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How do relativity and quantum mechanics contradict each other?

  1. Oct 16, 2010 #1
    I didn't think this question really belonged in either sub-section so I put it here. I hope that's OK. I've always heard that they contradict each other but I've never understood how. What predictions do they make differently?
  2. jcsd
  3. Oct 16, 2010 #2
    The biggest issue is that the Schrodinger equation (the fundamental equation of QM) is not lorentz-invariant. This means that the equations of QM are different for two observers moving at a relative velocity to one another---which is clearly unacceptable for relativity.

    Additionally, QM always maintains a conserved particle number. From relativity we learn that [tex]E=\gamma mc^2[/tex], and thus whenever the energy of a system (e.g. a pair of photons) is greater than the rest mass energy of another particle-pair (e.g. electron-positron pair), we can expect some probability of particle creation.
  4. Oct 16, 2010 #3
  5. Oct 17, 2010 #4
    some one told me yesterday that massive particles indeed can reach the speed of light, is this true?
  6. Oct 17, 2010 #5
    99.99...% the speed of light and as many "9"'s you can afford, but never 100% the speed of light.

    Now frankly, it does make sense that anything massive could never go as fast as something that is not.
  7. Oct 17, 2010 #6
    I'm pretty sure the dirac equation is fully relativistic.

    The Dirac equation is still missing other features... e.g. remember it only applies to spin-1/2 particles, and its still not a field theory---so again, it has issues with varying particle number.
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