# Lorentz Transformation if the invariance of c is explained

• I
Please tell me if Lorentz Transformation would be altered in any way if the invariance of c is explained, instead of postulated.

## Answers and Replies

FactChecker
Gold Member
The mathematical derivation of the Lorentz transformation is the same as long as c is constant. It does not depend on why c is constant (explained or postulated).

The mathematical derivation of the Lorentz transformation is the same as long as c is constant. It does not depend on why c is constant (explained or postulated).
Great! Thank you.

What about the rest of the math in relativity (both special and general)?

Grinkle
Gold Member
@DanMP I'm not comprehending your question. Can you give some conceptual example to show how you imagine SR or GR might change if a physical cause for constant c were identified?

A potential simple answer is that nothing SR or GR will ever change because they successfully predict within their domains, just like Newtonian mechanics did not change when relativity came on the scene. I might be totally missing your question, though.

PeroK
Homework Helper
Gold Member
2021 Award
Please tell me if Lorentz Transformation would be altered in any way if the invariance of c is explained, instead of postulated.

The invariance of the speed of light is essentially explained by Maxwell's theory of electromagnetism. Reconciling that theory with Classical Mechanics, in the form of the Galilean transformation, was problematic. The invariance of the speed of light is, however, consistent with the Lorentz Transformation.

You can develop SR from several starting points: invariance of the speed of light; the Lorentz Transformation; the velocity addition formula; to name but three. It doesn't have to be done the way it was first done by Einstein in 1905.

Great! Thank you.

What about the rest of the math in relativity (both special and general)?

GR does not have the invariance of the speed of light as a postulate. It does, however, assume that light travels on null paths. But, that is not fundamental to the development of the theory; only to the behaviour of light within the theory.

Ibix
What about the rest of the math in relativity (both special and general)?
If I postulate 2+2=4, is that result in any way affected if I, instead, postulate 1+1=2 and treat 2 as derived instead of fundamental?

The only way physics would be affected by an explanation for the invariance of c would be if it turns out that the explanation shows that c isn't invariant. Presumably it would also provide an explanation as to why c is close enough to invariant that we have so far not noticed.

Dale
@DanMP I'm not comprehending your question. Can you give some conceptual example to show how you imagine SR or GR might change if a physical cause for constant c were identified?
Maybe I'll post my explanation for the invariance of c. The basic idea is that we rely on atoms/molecules when it comes to measure anything, including time intervals and distances in space (our instruments are made of atoms/molecules), but atoms/molecules are structures held together by electromagnetic forces, with the photon as the force carrier ... So, we are measuring the speed of light using something that depends on it ...

I don't expect that the math of SR or GR would change in any way by replacing a postulate with an explanation stating the same thing, but when I wrote this in another forum, I was not believed, so I'm here to ask for experts opinion.

Nugatory
Mentor
I don't expect that the math of SR or GR would change in any way by replacing a postulate with an explanation stating the same thing, but when I wrote this in another forum, I was not believed, so I'm here to ask for experts opinion.
Work all the way through this line of thought (and "all the way" is a very long hard slog with not much reward at the end) and you will come up with the Lorentz Ether Theory. LET makes the same predictions as special relativity so we can't say that it is exactly wrong; but it is a very poor base on which to build any deeper understanding of general relativity or relativistic quantum mechanics so is generally rejected by physicists.

We have a policy prohibiting discussions of LET here: https://www.physicsforums.com/insights/pfs-policy-on-lorentz-ether-theory-and-block-universe/

GR does not have the invariance of the speed of light as a postulate. It does, however, assume that light travels on null paths. But, that is not fundamental to the development of the theory; only to the behaviour of light within the theory.
I don't quite understand this. The invariance of c is not used/necessary in GR?

Ibix
Maybe I'll post my explanation for the invariance of c. The basic idea is that we rely on atoms/molecules when it comes to measure anything, including time intervals and distances in space (our instruments are made of atoms/molecules), but atoms/molecules are structures held together by electromagnetic forces, with the photon as the force carrier ... So, we are measuring the speed of light using something that depends on it ...
So what? You can construct a theory in which there is a finite invariant speed but light does not travel at it (Proca's work). Experiment does not match it. You can construct a theory in which there is no finite invariant speed (Newton). Experiment does not match it. You can construct a theory that does not respect the principle of relativity (ether theories are one such type). Experiment does not match it.

As Nugatory notes, you can construct theories with extra hidden elements that don't change anything, but why bother?

Ibix
I don't quite understand this. The invariance of c is not used/necessary in GR?
There are no global inertial frames in general relativity, so "the same speed in all inertial frames" doesn't have inertial frames to work with. It's still true locally - light will always pass you at c.

Dale
Mentor
2021 Award
It doesn’t matter why the two postulates hold. Provided they do hold then SR is valid and vice versa

Work all the way through this line of thought and you will come up with the Lorentz Ether Theory. LET makes the same predictions as special relativity so we can't say that it is exactly wrong; but it is a very poor base on which to build any deeper understanding of general relativity or relativistic quantum mechanics so is generally rejected by physicists.
No, my explanation has nothing to do with LET. Maybe I'll post it tomorrow.

There are no global inertial frames in general relativity, so "the same speed in all inertial frames" doesn't have inertial frames to work with. It's still true locally - light will always pass you at c.
This is great. It is exactly what my explanation concludes. Thank you!

Nugatory
Mentor
No, my explanation has nothing to do with LET. Maybe I'll post it tomorrow.
Don't. That will put you on the wrong side of the Physics Forums rule prohibiting posting theories that have not been previously published in an appropriate peer-reviewed journal.

Dale
Nugatory
Mentor
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