Inertial Frames distinguished by proper times

[yogi]

Likewise for the conversation Robphy- but post # 30 was not directed to you.

My intent was to try to nail down the fundamental difference between apparent time dilation and actual time dilation in one way travel experiments, and I argued that a clock in an orbiting satellite is a perfectly good inertial frame - just as is a clock that is put in uniform linear motion. But in the latter case one doesn't have a convenient experimental platform because pulses transmitted between linearly moving frames must be Doppler compensated, and the changing distance between sources and receivers must also be accounted for. So my shift was intended to get some resolution or agreement as to the relative rate of time passage in the case of GPS and then carry this over to flat spacetime as per my original post.

I apologize if anything I said that may have offended you - I have always found your posts to be cordial and well thought out

Regards

Yogi

 

[Ich]

Yogi,

even if my posts lack the cordiality you seem to expect they could help you if you tried to understand SR. I became more aggressive when I found that you exhibit more and more a crackpot attitude that doesn´t fit in with this forum.
You claimed in former threads that an orbiting frame is a perfect (SR) inertial frame. You have been told that you´re wrong. Still you come back here and claim the same.
Likewise, you have been told repeatedly that initial acceleration woud not decide who is ageing more slowly. Still you ignore that.
In this thread, I tried (not for the first time) to give you clues to understand how SR works. You (obviously) took it as a personal attack and repeated even more aggressive your false claims.
That´s not how it works.
Just TRY to listen to the people you are discussing with. Then they´ll stay in tune.

 

[robphy]

Yogi,
Yes, I know that #30 wasn't directed to me.
I wasn't offended in any way from anything you said.
It's just that I felt that this thread was veering off the initial question without resolving it... and it wasn't clear [to me] where it was going. So, I was going to take a break from it.

robphy

 

[yogi]

Yogi,

.
You claimed in former threads that an orbiting frame is a perfect (SR) inertial frame. You have been told that you´re wrong. Still you come back here and claim the same...

There are many references that support what I have said - take a look at Road to Reality p 394, or Spacetime physics pp 26-31 if you want some authority as to the validity of orbiting satellites as free float inertial frames. In fact, they are preferable to Earth in many respects - and we normally consider the Earth as a good inertial frame for making relativistic experiments. I know there are limitations - they are not good inertial frames on a large scale where tidal forces are significant - but for the small volume inside a GPS satellite - they are as good as need be. Until you can sight me some authority to the contrary, I think I will go along with Penrose and Wheeler


As for your comment re the initial acceleration, I have said this is a direct consequence of Einstein's explanation in part 4 of his 1905 paper - I urge you to read it ... when two spaced apart clocks are synchronized and one is quickly accelerated to a constant velocity and then travels to the location of the other clock, the one which has been put in motion will be out of sync (read less time) with the other when they are compared. But Einstein doesn't stop there - he gives several more examples - concluding that a clock at the equator will run faster than one at the pole.

I would like to engage in a discussion where the responses do not turn into a shouting match - if anything I have asserted is in violation of a confirmed experiment, please advise. If you have an explanation of why the two clocks in Einstein's illustration are reading different times at the end of the experiment, I would like to hear it. But remember, they are being compared in the same rest frame at the end of the experiment and the one which has been accelerated into uniform motion reads less (this is not a reciprocal situation just as the two readings on the twin's clocks (in a round trip journey) is not reciprocal.

 

[robphy]

There are many references that support what I have said - take a look at Road to Reality p 394, or Spacetime physics pp 26-31 if you want some authority as to the validity of orbiting satellites as free float inertial frames. In fact, they are preferable to Earth in many respects - and we normally consider the Earth as a good inertial frame for making relativistic experiments. I know there are limitations - they are not good inertial frames on a large scale where tidal forces are significant - but for the small volume inside a GPS satellite - they are as good as need be. Until you can sight me some authority to the contrary, I think I will go along with Penrose and Wheeler

I happen to have these on my shelf right now.
Certainly, as you say, it is valid to regard "orbiting satellites as free float inertial frames"... and yes, "they are preferable to Earth in many respects". In addition, I agree that "they are not good inertial frames on a large scale where tidal forces are significant - but for the small volume inside a GPS satellite - they are as good as need be."

So, for a single satellite, there's no problem... you can locally apply SR at any event.

For two satellites meeting at an event, there's no problem... you can locally apply SR at that meeting event.

The problem is that when you try to consider two satellites at different altitudes and you have to correct one because of its altitude, then you are now certainly outside "the small volume inside a GPS satellite". So, with the two satellites taken together in one frame, special relativity doesn't apply.

 

[yogi]

robphy, yes - what you say is quite correct- - I noticed after posting #39 that Rindler uses a strict definition of an ideal inertial frame as being one totally removed from all G fields (this may have been what hurkyl was referring to in a previous thread). Rindler, however, then goes on to say, as a practical matter we don't have access to this utopia so we do our experiments in a less than perfect environment. So with that understanding, perhaps we can ask the question of whether there is any difference between the principles involved in 1) the measured loss of time between a velocity uncompensated orbiting clock S2 and the ground E clock...and 2) the predicted time loss in the linear experiment where one clock is put in motion after being initially synchronized with a distant clock which remains at rest (as per Einstein part 4 of 1905).

 

[Ich]

Hi yogi, I´ve been away for two weeks.

I have one problem with our discussion: I already told you almost everything I have to tell, and you did ignore it. It´s ok for me to start again and discuss things until we come to a solution. But I will not tell everything a third time. So I expect that you address the points I make explicitly and that you tell me either that you agree or where you don´t (and why).

There are many references that support what I have said - take a look at Road to Reality p 394, or Spacetime physics pp 26-31 if you want some authority as to the validity of orbiting satellites as free float inertial frames. In fact, they are preferable to Earth in many respects - and we normally consider the Earth as a good inertial frame for making relativistic experiments. I know there are limitations - they are not good inertial frames on a large scale where tidal forces are significant - but for the small volume inside a GPS satellite - they are as good as need be. Until you can sight me some authority to the contrary, I think I will go along with Penrose and Wheeler

1. Nobody doubts that there is a local IF valid for the satellite. But it is never (not even for an infinitesimal time) valid at the center of earth. Therefore you can´t use SR to compare satellite and center time. GR will give you the correct result.
2. It is still possible and instructive to examine the problem in SR if you treat the satellite´s orbit as a polygon.

As for your comment re the initial acceleration, I have said this is a direct consequence of Einstein's explanation in part 4 of his 1905 paper - I urge you to read it ... when two spaced apart clocks are synchronized and one is quickly accelerated to a constant velocity and then travels to the location of the other clock, the one which has been put in motion will be out of sync (read less time) with the other when they are compared. But Einstein doesn't stop there - he gives several more examples - concluding that a clock at the equator will run faster than one at the pole.

I read and understood the paper. I agree with everything that Einstein said but not with your understanding that initial acceleration somehow decides which clock will read less time. An example:
3. Two synchronized clocks are accelerated by the same amount to +v and -v. After some time, clock 2 accelerates to +v. You bring both clocks slowly together and compare times: clock 2 shows less. So in this case it´s final acceleration which breaks the symmetry.

If you have an explanation of why the two clocks in Einstein's illustration are reading different times at the end of the experiment, I would like to hear it. But remember, they are being compared in the same rest frame at the end of the experiment and the one which has been accelerated into uniform motion reads less (this is not a reciprocal situation just as the two readings on the twin's clocks (in a round trip journey) is not reciprocal.

4. It´s instructive to see that even in a symmetric setup the time of the "moving" reference frame goes faster than your own, if you observe it at your position. I´m convinced that you are unaware of this fact.

 

[yogi]

Ich - your point 1 - a clock on a tower at the North pole can be used as one IRF, and a GPS satellite at the same orbital height as a second.

point 2 - you don't need to construct a polygon - the free falling orbiting frame works fine - it can be an ellipse with any eccentricity - it is a perfectly good IRF because for any experiment conducted therein inertia is isotropic

point 3 - I disagree - the situation is changed anytime any clock undergoes acceleration. But it is not the acceleration per se that affects the difference in time when the two clocks are later compared; acceleration is simply a means employed to change the speed between two clocks.

point 4 - I am fully convinced that observers in equivalent inertial frames will measure the apparent rate of the other guys clock to be running slower. But ...the whole post is not about apparent time dilation, it is about what happens when two at rest separated clocks are synchronized in the same frame, and one is put in motion (accelerated) and when it reaches the other clock, it reads less. Read part 4 of the 1905 paper again. In this description of what happens (I think Einstein used the word peculiar) there is only one acceleration - at the beginning. This is why I have consistently maintained over the course of numerous threads, you cannot sync two clocks on the fly - you can read the time of a passing clock by its hands when it is near - but you cannot be guaranteed that the other clock will be running at the same rate. At the end of the one way journey the two clocks read differently - the clock put in motion does not have to slow down at the end to be read - it can be read by the clock which has not moved and a comparison made as it passes by - but that is not true at the beginning - the initial conditions (namely synchronization followed by an acceleration) is vital to the conclusion reached by Einstien - namely, that one clock reads more than the other at the end of the one way voyage

 

[Ich]

1. Yes, that´s two IRFs. But one of those is only locally (and only for a short time) valid and does not include the north pole most of the time. What you try to do is to compare clocks in the two frames, using only SR. That is only possible if both clocks are always covered by both IRFs.
Relativity is a theory of relations (as the name implies). To calculate something, it is not sufficient that both observers are in a local IRF. You have to specify how these IRFs move relative to each other. And SR only deals with linear motion and global IFRs. Everything else is curved spacetime, and therefore you also start with a broken symmtery (see 2.).
2. Same problem. Gravity is not included in SR, and a IRF that travels in circles certainly does need gravity. To calculate "clock rates", you need GR, even if you can use weak field approximations. If you trie to get around that, you only confuse yourself. Why don´t you calculate circular motion the way SR allows it?
3. You disagree with what? I only said that the situation is symmetric until clock 2 accelerates. At this point you decide in which frame to compare clocks and which clock "really" loses time. Note: the decision is made as the last step of the experiment. Initial acceleration has nothing to do with it. Do you agree with that?
4.

the initial conditions (namely synchronization followed by an acceleration) is vital to the conclusion reached by Einstien - namely, that one clock reads more than the other at the end of the one way voyage

No, it is not. You can: a) sync two separated clocks at rest. b) sync a moving clock on the fly with the first clock when they meet. c) compare its reading with the second clock when they meet. The outcome is the same, and no acceleration is involved.

you cannot sync two clocks on the fly - you can read the time of a passing clock by its hands when it is near - but you cannot be guaranteed that the other clock will be running at the same rate.

Just to be sure we speak of the same thing: "sync" means that you set the clock to a certain value, it has nothing to do with clock rates.

 

[Hurkyl]

2. It is still possible and instructive to examine the problem in SR if you treat the satellite´s orbit as a polygon.

Minor nitpick -- "thou shalt not use calculus" is not one of the postulates of SR. There is no reason to restrict one's self to polygonal curves aside from computational simplicity.

 

[Ich]

No, but it is what Einstein proposed in the paper yogi is referring to, and you can learn a lot when you calculate the effect of small translations and rotations. The result is the same, but you can see how it is achieved.

 

[yogi]

Ich - We are using the word sync differently - both definitions are valid - I am using it mean: "to render synchronous in operation" That is why I am claiming, in general, two clocks cannot be synchronized "on the fly" They must both be in the same reference frame (at rest wrt each other). When one is accelerated after using Einstein synchronization, I claim they will not be running in sync thereafter.

 

[yogi]

Post 44 - item 1. Exactly - each clock is a valid local IRF. If the orbit bothers you - forget it - consider the case where two spaced apart clocks are synchronized (using my definition that they are running at the same rate) and one is later accelerated to a uniform velocity v wrt the other. I claim the two clocks are no longer in sync and that to this extent the fames are no longer equivalent. Inertial experiments are the same when carried out in each frame, but the clock in the frame that was put into motion runs at a slower rate than the clock which remained in the rest frame in which the clocks were originally synchronized. I am aware there is an alternative explanation of why the two clocks do not read the same when the moving clock reaches the stationary clock - but I think it is fallacious

 

[Ich]

#47: good to know; I already got the impression that we´re not talking the same things. I suggest that we use the definition I gave, because it´s highly unusual to fiddle with clock rates. From Wikipedia: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. There is nothing to tune.

 

[Ich]

#48: Wonderful, a precisely stated claim. Let´s discuss it.

To avoid misunderstandings. we´re talking about SR here and not some personal theory how things should be.

You claim that the accelerated clock ticks slower than the one staying "at rest". That means, the amount of time lag is proportional to the time you let the clocks fly until you compare them.
How do you deal then with the following prediction of SR:
If you accelerate the second clock to match the velocity of the first clock immediatly before you compare them, the second clock will read less exactly the amount that you think the first one would.
What SR says is that moving frames are equivalent (regardless which one accelerated) until you decide in which frame you want to compare the clocks. That contradicts your claim.

 

[yogi]

Ich - I think you are trying to imply things I have not said. If you are saying that two separated clocks (say A and B) at rest wrt each other, and A is given a brief acceleration toward B, and travels most of the distance at constant velocity v, but just before reaching B, B is accelerated in the same direction to a velocity v, so now both A and B are moving together at velocity v relative to some object in the original frame of reference. Then A and B now run at the same rate because they are in the same frame (I hope we agree on that) but they do not read the same time - When B pulls alongside A, the time on the A clock will be less than the time on the B clock (do we agree on this)?

In fact, it is not necessary to wait until A is near B. For example, if A is at the origin of the X axis, and B is at X = 100 miles and both blast off in the direction of the + X axis at the same time with identical accelerations for identical time periods (their integrating accelerometers are set to cut off at the same velocity) Both will have reached a velocity v in the direction of the + X axis, so do you think there will be any difference in the reading on A's clock relative to B's clock now that they are traveling together in the same frame but still equally separated?

 

[Ich]

§1: Maybe I managed to misunderstand your claim. I agree with you that A will read less time.
What I had in mind was the following setup: A and B start at the same point, A being accelerated. A should "tick at a slower rate" from then. If you then accelerate B to match velocity with A, A and B should tick at the same rate. So if you bring A and B together, you would expect A to read less. SR says B will read less.

§2: We better don´t use accelerating frames. One has to be extremely careful with the setup and the calculations. For example, in your setup the distance between A and B would increase, and A will indeed read less time as he was at the bottom of a "gravity well". I think your §1 is enough to decide whether your view is consistent with SR´s.

 

[yogi]

§1: Maybe I managed to misunderstand your claim. I agree with you that A will read less time.
What I had in mind was the following setup: A and B start at the same point, A being accelerated. A should "tick at a slower rate" from then. If you then accelerate B to match velocity with A, A and B should tick at the same rate. So if you bring A and B together, you would expect A to read less. SR says B will read less.

After B accelerates to the same speed as A (same direction) then A and B will run at the same rate (I guess we agree on that). They are separated in space, but both are in the same frame at rest wrt each other (I assume we agree on that) My question is: "How do you propose to bring them together?" What if they are not brought together - each simply interrogates the other with radio signals? If they are not brought together, which clock will read more time?

 

[Ich]

We agree on both points.

My question is: "How do you propose to bring them together?" What if they are not brought together - each simply interrogates the other with radio signals? If they are not brought together, which clock will read more time?

To compare clocks, you either interrogate them with radio signals (same procedure as Einstein suggested in his paper) or you bring them together by slow transport (v<<c). It is a feature of SR that both procedures will give the same result: A will read more time.

 

[yogi]

Ich: That is interesting - let's see - we could actually do an orbiting version of what you suggest - let's launch a GPS satellite clock that has been corrected for height but not velocity - the two clocks are in sync in the Earth frame before launch - A is accelerated into orbit and flys for one year, during which time A will run slower than the B clock on earth. One year later we launch the B clock into an identical orbit (after correcting for altitude) and now A and B are side-by-side, so both are running at the same rate, but there will be a difference in the lapsed time accumulated on the A clock and the B clock during the one year that passed between the two launches. Are you saying the A clock will read more time, or are you saying the analogy is flawed?

I am assuming in the linear case that you proposed, the conclusion that A will read more time was arrived at using the methodology adopted by Einstein (1918) and Born to explain the twin thing. If so, I will comment upon that.

 

[Ich]

No, you could not do an orbiting version of this. I can explain later why not and how SR explains the effect in circular motion.
But for now I strongly suggest that we stop complicating things until we got the basics right.
I don´t know the methodology of Einstein and Born. It is simply the old simultaneity thing: Until A and B join frames, each one is equally right (or wrong) to say that the other´s clock is ticking slower. When B suddenly accelerates, A did not change his view of things. That means, B is still (nearly) at the same position, and his clock (nearly) shows the same time as before the acceleration. So the result that B shows less time still holds.
But B´s notion of simultaneity changed drastically. "Now" A´s clock is ahead of his, and this won´t change if the clocks are brought together.
WARNING: the following may be unintelligible. Ignore it, if you can´t make sense of it. It´s kind of a metaphor, but not too far from truth.
There is nothing important happening with A´s and B´s clock at this time. It is more like B suddenly recognized that his time was "flowing in the wrong direction" all the time. But which direction is the right one is decided only when you decide in which frame you want to compare clocks. If it would have been B´s frame, A´s time would have been flowing in the wrong direction.

 

[yogi]

Until A and B join frames, each one is equally right (or wrong) to say that the other´s clock is ticking slower. When B suddenly accelerates, A did not change his view of things. That means, B is still (nearly) at the same position, and his clock (nearly) shows the same time as before the acceleration. .

If I correctly picture what you painted - A and B are synchronized at the origin of an x-y coordinate system and A first accelerates to a velocity v along the positive x-axis - the A clock will run slower as long as this condition persists - for example, A could travel for a long time at v = 0.5c relative to B and would wind up with less accumulated time when arriving at Altair (we assume Altair is at rest relative to the origin of the coordinate system). Now just before A reaches Altair, B quickly accelerates to 0.5c wrt the coordinate axis 0,0 in the same direction (along the + axis toward Altair) - and you say that B's clock shows the same (nearly) time as it did before B commenced accelerating (OK agreed). So during A's long journey 1) the A clock either ran slower than the B clock, or 2) the spatial distance D between the origin and Altare is contracted from A's point of view so his clock only recorded a time L/v. (where L is the contracted length). Either way, before B accelerates, do you agree that A's clock will have recorded less time as A nears Altair (not yet decelerating) than clocks at rest with respect to the origin of the coordinate system where B has remained at rest? If so, then I do not understand how you arrive at a result that predicts B will show a Real (not apparent) lesser time than A after B completes his short duration of acceleration.

 

[Ich]

If I correctly picture what you painted - A and B are synchronized at the origin of an x-y coordinate system and A first accelerates to a velocity v along the positive x-axis - the A clock will run slower as long as this condition persists - for example, A could travel for a long time at v = 0.5c relative to B and would wind up with less accumulated time when arriving at Altair (we assume Altair is at rest relative to the origin of the coordinate system).

No, you start again mixing "observer" and "observer´s rest frame". It may sound like nitpicking, but it is crucial to understand the difference:
A will read less time than a clock positioned at Altair which is synchronized with B in their common IF. It will not read unambiguously less than B´s clock, because B himself is not at Altair, and comparing times at different positions is a very special thing in relativity.

Now just before A reaches Altair, B quickly accelerates to 0.5c wrt the coordinate axis 0,0 in the same direction (along the + axis toward Altair) - and you say that B's clock shows the same (nearly) time as it did before B commenced accelerating (OK agreed).

Yes.

So during A's long journey 1) the A clock either ran slower than the B clock, or 2) the spatial distance D between the origin and Altare is contracted from A's point of view so his clock only recorded a time L/v. (where L is the contracted length). Either way, before B accelerates, do you agree that A's clock will have recorded less time as A nears Altair (not yet decelerating) than clocks at rest with respect to the origin of the coordinate system where B has remained at rest?

Again, don´t compare clocks at different positions. That´s where all the trouble comes from. I agree that A will read less time than a clock synchronized with B when A passes it, eg the Altair clock when A is at Altair.

If so, then I do not understand how you arrive at a result that predicts B will show a Real (not apparent) lesser time than A after B completes his short duration of acceleration.

And again, B is not at Altair. A will read more time than a clock at Altair which is synchronized with B after B´s acceleration. B´s "simultaneity plane" or however you call it shifted during acceleration.
If you then bring A and B slowly together, the result stays the same: B will Really read less than A.

 

[yogi]

All the clocks in the coordinate frame can be synchronized prior to A's initial acceleration - So if we add a clock at Altair (call it D) it can be synced with A and B and will read the same as A and B before any accelerations have taken place. When A is accelerated, B and D are still in sync (reading the same time and logging time at the same rate).

1) When A arrives at D, A will read less than D. Do we agree on this?
I think from your post above, the answer must be yes

2) If Yes, do you agree that B and D still read the same time (prior to B's acceleration). If not, how did they get out of sync?

3) If yes to no 2 above, do you agree that A reads less than B immediately prior to B's acceleration?

- probably not - but in any case you conclude that after B's acceleration B will read less than A...and that is where we part company

Invariably the analysis of these interesting problems skips from actual real times (local times or proper, whatever you want to label them) logged by a clock to an apparent observation that typically involves a rapid shift in the slope of the plane of simultaneity

...so in the distant inertial system of A, the time on B's clock has rapidly changed as viewed by A - actually B's clock would have to lose a lot of time (run backwards) during a short period of acceleration - because prior to the acceleration, B clock should read the same as D clock - but physically the B clock cannot run backwords just to accommodate the book-keeping. While some folks are comfortable with such abstractions, I am not. To me the interest in these problems is in finding an explanation that is consistent with a physical reality.

 

[Hurkyl]

so in the distant inertial system of A ... because prior to the acceleration, B clock should read the same as D clock

The B clock and the D clock have never read the same time, as measured by any inertial reference frame in which A is stationary for its journey.

To me the interest in these problems is in finding an explanation that is consistent with a physical reality.

Coordinate charts are not physical reality. It is not inconsistent with reality for things to run backwards according to a coordinate chart. (Though technically such a thing is a generalization of a coordinate chart)

 

[yogi]

The B clock and the D clock have never read the same time, as measured by any inertial reference frame in which A is stationary for its journey.

In the quote you left out most of what I was saying - so it comes out wrong - B clock reads the same as D clock in the BD frame prior to B's acceleration. I did not say B and D are to be read in the A frame - B and D were synchronized initially and they stay in sync until B is accelerated. A reads less than D when A arrives at D, B reads the same as D prior to B's accelertion (B and D are still at rest in the same frame).

The real time lost on A's clock during the journey relative to B (analogous to the stay-at-home twin) is not going to be altered by B accelerating after the game is over- B can accelerate to v and immediately decelerate to 0 and wind up back in the BD frame only slightly displaced from the 0,0 origin - this will not influence any clock involved except to a small degree B - it doesn't wipe out the years of time lost by the A clock.

 

[Hurkyl]

I did not say B and D are to be read in the A frame

Then I am clueless as to what anything in your last paragraph of #59 means.

 

[Ich]

We are always encoutering the same problem: You compare times at different locations and treat the results as if they were invariant physical realities. This is not consistent with SR:

So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

Example:

3) If yes to no 2 above, do you agree that A reads less than B immediately prior to B's acceleration?
- probably not - but in any case you conclude that after B's acceleration B will read less than A...and that is where we part company

You compare the reading of two clocks. One is defined adequately: B`s reading at the time and place where he starts accelerating. The value is observer-independent as it represents a proper time.
The other reading is not defined sufficiently: When do you read A´s time? Obviously "at the same time". And what does "at the same time" mean? Prior to B´s acceleration it means, for example, "when A passes D". After B´s acceleration it may mean "when A passes the next star behind Altair" (we used no numbers until now, so that will do). Of course A will read then more time.
But what happened? Did B "run backwards in time"? Did A "jump forwards in time"? No. We simply compared different things and came to different results.

Invariably the analysis of these interesting problems skips from actual real times (local times or proper, whatever you want to label them) logged by a clock to an apparent observation that typically involves a rapid shift in the slope of the plane of simultaneity

All the readings I mentioned are, of course, readings of proper time. Actual real times. Invariant. So where do all those "apparent" time shifts and all this come from?
You ask "which clock reads less?", and think implicitly that this question must have one invariant answer. That´s where you and SR part company.
I encourage you: try to find a paradox in my setup without comparing times at different locations. Use as many clocks as you like, sync them in which frame you like, and compare the readings of any two clocks which are at the same position.
The result will confirm that B reads less than A when they are brought together. It will contradict your claim that A reads less due to initial acceleration. In fact, it is completely irrelevant wheter A accelerated or not.

 

[yogi]

"All the readings I mentioned are, of course, readings of proper time. Actual real times. Invariant. So where do all those "apparent" time shifts and all this come from?
You ask "which clock reads less?", and think implicitly that this question must have one invariant answer. That´s where you and SR part company.
I encourage you: try to find a paradox in my setup without comparing times at different locations."

The local reading on a clock can be compared with the local reading on another clock which is displaced (separated) as long as they are not in relative motion. There is no mystery - until B accelerates, B and D read the same (they are at rest in the same frame). When A reaches D, D and A can each communicate to the other what their own local clock reads. If v = 0.5c, gamma = 0.866, so if D clock reads 100 years at the time of A's arrival, A clock will read 86.6 years. And since B has remained in sync with D all during the time of A's flight, B will also read 100 years, as will every other clock that has remained at rest wrt B and D. if you don't agree with this, tell me what you think B clock will read at the time A arrives at D.

B of course, does not have access to the information that A has arrived - nonetheless, B will know when to accelerate by the reading on his own clock - that is, since he knows v and he knows the distance to D as measured in the rest frame, he will know that he should accelerate when his own clock reads 100 years.

 

[yogi]

Then I am clueless as to what anything in your last paragraph of #59 means.

Sorry - to clarify - A and D can each read the other as A passes D. A does not directly read B at this time - the time on B is established (determined) by the prior synchronization of B and D. This holds good until B accelerates.

 

[yogi]

Here is a simple experiment to demonstrates that the first clock to be accelerated records less time - create two pions in the lab - immediately accelerate them to 0.999c and observe that on average they travel 15 meters which corresponds to a life extension of 20 times their at rest half life. Now create two pions A and B and immediately accelerate A to 0.999c. After pion A has traveled one meter, accelerate pion B to 0.999c Which one decays last (or to put it another way, which travels the farthest before decaying)? Obviously A.

 

[Ich]

if you don't agree with this, tell me what you think B clock will read at the time A arrives at D.

That´s easy:
B reads
-50 years for an ultrafast observer traveling B->D
-74.7 years for A
-100 years for D
-150 years for an ultrafast observer traveling D->B
-any value between those for other observers.
always assuming that B does not accelerate after 100 years.
And, as if it couldn´t be worse, check this out:
Clock E, comoving and synchronized with A but 43.3 LY behind (so that it meets B at the same time A meets D), proves without doubt that at the time A meets D, B reads 74,7 years - less than A.
"Proves without doubt" means that, following your argumentation, you are of course allowed to compare A and E as they are in the same frame:

The local reading on a clock can be compared with the local reading on another clock which is displaced (separated) as long as they are not in relative motion. There is no mystery - until B accelerates, B and D read the same (they are at rest in the same frame).

Do you agree that there must be something wrong with your view?

 

[yogi]

Something is wrong with someone's view. Clocks do not run backwards.

 

[Ich]

Something is wrong with someone's view. Clocks do not run backwards.

Very helpful, thanks.
I´ll return to the guided discussion style.
1.

B reads
-50 years for an ultrafast observer traveling B->D
-74.7 years for A
-100 years for D
-150 years for an ultrafast observer traveling D->B
-any value between those for other observers.

Do you agree that this is what SR says about B´s reading at the time A meets D?

Somehow you seem to have the notion that of all those values, 100 years is the "real" one, because B and D are at rest wrt each other.

2.

Clock E, comoving and synchronized with A but 43.3 LY behind (so that it meets B at the same time A meets D), proves without doubt that "at the time" A meets D, B reads 74,7 years - less than A.

E and A are at rest wrt each other. Do you agree that
a) SR says that B reads less than E "at the time" A meets D and
b) the statement "B reads less than A" is just as real as the statement "A reads less than B", because both are backed by clocks at rest wrt each other?

3. Do you agree that, as we get to contradictory statements, the notion of "absolute simultaneity" is for the circular file, even if both observers are at rest? (that´s why I quoted Einstein. He is very clear about this)

 

[yogi]

If you try to judge time on a distant clock in relative motion wrt the frame in which the meaurment is being made, you get apparent readings. Real time on a clock is proper time - proper time is local time - that read by an observer at rest wrt the clock. At the start of the experiment, A,B and D are all at rest and set to zero. All real times read on any of these clocks thereafter must be positive.

You posed this problem of a second high speed particle starting out at a later time than a first particle. I claim the local time on the clock that started last will be greater than the one that started first - you say otherwise.

In post #66 I suggested you think about it in terms of the physics of local time. Let's do it again - create two pions A and B at the same point - each has an average lifetime in the lab of 0.02 usec. Accelerate A immediately to 0.99c. Wait 0.01 and then accelerate B to 0.99c. Which one do you think will travel the longer distance?