The discussion centers on the breakdown of general relativity (GR) at the Planck scale, emphasizing the need for a theory of quantum gravity (QG). Participants highlight that the Planck scale is derived from fundamental constants such as the speed of light, Planck's constant, and Newton's gravitational constant, suggesting it is a natural transition point where quantum effects become significant. The concept of "quantum foam," proposed by physicist John Wheeler, is explored as a potential model for spacetime at this scale, indicating a departure from traditional smooth manifold descriptions. The conversation concludes that while GR and quantum mechanics (QM) currently appear inconsistent, the Planck scale serves as a critical threshold for understanding these discrepancies.
PREREQUISITESPhysicists, cosmologists, and students of theoretical physics interested in the intersection of general relativity and quantum mechanics, particularly those exploring the implications of the Planck scale on our understanding of the universe.
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