Solving Basic SR Confusion for Twin Paradox

[robphy]

I would concur Rob, the distinction between GR and SR gets blurred in this example. If we say that whenever we introduce a consequence of acceleration, we are tacitly relying upon GR

No, we are only relying on GR if we try to consider things from the non-inertial "frame" of the accelerating object. But we can perfectly well use inertial frames to calculate the elapsed time on an accelerating clock and figure out the age difference.

In both of these quoted statements, "GR" is being referenced with respect to its methods (e.g., the use of noninertial coordinates systems), akin to methods in Riemannian geometry (e.g., the use of non-Cartesian coordinates), which can be applied to both flat spacetimes (like Minkowski spacetime) and curved spacetimes. Thus, these uses of the term "GR" are not the modern geometrical interpretation [as found in Wald] which is more focused on geometrical structures rather than merely its methods.

 

[yogi]

Jesse: "And if we did know which was accelerated at some distant time in the past, would this affect your answer about which clock was running faster, even if the acceleration happened millions or billions of years ago and they've both been coasting since? This is something I've never been clear on about your arguments, so please give me a yes or no answer"

That is a question that is pondered in many articles that attempt to find an answer to real time dilation - it implies there are intrinsic clock rates tied to every object, and the rate at which time passes relative to other objects depends upon their relative velocity -

What I would say again, is that a careful reading of Einstein's examples in part IV of the 1905 paper can only lead to the conclusion that an asymmetry is created when one of two synchronized clocks is accelerated. The peculiar results Einstein refers to are real age differences as measured by two clocks at rest in the same frame - not apparent time dilations observed between two relativly moving frames while they are in motion. When one of two spaced apart synchronized clocks A at rest in the same frame is briefly accelerated to a velocity v toward the other clock B, it will be found that the A clock, after coasting for a time that is long compared with the acceleration duration, A clock will have accumulated less time when it reaches B. He tells you the clocks will be out of sync when compared in the same frame. There is no ambiguity is what is being conveyed - although you always want to weasel word it to introduce a different experiment to avoid the consequences.

I will answer some of the other questions you have posed later - right now I cannot give you a yes or no to your question because there are different ways to arrive at the results predicted by Einstein.

 

[yogi]

Jesse - there is an aspect of what I have said in post 32 that deserves more comment. Einstein interpreted the peculiar results based upon a manipulation of transforms that were derived by considering inertial frames in relative motion as equivalent - so his conclusion that there would be an age difference in the case of one of two accelerated clocks is fiat - it does not follow from the derivation - that bothers me and a lot of people - maybe you also. But Einstein was intuitive - he knew the result had to conform with the experiments and his own view of the impossibility of detecting motion wrt space - at some point time dilation had to be real - so he simply derives the result based upon an inconsistent premise and labels it as peculiar. This is the way things stood for 13 years - and after thousands of critical words had been written on the subject - then in 1918 he attempted to rationalize the 1905 result based upon GR - introducing a pseudo G force, he sanctified the 1905 result by providing a cause that explained the asymmetry.

 

[pervect]

This reasoning in #33 is really baroque.

The easy route is this: clocks always tick at 1 second per second. Philosophically, clocks do not tick at "different rates" at all. (I don't generally like to get into philosophy too much, but this is basically a large part of the problem here).

This is where yogi is confused. By taking the philosohical view that clocks always tick at 1 second per second, it becomes clearer that in order to compare different clocks, one needs to specify a means by which the comparison is to be made.

The apparent rates of the clocks are not dependent on the clocks themselves, the apparent rates are dependent on the comparison process

This philosphical confusion on yogi's part has been going on for a long time, so I suppose this post won't clear it up, but it's worth another shot. Yogi insists that the apparent rate difference between clocks depends only on the clocks. This is wrong. The apparent rate difference depends both on the clocks, and the means by which they are compared.

When in #32 yogi asks

And if we did know which was accelerated at some distant time in the past, would this affect your answer about which clock was running faster, even if the acceleration happened millions or billions of years ago and they've both been coasting since?

The answer is "it depends on how you compare them".

 

[yogi]

Pervect - you are misreading what has been said - your quoting from post 32 was a question posed by Jessee - not me. I have not answered the question because it is undefined as presented. Secondly, there is no mystery in comparing clocks brought to rest in the same frame to see if one has accumulated more time in a particular experiment than another. At no time do I suggest we make comparisions of clocks while they are in relative motion. What is at issue in Einstein's examples in Part IV is why two clocks initially in sync are out of sync at the end of the travel period. Einstein in 1905 does not discuss acceleration as factor - in fact he is dismissive of its influence by relegating it to a short duration relative to the overall travel time. Real age differences occur in the one way travel experiment - clocks measure the age difference - where do I imply that the clocks are affected - Einstein uses the clock as the thing that measures time, and so have I. We all know that clocks tick at one second per second in their own frame - where did I say otherwise?

 

[yogi]

Jesse - in your your post 26 you state:
" No, I just deny the implications you draw from these examples, implications which Einstein never remotely states himself, and which in order to endorse would require him to deny the basic premises of his own theory."

Well, when I use the same language as Einstein and recount the same experiment, you are of course free to say that I have misinterpreted his teachings. But I am no different that the thousands who have attempted to rationalize his "peculiar results" with the underlying foundations of SR.
Recall that Einstein, in commenting upon the peculiar results, does not attempt to explain them - nor does he suggest that we make measurments during the experiment - there is a start event where both clocks are in sync in the same frame and there is an end event where both clocks are in the same fame but "out of sync" Since I do not know how that can happen, I assume there is something different about the two frames that occurred during the experiment. We do not like the idea of a preferred frame, so we fall back upon the idea that acceleration somehow modified the characteristics of one frame or the other. If that is a Cardinal Sin, then please tell me how I can avoid hell.

Again from the same post, you state: "You get a real difference of the times on both clocks, but that doesn't tell you anything about which actually accumulated more time since the moment the clock accelerated, since different frames disagree about the initial time on the non-accelerating clock at the moment the first clock accelerated (since they disagree about simultaneity), and there is no reason to prefer the point of view of the frame where they were initially at rest over other inertial frames except your own prejudices which you never provide the slightest reasoned argument for."

Well, cannot the time on the non-accelerated clock be checked by an adjacent clock which is in sync with the clock that is located at the final destination? Maybe I am not understanding your objection. When Einstein set up the thought experiment, he didn't address this - so I sort of figured he knew what he was doing - and skipped over it myself.

So is this the bases for your criticism of my analysis or should it be directed to Einstein's sloppyness?

 

[JesseM]

Well, when I use the same language as Einstein and recount the same experiment, you are of course free to say that I have misinterpreted his teachings.

But you don't use the same language, you say things like "both clocks cannot be ticking slower than the other" which Einstein never hinted at. Also, your whole argument is based on discounting the relativity of simultaneity, and saying that if two clocks are "synchronized" in their own rest frame, this means they are synchronized in some universal, frame-independent sense, so that if you accelerate one to meet the other and it shows a smaller time, we are somehow forbidden to explain this from the perspective of a frame where the clocks were not synchronized at the moment the clock was accelerated. But Einstein was clear to use "synchronous" only in a frame-dependent, relative sense:

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2*tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

I can really think of nothing in this description that I would modify if I wanted to describe the same experiment myself--does this mean you think that I am in secret agreement with you about there being a real truth about which clock was ticking slower? If not, exactly what is there in this description that makes you think Einstein was thinking this way? How do you think a person like me, who clearly doesn't believe there is a definite truth about which clock was ticking slower after the acceleration, would describe the experiment differently?

Recall that Einstein, in commenting upon the peculiar results, does not attempt to explain them

What do you mean "explain" them? What needs explanation?

nor does he suggest that we make measurments during the experiment - there is a start event where both clocks are in sync in the same frame and there is an end event where both clocks are in the same fame but "out of sync" Since I do not know how that can happen, I assume there is something different about the two frames that occurred during the experiment.

Don't know how what can happen? And what "two frames" are you talking about? No second frame was used in analyzing the experiment. Of course you could analyze it from a different frame, like the frame where clock A was at rest during the time it was closing in on clock B, but this frame would predict exactly the same thing about the times on each clock when they meet. So, for someone who accepts relativity, there is no mystery here--maybe there is a mystery to you because you are unwilling to accept the relativity of simultaneity, but stop projecting that onto people like Einstein when they give absolutely no indication of agreeing with you in their words.

We do not like the idea of a preferred frame, so we fall back upon the idea that acceleration somehow modified the characteristics of one frame or the other.

No, as long as we stick to inertial frames, we don't have to say acceleration modified any frames at all. The laws of physics in the frame where clock A was at rest during the time it was moving in the "stationary frame" are exactly the same as in the stationary frame.

Again from the same post, you state: "You get a real difference of the times on both clocks, but that doesn't tell you anything about which actually accumulated more time since the moment the clock accelerated, since different frames disagree about the initial time on the non-accelerating clock at the moment the first clock accelerated (since they disagree about simultaneity), and there is no reason to prefer the point of view of the frame where they were initially at rest over other inertial frames except your own prejudices which you never provide the slightest reasoned argument for."

Well, cannot the time on the non-accelerated clock be checked by an adjacent clock which is in sync with the clock that is located at the final destination? Maybe I am not understanding your objection. When Einstein set up the thought experiment, he didn't address this - so I sort of figured he knew what he was doing - and skipped over it myself.

So is this the bases for your criticism of my analysis or should it be directed to Einstein's sloppyness?

Einstein wasn't being "sloppy", he just didn't feel the need to analyze the same problem from the point of view of multiple frames. If you want to analyze things from the point of view of a different frame K'' where clock A was at rest after it accelerated (during the time interval when it was moving towards B at velocity v as seen in the 'stationary' frame' K), then in this frame K'' clock B was not synchronized with clock A at the moment clock A accelerated. You could indeed check this with clocks adjacent to A and B which are at rest in frame K''--if we call two clocks at rest and synchronized in this frame C and D, and if clock C was adjacent to clock A when C read 12:00 and A also read 12:00 at that moment, then if clock D was adjacent to B when D read 12:00 as well, clock B would read some significantly later time at this moment. Einstein spent the whole first section of his paper explaining how simultaneity should be defined physically in a given frame, so if you have really understood and assimilated that section this shouldn't seem strange to you.

 

[yogi]

From Jesse's post 37: "But you don't use the same language, you say things like "both clocks cannot be ticking slower than the other" which Einstein never hinted at."

That is simply a general statement made by numeros authors (including Brian
Green) that reflects the impossibility of such a situation - I assumed you you recognize it The point is the comment is introductory to the analysis - while the clocks are in relative motion, each observer can set up an experiment that indicates that the other guys clock is running slow - that has nothing to do with Einstein's experiment that you have recited.

I will treat each of your comments in a separate post

 

[yogi]

From Jessee's post 37. "I can really think of nothing in this description that I would modify if I wanted to describe the same experiment myself--does this mean you think that I am in secret agreement with you about there being a real truth about which clock was ticking slower? If not, exactly what is there in this description that makes you think Einstein was thinking this way? How do you think a person like me, who clearly doesn't believe there is a definite truth about which clock was ticking slower after the acceleration, would describe the experiment differently?"

Can I conclude from your statement that there is no difference between the time accumulated by the A clock and the B clock? In other words, we start with A and B separated but in sync - A moves to B, and stops. Both clocks are in the same frame as they were before the motion, but they are now together. Do they read the same?

 

[yogi]

From Jesse's post 37: "What do you mean "explain" them? What needs explanation"

Oh, about 10,000 articles that were written between then and now If it didn't need explaining, why did Einstein take the time to write his 1918 article explaining it?

 

[yogi]

From Jessee's post 37: "Don't know how what can happen? And what "two frames" are you talking about? No second frame was used in analyzing the experiment. Of course you could analyze it from a different frame, like the frame where clock A was at rest during the time it was closing in on clock B, but this frame would predict exactly the same thing about the times on each clock when they meet. So, for someone who accepts relativity, there is no mystery here--maybe there is a mystery to you because you are unwilling to accept the relativity of simultaneity, but stop projecting that onto people like Einstein when they give absolutely no indication of agreeing with you in their words."

The second frame is the one in which the A clock is at rest during the coasting phase - it is not mentioned because as I have said many times, the peculiar results are due to the fact that one of two separated clocks originally in sync is put into motion - once in motion, a second frame is created. When the clock put in motion is stopped, it is then in the original frame - during the experiment, B clock was one frame and A clock was in the other. Einstein predicts that the two clocks are now out of sync -

Einstein does not mention simultaneity in describing the time differences - but if you insist, there is no problem in synchronizing two clocks in the same frame initiall nor is there any problem in reading them in the same frame after the moved clock is returned - simultaneity is an issue in relatively moving frames - here both measurmentws are made while both clocks are at rest in the same frame

 

[yogi]

Jessee --Before posting more - our whole difference turns on your answer to post 39. If you do not believe Einstein intended to predicta real substantive temporal difference (as you have asserted in one of our previous discussions- then fine - we can discuss that - if you think the moved clock accumulated less time, then tell me how that can happen if the frames are identical

 

[JesseM]

That is simply a general statement made by numeros authors (including Brian
Green) that reflects the impossibility of such a situation

Are you claiming that numerous authors, including Brian Greene, say it is impossible that there is not a single truth about which clock is running slower? I've asked you to provide such a quote before, and you never do. Please provide one, I think we will see that, as with the Einstein quote, you are simply reading in implications that weren't intended by the author.

"I can really think of nothing in this description that I would modify if I wanted to describe the same experiment myself--does this mean you think that I am in secret agreement with you about there being a real truth about which clock was ticking slower? If not, exactly what is there in this description that makes you think Einstein was thinking this way? How do you think a person like me, who clearly doesn't believe there is a definite truth about which clock was ticking slower after the acceleration, would describe the experiment differently?"

Can I conclude from your statement that there is no difference between the time accumulated by the A clock and the B clock?

Of course not, what about my statement would possibly lead you to conclude I would think that? Once again you have a knack for reading implications in that are not even remotely suggested by the text you quote.

The second frame is the one in which the A clock is at rest during the coasting phase - it is not mentioned because as I have said many times, the peculiar results are due to the fact that one of two separated clocks originally in sync is put into motion - once in motion, a second frame is created.

It is meaningless to talk about frames being "created", since frames are just coordinate systems, there is no need to have an object at rest in a particular frame in order to analyze a problem from that frame.

When the clock put in motion is stopped, it is then in the original frame

It is at rest in the original frame, but again, you are not somehow forced to use one frame or another by the motion of the objects, you can continue to analyze the situation from the frame where the A clock was at rest during the coasting phase, or you could analyze the situation from the perspective of a frame where neither A or B was at rest at any time in the entire experiment, it doesn't matter. This is analogous to the fact that you don't have to put the origin of your spatial axes at the position of one of the clock, you could have the origin be light years away from either clock. You are completely free in your choice of inertial coordinate systems to analyze any problem, they're just coordinate systems and nothing more!

Einstein does not mention simultaneity in describing the time differences

He doesn't mention the different definitions of simultaneity in different frames in that particular example (although the entire opening of the paper deals with simultaneity issues), but that's because he isn't interested in analyzing the problem from different frames, he just picks the one that's most convenient. And he does specify that when he says the clocks are "synchronous" before A accelerates, this is just relative to the stationary frame K, he doesn't use "synchronous" in a frame-independent sense.

but if you insist, there is no problem in synchronizing two clocks in the same frame initiall nor is there any problem in reading them in the same frame after the moved clock is returned - simultaneity is an issue in relatively moving frames - here both measurmentws are made while both clocks are at rest in the same frame

I didn't say anything about there being a problem, I just pointed out that you're wrong to claim the experiment somehow shows the A clock was ticking slower than the B clock between the acceleration and the two clocks meeting in any absolute frame-independent sense, since you could certainly analyze the problem from a different frame where A was ticking faster than B during this period (though Einstein didn't choose to do this). My point about synchronization was that in this frame A would not be synchronized with B, in fact B would be ahead of A at the moment that A accelerated, which would explain why B could still be ahead of A when they met even though B was ticking slower in this frame. This is a perfectly straightforward result in relativity, there is absolutely no reason to think Einstein would dispute it (he spent the whole first part of the paper discussing how different frames define simultaneity differently), and likewise there is nothing in Einstein's words to suggest he thinks A was ticking slower than B in any absolute sense.

 

[JesseM]

Jessee --Before posting more - our whole difference turns on your answer to post 39. If you do not believe Einstein intended to predicta real substantive temporal difference (as you have asserted in one of our previous discussions- then fine - we can discuss that - if you think the moved clock accumulated less time, then tell me how that can happen if the frames are identical

My claims are simply the straightforward claims of relativity. From relativity, you can certainly predict that the A clock will show an earlier time than the B clock when they meet--if the B clock reads 4:00, the A clock might read 3:00. But it is also clear in relativity that there is no frame-independent answer to whether A or B "accumulated more time" between the time A accelerated and the time A reached B, because different frames disagree what the time was on B at the "same time" that A accelerated, due to the relativity of simultaneity. For example, if A read 2:00 at the time it accelerated, one frame might say that this event was simultaneous with B reading 2:00, another might say it was simultaneous with B reading 3:30. In both frames A accumulated 3:00 - 2:00 = one hour between the moment of acceleration and the moment of reaching B, but in the first frame B accumulated 4:00 - 2:00 = 2 hours (more than A), while in the second frame B accumulated 4:00 - 3:30 = half an hour (less than A). There is no reason to prefer one frame's answer to another, so there is no single objective truth about who "accumulated more time", even though all frames agree that at the time they meet A reads 3:00 and B reads 4:00.

 

[yogi]

My claims are simply the straightforward claims of relativity. From relativity, you can certainly predict that the A clock will show an earlier time than the B clock when they meet--if the B clock reads 4:00, the A clock might read 3:00. But it is also clear in relativity that there is no frame-independent answer to whether A or B "accumulated more time" between the time A accelerated and the time A reached B, because different frames disagree what the time was on B at the "same time" that A accelerated, due to the relativity of simultaneity. For example, if A read 2:00 at the time it accelerated, one frame might say that this event was simultaneous with B reading 2:00, another might say it was simultaneous with B reading 3:30. In both frames A accumulated 3:00 - 2:00 = one hour between the moment of acceleration and the moment of reaching B, but in the first frame B accumulated 4:00 - 2:00 = 2 hours (more than A), while in the second frame B accumulated 4:00 - 3:30 = half an hour (less than A). There is no reason to prefer one frame's answer to another, so there is no single objective truth about who "accumulated more time", even though all frames agree that at the time they meet A reads 3:00 and B reads 4:00.

It is true, one can analyse the two clocks A and B from different frames that are in relative motion wrt to A and B - and if you keep track of the apparent rates of clocks at all stages of the experiment, you will arrive at the same answer. But this obscures the point I have been laboring - for example, when a turn around twin changes from an outbound rf to the inbound rf, he sees the clock carried by the stay-at-home twin suddenly read more time - of course the change of direction by the turn around twin cannot affect the watch carred by the stay at home twin - it is simply a book keeping process that works to arrive at the correct age difference when the two twins reunite. The point is, there are many methods of arriving at the correct age difference, but they do not explain the age difference. That is why Einstein wrote the 1918 paper - if SR explained the results of the age difference, Albert would certainly not have felt the need to provide a constructive explanation. Following suit, others such Max Born, Dennis scima, Ron Lederman, have taken the position that SR cannot explain real time dilation. We get back once again to Rindler's comment that I have previously quoted -

This isn't just a case where there are several correct ways of working the same problem that all give the same answer. If Einstein's 1918 and Born's analysis is correct, then doing the problem in different frames that are always inertial and always identical should not work. The fact that "it does," to me, means there is a missing connection.

You wanted some quotes from authors that have said "two clocks cannot each be slower than the other" Some of my library is at my present location, much of it is elsewhere - I will try to find a couple.

 

[JesseM]

It is true, one can analyse the two clocks A and B from different frames that are in relative motion wrt to A and B - and if you keep track of the apparent rates of clocks at all stages of the experiment, you will arrive at the same answer. But this obscures the point I have been laboring - for example, when a turn around twin changes from an outbound rf to the inbound rf, he sees the clock carried by the stay-at-home twin suddenly read more time

He doesn't see that, what he sees is explained on the doppler shift explanation of the twin paradox page. Presumably what you're referring to is a switch of coordinate systems before and after acceleration (or equivalently, a single non-inertial coordinate system), each time using the inertial coordinate change where the twin is at rest. But I don't think this type of coordinate switch has any deep physical meaning, any more so than the fact that if you switch between a coordinate system whose spatial origin is centered on the ship to one whose spatial origin is 1000 light years away, the ship's coordinate position will suddenly jump by 1000 light years.

The point is, there are many methods of arriving at the correct age difference, but they do not explain the age difference. That is why Einstein wrote the 1918 paper - if SR explained the results of the age difference, Albert would certainly not have felt the need to provide a constructive explanation.

Is the 1918 paper you're talking about available online? If you're just talking about the general relativity explanation of the twin paradox, I don't see how this explanation is any more "constructive" than the one in SR, it's just a different method of calculating the answer based on a non-inertial coordinate system, as opposed to SR's method of calculating the answer in an inertial system. Neither method suggests there is an "objective truth" about which clock is "accumulating time more quickly" during a given phase of the journey (the outbound leg, say), although they all agree on the time both clocks show when they reunite at a single point in spacetime (presumably you could choose many different non-inertial coordinate systems to analyze the problem and they'd disagree about the rate each clock was ticking at different times). Do you think Einstein's 1918 paper does suggest such an objective truth? If not, are we or are we not discussing your claim that there must be some objective truth about which of two clocks is accumulating time faster?

Following suit, others such Max Born, Dennis scima, Ron Lederman, have taken the position that SR cannot explain real time dilation.

Given your strange way of interpreting quotes, I don't trust you that they take this position unless you can show me a quote. Some physicists may suggest SR is incomplete because (in non-tensor form) it doesn't have the same laws in non-inertial coordinate systems as in inertial ones, but this is different from saying that GR can "explain real time dilation" whereas SR cannot, and it definitely doesn't suggest there is an objective truth about which of two separated clocks is accumulating time faster.

We get back once again to Rindler's comment that I have previously quoted

Are you still talking about this quote?

"Granted that the motions of A and B are not symmetric, yet it could be maintained they are symmetric most of the time...the three asymmetric activities can be confined to arbitrarily short times...how is it then that such a large asymmetic effect can arise, and, morover, one that is proportional to the symmetric portions of motion? " The reason is that accelerations, however brief, have immediate and finite effects on A but not B."

Context would be helpful here. Which object accelerated, A or B? When he says "immediate and finite effects" is he talking about the "jumping of clocks" in some non-inertial coordinate systems which you talked about earlier, or something else?

This isn't just a case where there are several correct ways of working the same problem that all give the same answer. If Einstein's 1918 and Born's analysis is correct, then doing the problem in different frames that are always inertial and always identical should not work.

Why shouldn't it? My understanding is that the "GR" analysis of the twin paradox just adds a new way of analyzing the problem in non-inertial coordinate systems, there's no reason it should invalidate the old way. And again, using the GR method you can presumably analyze the same physical situation using different non-inertial frames, and I'm sure they'd disagree about the rate the clocks were ticking at different moments.

 

[yogi]

Jesse - what do you think of this:

An observer A, traveling into space in a rocketship, accelerates during a period T1 until he attains a speed v relative to the frame G of the fixed stars. He then falls freely towards some distant celestial object, where he reverses his motion during a period T2, and returns freely to Earth with the same speed as before. Finally he decelerates during a period T3 and lands. If for example v = square root of 3 times c over 2, A's clocks will have gone at half-rate compared with those of G during his free motion.

 

[yogi]

Jesse from your post 46: "He doesn't see that, what he sees is explained on the doppler shift explanation of the twin paradox page."

Yes he does if you draw the lines of simultaneity

 

[yogi]

Jesse - again from post 46: "Is the 1918 paper you're talking about available online? If you're just talking about the general relativity explanation of the twin paradox, I don't see how this explanation is any more "constructive" than the one in SR, it's just a different method of calculating the answer based on a non-inertial coordinate system.."

Actually, I don't think it is available for free on line, but there are several almost complete excerpts. A primary theory would be SR or the 2nd law oif thermodynamics, a constructive theory would be created by adding up all kinetic energies of the individual motions of the molecules to reach the same conclusion, or in the case of relativity, to account for the time dilations during each acceleration taking into account the distance between the two clocks

 

[yogi]

Jesse - more on my comment in post 48 from Wikipedia see last line:

"In the spacetime diagram on the right, the first twin's lifeline coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnover, the traveling twin calculates the age of the resting twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnover, if he recalculates, he'll measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the lifeline of the resting twin. The resting twin has suddenly "aged" very fast, in the reckoning of the traveling twin."

 

[JesseM]

Jesse - what do you think of this:

An observer A, traveling into space in a rocketship, accelerates during a period T1 until he attains a speed v relative to the frame G of the fixed stars. He then falls freely towards some distant celestial object, where he reverses his motion during a period T2, and returns freely to Earth with the same speed as before. Finally he decelerates during a period T3 and lands. If for example v = square root of 3 times c over 2, A's clocks will have gone at half-rate compared with those of G during his free motion.

I'd say the person writing the quote is working from within G's rest frame, which is certainly the most natural frame to use when analyzing this sort of the problem, although this should have been stated more clearly.

Jesse from your post 46: "He doesn't see that, what he sees is explained on the doppler shift explanation of the twin paradox page."

Yes he does if you draw the lines of simultaneity

They aren't "the" lines of simultaneity, they are just what you get if you stitch together the lines of simultaneity from two different inertial frames, as I said in my last post. But this doesn't uniquely define the "perspective" of the accelerating twin--in basic SR you're only allowed to use purely inertial frames, and once you bring in non-inertial coordinate systems you're free to use any smooth coordinate system you want, you could draw the lines of simultaneity as wavy lines and it'd be just as valid.

Actually, I don't think it is available for free on line, but there are several almost complete excerpts.

Can you link to some please?

A primary theory would be SR or the 2nd law oif thermodynamics, a constructive theory would be created by adding up all kinetic energies of the individual motions of the molecules to reach the same conclusion, or in the case of relativity, to account for the time dilations during each acceleration taking into account the distance between the two clocks

I don't understand what you mean by "taking into account the distance between the two clocks". Does this notion of primary vs. constructive come from Einstein's paper? Are you claiming that Einstein says there is some objective truth about which of two distant clocks is ticking faster? If so I really don't believe that, I'd need to see some quotes where you think he suggests this.

Jesse - more on my comment in post 48 from Wikipedia see last line:

Again, the wikipedia quote is just saying what happens if you stitch together his inertial rest frame before the acceleration and his inertial rest frame afterwards. But there isn't really any justification in SR or GR for saying this uniquely defines the "perspective" of an accelerating observer.

 

[yogi]

Jesse from post 51: They aren't "the" lines of simultaneity, they are just what you get if you stitch together the lines of simultaneity from two different inertial frames, as I said in my last post. But this doesn't uniquely define the "perspective" of the accelerating twin--in basic SR you're only allowed to use purely inertial frames, and once you bring in non-inertial coordinate systems you're free to use any smooth coordinate system you want, you could draw the lines of simultaneity as wavy lines and it'd be just as valid.

What I was referring to was the last line of post #50 - the turn around twin perceives a big jump in the time on the clock of the stay at home twin - and as I said, that type of analysis gets the right answer, but it skirts the issue of what is taking place at all times in the frames of the two clocks.

Let us go back to post 47 - you agree with that I think. So in the last line, it states that A's clock will have gone at half rate compared to B's during the free motion. Are you also saying that if we attach a coordinte system (frame ) to B, then by B's reckoning A's clock is going at half rate during the coasting periods?

 

[JesseM]

What I was referring to was the last line of post #50 - the turn around twin perceives a big jump in the time on the clock of the stay at home twin

But as I said, this is not the single correct way to define the traveling twin's "perspective", it's just one choice of non-inertial coordinate systems in which the traveling twin is at rest (one obtained by stitching together two inertial coordinate systems), you're free to pick any number of others, including ones where there is no such "jump", or where the Earth-clock ticks slowly for almost the entire trip but super-fast for the last minute before the traveling twin arrives at Earth.

Let us go back to post 47 - you agree with that I think.

What I said was that it is an accurate description of what happens in G's inertial rest frame (G was the one who moved inertially, A was the one who moved away and then turned around to rejoin G). But I also said I thought the author was being a bit sloppy by not specifying which frame was being used, even if G's frame is the most "natural" one to use in that scenario. (But I suppose the quote could also just be interpreted to mean that the total time elapsed on A's clock between the time of departing a G-clock and reuniting with it would be half the time elapsed on the G-clock, in which case we wouldn't have to worry about the perspective of different frames at all since they all agree on this).

So in the last line, it states that A's clock will have gone at half rate compared to B's during the free motion. Are you also saying that if we attach a coordinte system (frame ) to B, then by B's reckoning A's clock is going at half rate during the coasting periods?

By B do you mean G? Again, I think the quote was already speaking from the perspective of G's inertial rest frame.

 

[yogi]

Yes - I meant G - G is the inertial frame of the Earth and fixed stars that this persons uses - we can put a clock B at rest in G and it stays put.

Now let us focus on the first part of the trip - A accelerates relative to G to velocity v, and coasts. What do you think of the last line - is the A clock running at half speed as reckoned by B during the coasting phase?

 

[yogi]

PS - Jesse. I thought I had copied the Wikipedia article about the Einstein 1918 paper in a post - but somehow it didn't show up - anyway, it is a decent summary of the paper from the standpoint of the accelerating twin.

 

[JesseM]

Now let us focus on the first part of the trip - A accelerates relative to G to velocity v, and coasts. What do you think of the last line - is the A clock running at half speed as reckoned by B during the coasting phase?

Like I said, I think it's correct if it refers to how things work in G's inertial rest frame, or if it refers to the total time elapsed on A's clock between the time it departs from a clock at rest in G and the time it reunites with it. But there is no frame-independent sense in which we can say that A's clock was running at half the rate of G's during a particular phase of the trip, like the outbound leg.

PS - Jesse. I thought I had copied the Wikipedia article about the Einstein 1918 paper in a post - but somehow it didn't show up - anyway, it is a decent summary of the paper from the standpoint of the accelerating twin.

What's the title of the wikipedia article?

 

[yogi]

Jesse - here is the link to the wikipedia article - You have already seen it probably many times - the 1918 paper is discussed near the bottom
http://en.wikipedia.org/wiki/Twin_paradox

 

[yogi]

Like I said, I think it's correct if it refers to how things work in G's inertial rest frame, or if it refers to the total time elapsed on A's clock between the time it departs from a clock at rest in G and the time it reunites with it. But there is no frame-independent sense in which we can say that A's clock was running at half the rate of G's during a particular phase of the trip, like the outbound leg.

Well, there may be no frame independent sense - and there are always sync issues that will be different as to the start and stop components that define a spacetime interval as viewed from relatively moving inertial frames - but the interval (the spacetime distance between the end of the acceleration and turn around point) will be the same in the G frame and the frame attached to A. From G's point of view, the B clock interval is entirely temporal, whereas from G's point of view the A clock interval is a combination of spatial and temporal components. Now, if we attach a coordinate system to A, and measure the same interval in the A frame and G frame, I think you are saying there is no difference as to what A would measure from A's frame and what G measured from G's frame since we cannot tell which frame is in motion. Ergo, there is no reason to believe the A clock will have accumulated less time when it begins its turn around

At least I think that is what you are saying. Correct me if I am wrong - actually I don't think I need to tell you that.

 

[wisp]

#52...
What I was referring to was the last line of post #50 - the turn around twin perceives a big jump in the time on the clock of the stay at home twin - and as I said, that type of analysis gets the right answer, but it skirts the issue of what is taking place at all times in the frames of the two clocks.

The answer could be that the stay at home twin was in the preferred rf, so the outward-bound twin’s clock runs slow all the time it's moving. Then at turn around the moving twin’s clock would continue to run slow and there wouldn’t be a big jump in the time on the clock of the stay at home twin.

PS: SR doesn't allow for a preferred rf, but it doesn't prove it cannot exist.

 

[JesseM]

But there is no frame-independent sense in which we can say that A's clock was running at half the rate of G's during a particular phase of the trip, like the outbound leg.

Well, there may be no frame independent sense

If there's no frame-independent sense in which one clock is running slower than the other, and if at any given moment there are equally valid frames where A's clock is running slower than G's and frames where G's clock is running slower than A's, then what are we debating here exactly? I was just trying to debate your statement that two clocks cannot each be running slower than the other, that there must be an actual physical truth about which was "really" running slower at a given moment.

From G's point of view, the B clock interval is entirely temporal, whereas from G's point of view the A clock interval is a combination of spatial and temporal components.

I guess B is a clock at rest in G's frame? If so, I agree.

Now, if we attach a coordinate system to A, and measure the same interval in the A frame and G frame, I think you are saying there is no difference as to what A would measure from A's frame and what G measured from G's frame since we cannot tell which frame is in motion. Ergo, there is no reason to believe the A clock will have accumulated less time when it begins its turn around

I don't remember saying anything remotely like that--what specific quote gave you this impression? All I've been saying is that you can come up with equally valid coordinate systems where at any given moment, or doing any particular phase of the trip (like the outbound leg), one frame says clock A was running slower and another frame says clock B was running slower. But of course all frames will agree on the total elapsed time on each clock between A and B leaving each other and A and B reuniting (specifically, they'll all agree that A shows less elapsed time), because these are physical events and all frames make the same physical predictions!