The discussion revolves around the assertion that general relativity (GR) breaks down at the Planck scale, exploring both theoretical implications and the nature of quantum gravity (QG). Participants examine the reasons behind this claim, the significance of the Planck scale, and the relationship between GR and quantum mechanics (QM).
Participants do not reach a consensus on the nature of the breakdown of GR at the Planck scale, with multiple competing views and ongoing debates about the implications of quantum foam, the significance of the Planck scale, and the relationship between GR and QM.
Limitations in the discussion include unresolved assumptions about the nature of spacetime at the Planck scale, the dependence on definitions of quantum gravity, and the lack of experimental evidence to support various claims.
We teach that to physics students as well. But that is just the lowest level of using dimensional information. Often physicists just refer to that as "checking units". It is a useful tool to find where an error occurred in a calculation.yogi said:In Engineering, dimensional analysis is exactly what Jesse described - by keeping track of the units you can check the vaidity of both sides of an equation, and quickly spot an error - some of the literature regarding Planck units has appropriated the term "dimensional analysis' - but it is actually a case of "dimensional inference"
JesseM said:Thanks for the explanation Justin. I think you may be right that I was posing a false dichotomy, the notion of "dimensional analysis" you're describing does involve some physical intuitions such as the choice of "relevant" parameters, and also general ideas like the notion that quantum gravity should have a characteristic length scale (whereas it doesn't have a characteristic mass scale), but it comes short of more detailed physical arguments.
No, not saying the Planck mass is meaningless, but it would be a mistake to think that quantum gravity is needed anytime you are analyzing a system with less mass than the Planck mass (though you do if the mass is compressed down to around the Planck length), whereas quantum gravity would be needed anytime you're analyzing interactions on the scale of the Planck length or Planck time--that's exactly what I meant when I said you still needed some basic physical intuitions to do dimensional analysis, even if you don't need detailed physical arguments.yogi said:The same 3 constants (G, C and h) also lead to a unit of mass - are you saying its ok to ignor the mass that falls out of the combination as meaningless - but not the length