Understanding Einstein's second postulate of special relativity

• I
• Erland
In summary: Einstein singled out and called "stationary". The second postulate is about the independence of the speed of light from the motion of the light source, as seen by an observer in the "stationary" frame. This "stationary" frame is arbitrary and does not exist in reality, but it is used for pedagogical purposes to better understand the postulate. The first postulate states that the laws of physics are the same in all inertial frames, and together with the second postulate, this leads to the conclusion that the speed of light is the same in all inertial frames. However, this conclusion should not be
Sagittarius A-Star said:
He omitted "is always propagated in empty space with a definite velocity c".
He said "the speed of light in a vacuum". He didn't label it as ##c##, but so what?

vanhees71
PeterDonis said:
He said "the speed of light in a vacuum". He didn't label it as ##c##, but so what?
Also, he did not say: "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity".

Dale said:
Einstein was not a prophet and his words are not holy writ.
Curious how frequently this paper crops up. We don't learn mechanics from Newton's principia, or electrodynamics from Maxwell's original writings (which are similarly confusing when seen through a modern lens).

berkeman, vanhees71, PeroK and 4 others
Sagittarius A-Star said:
Also, he did not say: "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity".
What he said was equivalent to that. There is no requirement that the postulate be stated in exactly the same words every time.

vanhees71 and Sagittarius A-Star
PeterDonis said:
There is no requirement that the postulate be stated in exactly the same words every time.
This is an important point. The words of a postulate serve as a useful mnemonic, they can vary. What really matters is the math.

$$0=-c^2 \Delta t^2+\Delta x^2 + \Delta y^2 + \Delta z^2=- c^2 \Delta t’^2+\Delta x’^2 + \Delta y’^2 + \Delta z’^2$$

vanhees71 and Sagittarius A-Star
Dale said:
Yes. And if the aether is a medium for light like air is a medium for sound, then this does not violate the first postulate.
Then we would have one intertial frame where there can be no aether drag which can influe the light speed, but other intertial frames with aether drag which influe the light speed. Seems to me that the laws of physics are different in those frames, hence violating the 1st postulate.

vanhees71
Erland said:
Then we would have one intertial frame where there can be no aether drag which can influe the light speed, but other intertial frames with aether drag which influe the light speed. Seems to me that the laws of physics are different in those frames
No, they're not; the laws just include terms in the equations that reflect the state of motion of the aether. Just as the laws of physics for sound in air have terms in the equations that reflect the state of motion of the air. The laws themselves are still relativistically invariant; but particular solutions of those laws will have particular states of motion for the medium (aether or air).

Dale
Erland said:
Then we would have one intertial frame where there can be no aether drag which can influe the light speed, but other intertial frames with aether drag which influe the light speed. Seems to me that the laws of physics are different in those frames, hence violating the 1st postulate.
Then according to that logic sound violates the 1st postulate

Dale said:
Then according to that logic sound violates the 1st postulate
No, the problem doesn't arise for sound. There is no inertial frame in which air cannot move.

Dale
Erland said:
There is no inertial frame in which air cannot move.
But for any state of motion of air, there is some inertial frame in which the air is at rest. The same applies to aether.

I strongly suggest that you take a step back and think very carefully about the position you are taking.

PeterDonis said:
But for any state of motion of air, there is some inertial frame in which the air is at rest. The same applies to aether.

I strongly suggest that you take a step back and think very carefully about the position you are taking.
Well, there is some inertial frame in which some local volume of air happens to be at rest at some time. There is no inertial frame in which all air always must be at rest.

Erland said:
There is no inertial frame in which all air always must be at rest.
Nor is there a single inertial frame in which all aether must always be at rest. There was nothing in aether theory that prevented the state of motion of the aether from varying from place to place. (That's to the extent that "aether theory" was a well-defined theory in the first place.)

Dale
PeterDonis said:
Nor is there a single inertial frame in which all aether must always be at rest. There was nothing in aether theory that prevented the state of motion of the aether from varying from place to place. (That's to the extent that "aether theory" was a well-defined theory in the first place.)
The 2nd postulate, in "my" interpretation, says that there is at least one intertial frame in which the light speed always is measured to c. If there is an aether, this means that it must be at rest in this frame. Of course, a consequence of the postulates is that we can do better without the aether hypothesis.

Erland said:
The 2nd postulate, in "my" interpretation
The 2nd postulate is a postulate of SR, not aether theory. Unless you can give a reference to back up "your" interpretation of that postulate as a postulate of SR, your comments based on it are personal speculation and are off limits here.

Erland said:
The 2nd postulate, in "my" interpretation, says that there is at least one intertial frame in which the light speed always is measured to c. If there is an aether, this means that it must be at rest in this frame. Of course, a consequence of the postulates is that we can do better without the aether hypothesis.
Either there exists a finite invariant speed or not.
• If not, the assumed invariance of causality implies t'=t, that means the Galilei transformation must be valid.
• If yes, the only possible transformation between inertial frames is the Lorentz transformation.
The role of the 2nd postulate is to separate between these two possibilities.

A.T.
Sagittarius A-Star said:
Either there exists a finite invariant speed or not.
• If not, the assumed invariance of causality implies t'=t, that means the Galilei transformation must be valid.
• If yes, the only possible transformation between inertial frames is the Lorentz transformation.
The role of the 2nd postulate is to separate between these two possibilities.
This is what it boils down to, nicely visualized below:

Sagittarius A-Star
Erland said:
In Einstein's 2nd postulate, it is the motion of the light source that is important, not the motion of the observer.
The motion of the source relative to the observer is determined by the motion of the observer relative to the source. So it doesn't matter how you formulate this. But the bottom line is that you have to replace the Galilean Transformation with Lorentz Transformation.

@Erland , are you asking us a question or trying to tell us something?

To me he's trying to convince us he's found a loophole in Einstein's argumentation. A softer (or less direct) way to say he was wrong, or perhaps not fully right. We just kept telling him "no, Einstein's wording of his 1905 article is fine, it is just that we in 2023 use a simpler, newer version of his conclusion(s)".

russ_watters
PeterDonis said:
The 2nd postulate is a postulate of SR, not aether theory. Unless you can give a reference to back up "your" interpretation of that postulate as a postulate of SR, your comments based on it are personal speculation and are off limits here.
Actually, it was Dale, not me, who first mentioned the aether in this thread.

And in fact, I can give a reference to back up my "interpretation". I hope that Einstein isn't regarded as completely obsolete today. He writes in his 1905 paper, section 3, where he is deriving the Lorentz transformation:

"With the help of this result we easily determine the quantities
,
,
by expressing in equations that light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system."

So, he justifies the claim that the light speed is c measured in the "moving system", by saying that it is "required by the principle of constancy of the velocity of light (2nd postulate), in combination with the principle of relativity (1st postulate)".
He doesn't justify this by the 2nd postulate alone, he also invokes the 1st postulate. I cannot interprete this in any other way than that he in the 2nd postulate only claims that the light speed is measured to c in the "stationary" frame, and that the 1st postulate is needed to conclude this for other intertial frames too.
Just as I have claimed all the time.

But, if Einstein is completely passé today, then the postulates might be reformulated in most standard texts. Not to the better, in my opinion.

Dale
Erland said:
The 2nd postulate, in "my" interpretation, says that there is at least one intertial frame in which the light speed always is measured to c. If there is an aether, this means that it must be at rest in this frame. Of course, a consequence of the postulates is that we can do better without the aether hypothesis.
This doesn’t fix the problem I pointed out. A rigid aether would still be a medium and would still make your formulation of the 2nd postulate fail for the reason I identified.

This is getting tiresome.

Erland said:
Actually, it was Dale, not me, who first mentioned the aether in this thread.
I mentioned it because it is a counter example that shows why your formulation of the 2nd postulate (together with the standard formulation of the 1st postulate) does not imply the Lorentz transform. This is one of the reasons why the community shifted away from Einstein’s original formulation.

I had no idea that you wouldn’t understand the issue and we would still be discussing it. Frankly, if you don’t understand the problem then you are not qualified to be reformulating the postulates

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berkeman
Erland said:
I can give a reference to back up my "interpretation".
I don't see how it does. But in any case:

Erland said:
I hope that Einstein isn't regarded as completely obsolete today.
This was already answered earlier in the thread. The short version: we have had more than a century of theoretical development since Einstein. That development includes many refinements in the formulation of SR. Reading Einstein without paying any attention to those developments is not a good way to approach the subject.

Dale
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