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Using imaginary time to unify QM and GR

  1. Jul 13, 2012 #1
    I find this passage from A Brief History of Time a bit hard to believe. When he talks about using imaginary time for the purposes of calculation, is it the same like in the Schro eq which uses an imaginary number? How plausible is the following passage? Is using imaginary time a common practice?
    Further on he writes:

     
    Last edited: Jul 13, 2012
  2. jcsd
  3. Jul 13, 2012 #2
    Take a look at the wikipedia page on imaginary time:

    http://en.m.wikipedia.org/wiki/Imaginary_time#section_2

    Essentially, it's related to a concept pushed by Hawking and Jim Hartle. That is, the 'wavefunction of the universe'. Whereas wavefunctions for particles represent the probability of finding a particle in a particular location or having taken a certain path, the wavefunction of the universe would encode the probability of certain ways the universe could evolve.

    Gravitationally singularities disappear in imaginary time, which I'd have to say is why Hawking says it is crucial.
     
  4. Jul 14, 2012 #3
    Yes, definitely. In addition to the quantum cosmology applications of Euclidean time mentioned by Mark M, there is also the widespread use of instantons as contributions to path integral calculations, for example in Yang Mills theory.
     
  5. Jul 14, 2012 #4
  6. Jul 14, 2012 #5
    Imaginary time can be obtained from real time in quantum mechanics by applying a Wick rotation by [itex] \frac {\pi} {2} [/itex] through the complex plane so that imaginary time, [itex] \tau [/itex], is given by [itex] \tau = it [/itex].
     
  7. Jul 15, 2012 #6
    Yes, it gives spacetime a positive definite signature (i.e. makes it euclidean). Einstein used it originally in relativity. It is more used by particle physicists.
     
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