Understanding Einstein's second postulate of special relativity

[Sagittarius A-Star]

You do realize that he is just stating one of the postulates of SR, correct?

No, he omits a part of it and wrote only the part, that is not crucial.

2. 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.

Source:
https://en.wikipedia.org/wiki/Postulates_of_special_relativity

 

[PeterDonis]

omits a part of it and wrote only the part, that is not crucial.

What you quoted from Wikipedia says the same thing @vanhees71 said. The second sentence is not an additional part of the postulate; it's just a rewording of the first sentence. That's why the "Or" is there in between.

 

[Sagittarius A-Star]

What you quoted from Wikipedia says the same thing @vanhees71 said. The second sentence is not an additional part of the postulate; it's just a rewording of the first sentence. That's why the "Or" is there in between.

He omitted the first half of the first sentence.

 

[PeterDonis]

He omitted the first half of the first sentence.

No, he didn't. He said "for any inertial observer".

 

[Sagittarius A-Star]

No, he didn't. He said "for any inertial observer".

He omitted "is always propagated in empty space with a definite velocity c".

 

[PeterDonis]

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?

 

[Sagittarius A-Star]

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".

 

[ergospherical]

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).

 

[PeterDonis]

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.

 

[Dale]

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.

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

 

[Erland]

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.

 

[PeterDonis]

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]

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

 

[Erland]

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.

 

[PeterDonis]

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.

 

[Erland]

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.

 

[PeterDonis]

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.)

 

[Erland]

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.

 

[PeterDonis]

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.

 

[Sagittarius A-Star]

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.]

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:

 

[A.T.]

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.

 

[Vanadium 50]

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

 

[dextercioby]

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)".

 

[Erland]

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]

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.

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

 

[PeterDonis]

I can give a reference to back up my "interpretation".

I don't see how it does. But in any case:

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.

 

[PeterDonis]

After moderator review, this thread is closed.