Questions on General Relativity and Beyond

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Discussion Overview

The discussion centers around the nature of General Relativity (GR) as a theory of geometry and whether future theories beyond GR must also adhere to a geometric framework. Participants explore the implications of geometry in various theoretical frameworks, including string theory and loop quantum gravity (LQG).

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that while GR is fundamentally a theory of geometry, it is uncertain whether subsequent theories must also be geometric in nature.
  • One participant notes that string theory incorporates geometry, but this geometry may not directly represent spacetime, suggesting that spacetime geometry could be emergent rather than fundamental.
  • In contrast, LQG and Asymptotic Safety maintain that spacetime geometry remains fundamental even at high energies, though the correctness of these theories is still in question.
  • Another participant reflects on the evolving nature of language and mathematics, suggesting that the definition of geometry may change over time based on collective consensus within the scientific community.
  • There is a discussion about the interaction between geometry and matter in GR, with a participant advocating for a more inclusive definition of geometry that encompasses dynamic interactions with matter.

Areas of Agreement / Disagreement

Participants express differing views on whether future theories must be geometric, with some advocating for the necessity of geometry while others suggest alternative frameworks could yield similar results. The discussion remains unresolved regarding the fundamental nature of geometry in future theories.

Contextual Notes

The discussion highlights the dependence on definitions of geometry and the evolving nature of language in physics, with no consensus on the implications of these factors for future theoretical developments.

Drakkith
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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.
 
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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).
 
Drakkith said:
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.
 
Awesome, thanks guys.
 

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