Exploring the Invariable Speed of Light: Einstein's Velocity Addition Formula

[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:

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

This is not [tex]\gamma[/tex]

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/[tex]\sqrt{(c^2 - v^2)/c^2}[/tex]

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/[tex]\sqrt{(c^2 - v^2)/c^2}[/tex]

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'/[tex]\gamma[/tex]

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'/[tex]\gamma[/tex]

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