# What do I need to build special relativity?

If I postulate the principle of relativity and the constancy of the speed of light for every inertial observer can I then prove all SR? Or do I need some other postulate?

For example: do I need to also postulate the structure of the Lorentz transformations or the Lorentz transformations derive completely only from this two basic postulates. (Do I have to also postulate, for example, that the transformation are linear to prove them from the two starting postulates?)

You can not prove all of SR. You can derive the Lorentz transformation using those two postulates plus linearity. The Lorentz transformation then gives you time dilation, length contraction and relativity of simultaneity. But this is not all of SR. You can not get the relativistic formula for momentum and the well-known formula $$E=mc^2$$ without also postulating conservation of momentum and energy, and using some definition of momentum and energy.

• I'd just add that linearity is a consequence of assuming space homogeneity Oct 15, 2020 at 19:03

By more modern standards, if you are looking for a proof (and not just handwaving arguments), you'll need to clearly state assumptions about the "space[time]" and other mathematical structures that model the physics that you are using as your starting point, and formulate your postulates in precise terms with those structures.

(Don't assume that "we all know that THIS [term] means THAT".
Clearly state the assumptions... A successful proof rests on the details.)

You might find enlightening this diagram describing various pathways to the Lorentz Transformations. (Sorry I don't have a nicer scan.) (from "Spacetime and electromagnetism : an essay on the philosophy of the special theory of relativity"
by J R Lucas & P E Hodgson, Oxford University Press, 1990.)

No, the two starting postulates are the only required thing. Lorentz's transformations are also derived from them.

• But for example on Morin's textbook is stated that we have to postulate the linearity of LT. Aug 3, 2020 at 13:47
• This would be a more useful answer if you provided a bit more info on how Lorentz equations derive from those axioms. Aug 3, 2020 at 13:47
• I know but I have little time now. I just posted the answer because some users strongly dislike comments which kind of answer hthe question haha, but I must said that I found a lot of "how SR is derived" in this site, just search for it. Aug 3, 2020 at 13:49
• It seems to me that “including GR” is too strong a statement... the two postulates do not not imply spacetime curvature or anything about the causal structure and the global topology of the spacetime. (GR admits solutions that do not have the topology of $R^4$.) Aug 5, 2020 at 14:33