Derive Special Relativity: Alternative Paths

[user_12345]

The only way I know of to derive special relativity is to start with the two postulates, derive the Lorentz transformations, and rewrite the laws of physics consistent with those transformations.
Are there alternative ways to derive special relativity?
Thank you.

 

[dextercioby]

See this relatively recent discussion and links within.
https://www.physicsforums.com/threa...-independence-of-einsteins-sr-axioms.1000017/

 

[PeroK]

Here's a derivation from only the homogeneity and isotropy of spacetime:

http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

 

[Ibix]

State the interval and assert it is invariant; deduce the transforms that make it so.

Start from the principle of relativity and derive Galilean or Einsteinian relativity. Assert that we don't live in a Galilean universe.

 

[Grasshopper]

I found this colelction here on physicsforums.com from a suggestion from one of the respected members (can't remember who for credit, sadly), and I love this particular derivation because it derives a general case for transformation laws in an isotropic and homogeneous spacetime, and then you can select Galilean relativity or special relativity based upon whether you set a particular constant equal to 0 or 1.

https://www.mathpages.com/rr/s1-07/1-07.htmEDIT - regarding the source, all I can say is it's recommended by Fields Medal winner Timothy Gowers if that carries any weight, and as I said, someone here with one of those icons next to their name showed me this.

 

[hartmutneff]

The reason why we need special relativity is, that wave equations are not invariant under galilean transformations. The reason for this is, that the veolcity of a wave is determined by the medium. That means that an observer with a relative speed to the medium v>0, simply observes the wave going at the wrong speed. So he cannot describe the wave correctly. Now, with a medium, one can always get away with saying that the medium is the relevant reference frame and that therefore we don't have to worry about galilean transformations.
With light, things are different, since light doesn't require a medium. Hence, either the wave equation of light is wrong or the galilean transformation.

Since the partial derivatives are coefficients of a dual vector, the transformation that will leave this equation invariant, will be orthogonal with the metric of special relativity (due to the relative minus sign between the time and space components).
One can now simply generalize the galilean transformation, by putting variables in front of each term, and then use the chain rule of the partial derivatives to work out the Lorentz transformation.

Only the wave equation with velocity c is then invariant under the so found Lorentz transformation. All wave equation with speeds different to c are still not invariant. This means that the speed of light has to be the same for all observers, or otherwise we still wouldn't have an invariant description of light.

I hope this helps.

 

[vanhees71]

For a quick treatment of relativistic waves in a medium, see

https://itp.uni-frankfurt.de/~hees/pf-faq/rela-waves.pdf

 

[hartmutneff]

Or in written form, hoping that I didn't make mistakes...