# Special relativity vs Lorentz invariance

PAllen
2019 Award
I would say, at least the following define what I would consider 'standard SR':

1) Lorentz covariance with c is a universal principle that must apply to all physical laws, and that light traveling at c is true only to the extent Maxwell equations are exact (that is Lorentz covariance is more fundamental, and there could be a Lorentz covariant alternative to Maxwell's equations in which light travels at c-epsilon, which is found to be true without abolishing SR).

2) No information (matter and energy are special cases) of any kind can travel > c (the Lorentz constant) in an inertial frame. This makes the null cone structure of spacetime fundamental, and is definitely a prediction in that it applies to all conceivable mechanisms (now and 'forever' unless dis-proven). This makes the causal structure of spacetime fundamental, allowing SR to be built from this starting point.

(Note that all predictions of these are still compatible with suitably generized LET, as far as I know).

Dale
martinbn
I would say, at least the following define what I would consider 'standard SR':

1) Lorentz covariance with c is a universal principle that must apply to all physical laws, and that light traveling at c is true only to the extent Maxwell equations are exact (that is Lorentz covariance is more fundamental, and there could be a Lorentz covariant alternative to Maxwell's equations in which light travels at c-epsilon, which is found to be true without abolishing SR).

2) No information (matter and energy are special cases) of any kind can travel > c (the Lorentz constant) in an inertial frame. This makes the null cone structure of spacetime fundamental, and is definitely a prediction in that it applies to all conceivable mechanisms (now and 'forever' unless dis-proven). This makes the causal structure of spacetime fundamental, allowing SR to be built from this starting point.

(Note that all predictions of these are still compatible with suitably generized LET, as far as I know).
Couldn't one just say that standatd SR says that space-time is Minkowski space?

Dale
PeroK
Homework Helper
Gold Member
I think that his assumption was that matter too (not just the EM field) obeys Lorentz covariant equations. I think that it's enough to derive all the rules of SR. But I would like to see what others think, is it really enough (as I think it is) or is something more needed?
I don't think that Einstein specifically assumed anything like this. His 1905 paper is available online, so you can read exactly what he published.

Naively, it was all based on a simple assumption about the invariance of the speed of light and, implicitly, some assumptions about isotropy and homogeneity of space and time.

A more modern approach might ignore EM radiation and from principles of isotropy and homogeneity of space and time alone demonstrate only the two candidates: Newtonian space and time with the Galilean transformation and no invariant speed; and, Minkowski spacetime with the Lorentz Transformation based on a universal constant ##c##, which can be seen to be an invariant speed.

I don't think you need any more than that.

PeroK
Homework Helper
Gold Member
Invariance under what?
Between inertial reference frames: "in which the equations of Newtonian mechanics hold good".

Dale
Mentor
So I want to better understand what exactly did he assumed in addition to the Lorentz covariance of Maxwell equations?
This sounds like a historical or biographical question rather than a scientific question.

I think that his assumption was that matter too (not just the EM field) obeys Lorentz covariant equations.
I think that is clear when he referred to a frame where the equations of mechanics hold good, which is why I specifically mentioned it in post #2. That was one of the two key insights I mentioned that others were missing at the time.

He had to assume something more (which later turned out to be true). So I want to better understand what exactly did he assumed in addition to the Lorentz covariance of Maxwell equations?
I don't think that he did. He just had to not be silly in proposing that the then known laws of acoustics were Lorentz covariant. Frankly, your assertion to the contrary is ludicrous.

At this time I am closing this thread. If you find some professional scientific publications on this topic please PM me and we can reopen the thread. I am not interested in permitting a discussion based on personal speculation like claims that the laws of sound are Lorentz covariant.

Last edited:
martinbn and PeterDonis