Constancy of c - second postulate

[John232]

https://www.youtube.com/watch?v=DRDN7ceu6UU

Wow, this video is amazing, they actually solve for the Lorentz and assigned the time vairables correctly in the light clock experiment like I mentioned in another thread. Every other source I have seen on this doesn't. Guess you can't win them all.

I would have to say that Newton rigged physics to allow the equation of velocity to work for light, he did this by dividing the amount of length something traveled by the amount of time it traveled. It's funny people say Einstein overturned Newtonian Physics, but to start out he had to use this same equation to do it.

Say you drew the line of velocity on a coordinate plane, the line is true from -∞ to ∞. If you draw out the function for the lorentz transform on a coordinate plane, it has a hole at c. At the hole the two sides of the triangle become the same line, this line then gives the same values for spacetime dialation, so then you get your original equation for velocity. The concept of v=d/t may be more true for light than it is for anything else in the known universe.

You could show this by drawing where these two functions intersect at v=c. The Lorentz Transformation isn't true, but the velocity equation is true at this point.

 

[Dale]

The Lorentz Transformation isn't true, but the velocity equation is true at this point.

Then kindly explain the outcome of each of these experiments without using the Lorentz transform or formulas derived from it:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[ghwellsjr]

In his 1905 paper, near the end of section 1, Einstein makes the following statement:

He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "t_A" is the time the light starts from the clock at "A" and "t'_A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.

Yes, I understand all of that, but that was not what I was asking. I was asking how the constancy of the measured two-way velocity follows from the first postulate as you claimed. Einstein did the definition of simultaneity using the two-way speed of light in the section before introducing his postulates, so it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

 

[Dale]

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

 

[ghwellsjr]

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

It's not my claim, I got it from Einstein.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

It's not my claim, I got it from Einstein.

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

 

[ghwellsjr]

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

Whenever Einstein discusses the second postulate, he always specifically refers to 1C and not 2C. He always uses terms like "propagation of light" or "a ray of light" or "how light travels" or "the progress of light" or "tracking light" or other similar terms. The point about 2C is that it establishes the universal constant value of c, the speed of light, a value that needs to be determined before the second postulate can be introduced. The second postulate does not say anything about the value of c or how to determine it or even what its value is. Instead, it establishes that the two portions of the round-trip measurement of the speed of light (whatever that is) takes the same amount of time in either direction.

 

[Dale]

Yes, I understand the relationship between 2C and 1C and I understand that the second postulate refers to 1C. That is not a point of disagreement.

I can see how you can easily arrive at 2C from only the second postulate. I cannot see how you can arrive at 2C from only the first postulate. That is the point of disagreement, and so far nothing you have shown even remotely resembles proof of that point.

I am not looking for more quotes from Einstein's OEMB, I am looking for a clear derivation that starts only with the first postulate and arrives at 2C. It is not in OEMB.

 

[ghwellsjr]

Yes, I understand that you can easily arrive at 2C from only the second postulate. That is not a point of disagreement.

I won't give you more quotes from Einstein's OEMB, but I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate. And I would like answers to my previous questions that you ignored.

Ok, here's the quote from the introduction:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

to which you replied:

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established.

and:

I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind.

So if he wasn't talking about 2C when he said (previously quoted in post #86):

In agreement with experience we further assume the quantity c to be a universal constant—the velocity of light in empty space.

then what "laws of electrodynamics and optics" was he referring to when he conjectured they "will be valid for all frames of reference for which the equations of mechanics hold good"?

And finally, I would appreciate answers to my previous questions:

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate.

I don't think that he was claiming that 2C comes out of the first postulate alone because none of those quotes are even a vague outline of a proof that 2C comes out of the first postulate.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity?

Not necessarily. The alternative is that Maxwells equations as written are not a law of nature, and that the real laws of electrodynamics were Galilean invariant.

Isn't that what Maxwell thought his equations would lead to?

I have no idea what Maxwell thought.

I have revisited the quotes and answered your questions, now answer mine: Can you or can you not provide a proof that 2C follows from the first postulate alone? I am not interested in history nor expert opinion (even Einstein's), either there is such a proof or there is not such a proof. To me the reasoning doesn't seem sound. I see no way to start only with the first postulate alone and follow a logical chain to get 2C

 

[harrylin]

[..] The alternative is that Maxwells equations as written are not a law of nature, and that the real laws of electrodynamics were Galilean invariant. [...]

Exactly, as I also mentioned - that is what Newton's theory of light had, and probably also Ritz's theory was Galilean invariant. The issue was how to match Maxwell's theory with the PoR.

Cheers,
Harald

PS: Maxwell thought that the speed of light was Galilean invariant in the same way as sound (to good approximation): that is also a law of nature, but it is expressed as the velocity relative to the medium.