Is Relativity a Complete Theory? Investigating Math Formulation

In summary, the conversation discusses whether or not the theory of relativity is complete in terms of its mathematical formulation. This includes the question of whether new mathematical tools need to be introduced or existing ones need to be reviewed. The answer to this question is uncertain and would require analysis from a mathematician or physicist. Additionally, there is discussion about how many attempts would need to be made to definitively determine if relativity is complete or not. This conversation was based on the book "General Relativity: A Concise Introduction" by Steven Carlip.
  • #1
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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  • #2
How could the answer to that question be determined?
 
  • #3
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?
 
  • #4
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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  • #5
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?
 
  • #6
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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  • #7
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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1. What is the theory of relativity?

The theory of relativity is a scientific theory developed by Albert Einstein in the early 20th century. It describes the relationship between space and time, and how they are affected by the presence of matter and energy.

2. Is relativity a complete theory?

This is a debated topic among scientists. Some argue that relativity is incomplete because it does not fully explain the behavior of subatomic particles. Others argue that it is complete within its own framework and can be combined with other theories to provide a more complete understanding of the universe.

3. What is the math formulation of relativity?

The math formulation of relativity is based on the concept of four-dimensional spacetime, where time is considered as a fourth dimension. It involves complex mathematical equations, including the famous E=mc² equation, to describe the relationship between space, time, and matter.

4. How does relativity differ from classical physics?

Relativity differs from classical physics in several ways. It takes into account the effects of gravity and the curvature of spacetime, whereas classical physics only considers the laws of motion in a flat, non-changing space. Additionally, relativity allows for the speed of light to be the maximum speed in the universe, while classical physics does not have this limitation.

5. What evidence supports the theory of relativity?

There is a significant amount of evidence that supports the theory of relativity. One of the most famous examples is the observation of the bending of light by massive objects, such as stars, which was predicted by Einstein's theory. Other evidence includes the accurate predictions of the precession of Mercury's orbit and the time dilation effects observed in experiments with atomic clocks.

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