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QM at the singularity

  1. Sep 24, 2014 #1
    I keep hearing that QM and GR don't play well together. For example, a singularity, a result of GR, is small enough for QM to apply but...it doesn't. I was hoping someone could explain exactly where the "equations fail." Unfortunately I'm so ignorant in this subject matter that I can't be more specific than that. I just know to ask that question because I heard Michio Kaku state that the equations fail on some TV show.
  2. jcsd
  3. Sep 24, 2014 #2


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    Science Advisor

    "Where" is hard to answer. If the volume is small enough so that both theories have to be used, the results are nonsense. For example total probabilities aren't 1.
  4. Sep 24, 2014 #3


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    I'll be damned ... Kaku actually said something that's true. A rare moment.

    The GR equations fail when you get to the singularity at the center of a black hole, in that they give an infinity (infinite density, 'cause all the mass goes to a point), which is not considered physically likely. The hope is that QM will eventually give a more accurate picture of whatever it is that happens at the center of the BH and the even further hope is that somehow this will be reconciled with GR so that the two theories (which are each in their own realm, amazingly good theories) will play nicely together.
  5. Sep 24, 2014 #4


    Staff: Mentor

    The issue is a bit more subtle than that:

    Basically Quantum Gravity is perfectly valid up to a certain cut-off about the plank scale. But then again so is QED - it breaks down in the so called electroweak region where the electroweak theory takes over. In fact the modern view of renormalisation - which is the trick used to get finite answers in theories like QED - is to take a cutoff very seriously and such theories are only valid to a certain cutoff. Quantum gravity is no different.

    The real issue is the interesting physics for QED occurs well below that cutoff - the interesting physics for Gravity is above the cutoff and physicists really want to peek behind it.

  6. Sep 25, 2014 #5
    Thanks all for the replies and the link to the article. I'll try to wrap my head around it when I'm not busy with my regular studies.

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