Why is the speed of light invariant despite relative motion?

[stevmg]

Look above your post, I wrote something for you personally.

I was too quick on the draw... I answered you before I could see your note about your blog. I have downloaded both .pdf files and do see where you used the closure formula. It appears that the "\gamma" was fortuitous as they did not know about it (I don't think) in 1887. Am I correct? Or, is this formula the basis upon which the now famous "\gamma" was derived?

Steve

 

[starthaus]

I was too quick on the draw... I answered you before I could see your note about your blog. I have downloaded both .pdf files and do see where you used the closure formula. It appears that the "\gamma" was fortuitous as they did not know about it (I don't think) in 1887.

The explanation I wrote for you uses SR, not the Lorentz-FitzGerald contraction from the late 1800's.
As you can see, you need both closing speed and the Lorentz transforms in order to explain the null result for MMX.

 

[stevmg]

The explanation I wrote for you uses SR, not the Lorentz-FitzGerald contraction from the late 1800's.
As you can see, you need both closing speed and the Lorentz transforms in order to explain the null result for MMX.

From what I see equations 1.1 - 1.4, the null result was explained without the Lorentz transforms. The "\gamma" arrived at was fortuitous (although correct.) There was no time-dilation except that which resulted from the calculations. c (as 30,000,000 m/sec) was never a limiting speed as it could be anything (except, of course, equal to or less than v)and this would work out. Thus, this would be true in a Galilean universe, too. t₂ - t₁ = 0

The corroboration with equations 1.5 and 1.6 using time dilation which is a result of the Lorentz-Fitzgerald contraction from the late 1800's shows the MMX experiment to be valid both ways - from a closue speed point of view and a SR point of view (I am using SR to refer to the later Einsteinian concept of SR and not the earlier concepts of Newtonian relativity.) Again, t₂ - t₁ = 0

That is a beautiful, understandible and succinct (you are quite good at being succinct - kind of like Calvin Coolidge - our 30th President - and this is not a put down) explanation of what you were talking about.

 

[stevmg]

starthaus -

I stand corrected on post #33 above. When the Lorentz transformations were derived, as I recall, an assumption was made about c + v and c - v (from closure velocity) which equated to c being constant and the gamma factor resulting:

\gamma =
\sqrt{(c^2 - v^2)/c^2}

This gamma factor was necessary to keep the light speed at c but would alter time and thus velocity. So, it was on the basis of closure velocities that Lorentz transforms were derived.

 

[starthaus]

From what I see equations 1.1 - 1.4, the null result was explained without the Lorentz transforms.The "\gamma" arrived at was fortuitous (although correct.)

There is nothing "fortuitous", the derivation follows modern SR exactly.

There was no time-dilation except that which resulted from the calculations. c (as 30,000,000 m/sec) was never a limiting speed as it could be anything (except, of course, equal to or less than v)and this would work out.

c=300,000,000 m/s , not 30,000,000m/s. The proof has nothing to do with the value attributed to c, yet it has everything to do with the SR assumption that light speed is:

-isotropic
-does not depend on the speed of the emitter (hence the closing speed equations I wrote are correct)

Thus, this would be true in a Galilean universe, too. t₂ - t₁ = 0

...only in the lab frame, not in the frame of an external observer (say, situated in the Sun).

The corroboration with equations 1.5 and 1.6 using time dilation which is a result of the Lorentz-Fitzgerald contraction from the late 1800's

Time dilation is not a consequence of the Lorentz-FitzGerald contraction.

shows the MMX experiment to be valid both ways - from a closue speed point of view and a SR point of view

I think you misunderstood my writeup, I explained that you need both colsing speed and the Lorentz transforms (SR) in order to explain the null outcome.

That is a beautiful, understandible and succinct (you are quite good at being succinct - kind of like Calvin Coolidge - our 30th President - and this is not a put down) explanation of what you were talking about.

Thank you. I hope that the above clears the last of your misunderstandings.

 

[starthaus]

starthau -

I stand corrected on post #33 above. When the Lorentz transformations were derived, as I recall, an assumption was made about c + v and c - v (from closure velocity) which equated to c being constant and the gamma factor resulting:

\gamma = \sqrt{(c^2 - v^2)/c^2}

This is not \gamma

This gamma factor was necessary to keep the light speed at c but would alter time and thus velocity. So, it was on the basis of closure velocities that Lorentz transforms were derived.

No, it wasn't. Einstein was much smarter than that. You need to read his 1905 paper. He used closing speed in a much smarter way.

 

[stevmg]

starthaus -

I stand corrected on post #33 above. When the Lorentz transformations were derived, as I recall, an assumption was made about c + v and c - v (from closure velocity) which equated to c being constant and the gamma factor resulting:


gamma = 1/\sqrt{(c^2 - v^2)/c^2}

I wrote my post before you got to me, but I did get the message.

If I can get to that 1905 paper, the one on electromagnetism, I will read it. For now, I'll let it slide until I have more time in the future.

I assume by your name that you read German. I'm not that good at it but I can get by because I lived there and wasn't one of those Americans who refuse to learn a different language. I assume the standard English translations are good enough if I get stuck, and I will.

 

[starthaus]

starthaus -

I stand corrected on post #33 above. When the Lorentz transformations were derived, as I recall, an assumption was made about c + v and c - v (from closure velocity) which equated to c being constant and the gamma factor resulting:


gamma = 1/\sqrt{(c^2 - v^2)/c^2}

This gamma factor was necessary to keep the light speed at c but would alter time and thus velocity. So, it was on the basis of closure velocities that Lorentz transforms were derived.

Not exactly, Einstein was much smarter than that.

I wrote my post before you got to me, but I did get he message.

If I can get to that 1905 paper, I will read it. For now, I'll let it slide until I have more time in the future.

I assume by your name that you read German. I'm not that good at it but I can get by. I assume the standard English translations are good enough.

See here

 

[stevmg]

starthaus -

Thanks a lot for the .pdf on Einstein's 1905 electromagnetics. When I get a chance to go over it in the next day or two I will. I had made a brief attempt to Google it but hadn't found it...

Annalen Physik doesn't lie around everywhere so many thanks.

- S

 

[stevmg]

There is nothing "fortuitous", the derivation follows modern SR exactly.




c=300,000,000 m/s , not 30,000,000m/s. The proof has nothing to do with the value attributed to c, yet it has everything to do with the SR assumption that light speed is:

-isotropic
-does not depend on the speed of the emitter (hence the closing speed equations I wrote are correct)





...only in the lab frame, not in the frame of an external observer (say, situated in the Sun).




Time dilation is not a consequence of the Lorentz-FitzGerald contraction.



I think you misunderstood my writeup, I explained that you need both colsing speed and the Lorentz transforms (SR) in order to explain the null outcome.


Thank you. I hope that the above clears the last of your misunderstandings.

300,000,000 m/sec - need that for another problem, thanks I was working from 300,000 km/sec and got zero's messed up.

In your blog, after equation 1.2, you use the fact that l₂ = l₂'/\gamma

That is from the Lorentz transformation, yes? Equation 1.1 is from pure closure velocity, yes?

equation 1.4 appears to be a combination of both as you already used the Lorentz transform (length contraction) earlier in the chain of derivation.

So, what you demonstrated here, with length contraction t₂ - t₁ = 0

What I recall from Spacetime Physics and Special Relativity books is that there was a quantity that was to be expected from the presence of moving across an ether:

which was not supposed to zero, if v were not too small, but they couldn't find it.

So, you basically showed here why they couldn't find it.

The Lorentz-Fitzgerald (c. 1898 or somewhere there) contraction which comes up with the length contraction used does the correction which brings this to the null value.

If that is right, then I "got it." I see what you mean about the lab frame and the Sun frame. In the Sun frame, you applied the correction. In the lab frame, you did not. But then you later showed that in the lab frame, the time dilation from Lorentz also worked.

 

[starthaus]

300,000,000 m/sec - need that for another problem, thanks I was working from 300,000 km/sec and got zero's messed up.

In your blog, after equation 1.2, you use the fact that l₂ = l₂'/\gamma

That is from the Lorentz transformation, yes? Equation 1.1 is from pure closure velocity, yes?

equation 1.4 appears to be a combination of both as you already used the Lorentz transform (length contraction) earlier in the chain of derivation.

So, what you demonstrated here, with length contraction t₂ - t₁ = 0

What I recall from Spacetime Physics and Special Relativity books is that there was a quantity that was to be expected from the presence of moving across an ether:

which was not supposed to zero, if v were not too small, but they couldn't find it.

So, you basically showed here why they couldn't find it.

The Lorentz-Fitzgerald (c. 1898 or somewhere there) contraction which comes up with the length contraction used does the correction which brings this to the null value.

If that is right, then I "got it." I see what you mean about the lab frame and the Sun frame. In the Sun frame, you applied the correction. In the lab frame, you did not. But then you later showed that in the lab frame, the time dilation from Lorentz also worked.

yes, you got it

 

[stevmg]

Thanks for your patient help (again, sorry about the typo of 30,000,000 vs 300,000,000 - I really annoyed myself by doing that.)

Part of my problem is understanding what knowledgeable folks like you as well as the "official" PF contributors always mean because I am not used to the terminology and context of what replies are written. As precise as we try to be there are always ways that things can be taken another way than intended with the resultant delay in comprehension. That's nobody's fault, but that's the way it is. I know that from medicine where I constantly had to go over things with nurses, patients and other colleagues in terms of full understanding (both theirs and mine) as a safety issue.

I am a physician (MD) and delving later in life into an area of science which always fascinated me yet never had time to go after. So far, no practical application in my life for this but who knows, maybe some principle in thought process will come in handy.

I will now delve into that 1905 electrodynamics paper which will be even more enlightening. Don't be surprised if I have some questions about that, too.

Thanks, again.

Steve G