General relativity breaks down at Planck scale

[yogi]

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"

 

[JustinLevy]

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"

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.

What I described above though: learning the form of the answer and learning the important scales, I believe are what is fully meant by dimensional analysis. At least there are some professors at my university that use it as such, as well as that book I mentioned earlier (which didn't discuss general relativity at all, it was a book on phase transitions).

 

[JesseM]

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.

 

[yogi]

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.

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

 

[JesseM]

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

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.