a possibility at high magnetic field strength, and is actively being sought with sensitive ellipsometry.
    see for ex,: http://www.spectro.jussieu.fr/QED2005/Talks/Chen.pdf

    Last edited: Oct 13, 2009
  8. Oct 13, 2009 #7
    The problem is easy to understand: as soon as the QED equations are non linear, the Lagrangian is not really quadratic function of E. There is no the principle of superposition of fileds: there is a reaction to an external field E. There is some sort of instability of any constant field E. The state decays into E plus electron-positron couples that weaken the original filed. Kind of tunnelling.
    Last edited: Oct 13, 2009
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