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I Why isn't the Planck-scale limit taken as a postulate?

  1. Aug 16, 2017 #1
    Layman question here, kindly provide layman-understandable answers. The problem of quantum gravity is often expressed as saying 'GR predicts a collapse into a genuine singularity, there is no known mechanism which would stop such a collapse', and 'QM has nothing to say about gravity, it can not answer what happens close to the hypothetical singularities'.

    But we have reasonable hints that the Planck scale imposes some limits to length and time dimensional extension. My question then is, why is it not considered as just a postulate, an assumption, that the energy density reaches a limit at the Planck-size volume, and it can not get any more dense than that?

    What sort of physics would it represent assuming such a postulate, and why are they rejected as an actual possibility? Why are we discarding this option and keep searching for some other quantum gravity options?
    Would taking the Planck-scale limit as a given postulate help in any way in reconciling GR and QM, and if not, why so?

    Thanks
     
  2. jcsd
  3. Aug 16, 2017 #2

    phinds

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    It does not, any more than the foot or the meter or the second does. There is no physical significance to the Plank units and they are not considered the smallest possible amount of anything.
     
  4. Aug 16, 2017 #3

    PeterDonis

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    Because energy density is not invariant; it depends on your choice of coordinates. You can't base a postulate on something that depends on your choice of coordinates. (Similar remarks apply to length and time.)

    Because there's no "option" to discard. See above.
     
  5. Aug 16, 2017 #4

    kimbyd

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    The problem with General Relativity is much deeper than just a length/energy limit. General Relativity assumes a matter distribution with exact energy, momentum, pressure, etc. Quantum mechanics doesn't work like that: particles can be in superpositions of multiple states, and the uncertainty principle limits how precisely these variables can be defined. There is no such thing as a superposition of gravitational fields in General Relativity, and if you try to make it so that there is one, the math (at least done in the simple way) doesn't work out.
     
  6. Aug 16, 2017 #5
    Thanks PeterDonis, so you are saying that Plank units for length and time are not fundamental in any way, that they are just a 'choice of coordinates' same as any other choice of units may be?
     
  7. Aug 16, 2017 #6

    PeterDonis

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    Not as far as we know at this point.
     
  8. Aug 16, 2017 #7
    Thanks. I have read that Planck units seem to be somehow 'fundamental', even to saying things such as that 'the Planck length is the smallest length we can make sense of' or that 'the Planck time is the smallest time interval we can make sense of'.
    So just to confirm, those things I read were just wrong?
     
  9. Aug 16, 2017 #8
    Yes, because we don't have empirically tested model that works on that scale. So we simply don't know.
     
  10. Aug 16, 2017 #9

    kimbyd

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    The best way to understand the Planck length is that there are some arguments that experiments on those scales should likely show large differences from General Relativity. These arguments come from assumptions about how gravity interacts with quantum mechanics, and are based upon the strength of gravity. The very short length scale/high energy stems from the fact that gravity is so incredibly weak compared to the other forces.

    Since we have no experiments which are able to probe anywhere near the Planck regime, it is entirely plausible that General Relativity fails to work long before you get to those scales. There are some models that do precisely this.

    There are good reasons to believe that General Relativity can't make sense of things at the Planck scale, but it may cease to make sense of things at much lower energies/longer length scales as well.
     
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