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Does the constancy of the speed of light for all observers naturally emerge from the Minkowski spacetime metric?

Do Einstein's two postulates of relativity emerge from the Minkowski spacetime metric?

Suppose we begin with Minkowski spacetime and the Minkoswki metric.
https://simple.wikipedia.org/wiki/Minkowski_spacetime

Can we then derive Einstein's two postulates of relativity?

  1. First postulate (principle of relativity)

The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.

  1. Second postulate (invariance of c)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body. OR: The speed of light in free space has the same value c in all inertial frames of reference.

Thanks! :)

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From the Minkowski metric plus the first assumption of Special Relativity, the rest may be derived.

That is, if it is assumed that physical laws are the same in all inertial reference frames, which was first proposed by Galileo, and taken up by Newton; plus the Minkowski metric for spacetime, we automatically obtain the invariant spacetime interval, Lorentz transformations, and the invariance of the speed of light.

You need to assume both the metric and the Principle of Relativity in order to obtain all of the physics. Otherwise you just have an abstract geometry.

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I beleive you have a huge confusion.

The Minkwoski metric only gives geometrical properties of the spacetime, and it basically states that the spacetime is not euclidean. What you are asking is similar to asking that Newton laws and classical mechanics comes from the fact that we live in an euclidean world (without time component).

The first postulate: "The laws of physics are the same in all reference frames".

Has nothing to do with geometry, is almost axiomatic. We want laws of physics that stay the same regardles of our chosen reference inertial frame. This goes way back to Galileo's principle of relativity, and Galileo's relativity is used for classical physics, and is valid up to relativistics speeds.

The second postulate: "The invariance of C"

Again, is not dependent on the geometry. After Maxwell published his equations, physicist noticed that when using Galileo's principle of relativity, the equations changed their form, which means that the light would no behave the same if you are at rest, or in a car. This only leaves 2 possibilities:

  1. There is a "universal" inertial reference frame
  2. Galileo's principle of relativity is wrong

So if you create a relativity principle so that Maxwell's equations stay the same across all reference frames (Laws of physics stay the same across reference frames), you get

  1. C is constant
  2. Einstein's relativity (Lorentz equations)
  3. Minkowski metric for the spacetime ($ct - \vec{r}$ )

Regards

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  • $\begingroup$ what happens if the first possibility is right and there is a universal FoR? Is relativity un-necessary? $\endgroup$ – user104372 Apr 18 '16 at 4:34
  • $\begingroup$ It's a bit more complex than that. We would still have Galileo's relativity, but to obtain any meaningful we may have to take all our observations to the universal frame of reference, and re-study the laws of physics there. We may also have different aws of physics on different reference frames, (much like non-inertial reference frames). So maybe we wouldn't have relativity as stated by Einstein, but we would still have some corrections to our standard equations $\endgroup$ – Joafigue Apr 18 '16 at 15:51

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