The Essential History of Special Relativity

The genesis of the theory of relativity was a long process that involved three major players and their critical reactions to the electrodynamics of moving bodies.

Lorentz made a key step when he sought to develop a mechanics that would obey the principle of relativity and Maxwell's...

Very Interesting

I enjoyed reading the axiomatization of physics.

I look forward to further posts.

I often wondered whether it was possible to build a spacetime with a recursive nature maybe you can answer that question sometime..

Thanks again

Peace

My very conventional solution of the equations for the three frame universe assumed that those equations were functional equations with independent velocity variables. I didn’t have to assume mathematical simplicity; I believe it’s obvious that infinity many other solutions also exist. If I had decided against finding a simple answer, then I would only be left with an extraordinarily complicated solution strategy. If I had pursued that rebellious strategy, which would only be regarded as being mischievous, then the construction of and all higher order universes would involve a recursive process that would depend on the previous steps taken.

To give you an idea of what some of those universes look like, begin with generalizing the Lorentz transformation written in terms of rapidity . Assume the more general form:





Next, suppose that a set of transformations of this type satisfy the properties of a mathematical group and conclude immediately that



Nontrivial solutions to this equation exist, but they all require the Axiom of Choice. The only continuous solutions are of the form where is a constant. The nontrivial solutions are discontinuous at every point.

Shubee

The clearest reason this is impossible is that Jean-Marc Lévy-Leblond and I come up with different conclusions. Please note this claim by Richard T. W. Arthur and his alleged agreement with Harvey R. Brown and Lévy-Leblond:

In my paper, The Axiomatization of Physics - Step 1, it’s already clear from the fundamental equations of that the most complete description of the simplest spacetime imaginable is given by nonlinear transformation equations.

I'm looking at Brown's book:

pages 26-27

and he seems to make a good case for linearity.

I'll have to find Lévy-Leblond's work on it and go back to your paper to make any kind of intelligent comment. The only derivation I've ever done is Einstein's special relativity and that was some time ago. So, this may take some time for me to properly follow.

-modest