# Can we deduce the principle of relativity from some more basic principles?

I was reading "Relativity" by Albert Einstein. In chapter 5 page 14, it is written that

If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to K' the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K.

We advance one step farther in our generation when we express the tenet thus: if, relative to K, K' is a uniformly moving co-ordinate system devoid of rotation, then natural phenomenon run there course with respect to K' according to exactly the same general laws as with respect to K. This Statement is called principle of relativity (in restricted sense).

This generalization is not obvious, well... At least for me. Are there some underlying principles which are used to derive or deduce this principle? moreover how such a generalization can be made(it is not that simple ... Is, it?) ?

• If there is a (are) more basic principle(s) from which the 'principle' of relativity can be deduced, would it (the principle of relativity) be a principle in fact? – Alfred Centauri Jul 29 '18 at 20:14
• @AlfredCentauri To my understanding, there is historically an example of a theoretical idea that was regarded as a principle in it's own right, that was later recognized as a consequence of a deeper phenomenon. The thermodynamical concept of entropy was superseded by describing thermal phenomena in terms of statistical mechanics. The fact that physicists have at some point decided to refer to the concept of relativity as 'principle of relativity' does not exclude the possibility that unknown to physicists a deeper concept exists. – Cleonis Jul 29 '18 at 23:20
• This depends on what you mean by "basic." There are certainly other axiomatizations besides Einstein's 1905 axioms, e.g., arxiv.org/abs/physics/0302045 . – user4552 Jul 30 '18 at 18:53

To my understanding, to formulate 1905 relativistic physics at all you have to make the assumption that Einstein made in 1905.

That assumption is the generalization that you mention. And yeah, it's very much non-obvious.

There is the equivalence class of coordinate systems with the property that for all members of that equivalence class Newton's laws of motion hold good.

Einstein's 1905 generalization:
Not only Newton's laws of motion will hold good: that equivalence class is an equivalence class for all laws of physics.

(Well, in 1905 the only other set of laws of motion was the theory of propagation of electromagnetic radiation: Maxwell's equations.)

Einstein proceeded to show that the apparent self-contradition does not happen if one accepts the following: the members of the equivalence class are related to each other by way of Lorentz transformation, not by way of Galilean transformation.

The thing is: the shift to relativistic physics is not a single new assumption, it is a coordinated set of new assumptions. To transit you have to accept the set of assumptions as a whole, and as you familiarize yourself with them you perceive that no self-contradiction arises.

So no matter how you approch it, at first sight it's going to be very non-obvious.

The basic reasoning is that the coordinate systems are just artefacts of the human mind, hence the physical laws should exhibit the same form independently of the coordinates chosen.

SR (special relativity) extended the Galilean principle from mechanics to all of the other physical laws (excluding gravity/accelerated systems).

Together with the invariance of the speed of light (second principle of SR), plus assumptions on the homogeneity and isotropy of vacuum, that allowed to work out the Lorentz transformation.