Generalize Special Relativity for Flat Spacetime

[Ans]

TL;DR Summary

Generalizations of special relativity for flat spacetime

I am looking for generalizations of special relativity for flat spacetime.
Of course, most well known generlaization of SR is general relativty.
There are many other generalizations of SR for curved spacetime. All what I found is for curved spacetime.
Are any more or less successfull attempts to generalize SR for flat spacetime? May be there is review article on the topic?

 

[robphy]

Possibly useful: https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation

 

[Dale]

I am not sure what it would mean to generalize special relativity for flat spacetime.

 

[Ans]

I am not sure what it would mean to generalize special relativity for flat spacetime.

I also don't know how it can be done and what it would mean. So I looking for is anyone did it somehow with some level of success, such as no internal logical contradictions and no obvious contradictions to experiments.

 

[Bandersnatch]

Isn't SR already plenty general for flat spacetime? You want it to be more general in what way?

 

[PeterDonis]

I also don't know how it can be done and what it would mean. So I looking for is anyone did it somehow with some level of success, such as no internal logical contradictions and no obvious contradictions to experiments.

If you don't even know what it would mean, how can you possibly know what you are even looking for?

 

[strangerep]

Are any more or less successful attempts to generalize SR for flat spacetime?

Adding to what others have already said, if you insist on "flat spacetime" then you imprison yourself in a straitjacket. The usual Minkowski metric for flat spacetime is usually derived from the "Relativity Postulate" and the "Light Postulate". (If you're not familiar with these, a bit of googling will turn up lots of references. The search should probably also turn up several older threads here on PF that discuss this stuff about postulates in more detail.)

Some treatments of SR assume Minkowski spacetime as an axiom, then proceed to explore the consequences. I prefer the more physics-oriented textbooks that start from the postulates and derive the concept of spacetime and its properties.

As for generalizations, one can actually drop the "Light Postulate" and (after a lot more math) discover that de Sitter spacetime is also compatible with the Relativity Postulate. But de Sitter spacetime has constant curvature, i.e., not flat. You can google for "de Sitter Special Relativity" if you want to know more about this.

There's also at least one other attempt called "Doubly Special Relativity", but I don't much about that.

 

[strangerep]

If you don't even know what it would mean, how can you possibly know what you are even looking for?

Heh, "if we knew what we were doing, it wouldn't be called research".

In @Ans's case, the discipline of structured concept analysis might help (meaning an inquiry/analysis of exactly what each word/phrase/concept means, where they came from, what assumptions they depend on, and what interdependencies might exist between them).

 

[martinbn]

Probably this is not what you are looking for, but since even you don't know what you are asking, this might count https://en.wikipedia.org/wiki/Teleparallelism