Is Relativity a Complete Theory? Investigating Math Formulation

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Discussion Overview

The discussion revolves around the completeness of relativity, specifically regarding its mathematical formulation. Participants explore whether the theory requires new mathematical tools or a review of existing ones, and how one might determine its completeness.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question if relativity is complete in terms of its mathematical formulation, suggesting that further investigation may be necessary.
  • Others propose that a good mathematician or physicist could analyze the theory to determine if new mathematical additions are needed.
  • A participant notes that the question may not be well-posed, indicating that classical covariant electrodynamics could be considered part of relativity, which might imply that the theory is not complete.
  • There is a repeated inquiry about how many attempts to analyze the theory would be required to reach a definitive conclusion about its completeness.
  • Another participant references a specific section from a book on general relativity, suggesting that there are ongoing discussions about the mathematical aspects of the theory.

Areas of Agreement / Disagreement

Participants express differing views on whether relativity is complete, with no consensus reached on the necessity of new mathematical tools or the adequacy of current formulations.

Contextual Notes

The discussion highlights the ambiguity in defining completeness and the potential dependence on interpretations of what constitutes relativity, particularly in relation to classical theories.

kent davidge
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Is it complete in the sense that there's nothing further to investigate in terms of its mathematical formulation?

I mean, in the sense that we don't need to introduce new mathematical tools or review existing ones for the theory.
 
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How could the answer to that question be determined?
 
Dale said:
How could the answer to that question be determined?
By a good mathematician or physicist analyzing and determining whether new additions are convenient?
 
As @Dale said, the question isn't well-posed. That said, if you regard classical (i.e., non-quantum) covariant electrodynamics as part of "relativity," then perhaps the answer is no.
 
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kent davidge said:
By a good mathematician or physicist analyzing and determining whether new additions are convenient?

How many such attempts would need to be made before you would say their results are definitive--either relativity is definitely complete or definitely not?
 
kent davidge said:
Is it complete in the sense that there's nothing further to investigate in terms of its mathematical formulation?

I mean, in the sense that we don't need to introduce new mathematical tools or review existing ones for the theory.
Why? Are you worried that you might need to learn more maths.
 
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kent davidge said:
Is it complete in the sense that there's nothing further to investigate in terms of its mathematical formulation?

I mean, in the sense that we don't need to introduce new mathematical tools or review existing ones for the theory.

Careful.

From the section "Mathematical relativity" in the final chapter "Next steps" of the very nice, very short, new book "General Relativity: A Concise Introduction" by Steven Carlip.

Carlip p110.jpeg

Carlip p111.jpeg
 
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