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## Speed of the light and dilation of time

 Quote by GAsahi It is good that now you are now sticking with the correct scenario, not with the two scenarios that have nothing to do with this thread. The issue is that BOTH observers measure redshift OR blueshift AT the SAME TIME , contrary to the claim by Gwellsjr that one of the observers measures redshift while the other measures blueshift (and vice-versa). Actually, this error has first been introduced by gjwellsjr at post 20. I pointed out to you this several times. This is the root of my disagreement with gjwellsjr. Do we really need 100+ posts to get this?
He said 'on average'. To be honest you don't even need to write a single equation to see why he must be correct - if it wasn't the case the two observers wouldn't measure a difference in the time interval.

 Quote by PAllen Since there seems to be enormous miscommunication about scenarios, let me give simple equations for what I think are the two distinct cases in this thread. Let us propose standard coordinates (t,x,y,z) in flat spacetime. r is an arbitrary radius, v an arbitrary speed. OP scenarios: stationary observer has world line (t,r,0,0). circular moving observer has world line (t,x,y,z) = (t, r*cos(vt/r), r*sin(vt/r),0)

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 Quote by GAsahi It is good that now you are now sticking with the correct scenario, not with the two scenarios that have nothing to do with this thread. The issue is that BOTH observers measure redshift OR blueshift AT the SAME TIME , contrary to the claim by Gwellsjr that one of the observers measures redshift while the other measures blueshift (and vice-versa). Actually, this error has first been introduced by gjwellsjr at post 20. I pointed out to you this several times. This is the root of my disagreement with gjwellsjr. Do we really need 100+ posts to get this?
I disagree with you. As normally used (Doppler measured in vacuo for light actually received by direct path), the pattern of doppler for circular and stationary (NOT CENTRAL) observer are different. Further, the very phrase 'at the same time' is seriously problematic. For who? The stationary observer? The circular moving observer? They obviously differ as to 'same time', and for the circular traveler, there is no unique way to even define global simultaneity.

I agree with what Gwellsjr said about doppler and about temporal relationships. #113 summarizes what is true for OP scenario.

 Quote by jcsd He said 'on average'.
"Average" has nothing to do with it, when A measures redshift, B measures redshift. When A measures blueshift, B measures blueshift. gjwellsjr has claimed (at least twice) that A measures redshift while B measures blueshift. I can't believe that it is already past 100 posts and people don't get it.

 Quote by PAllen I disagree with you. As normally used (Doppler measured in vacuo for light actually received by direct path), the pattern of doppler for circular and stationary (NOT CENTRAL) observer are different.
Yes, you have tried this hair splitting earlier. The point is that they both measure the same type (red OR blue) shift, NOT opposite shifts as gjwellsjr incorrectly claimed.

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 Quote by GAsahi "Average" has nothing to do with it, when A measures redshift, B measures redshift.
Yes "average" does have everything to do with it as that is what he said, I'm not sure redshift or blueshift had even been mentioned at this point.

 When A measures blueshift, B measures blueshift. gjwellsjr has claimed (at least twice) that A measures redshift while B measures blueshift.
The two observers have clocks that run at different speed and no objective "when".

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 Quote by GAsahi "Average" has nothing to do with it, when A measures redshift, B measures redshift. When A measures blueshift, B measures blueshift. gjwellsjr has claimed (at least twice) that A measures redshift while B measures blueshift. I can't believe that it is already past 100 posts and people don't get it.
People don't get it because it is wrong (except for your scenario of carefully inserted sequence of mirrors, and measuring only on that path). In any normal discussion, one refers to doppler measured through empty space by direct light path. In this case the doppler pattern is not symmetric between the two observers. As to 'same time', I noted in another response that this is not even meaningful.

 Quote by jcsd Yes "average" does have everything to do with it
It is a red herring.

 as that is what he said, I'm not sure redshift or blueshift had even been mentioned at this point.

 Quote by PAllen People don't get it because it is wrong (except for your scenario of carefully inserted sequence of mirrors, and measuring only on that path). In any normal discussion, one refers to doppler measured through empty space by direct light path. In this case the doppler pattern is not symmetric between the two observers.
Irrelevant, do you really think that the observers measure opposite shifts (one red, the other one blue)? Why is it so difficult for you to admit that you are defending an error?

 As to 'same time', I noted in another response that this is not even meaningful.
Hair splitting: throughout the revolution, both observers only see one type of shift if they maintain the direction of emitting signals.

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 Quote by GAsahi It is a red herring.
It's not a red herring, because that's what was said in the post that you objected to!

So I should start reading the thread at post 20, to see if redshift or blueshift was mentioned before post 20?

 Quote by jcsd It's not a red herring, because that's what was said in the post that you objected to!
I objected to his incorrect claim that the observers measure opposite type of shifts.

 So I should start reading the thread at post 20, to see if redshift or blueshift was mentioned before post 20?
Just start reading at post 20, ok?

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 Quote by GAsahi Irrelevant, do you really think that the observers measure opposite shifts (one red, the other one blue)? Why is it so difficult for you to admit that you are defending an error?
Because I am not in error. If we place on, each world line I describe for OP scenario, a monochromatic light source and a spectrograph recording light from the other, the recordings on the spectrographs would not have the same shape. What could be clearer than that?

 Quote by PAllen Because I am not in error. If we place on, each world line I describe for OP scenario, a monochromatic light source and a spectrograph recording light from the other, the recordings on the spectrographs would not have the same shape. What could be clearer than that?
You mean one would be blueshifted and the other one would be redshifted? Yes or No?

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 Quote by GAsahi You mean one would be blueshifted and the other one would be redshifted? Yes or No?
Both choices are wrong. Each graph would be a smooth, periodic function, but the shape would be different. If you try to compare the graphs at a meeting point, besides the difference in shape, the length of the graphs would be different (assuming identically constructed devices), because of the difference in accumulated proper time. Trying to say which point on one graph corresponds to which point on the other would get into exactly the issues I raised in #113, which is a summary of what I think the important features are.

 Quote by PAllen Both choices are wrong. Each graph would be a smooth, periodic function, but the shape would be different.
You are not answering the question, you are just attempting to evade it. Obviously there is a redshift from the emitted frequency since the observers are separating. Is the shift the same (towards red) or not? Yes or No?

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