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Why must charge be attached to mass?

  1. Dec 2, 2008 #1
    Why must charge be attached to mass?
    Why should the divergence of the electric field be attached to mass?
     
  2. jcsd
  3. Dec 2, 2008 #2

    Dale

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    That is a good question. I am sure there would be some problem with a charge moving at c, but I don't know what.
     
  4. Dec 3, 2008 #3

    Vanadium 50

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    The lightest object with charge is, experimentally, an electron. Since it has mass, everything else must as well. Do you find that dissatisfying?
     
  5. Dec 3, 2008 #4

    Vanadium 50

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    I don't think so. The photon carries weak hypercharge (the structure of the theory of weak hypercharge is identical to the theory of electric charge), and it moves at c just fine.
     
  6. Dec 3, 2008 #5
    That's a good question. Unfortunately, I don't have a good answer. These types of questions are good to ponder. They expand our thinking.

    Claude
     
  7. Dec 3, 2008 #6
  8. Dec 3, 2008 #7

    malawi_glenn

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    And why is that worth knowing in this discussion?
     
  9. Dec 3, 2008 #8
    Suppose you could make the mass of the electron as small as you please while keeping the charge the same. Then you could make the critical field strength above which you get fast Swinger pair creation as low as you want.

    The nonlinear corrections from QED to the Maxwell equations could be very large. Magnets could bend light so much that it would be clearly visible. The photon-photon cross section could be very large, so you could observe how light from different sources interact and scatter.

    The Coulomb potential would be modified. The fact that Gauss Law would not be valid would mean that electric fields would not be shielded by conductors.

    Black body radiation at room temperature would consist of photons and electrons and positrons.
     
  10. Dec 3, 2008 #9

    Dale

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    That would be inconvenient.
     
  11. Dec 4, 2008 #10
    I was interestest in how things might seem to work within the domain of classical differentiable fields on differentiable manifolds, but there's nothing objectionable in bringing quantum field theory into it.

    Could you explain how it is that if an electron has mass, so would other charged particles have mass?

    It seems that in stripping an electron of charge to obtain a neutrino, most but not all, of it's mass disappears. For whatever reason, the two seem intimately related. However--and I'm not equip't to talk about quantum field theory intelligently--I seem to recall that mass and charge enter into various qft's independently.
     
    Last edited: Dec 4, 2008
  12. Dec 4, 2008 #11

    ZapperZ

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    I'm hesitant to mention this, especially since I don't think this is the scope that is relevant here, and also because this is in the classical physics forum. But since people have already brought up "hypercharge" and QED, I suppose then it is fair game now.

    If you look at the Luttinger Liquid theory for 1D conductors, even under the smallest many-body coupling, a very interesting phenomenon has been predicted. The Landau Fermi Liquid quasiparticle (in an ordinary conductor, this quasiparticle is our renormalized electron) undergoes a "fractionalization", whereby the spin and charge are no longer "good quantum numbers". In fact, spin-charge separation is predicted[1]. This is where the spin and charge transport moves almost independently of each other. If you look at the dispersion curve for each one of them, they have no longer on top of each other, but disperses differently. For many, this signifies that the unit "carrier" in such a system has fractionalize - the spin and charge moves separately.

    There are several indications that this may have been observed. The violation of the Wiedemann-Franz law in several different systems[2] has been attributed to such spin-charge separation.

    Edit: I just realized that the point that I'm making with regards to the topic of this thread (mass and charge) didn't get made. (That'll teach me to post something in a hurry.) The point here is that these "observables", such as mass, spin, and charge, may, under certain circumstances, be "separated". Since we have seen spin and charge separation, I wouldn't be surprised that mass and charge might be separable as well. We haven't seen the latter yet, of course, since in most of these condensed matter systems, mass isn't that interesting yet. But if we can renormalize such masses, especially with the Fermi liquid system, via the effective mass from band structure, there's nothing here to indicate that such fractionialization can't occur with mass and charge.

    Zz.

    [1] T. Lorenz et al. Nature v.418, p.614 (2002).
    [2] G.Z. Liu and G. Cheng, PRB v.66, p.100505.1 (2002).
     
    Last edited: Dec 4, 2008
  13. Dec 4, 2008 #12

    Vanadium 50

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    The point is that once the lightest charged particle has mass, all charged particles have mass. It's not very profound.

    I don't think you want to think that way. A neutrino isn't just a "charged electron" any more than a proton is a "charged neutron". Several things change between neutrino and electron: weak isospin and the relationship between mass and flavor eigenstates.

    The point about weak hypercharge is that there exists an EM-like force that permits a charged, massless object. So the electron could have been massless. It just isn't.
     
  14. Dec 4, 2008 #13

    George Jones

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    I have been reading an essay by Penrose about his latest outrageous proposal about the Big Bang, and he mentioned the QED aspect of massless charged particles. From his essay in the book On Space and Time:

    "However, there cannot be massless charged particles in existence now, or else their potential presence would have become manifest in pair annihilation processes. This point was stressed to me by James Bjorken."
     
  15. Dec 4, 2008 #14
    Because the OP asked why must charge be associated with mass, and the link statement say's that that is not always the case. So I felt it was relevant.
     
    Last edited: Dec 4, 2008
  16. Dec 4, 2008 #15

    Defennder

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    Well to be unnecessarily pedantic, he asked why charges cannot be massless. He didn't ask why mass did not have to be associated with charges, something which your link would bear more relevance to.
     
  17. Dec 5, 2008 #16

    malawi_glenn

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    An atom is overall charge netural aswell as my coffe cup too...
     
  18. Dec 5, 2008 #17
    Within classical electrodymamics, it is implicitly assumed that all charges are attached to inertial matter. There are basically three pieces to electrodynamics: Maxwell's equations, the Lorentz force and unspoken massive charges.

    This creates a rather odd arrangment where massless first order fields of the 4-vector potential act upon massive second order fields of the 4-potential.

    Why should the electromagnetic field act upon back upon it's own first derivative--one that somehow has retarded velocity?

    But this builds the basis of field theory, in quantized form. Am I the only one who finds this too odd to be true?
     
    Last edited: Dec 6, 2008
  19. Dec 5, 2008 #18

    naima

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    In "The road to reality" Penrose also talks about zigzaging massless electrons!
     
  20. Dec 5, 2008 #19

    George Jones

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    There, he's talking about hypothetical, uncharged, massive, spin 1/2 particles.
     
  21. Dec 5, 2008 #20

    naima

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    Read fig 25.1

    massive electrons may be seen as massless zig and zag particles oscilating from one to the other.
    I think they are the L and R massless fermions upon which all the EW theory is based
    A few pages later another fig with their interaction with the Higgs field.
     
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