Questions on General Relativity and Beyond

[Drakkith]

To my understanding General Relativity is a theory of geometry. Is it mandatory that the next step beyond GR also be a theory of geometry, or is there/could there be something else that is believed to give the same results without using geometry?

I hope that makes sense.

 

[atyy]

GR is a theory of spacetime geometry. String theory has geometry, but the geometry doesn't have a direct interpretation as spacetime, so spacetime geometry is not fundamental, but is instead emergent at low energies. In contrast in LQG or Asymptotic Safety, the degrees of freedom up to arbitrarily high energies are spacetime geometry. We don't know which one is correct (if any).

 

[marcus]

To my understanding General Relativity is a theory of geometry. Is it mandatory that the next step beyond GR also be a theory of geometry, or is there/could there be something else that is believed to give the same results without using geometry?
...

If it gives the same results then people will probably call it geometry. And so it will be geometry.

Over time, language evolves, and mathematics (a kind of language) evolves. What geometry IS (the concepts, practices, definitions, proven theorems) has evolved. There is no fixed essence. The meaning of words is their accepted use. One has to allow people that mental freedom. The community of physicists and mathematicians will collectively decide what to call it, and therefore what it IS, when the time comes, as they always do. And they may call it geometry.

You say GR is a "theory of geometry", Dra. The main equation has geometry on the LHS and MATTER on the RHS and shows how they interact. But I see you do not all it a "theory of geometry-and-matter". I take that to be an omen or sign-of-the-times.
Maybe from now onward, we will talk like you, and when we say "geometry" we will tacitly include the thought that it is dynamic geometry interacting with matter that we really mean.

I would be in favor of that linguistic drift. It's nice to keep the number of syllables down so terms are easy to say, and for language to be concise.

 

[Drakkith]

Awesome, thanks guys.