Connection between Lorentz covariance and special relativity

[fezster]

s² = t² - x² - y² - z²

This equation is covariant (Lorentz covariance). The interval "s" is invariant (Lorentz invariance).

Can you derive everything in special relativity from these facts? Or am I mistaken about that?

 

[PeterDonis]

Can you derive everything in special relativity from these facts?

It depends on what you mean by "everything". You can derive everything about the spacetime structure, yes.

 

[fezster]

It depends on what you mean by "everything". You can derive everything about the spacetime structure, yes.

When I say everything, I mean can we explain all the phenomena that arises due to special relativity on the basis of just these facts.

So, if we can predict all the phenomena of special relativity from the spacetime structure, and everything about spacetime can be derived from these facts, then the answer would be yes. Is that right?

 

[PeterDonis]

if we can predict all the phenomena of special relativity from the spacetime structure, and everything about spacetime can be derived from these facts, then the answer would be yes. Is that right?

Yes, as long as you also stipulate that all of the other laws of physics must be covariant (for example, Maxwell's Equations governing the electromagnetic field). This is not a problem because we have covariant forms of all those other laws. But it should be noted that spacetime, by itself, is not everything.