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PeterDonis
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He said "the speed of light in a vacuum". He didn't label it as ##c##, but so what?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?Sagittarius A-Star said:He omitted "is always propagated in empty space with a definite velocity c".
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 "the speed of light in a vacuum". He didn't label it as ##c##, but so what?
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.
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".
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.
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.
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).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
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.
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
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.Erland said:There is no inertial frame in which air cannot move.
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 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.
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.
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 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 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
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. 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 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.
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.
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.
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. 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.
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 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.