Negative Energy Solutions to Photon Wavefunction

  1. Hello:

    My question is simple: Does not the standard differential wave equation from Maxwell's relations lead to both positive and negative energy solutions for a photon's E field? If so, then why do we always throw away the negative energy solutions? Is this just custom? I suspect it is. But when considering excitations of the vacuum, it appears to me that the negative energy solutions for the photon would be important. Are they thrown away by QED theorists?

    Could it be possible to create a zero energy superposition state with positive energy photons superposed to negative energy photons? And would that state not take zero energy to make, by definition? What would the wave function of such a state look like then?

    Maybe QED theorists treat negative energy photons as positive energy photons moving backwards in time.

    And when dealing with negative energy photons, is there not the apparent necessity of understanding how the E and B fields transform under energy inversion? So, perhaps the E and B fields of positive and negative photons don't superpose in such a simple manner.

    I believe this all relates to an important real-world physics problem, and I believe I know some of the answers I am seeking, but because I am an experimentalist, I am seeking advice from a "higher authority."

    Thanks for your help.

    RoKo
     
  2. jcsd
  3. Does it gives a negative solution?

    Long time ago I learnt that the Dirac equation for spin half electron gives negative energy solution.
     
  4. Yes, I believe that if you carefully work through the standard differential equation for the photon, you will see that there are negative energy solutions.

    Dirac did indeed get negative mass solutions for the electron and that led him eventually to come up with the idea for the positron. So, antiparticles have their basis with the negative mass electron.

    But I don't believe anyone has ever searched for either negative energy photons or negative mass electrons. Do they exist? I believe maybe they do.

    RoKo
     
  5. RoKo,

    Does it means that Dirac’s prediction don’t derived from the negative mass solutions, because positron has opposite charge not a mass.
     
  6. HallsofIvy

    HallsofIvy 40,918
    Staff Emeritus
    Science Advisor

    This is really a physics question, not mathematics, so I am moving it.
     
  7. Give me a solution in which E field has a negative energy.
    I mean classical, Maxwellian. No QED.
     

  8. Does not; the energy of an Electric field goes as E^2 (where E is the electric field), therefore there are only positive energy solutions....at least with Maxwell's eqns.

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