Speed of the light and dilation of time

[PAllen]

Correct.



Correct. If you paid attention, you would have noticed that the path is HALF circle, so you should have stopped here.



Try paying attention to the scenario, gjwellsjr had the two observers "looking at each other through a webcam". How do you think one connects webcams? Hint: through a fiberoptic cable.



You are assuming that the Earth is transparent, aren't you? Last I checked, it wasn't. :-)

I'm assuming the Earth isn't there as it is extraneous to the scenario. I described worldlines in empty (flat) spacetime.

As I recall, gwellsjr did, indeed, propose to consider the Earth transparent, so as to discuss doppler the way all the world except you does.

 

[GAsahi]

I'm assuming the Earth isn't there as it is extraneous to the scenario.

But it is THERE. Please stop making up scenarios.

As I recall, gwellsjr did, indeed, propose to consider the Earth transparent,

You are now making things up again. No person in his right mind would "make the Earth transparent". Why is it so difficult for you to admit you are wrong?

 

[PAllen]

But it is THERE. Please stop making up scenarios.




You are now making things up again. No person in his right mind would "make the Earth transparent". Why is it so difficult for you to admit you are wrong?

Because I'm not. I have been pretty clear what my assumptions and definitions are, and draw correct conclusions from them. I have granted that in the peculiar (to me) scenario you insist on, you are also right. Measuring doppler through a curved tube removes all utility it has in accounting for differential aging, so I have no interest in this scenario.

 

[GAsahi]

I have granted that in the peculiar (to me) scenario you insist on, you are also right.

Good, because the "peculiar" scenario is the one that has been in discussion before you butted in and it is the realistic scenario. Your "transparent Earth", isn't.

 

[PAllen]

Good, because the "peculiar" scenario is the one that has been in discussion before you butted in and it is the realistic scenario. Your "transparent Earth", isn't.

Obviously, we differ about the plausibility of such a tube. Beyond that, how is it instructive? All it shows is that finite signal times, if not accounted for, can lead to confusing results. If you pulled off the mirror tube scenario all the way to meeting time, what would be seen is:1) Stationary observer sees circular observer's clock right next to them behind theirs. Looking in the webcam, they an image of this clock even further behind.

2) Circular observer sees stationary clock right next to them ahead of theirs. Looking in the webcam, they see an image of this clock behind theirs.

Conclusion: webcams with long signal paths don't tell you much unless you compensate for signal delay. Any reasonable way of doing this suggests that time ran faster for the stationary clock over all, and there is no unuique way of locating the time differential along the different world lines.

 

[GAsahi]

Obviously, we differ about the plausibility of such a tube. Beyond that, how is it instructive?

It is instructive because it teaches you to read before butting in. It also teaches you not to make up cockamamie scenarios that involve "transparent Earth(s)".

1) Stationary observer ... Looking in the webcam, they an image of this clock even further behind.

2) Circular observer ... Looking in the webcam, they see an image of this clock behind theirs.

...which contradicts the claim made by gjwellsjr in post 20. Thank you for coming up clean.

 

[PAllen]

It is instructive because it teaches you to read before butting in. It also teaches you not to make up cockamamie scenarios that involve "transparent Earth(s)".

My scenario had no Earth at all because it was extraneous to the main issues. Moving the world lines to empty space allows easier understanding of the central issues.

 

[GAsahi]

My scenario had no Earth at all because it was extraneous to the main issues. Moving the world lines to empty space allows easier understanding of the central issues.

Agreed. But it is not the original scenario that sparked the argument. You need to learn to pay attention to what is being discussed, rather than making up your own scenarios.

 

[PAllen]

Agreed. But it is not the original scenario that sparked the argument. You need to learn to pay attention to what is being discussed, rather than making up your own scenarios.

Simplifying a proposed scenario is generally very instructive and normally done on these forums.

 

[ghwellsjr]

Try paying attention to the scenario, gjwellsjr had the two observers "looking at each other through a webcam". How do you think one connects webcams? Hint: through a fiberoptic cable.

I liked your idea of connecting two observers stationary at different points on the Earth through a fiberoptic cable but not when one of them is traveling on a very high speed train around the Earth thousands of times per second which is what the scenario is. I discussed in detail how this would work using radio signals transmitted through antennas in post #31.

 

[GAsahi]

I liked your idea of connecting two observers stationary at different points on the Earth through a fiberoptic cable but not when one of them is traveling on a very high speed train around the Earth thousands of times per second which is what the scenario is. I discussed in detail how this would work using radio signals transmitted through antennas in post #31.

The fiberoptic cable doesn't have to be unrolled, you can simply have it placed around the Equator and send the pulses from the current position(s) of the observers. Same idea as using mirrors, using GPS or using antennas located along the Equator.

 

[ghwellsjr]

Well then, why don't we say we have an electric train and we communicate through the third rail (or trolley line)?

 

[ghwellsjr]

1. Observer A accelerates in a straight line away from observer B. The two observers send light signals towards each other. B sends a ray that chases after A and A sends a ray back, along the line connecting them. Do they measure the waves as being:

A1. Mutual Redshift
B1. Mutual Blueshift
C1. One Redshift while the other Blueshift

2. Same problem as above but the trajectory is a half circle. The rays exchanged follow the circular arc.

A2. Mutual Redshift
B2. Mutual Blueshift
C2. One Redshift while the other Blueshift

If you paid attention, you would have noticed that the path is HALF circle, so you should have stopped here.

OK, we have two identical problems except that the first one is in a straight line and the second one is in a half circle.

For the first problem, we start with A and B mutually at rest in a common inertial Frame of Reference. They have identical synchronized clock/light systems. A quickly (let's agree on instantly to make life simpler for ourselves) accelerates to some speed away from B in a straight line for some distance as defined in our FoR. A and B will observe the same redshift in each others clock/light system for awhile. But during this time, A's clock/light system will be time dilated, meaning that it is running slower than it was before. When A reaches the target distance, he instantly stops. He immediately sees the clock/light system of B go back to normal (no Doppler) but B does not see the same thing. He continues to see the clock/light system of A to be redshifted for an additional length of time corresponding to the light transit time for the signal to go from A to B. After this time period is over, A and B will see the time on each others clock/light system as having accumulated different time deltas during the observed redshift periods. A will see B's clock as having accumulated more time than his own and B will see A's clock as having accumulated less time than his own. So even though they both observe the same amount of redshift, they observe the redshift for different periods of time and thus different amounts of accumulated time deltas and so none of your multiple choice answers is correct.

For the second problem, since the light is made to follow the same circular arc path that A traverses, it has the exact same analysis as the first problem and the same answer--which is none of the answers you provided.

Any more scenarios you'd like explained?

 

[GAsahi]

OK, we have two identical problems except that the first one is in a straight line and the second one is in a half circle.

The answers should be the same, in BOTH cases BOTH observers measure redshift . I simply introduced the first case as a warmup for the second case, in order to stop the nonsense about the "Transparent Earth".

. A and B will observe the same[/color] redshift in each others clock/light system for awhile.

Not "for a while", for the whole duration of the trip both observers measure redshift, contrary to your incorrect statement made at post 20 that started the whole thing.
Now, you are trying to sneak in words like "same", in order to have another crack at justifying your position. Of course that the observer in circular motion is not seeing the same[/color] amount of redshift, since he isn't perfectly equivalent to the inertial observer. The point is that BOTH observers measure redshift. Please don't try to move goalposts, I am very good at detecting such attempts.

So even though they both observe the same amount of redshift,

You should have stopped while you were still ahead, the point is (and has always been) that your statement that one observer measures redshift and the other one measures blueshift is false.

Any more scenarios you'd like explained?

Pass.

 

[ghwellsjr]

The answers should be the same. Since you got different answers, you continue to make mistakes.

I don't know why you are saying this. I thought it was very clear that I got the same answer for both of your problems.

Not "for a while", for the whole duration of the trip both observers measure redshift, contrary to your incorrect statement made at post 20 that started the whole thing.

You didn't make the trip in your two problems the same as the trip in post #20. In your two problems, A only went half way around instead of all the way around as in post #20.

Now, you are trying to sneak in words like "same", in order to have another crack at justifying your position. Of course that the observer in circular motion is not seeing the same[/color] amount of redshift, since he isn't perfectly equivalent to the inertial observer. The point is that BOTH observers measure redshift. Please don't try to move goalposts, I am very good at detecting such attempts.

Well since we both agree on this half of the trip, I'd like to do the other half where A returns to B for both of your problems. I just need to know if these two new problems will end up having the same answer to each other or different answers. In other words, for your second problem, are you going to insist that A sends and receives signals along the total path length that A traversed, meaning that it ends up twice as long as in your original statement of the problems? Or are you going to have A send and receive the signals ahead of himself or will you allow A to turn around and come back on the same path he left on?

You should have stopped while you were still ahead, the point is (and has always been) that your statement that one observer measures redshift and the other one measures blueshift is false.

I should not stop until we have completed the same problem that we had in post #20, not some new scenario that you dreamed up and claimed is the same. After I analyze the return half of the trip, I'll put them together and then we'll see where we stand.

 

[GAsahi]

You didn't make the trip in your two problems the same as the trip in post #20. In your two problems, A only went half way around instead of all the way around as in post #20.

I made it half circle in order to preclude further cheating. In the further posts, once I made sure there was no more cheating, I allowed it to be full circle.

Well since we both agree on this half of the trip, I'd like to do the other half where A returns to B for both of your problems. I just need to know if these two new problems will end up having the same answer to each other or different answers. In other words, for your second problem, are you going to insist that A sends and receives signals along the total path length that A traversed, meaning that it ends up twice as long as in your original statement of the problems?

It is really simple, the signals from A to B and from B to A are always sent along one path. So, when A completes the circle, the signal path is twice the length for the semi-circle. This precludes any attempt at moving goalposts.

Or are you going to have A send and receive the signals ahead of himself or will you allow A to turn around and come back on the same path he left on?

Not allowed.

I should not stop until we have completed the same problem that we had in post #20, not some new scenario that you dreamed up and claimed is the same. After I analyze the return half of the trip, I'll put them together and then we'll see where we stand.

You stand that you were wrong and that you are trying to move some goalposts.

 

[PAllen]

Looking at #19, which introduced the webcam question, the OP said nothing about the signal path connecting the webcams. For any reasonable scenario (and I consider a forever growing signal path as not reasonable for a cyclic situation), e.g. using GPS sattellites, what Gwellsjr describe in #20 and #31 would be correct. Only for the (IMO absurd) case created by GAsahi and not by the OP would it be true that the webcams show mutual ever growing mutual time dilation.

 

[GAsahi]

Looking at #19, which introduced the webcam question, the OP said nothing about the signal path connecting the webcams. For any reasonable scenario (and I consider a forever growing signal path as not reasonable for a cyclic situation), e.g. using GPS sattellites, what Gwellsjr describe in #20 and #31 would be correct. Only for the (IMO absurd) case created by GAsahi and not by the OP would it be true that the webcams show mutual ever growing mutual time dilation.[/color]

So, you are back to one last gasp attempt to prove that you are right, eh?
There is no mention of "ever growing" mutual time dilation, there is mention of mutual redshift. There is no "ever growing", so why do you try moving the goalposts again?
As to the way of connecting everything, the circum-equatorial "tube" is present from post 1.

 

[PAllen]

So, you are back to one last gasp attempt to prove that you are right, eh?
There is no mention of "ever growing" mutual time dilation, there is mention of mutual redshift. There is no "ever growing", so why do you try moving the goalposts again?
As to the way of connecting everything, the circum-equatorial "tube" is present from post 1.

Who appointed you dictator of someone else's thread? Only you get determine what scenarios are allowed for discussion? Giving a correct description of a stated scenario is not wrong because it differs from the only scenario you want to allow. So far as I see it, basically everything I've said, and everything Gwellsjr has said, is correct.

I find your whole attitude strange, especially as you have made a number of clearly incorrect statements (not related to scenario confusion - just bad math, and false critique of Gwellsjr's math).

[edit: as to ever growing time dilation, if there is only ever red shift seen via webcams, each sees the clock image in the web cam fall ever behind theirs, having ever larger disprepancy compared to clock comparisons at points where they meet on each circuit.]

 

[GAsahi]

Who appointed you dictator of someone else's thread? Only you get determine what scenarios are allowed for discussion?

The scenario introduced by the OP is what is being discussed. It is THIS specific scenario that ghwellsjr made the incorrect claim about what the two observers measure.
You have tried in vain to move the goalposts several times by introducing other scenarios. If you want to discuss your scenarios, open your own thread and I will be more than happy to discuss with you.

[edit: as to ever growing time dilation, if there is only ever red shift seen via webcams, each sees the clock image in the web cam fall ever behind theirs, having ever larger disprepancy compared to clock comparisons at points where they meet on each circuit.]

I was just pointing out that you keep trying to put words in my mouth. I never made the claim, so stick with what I wrote, don't move the goalposts, ok?

 

[PAllen]

So, you are back to one last gasp attempt to prove that you are right, eh?
There is no mention of "ever growing" mutual time dilation, there is mention of mutual redshift. There is no "ever growing", so why do you try moving the goalposts again?
As to the way of connecting everything, the circum-equatorial "tube" is present from post 1.

Post #1 describe travel in a tube. The OP, so far as I've seen, never specified anything about how webcams got their signal. There are many possibilities, and I find yours the least plausible and meaningful - precisely because it erases the real the differential aging that occurs.

 

[PAllen]

The scenario introduced by the OP is what is being discussed. It is THIS specific scenario that ghwellsjr made the incorrect claim about what the two observers measure.
You have tried in vain to move the goalposts several times by introducing other scenarios. If you want to discuss your scenarios, open your own thread and I will be more than happy to discuss with you.

The OP actually raised several variants in the first dozen threads, most of which are incompletely specified. You seem to claim that only you are allowed to specify the details of what the OP meant or was concerned about.

 

[PAllen]

I was just pointing out that you keep trying to put words in my mouth. I never made the claim, so stick with what I wrote, don't move the goalposts, ok?

You've stated that by your definition of how the webcam's operate, each always sees red shift and time dilation. Since the OP clearly stated multiple circuits by the train, that clearly implies that the discrepancy between the webcams and direct clock comparisons at meeting points is ever growing.

 

[ghwellsjr]

I made it half circle in order to preclude further cheating. In the further posts, once I made sure there was no more cheating, I allowed it to be full circle.

Forgive me for all these questions, but I am just now learning all the rules for goalposts and I really don't want to cheat.

It is really simple, the signals from A to B and from B to A are always sent along one path. So, when A completes the circle, the signal path is twice the length for the semi-circle. This precludes any attempt at moving goalposts.

Well that does make it really simple--everything is doubled from your half-circle problems.

Not allowed.

That's why I asked first.

You stand that you were wrong and that you are trying to move some goalposts.

Sorry, I can't make sense of this statement but why do you think I'm trying to move any goalposts? Haven't I been playing fairly by your rules?

 

[GAsahi]

You've stated that by your definition of how the webcam's operate, each always sees red shift and time dilation. Since the OP clearly stated multiple circuits by the train, that clearly implies that the discrepancy between the webcams and direct clock comparisons at meeting points is ever growing.

Don't attribute to me what someone else said or you think that person said.

 

[ghwellsjr]

Of course that the observer in circular motion is not seeing the same[/color] amount of redshift, since he isn't perfectly equivalent to the inertial observer. The point is that BOTH observers measure redshift.

OK, so now you have agreed that after A makes one complete loop around and has rejoined B, they both have observed the same redshift but A stops seeing it as soon as he stops but B continues to see the redshift for a longer period of time, in fact, the period of time that it takes for light to travel around the fiberoptic loop.

Now I don't want to cheat or be accused of moving any goalposts or even wanting to move any goalposts but I just don't have any idea how you make the transition to the actual scenario where A does not stop but rather passes by B and continues around the loop a second time. Could you please explain how the redshift works for both A and B and how it correlates to the actual time the A and B can see on each others clocks as they A passes by B?

 

[GAsahi]

OK, so now you have agreed that after A makes one complete loop around and has rejoined B, they both have observed the same redshift but A stops seeing it as soon as he stops but B continues to see the redshift for a longer period of time, in fact, the period of time that it takes for light to travel around the fiberoptic loop.

The above means that you realized your mistake in claiming that one observer measures redshift while the other measures blueshift. This is progress.

Now I don't want to cheat or be accused of moving any goalposts or even wanting to move any goalposts but I just don't have any idea how you make the transition to the actual scenario where A does not stop but rather passes by B and continues around the loop a second time. Could you please explain how the redshift works for both A and B and how it correlates to the actual time the A and B can see on each others clocks as they A passes by B?

Huh? The situation repeats identically. The period of the phaenomenon is 2 \pi. Both A and B measure redshift as soon as A starts accelerating away from B.

 

[ghwellsjr]

The above means that you realized your mistake in claiming that one observer measures redshift while the other measures blueshift. This is progress.

But it's only a tiny bit of progress. I still have a long way to go to learning all the goalpost rules. And thank you for not accusing me of trying to cheat this time. I really don't want any cheating going on.

Huh? The situation repeats identically. The period of the phaenomenon is 2 \pi. Both A and B measure redshift as soon as A starts accelerating away from B.

I see, so you're say that A stops when he reaches B so that B can finish seeing the redshift coming from A traveling all the way around the fiberoptic loop and then A accelerates away from B a second time. Now I realize that as soon as A stops, the redshift that he sees coming from B also immediately stops (no more Doppler) but how does A know when B stops seeing the redshift so that he can start up again? Is he sneaking a peek at B's webcam? Wouldn't that be cheating?

 

[GAsahi]

But it's only a tiny bit of progress.

Yes, you are a slow learner.

I still have a long way to go to learning all the goalpost rules. And thank you for not accusing me of trying to cheat this time. I really don't want any cheating going on.

I see, so you're say that A stops when he reaches B so that B can finish seeing the redshift coming from A traveling all the way around the fiberoptic loop and then A accelerates away from B a second time. Now I realize that as soon as A stops, the redshift that he sees coming from B also immediately stops (no more Doppler) but how does A know when B stops seeing the redshift so that he can start up again?

A goes around in circles, nothing to do with B.

Is he sneaking a peek at B's webcam? Wouldn't that be cheating?

Where is this going? Are you just trolling now?

 

[ghwellsjr]

Yes, you are a slow learner.

If you quit teaching, then I'll never learn.

Where is this going?

I have no idea where this is going. You have all the rules and until you disclose them, I can't know them.

Are you just trolling now?

Not me, must be someone else.