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Negative energy in Dirac theory

  1. Dec 26, 2008 #1
    Can anyone explain what's negative energy mean in Dirac theory?
    Does it imply anti-particle travel backward in time?
  2. jcsd
  3. Dec 26, 2008 #2
  4. Dec 27, 2008 #3


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    Hi feynmann! smile:

    It's not physical, it's just maths …

    once you accept that a positron is a version of an electron,

    you have to explain the differences either by saying it has negative energy,

    or by saying that it's the anti-particle of the electron (defined as meaning that it behaves the same as an electron provided you "run the film backward", and reverse charge and parity). :smile:
  5. Dec 27, 2008 #4


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    wait a minute, a statement such as "It's not physical, it's just maths" must be explained further.

    Math is the language of physics, so what does such a statement really tell you?

    The negative energy solutions in the dirac equation WAS inteperted as "just math", but not by dirac, who postulated the existence of antimatter. Then we have the Feynman-Stueckelberg interpretation that the field is propagating backwards in time means that the antiparticle has same mass and spin as the particle, but opposite electric charge.

    So clearly, there is something more than "just maths" regarding the negative solutions to the dirac equation.
  6. Dec 27, 2008 #5


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    Hi malawi_glenn! Merry fishmas! :smile:
    ooh, i disagree … Dirac saw mathematically that energy could be negative,

    and he rejected that as non-physical,

    and had to invent/postulate a new physical state so that energy was always positive.

    The negativity of energy is a physical impossibility, even for Dirac.
    hmm … that's my "run the film backward" example …

    but are you saying that that interpretation, in which fields propagate backwards in time, is physical?

    i'd reply that, by definition, that's non-physical, and purely mathematical. :smile:
  7. Dec 27, 2008 #6


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    It depends on where one puts the zeroth level, I would say. But you are ofcourse correct, I just wanted to raise this discussion so that the OP get the impression "why" something "is just maths".

    "What is the difference of beeing physical and just mathematical?"

    is the question I would like to ask, what defintion are you referring to?
  8. Dec 27, 2008 #7
    Indeed, allowing energy to permit negative values is very problematic - if we permit these values, there is nothing in priniciple to stop a system decaying away to a negative infinity of energy. Consider an electron decaying away to negative infinity in energy - emitting infinitely many photons in the process.

    Dirac interpreted this by postulating that all the negative energy states were full. Though it would be possible to free up these states with the input of positive energy. Dirac interpreted these unfilled negative energy states as anti-particles.

    Feynmann came up with an alternative interpretation by considering the possibility of a negative in time instead of energy.

    I should add that the idea of a particle travelling backwards in time does not have any horrible implications for causality or anything, it is merely a way of interpreting the particles behaviour and does not mean that if I were made of anti-matter I would experience time passing in the opposite direction to anyone else.
  9. Dec 29, 2008 #8
    So Feynmann and Stueckelberg essentially coupled energy in this case to another variable which has time as the dimension? That seems very arbitrary without having physical evidence to lead to that conjecture. Wouldn't spatial displacement (length) be a more obvious coupling?
  10. Dec 29, 2008 #9


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    Where does this leave researchers such as Richart Slusher and Bernard Yurke, who have done work indirectly measuring negative energy? Of course, these researchers are carefull to point out that the "negative energy" they are studying has little or nothing to do with antimatter (or the Cosmological Constant).
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