- #36

#### PeterDonis

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He said "Sagittarius A-Star said:He omitted "is always propagated in empty space with a definite velocity c".

**the**speed of light in a vacuum". He didn't label it as ##c##, but so what?

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- Thread starter Erland
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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

- #36

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He said "Sagittarius A-Star said:He omitted "is always propagated in empty space with a definite velocity c".

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- #37

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

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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).Dale said:Einstein was not a prophet and his words are not holy writ.

- #39

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What he said was equivalent to that. There is no requirement that the postulate be stated in exactly the same words every time.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".

- #40

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

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

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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.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.

- #42

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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 particularErland 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

- #43

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Then according to that logic sound violates the 1st postulateErland 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.

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

- #45

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But for any state of motion of air, there isErland said:There is no inertial frame in which air cannot move.

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

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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 said:But for any state of motion of air, there issomeinertial 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.

- #47

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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 said:There is no inertial frame in which all air always must be at rest.

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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.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.)

- #49

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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

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Either there exists a finite invariant speed or not.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.Ifthere 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.

- 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.

- #51

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This is what it boils down to, nicely visualized below:Sagittarius A-Star said:Either there exists a finite invariant speed or not.

The role of the 2nd postulate is to separate between these two possibilities.

- 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.

- #52

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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 said:In Einstein's 2nd postulate, it is the motion of the light source that is important, not the motion of the observer.

- #53

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

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Actually, it was Dale, not me, who first mentioned the aether in this thread.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.

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

So, he justifies the claim that the light speed is

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

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.

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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.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.Ifthere 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 is getting tiresome.

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.Erland said:Actually, it was Dale, not me, who first mentioned the aether in this thread.

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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- #57

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

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.Erland said:I hope that Einstein isn't regarded as completely obsolete today.

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After moderator review, this thread is closed.

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