The case for True Length = Rest Length

[ghwellsjr]

Well, during periods of twin B inertial motion, the reciprocity always exists and can be observed. However when twin B undergoes proper acceleration, it's another story ...

The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration. However, this "overall experience" is the superposition of 2 relativistic effects ...

(1) the reciprocity of slower ticking clocks, and

(2) the change in relative simultaneity between the 2 POVs.​

So, the reciprocity of moving clocks always holds mathematically (as ghwellsjr stated), however the change in relative simultaneity counters that effect (from B's POV), twice over ... and so the reciprocity of moving slower-ticking-clocks cannot be observed, and can only be deduced as the superposition of 2 relativitic effects that concurrently concur.

That said, I see you and ghwellsjr both as correct. However, if you think that relative clock rates are illusionary effect, in this you are mistaken. Whether inertial or undergoing proper acceleration, what a clock presently reads dictates its real time and thus the proper time experienced by the clock since the 1st of 2 spacetime events.

GrayGhost

Your statement:

The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration.​

is not correct.

Twin B (the traveling twin) never experiences twin A's clock wildly spinning and by that I mean twin B never observes twin A's clock wildly spinning. During the acceleration period twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate higher than his own. If the acceleration is instant, the transition will be instant. If it is gradual, the transistion will be gradual. If the acceleration is in two parts where twin B decelerates to a stop and stays there for awhile and then accelerates in the back-home direction, the transition will be in two parts, first twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate identical to his own and stay there for awhile and second twin B will see twin A's clock transition from the same rate as his own to a higher rate than his own.

And twin A will see identical transitions in the tick rates of twin B's clock, except that instead of them occurring at the half-way point in the trip, they occur closer to the end of the trip. It's only this lack of symmetry in when the transitions occur that accounts for the twin's observations of the difference in aging when they finally reunite.

Keep in mind that there are similar transitions that occur during twin B's initial acceleration and final deceleration but all these acceleration periods only complicate the issue which we are discussing which is the reciprocal time dilation that each twin observes of the other one's clock. If we make the accelerations be instant, then we can say that each one always observes the same time dilation of the other one's clock during the entire trip. If we insist on making the accelerations take time, then we have to put in a little caveat that the time dilation will not be reciprocal nor be constant during the entire trip but the effect is quite minor and really doesn't impact the point of the discussion.

 

[ghwellsjr]

And keep in mind, I explained what each twin sees without bringing Special Relativity into the picture. You can also explain the Twin Paradox, as I said before, by using any frame of reference. But you have to be careful to illustrate in that frame what each twin actually sees and it will be exactly the same as I described without using SR. It doesn't matter which frame you use to analyze a scenario, they all agree on what each observer sees.

ghwelsjr, I was pretty much following everything you've been saying, except I don't follow what you mean about not using special relativity to explain the twin paradox. I've always understood the twin example as following from application of the knowledge of special relativity (I did rely upon it in my spacetime diagram above--post 102).

I'm not saying that my knowledge of Special Relativity hasn't influenced my thinking about how to explain the twin paradox without using SR, in fact, it is from SR that we learn how to properly understand Relativistic Doppler which is what I have been using. It's just that I have not established a frame of reference to explain what each observer sees of the other one's clock during each part of the trip. Do you think if you were the traveling observer, you would need to think about a frame of reference when you watch something? I don't think you go around all day long giving any thought to what frame of reference you should be considering your observations to be made in. And the point is, when you do invoke SR and establish a frame of reference, it does not in any way change what the observers see, it merely adds another level of complexity to the issue at hand which is: what do the observers see?

 

[rjbeery]

ghwellsjr, I'd like to apologize only for the reason that our discussion seems to have taken on a small bit of defensive posturing. Our mutual goal should be to further our understanding of Physics rather than to play a game of "speech and debate", parsing each others' words for errors.

That being said, since you're asking explicitly, I'll explain my position one last time. First of all, if you can't see my graphic of lines of simultaneity, let me try again, because it's important...

See that "gap" in the stationary twin's world from the traveling twin's perspective? If you study this for a bit you'll realize that ALL of their relative age differential exists because of this gap. (Note: the only reason the stationary twin appears to age "instantly" is because the graph shows, as most do, that the traveler turns around "instantly". A more reasonable rate of acceleration while turning around would produce a period of extremely fast aging for the stationary twin, yet one devoid of an unnatural gap.)

The picture is from Wikipedia, but you can read more about this analysis here:
http://chaos.swarthmore.edu/courses/PDG/AJP000384.pdf

That's my perspective. All age differential is due in toto to the frame change caused directly by acceleration of one of the twins. Now, on to what you're saying...

They all agree that each party views the other party's clock as running slower than their own during the entire trip and yet when they re-unite, the traveling twin's clock has progressed a lesser amount of time.

First of all, this isn't right and doesn't even coincide with the very lengthy explanations you have subsequently given. I suspect it was a mental lapse that you corrected when you did a thorough walk-through.

The reciprocity is not broken just because one of them accelerated.

Yet...

The stationary twin has no knowledge of the traveling twin's turn around until long after it has occurred at which point he will also observe a similar change in tick rate but it also calculates to the same time dilation factor as before.

What you're saying is that Twin B sees an effect that Twin A does not "until long after it has occurred"...that's the very definition of a break in symmetry!

There are many ways to analyze the Twin Paradox, but trying to do so using only SR concepts devoid of acceleration will ultimately fail. The "cause" of the age differential is acceleration, period. That is and continues to be my point, and if you or anyone else has an interpretation of the Twin Paradox that does not involve a frame change based caused by acceleration I would be fascinated to learn of it. Thanks

 

[PAllen]

Didn't spot any errors. However, see my post #98 for more aspects of the situation. In your scenario, a key point is to imagine cameras on the inside of each barn door taking pictures every nanosecond, previously synchronized to extreme precision (in the barn frame). These cameras will have a period where one photographs the front of the rod and the other the back. However, the camera snapping the approaching rod will see it extending out the barn (or in my more extreme scenario, before it has even entered the barn). All the same, the other camera will simultaneously show the back of the rod. Also, the readout from my proposed tissue detectors will clearly show the rod inside the barn. As, for the cameras, it is easy to understand that the camera snapping the approaching rod is showing a very stale image, and thus concluding that the two cameras together 'prove' the rod was in the barn.

This all shows the even in one frame, you better clearly define how you measure something and how you interpret those measurements. Different, perfectly reasonable choices can lead to different results.

Addendum: There will be a point in time where both head on and tail on cameras see the rod inside the barn. In may be only when the rod just about the smash the camera it is approaching.

 

[bobc2]

That's my perspective. All age differential is due in toto to the frame change caused directly by acceleration of one of the twins. Now, on to what you're saying...

The "cause" of the age differential is acceleration, period.

rjbeery, with due respect I really don't see how that comes out of our analysis. Certainly the change in velocity of the returning twin is a result of acceleration. But, it is the final velocity that is to be associated with the subsequent shortcut to the final destination.

That is and continues to be my point, and if you or anyone else has an interpretation of the Twin Paradox that does not involve a frame change based caused by acceleration I would be fascinated to learn of it. Thanks

But, I really have already presented the spacetime diagram that shows clearly the effect of the short cut through spacetime accounting for the difference in twin ages (post #111 pg 7 above). Your spacetime diagram does not include the hyperbolic calibration curves necessary to follow the progression of proper time for the return trip. You can easily come to the wrong conclusions without correctly representing the proper time. If you will add in the two sets of hyperbolic calibration curves onto your spacetime sketch, then the effect of shortcuts thru spacetime will become clear.

 

[bobc2]

Didn't spot any errors. However, see my post #98 for more aspects of the situation. In your scenario, a key point is to imagine cameras on the inside of each barn door taking pictures every nanosecond, previously synchronized to extreme precision (in the barn frame). These cameras will have a period where one photographs the front of the rod and the other the back. However, the camera snapping the approaching rod will see it extending out the barn (or in my more extreme scenario, before it has even entered the barn). All the same, the other camera will simultaneously show the back of the rod. Also, the readout from my proposed tissue detectors will clearly show the rod inside the barn. As, for the cameras, it is easy to understand that the camera snapping the approaching rod is showing a very stale image, and thus concluding that the two cameras together 'prove' the rod was in the barn.

This all shows the even in one frame, you better clearly define how you measure something and how you interpret those measurements. Different, perfectly reasonable choices can lead to different results.

PAllen & Mentz114, did you guys find something wrong with my post #102 pg 7, or were you just interested in understanding the example strictly from the standpoint of observer measurements?

 

[PAllen]

PAllen & Mentz114, did you guys find something wrong with my post #102 pg 7, or were you just interested in understanding the example strictly from the standpoint of observer measurements?

Nothing wrong with your picture. However, it didn't address measurement techniques or light delays which Mentz and I were interested in. In particular, it is interesting to note that in my extreme example, if a 100 meter pole is going fast enough to be measured at 8 meters, at the point where it is in the middle of 10 meter barriers, a picture snapped at that point by the camera on the barrier being approached will show the rod/rocket as it was about 20 meters before it reached the barn/barrier. At the same moment, the other camer will capture its tail. I find that interesting. However, when the rod is 1 centimeter from barrier being approached, a camera at that moment would capture the rod as inside the barn (about 30 cm away).

 

[rjbeery]

The "cause" of the age differential is acceleration, period.

Certainly the change in velocity of the returning twin is a result of acceleration. But, it is the final velocity that is to be associated with the subsequent shortcut to the final destination.

Bob...if the final velocity is what allows the subsequent shortcut to the final destination, as you call it, do you have a way for the traveling twin to obtain such a velocity that does not involve acceleration? We're arguing the same thing. I said it's a change in frames, you say it's "final velocity"; they are both the SAME THING, and they both DEMAND an acceleration.

The age differential demands unequal acceleration. Do you disagree with this?

 

[bobc2]

Bob...if the final velocity is what allows the subsequent shortcut to the final destination, as you call it, do you have a way for the traveling twin to obtain such a velocity that does not involve acceleration? We're arguing the same thing. I said it's a change in frames, you say it's "final velocity"; they are both the SAME THING, and they both DEMAND an acceleration.

The age differential demands unequal acceleration. Do you disagree with this?

I certainly agree with you that there is no increased velocity without acceleration. However, my attention is still on the shortcut through spacetime associated with the velocity (during which time there is no acceleration). That aspect of the spacetime diagram is clear when you include the hyperbolic calibration curves that allow you to calibrate proper time along the returning twin's path.

Some of your comments give me the impression that you are thinking that somehow the round trip twin's acceleration has something to do with the other twin's proper time along the other twin's world line. Of course it affects the round trip twin's coordinate view of the other's proper time clock. But, each twin moves along his own world line at the speed of light, and proper time will accumulate along a path for each observer--so that the final times for each (at their reunion) will depend on their individual paths followed through spacetime. You can follow the progression of these proper times if you include the hyperbolic calibration curves for the round trip twin.

 

[bobc2]

Nothing wrong with your picture. However, it didn't address measurement techniques or light delays which Mentz and I were interested in. In particular, it is interesting to note that in my extreme example, if a 100 meter pole is going fast enough to be measured at 8 meters, at the point where it is in the middle of 10 meter barriers, a picture snapped at that point by the camera on the barrier being approached will show the rod/rocket as it was about 20 meters before it reached the barn/barrier. At the same moment, the other camer will capture its tail. I find that interesting. However, when the rod is 1 centimeter from barrier being approached, a camera at that moment would capture the rod as inside the barn (about 30 cm away).

You are certainly right about that. I did not include any presentation about observers' actual measurements. My perspective was focused on the juxtaposition of two 4-dimensional objects and the implications about the events related directly in terms of the two coordinate systems.

You and Mentz114 do well in analyzing the actual measurements performed by the observers. To many that is the real business of physics.

 

[JesseM]

There are many ways to analyze the Twin Paradox, but trying to do so using only SR concepts devoid of acceleration will ultimately fail.

What do you mean when you say "only SR concepts devoid of acceleration"? I'd say that methods to deal with proper time along the worldlines of accelerating objects are already part of the standard "SR concepts", would you disagree?

The "cause" of the age differential is acceleration, period. That is and continues to be my point, and if you or anyone else has an interpretation of the Twin Paradox that does not involve a frame change based caused by acceleration I would be fascinated to learn of it. Thanks

It sounds like you may be conflating "acceleration" and "frame change" here, while the fact that one twin accelerated is crucial to resolving the twin paradox, it is totally unnecessary to use more than one inertial frame to calculate the elapsed time along each twin's worldline, since it's a simple matter to analyze an accelerating object from the perspective of a single inertial frame.

 

[ghwellsjr]

ghwellsjr, I'd like to apologize only for the reason that our discussion seems to have taken on a small bit of defensive posturing. Our mutual goal should be to further our understanding of Physics rather than to play a game of "speech and debate", parsing each others' words for errors.

That being said, since you're asking explicitly, I'll explain my position one last time. First of all, if you can't see my graphic of lines of simultaneity, let me try again, because it's important...

The picture is from Wikipedia, but you can read more about this analysis here:
http://chaos.swarthmore.edu/courses/PDG/AJP000384.pdf

That's my perspective. All age differential is due in toto to the frame change caused directly by acceleration of one of the twins. Now, on to what you're saying...

First of all, this isn't right and doesn't even coincide with the very lengthy explanations you have subsequently given. I suspect it was a mental lapse that you corrected when you did a thorough walk-through.


Yet...

What you're saying is that Twin B sees an effect that Twin A does not "until long after it has occurred"...that's the very definition of a break in symmetry!

There are many ways to analyze the Twin Paradox, but trying to do so using only SR concepts devoid of acceleration will ultimately fail. The "cause" of the age differential is acceleration, period. That is and continues to be my point, and if you or anyone else has an interpretation of the Twin Paradox that does not involve a frame change based caused by acceleration I would be fascinated to learn of it. Thanks

Yes, our mutual goal is to further our understanding of Physics.

I can see your new graphic, thanks for fixing that.

Now let me be clear in what you are saying because JesseM thought you were "just arguing that the acceleration explains why one twin has aged less in total when they reunite, which is not the same as saying all the differential aging occurred 'during the acceleration'". But you are saying that "all the differential aging occurred 'during the acceleration'", correct?

Now you referenced a very interesting paper in defense of your position. I have a lot of comments I could make about this paper but I will refrain and instead simply address your claim that it supports your position.

Look at the abstract. It says (in reference to the many different explanations of the twin paradox):

these are merely specific examples of an infinite class of possible accounts, none of which is privileged.​

Then in section VI entitiled THE ROLE OF ACCELERATION CRITICIZED they start off by saying:

...discussions which try to pin the age difference to the direction-reversing acceleration are misconceived.​

Are they talking about you, rjbeery?

And finally, in the conclusion they say:

One can conclude that any explanation of relative aging that stays within the bounds set by the light cone is equally valid.​

Unless I have misunderstood you, you are claiming that there is only one right way to understand the twin paradox and that is to attribute all of the aging of the stationary twin to the acceleration duration at turn-around. Please let me know if I am mixed up about what you are claiming.

Now if you look at their discussion beginning with "David Bohm" on the second page and continuing for two paragraphs (including Figures 2 and 3) and picked up again in the last column of section IV, you will see exactly the explanation that I was giving you of what each twin sees. Does this carry any weight with you in seeing that what I am explaining is correct?

You then say that you "suspect it was a mental lapse" that caused me to correct my "very lengthy explanations". Come on now, rjbeery, is this in accord with your apology to me of "a small bit of defensive posturing"? I am sincerely trying to "further our understanding of Physics".

You have to understand that I'm explaining two different things here. First I'm explaining what each twin sees. And second I'm explaining what each twin interprets from what he sees. In my most recent posts, I focused only on what each twin sees because when I did both it seemed only to confuse and I thought it might be advantageous to focus on one thing at a time and to see if we could arrive at agreement on that one point. You still have not answered my direct question to you if you agree with my statements of what each twin sees.

But earlier I had also explained what each twin interprets from what they see and with the added assumed knowledge that the traveling twin knows that the stationary twin will remain stationary throughout the trip and that the stationary twin knows that the traveling twin will turn around at some point and come back to him. Using Relativistic Doppler and ignoring the minor effects of acceleration, the traveling twin can use his measurement of his twin's clock rate to calculate the relative speed between them and from that calculate his twin's relative Time Dilation Factor. At the same time, the stationary twin can do the same thing for the traveling twin and they both get the same answer. Then at the turn-around point, which happens exactly half way through the trip, the traveling twin will see an increase in the rate of his twin's clock and from this he can calculate their relative speed and from that he can calculate his Twin's relative Time Dilation Factor and it will be the same as it was before (we are assuming that his relative inbound speed is the same as his outbound speed). Meanwhile, the stationary twin does not see anything happen differently but my point is that the reciprocal relative Time Dilation (which is what you were talking about) remains unchanged from before the turn-around and after the turn-around. Finally, some time later, the stationary twin sees the rate of the clock from his twin increase and he calculates the new speed and finds that it is exactly what it was before (just in the opposite direction) and from that he again calculates the relative Time Dilation of his twin and sees that it is the same as before.

I'm going through all of this because you said there was a contradiction if we used Special Relativity and you asked me to explain how there could be a constant reciprocal time dilation between the two twins throughout the entire trip and yet the traveling twin ages less than the stationary twin.

Finally, the break in symmetry does occur in the counting of each clock's time by the other twin but it does not occur in the time dilation which is what you claimed.

Now, even though my repeated explanation is given without any consideration for SR and without any assumed frame of reference, let alone with any frame change, it is easy enough to use SR to analyze the situation from an inertial frame of reference in which the stationary twin is at rest:

In the stationary twin's rest frame, his clock ticks away at the normal rate. There is no time dilation for him or his clock. The traveling twin's clock ticks away at a slower rate calculated by the time dilation factor based on his instanteous speed. If we want we can have him accelerate with any profile but it will make the calculations a little more difficult. He and his clock will experience time dilation throughout the entire trip. When he turns around, he can accelerate with any profile and we can use his instantaneous speed to calculate his time dilation factor. (Only if he comes to rest in the frame under consideration before continuing to accelerate back home will he no longer experience time dilation.) As he approaches his twin, he decelerates with any profile until he comes to rest and we can calculate exactly what his clock will read and it will have a lower elapsed time than the stationary twin has on his clock. Please note that this explanation does not reveal to us what each twin measures, only what we arbitrarily assign to times, speeds, distances, etc during the scenario. If we wanted to, we could do some more work and show that what each twin observes corresponds to my earlier explanation done with Relativistic Doppler.

Now if we wanted to, we could analyze the situation from another inertial frame of reference. Here are some possible (sensible) candidates:

A reference frame in which the traveling twin is at rest during his outbound trip.
A reference frame in which the traveling twin is at rest during his inbound trip.
A reference frame in which both twins are traveling in opposite directions during the outbound portion of the trip.
A reference frame in which both twins are traveling in opposite directions during the inbound portion of the trip.

(The first two of these were actually considered favorably in the paper you referenced along with the one I explained in detail.)

We could either reformulate the problem in anyone of those frames (possibly giving us a different scenario) or we could use the Lorentz Transform to show us what the same scenario would look like in different frames.

We could also analyze the situation from a non-inertial frame of reference or by switching frames which is what you propose to do but the math gets extremely complex or with a crazy inertial frame (for example, one in which the starting point is traveling at half the speed of light at 90 degrees to the direction of that the traveling twin will go).

The point is that every one of these SR analyses will describe exactly the same thing in terms of what each observer experiences, that is, what they see and measure. My point is why bother with a complex frame of reference when you can do it with a simple one.

 

[GrayGhost]

Your statement: The overall experience per twin B is twin A's wildly spinning distant clock during periods of twin B's own proper acceleration is not correct. Twin B (the traveling twin) never experiences twin A's clock wildly spinning and by that I mean twin B never observes twin A's clock wildly spinning.

In this you are mistaken, and so we disagree. The twins graphic rjbeery just threw up tells the story there. Not only can twin A's clock spin wildly per B "per the math" during B's own rapid proper accelerations (pos or neg), but twin B will also observe this similarly.

Inertial observers (eg twin A) indeed predict (and record) a change in a moving clock's rate due to the change in speed, but never does the moving clock tick faster than his own. However, observers who undergo rapid accelerations (eg twin B) "also" predict (and record) wild changes in distant luminal inertial clocks (A's clock), due to the rotation of their own sense-of-simultaneity during their (B's) own rapid proper acceleration. For twin B they are superpositional effects.

I might add ... not only does twin A's distant luminal clock spin wildly during B's own rapid proper acceleration, eg the turnabout point, but twin A also flies wildly across the heavens (per B). Twin A doesn't do this on its own, but rather only because twin B's POV has changed while rapidly accelerating. The always inertial observer never experiences (or records) any such effect, because their sense-of-simultaneity never rotates since they never undergo proper acceleration.

During the acceleration period twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate higher than his own. If the acceleration is instant, the transition will be instant. If it is gradual, the transistion will be gradual. If the acceleration is in two parts where twin B decelerates to a stop and stays there for awhile and then accelerates in the back-home direction, the transition will be in two parts, first twin B will see twin A's clock transition from a tick rate lower than his own to a tick rate identical to his own and stay there for awhile and second twin B will see twin A's clock transition from the same rate as his own to a higher rate than his own.

ghwellsjr, nothing you say here changes or counters what I said prior.

GrayGhost

 

[harrylin]

In this you are mistaken, and so we disagree. The twins graphic rjbeery just threw up tells the story there. Not only can twin A's clock spin wildly "per the math" during B's rapid proper accelerations (pos or neg), but twin B will also observe this similarly.

Just my 2cts as I'm not following this discussion:

I suppose that gwellsjr speaks of the clock frequencies that will be seen, as affected by Doppler*. You appear to speak of clock frequencies that will be inferred, after correcting for Doppler.

*http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

Cheers,
Harald

 

[JesseM]

In this you are mistaken, and so we disagree. The twins graphic rjbeery just threw up tells the story there. Not only can twin A's clock spin wildly per B "per the math" during B's own rapid proper accelerations (pos or neg), but twin B will also observe this similarly.

What "math" exactly? There is no single inertial frame where A's clock advances rapidly during B's acceleration, the rapid advancing of A's clock during B's acceleration only happens if you design a particular type of non-inertial coordinate system for B, one where the definition of simultaneity at any given point on B's worldline matches that of B's instantaneous inertial rest frame at that point, will it necessarily be true that A's clock advances rapidly during B's acceleration. But with non-inertial coordinate systems, unlike inertial ones, there is no single "correct" way to construct a coordinate system for a given non-inertial observer, you could easily design a different non-inertial coordinate system which had B at a constant coordinate position (so it was still a 'rest frame' for him) but where A's clock does not advance any faster during the acceleration than during other sections of the journey. And of course, if we're talking about what B sees visually rather than what is "observed" in terms of the coordinates of B's frame, then the answer is given by the Doppler shift analysis (illustrated nicely in the second diagram here) which doesn't require any rapid advancement during the acceleration phase, it just says that visually B sees A's clock running fast throughout the entire trip back.

 

[Dale]

When I say illusion I mean that the property of an object being measured isn't its "true" value, but that doesn't mean that the "illusion" has no physical consequences. As an example, I had to fit an ottoman through a door the other day which would not fit because the ottoman was wider than the doorway. I rotated the ottoman, such that its foreshortened length was able to fit. Did I actually change the length of the ottoman, or was its foreshortening "illusory"? The illusory effect of foreshortening has physical consequences.

You have a very weird definition of "illusion", but I suppose that is not surprising given your odd compulsion to label things other things "true". You still have not answered the question that I have asked 3 times now:

Why do you feel the need to change the term from "rest length" to "true length"? After all, your "true length" is exactly the same as the standard "rest length", so why do you feel the need to invent a new term when a standard one already exists.

In the end it's nothing more than a (possibly unnecessary) semantic convention

Exactly.

It's a bit nonsensical to assign any true or intrinsic value to a measured property if it leads to a logical contradiction.

I agree.

 

[Dale]

I had a good look at the barn-pole scenario and this is what I got. I hope I haven't made an error but I'm sure someone will tell me if I have.

The observer in the middle of the barn visually sees the pole completely inside the barn with both barn doors closed for a short period of time.

 

[bobc2]

What if we get back to basics. It seems like the concept we could be working off of should be fairly straight forward. The symmetric coordinate spacetime diagram (upper left) follows directly from the postulate that the speed of light is constant. Physics is the same for blue and red coordinates. The Minkowski metric is derived easily from the Pythagorean theorem (upper right). Then we have the Triangular Inequality (lower left), from which follows any twin example you wish to present (lower right). Paths 2, 3, 4, and 5 are all shorter than path 1.

By the way, you can see from the below sketches that there is no need at all to even talk about how each observer views the other throughout the trips to resolve the twin paradox (which just boils down to Minkowski path lengths from start to the reunion). The observers need only compare clocks at the start and at the end--and the proper times resulting from chosen paths explain it all.

[Edit] rjbeery: Now, having made the point about shortcuts through spacetime as about as well as I could, it's time to acknowledge your point about the role of acceleration. I understand how you could focus on the role of acceleration. You could point out that at the conclusion of the transient acceleration, you have now put the observer very close to the final target. Sure, the observer now takes the shortest path--but I'm sure you would want to give credit to the acceleration for putting the observer in that position of such close proximity to the target--making it easy for the observer to get to the final target from that orientation in such a short proper time and 4-D metric distance. You might then engage in a discussion that addresses the question, "How did the acceleration get the observer so close to the final target?" Did the acceleration move the observer closer? Or did the acceleration simply rotate the observer, pointing him in the direction of the shortest distance (similar to pointing an aircraft in the direction of a geodesic, giving it the shortest flight from point A to point B on the spherical surface--notwithstanding that SR uses a flat spacetime--but consider JesseM's pseudo-gravitational field and Rindler coordinates comments)?

 

[GrayGhost]

What "math" exactly? There is no single inertial frame where A's clock advances rapidly during B's acceleration, the rapid advancing of A's clock during B's acceleration only happens if you design a particular type of non-inertial coordinate system for B, one where the definition of simultaneity at any given point on B's worldline matches that of B's instantaneous inertial rest frame at that point, will it necessarily be true that A's clock advances rapidly during B's acceleration.

Yes, that's what I said. Wrt "what math", that be the LTs.

But with non-inertial coordinate systems, unlike inertial ones, there is no single "correct" way to construct a coordinate system for a given non-inertial observer, ...

Well, I disagree there is "not a single correct way".

First, we maintain that the 2-way speed of light is c, as well as the 1-way speed of light, because that's what SR requires. The LTs may be applied to the twin B experience, however one must account for the change in twin B's own sense of simultaneity as he undergoes the proper acceleration. Conceptually, it's very easy ... the B POV must always match "what the LTs predict of the B POV per the A POV". All points in spacetime are mappable between the 2 systems, and all must agree. Granted, the B POV is less convenient than an all-inertial POV, but its no less preferred a POV in so far as its ability to predict accurate spacetime solutions.

you could easily design a different non-inertial coordinate system which had B at a constant coordinate position (so it was still a 'rest frame' for him) but where A's clock does not advance any faster during the acceleration than during other sections of the journey. ...

You can do anything you like mathematically JesseM, but the only important thing is that it remains consistent with the special theory. If the B experience does not match precisely "what the twin A predicts of the B experience" (per the LTs), then it is not consistent with SR.

And of course, if we're talking about what B sees visually rather than what is "observed" in terms of the coordinates of B's frame, then the answer is given by the Doppler shift analysis (illustrated nicely in the second diagram here) which doesn't require any rapid advancement during the acceleration phase, it just says that visually B sees A's clock running fast throughout the entire trip back.

The gravitational time dilation portrayed on the illustration supports my point. Terrance's clock must advance wildly (per Stella) when Stella executes the rapid turnabout. I'm talking about the mapping spacetime between Stella and Terrence, not doppler effects.

Harrylin's right in that my posts here have been wrt the time readouts of the A & B clocks "in the present instant of time", for any instant. Doppler effects produce a different appearance because of the light transit time. However the negation of the light transit time tells the story of what the distant luminal (A) clock then reads (at any instant) per B. IOWs, I'm not mapping doppler effects to doppler effects, but rather the readout of the clocks in spacetime.

GrayGhost

 

[JesseM]

What "math" exactly? There is no single inertial frame where A's clock advances rapidly during B's acceleration, the rapid advancing of A's clock during B's acceleration only happens if you design a particular type of non-inertial coordinate system for B, one where the definition of simultaneity at any given point on B's worldline matches that of B's instantaneous inertial rest frame at that point, will it necessarily be true that A's clock advances rapidly during B's acceleration.

Yes, that's what I said. Wrt "what math", that be the LTs.

The LTs don't deal with non-inertial coordinate systems like the one I described.

Well, I disagree there is "not a single correct way".

First, we maintain that the 2-way speed of light is c, as well as the 1-way speed of light, because that's what SR requires.

Only in inertial frames does SR require this, not in non-inertial frames (for example, the speed of light is not constant in Rindler coordinates which are still considered to be part of SR rather than GR since they are defined on flat spacetime). And as I said there is no inertial frame where A's clock suddenly starts moving forward very rapidly when B accelerates, that would only be true in the type of non-inertial frame above.

Conceptually, it's very easy ... the B POV must always match "what the LTs predict of the B POV per the A POV".

In relativity when physicists talk about the "point of view" of an observer, then assuming they aren't just talking about visual appearances, they must be talking about some coordinate system that by convention we choose to associate with that observer, like the inertial rest frame of an inertial observer. There are no physical considerations that demands we must consider a particular coordinate system to represent the "point of view" of an observer, especially in the case of a non-inertial observer. If you choose to call the coordinate system I described the "point of view" of the accelerating observer you're free to do so, but I am equally free to pick some completely different coordinate system with a different simultaneity convention and call that the "point of view" of the accelerating observer.

You can do anything you like mathematically JesseM, but the only important thing is that it remains consistent with the special theory. If the B experience does not match precisely "what the twin A predicts of the B experience" (per the LTs), then it is not consistent with SR.

I'm not sure what you mean by "experience", again if you are just talking about coordinate systems rather than visual appearances, then this is another word like "POV" that we are free to define relative to whatever coordinate system we like. You badly misunderstand what "consistent with the special theory" means if you think that being consistent with SR means we can't use non-inertial coordinate systems where the speed of light is non-constant. In fact if you did the analysis, you'd see that even in the non-inertial coordinate system you prefer where the definition of simultaneity always matches that of the instantaneous inertial rest frame, the coordinate speed of light is actually not constant during the acceleration phase...for example if the acceleration phase involves constant proper acceleration this section of the trip would be covered by a chunk of the Rindler coordinate system, which is based on considering a family of observers with constant proper acceleration and making sure the definition of simultaneity always matches their instantaneous inertial rest frames.

The gravitational time dilation portrayed on the illustration supports my point.

It isn't really "gravitational time dilation" as that term is used by modern physicists, since there is no spacetime curvature here. The equivalence principle analysis from this twin paradox page refers to it time dilation from a "pseudo-gravitational field", and explains that without spacetime curvature this sort of analysis is still considered part of SR.

 

[GrayGhost]

JesseM,

I never said there is an inertial frame where A's clock suddenly starts moving forward very rapidly when B accelerates. I simply said "from the B POV" this is what must happen. I know that there is no gravitational dilation in the twins scenario, but since "that's what they labeled it" on their own graph, I merely referred to it since it supports what I've been saying here.

As you know, SR can be used to analyse the classic twins scenario. Also, Rindler diagrams do not alter the LTs in any way. They simply present the lines of simultaneity for accelerating worldlines.

The twins scenario may well be a pre-planned controlled roundtrip flight test if desired (not that it matters). Via the LTs, and for any moment, twin A can determine (via integration) not only what time the moving B clock must then read, but also the separation between A and B, per B. From this data, we can easily determine what B determines of A's clock wrt time and range, for any instant. The twin B experience must agree with twin A's LT predictions of B. Again, I'm not talking doppler effects here. I'm talking about the mapping each point in spacetime between the 2 systems.

If you happen to choose a different sense-of-simultaneity that differs from what relativity requires, then although you may obtain the same end result (final relative age differential), I do not see that you can obtain correct results for any arbitrary point along twin B's trek. Again, what B holds of the A clock at any instant (and its relative range), must precisely match "what twin A predicts the B experience to be" using the LTs.

You disagree?

GrayGhost

 

[PAllen]

JesseM,

I never said there is an inertial frame where A's clock suddenly starts moving forward very rapidly when B accelerates. I simply said "from the B POV" this is what must happen. I know that there is no gravitational dilation in the twins scenario, but since "that's what they labeled it" on their own graph, I merely referred to it since it supports what I've been saying here.

As you know, SR can be used to analyse the classic twins scenario. Also, Rindler diagrams do not alter the LTs in any way. They simply present the lines of simultaneity for accelerating worldlines.

The twins scenario may well be a pre-planned controlled roundtrip flight test if desired (not that it matters). Via the LTs, and for any moment, twin A can determine (via integration) not only what time the moving B clock must then read, but also the separation between A and B, per B. From this data, we can easily determine what B determines of A's clock wrt time and range, for any instant. The twin B experience must agree with twin A's LT predictions of B. Again, I'm not talking doppler effects here. I'm talking about the mapping each point in spacetime between the 2 systems.

If you happen to choose a different sense-of-simultaneity that differs from what relativity requires, then although you may obtain the same end result (final relative age differential), I do not see that you can obtain correct results for any arbitrary point along twin B's trek. Again, what B holds of the A clock at any instant (and its relative range), must precisely match "what twin A predicts the B experience to be" using the LTs.

You disagree?

GrayGhost

I disagree with a lot of the above, and know that JesseM is making important points. I would like to ask a few other questions for you to think about. Note that ghwellsjr has pointed out that B never see (through a telescope, for example) A's clock rapidly advance. You have argued that this is a visual effect and that B 'must' interpret A's clock to rapidly advance (instantaneously in the instant turnaround scenario). I would like you to outline exactly how B should interpret some measurements they make to justify this without resorting to 'must interpret reality according to LT of A's perspective via B's instantaneous velocity'.

Consider the following:

1) At the moment of turnaround, parallax and subtended angle suggest A has instantly moved further away. Interpreting this via lightspeed delay, 'must' B conclude they are suddenly re-seeing a blue version of events they've already seen? This would follow from a constant lightspeed interpretation A being suddenly much farther away. Except that images contradict this - they are not re-seeing older events. Further, instant travel is precluded.

2) On the other hand, if B factors out blueshift, they still see an increase in luminosity of A (see relativistic beaming). So they should instead conclude that A has jumped closer, rather than farther? This leads to inverse paradoxes from (1).

3) If they in fact use the assumption of two way lightspeed and one way lightspeed being constant, and continuously bounced signals off of A, they would see interpret something completely different (see Dolby and Gull re radar coordinates). Here, they would interpret a very smooth simultaneity history, factoring in that B knows he hasn't been 'eternally' moving at his current velocity relative to A (and LTs are specifically derived for eternally inertial observers).

There is, in fact, no reasonable interpretation of direct measurements made by B that leads to the Fermi-Walker coordinates that you are proposing as the only valid choice. Note that there is no wrong physical prediction resulting from using Fermi-Walker coordinates correctly, but there is also no simple physical interpretation of measurements that supports them for this scenario. (Actually, there are imaginary measurements that support them: maintaining set of clocks with Born rigid relationships between them; however, this has little relation to achievable measurements).

 

[rjbeery]

The participation on this forum is fantastic, and the feedback is of a high caliber, but it's also exhausting.

DaleSpam: There is no point beyond me giving you something to ponder. Speaking of arbitrary, I find it arbitrary to NOT correct for SR-related length contraction when we DO correct for size at a distance, width at an angle, sound pitch of an engine speeding by, color for binary rotating stars, and Doppler effects of Gendanken space-walkers with clocks. I'm just seeking some logical consistency really, but the convention itself bears no consequences on Science one way or the other.

ghwellsjr and bobc2: Holy crap, you guys win by attrition I guess. I don't know where you find the time to write all that...

 

[GrayGhost]

PAllen,

I'll think carefully about your post before responding. Thanx.

GrayGhost

 

[JesseM]

I never said there is an inertial frame where A's clock suddenly starts moving forward very rapidly when B accelerates. I simply said "from the B POV" this is what must happen.

Yes, and I explained that the question of what coordinate system we choose to represent as the "POV" of a non-inertial observer is purely a matter of convention.

As you know, SR can be used to analyse the classic twins scenario. Also, Rindler diagrams do not alter the LTs in any way. They simply present the lines of simultaneity for accelerating worldlines.

There are other commonly-used non-inertial coordinate systems which give a different view of simultaneity with distant clocks than the one in the instantaneous inertial frame, like Marzke-Wheeler coordinates where simultaneity is based on the use of radar signals. (If the non-inertial observer sends out a signal at time T1 according to their clock, and the event of it bouncing off some distant object is labeled E, and the reflected signal returns to the observer at time T2 on his clock, then he will say that E occurred at a time halfway between T1 and T2. The linked paper shows on p. 10 what this imples for simultaneity in a twin paradox scenario.) Would you say that these coordinate systems "alter the LTs"? I don't even understand the meaning of that phrase, since the idea that light has a coordinate speed of c is built into the LT but apparently it doesn't bother you that light can have a variable coordinate speed in Rindler coordinates.

If you happen to choose a different sense-of-simultaneity that differs from what relativity requires

Relativity doesn't "require" anything about what definition of simultaneity is used in a non-inertial frame, this is a totally imaginary requirement you have invented.

then although you may obtain the same end result (final relative age differential), I do not see that you can obtain correct results for any arbitrary point along twin B's trek.

This sounds like a circular argument, are you just defining "correct results" to mean agreement with simultaneity in the instantaneous inertial rest frame at each point? Again this is a requirement that you have just invented, all that physicists care about when using non-inertial coordinate systems is that they agree with inertial ones about coordinate-invariant facts, not coordinate-dependent ones like simultaneity or the coordinate speed of light.

Again, what B holds of the A clock at any instant (and its relative range), must precisely match "what twin A predicts the B experience to be" using the LTs.

Nope, there is no recognized requirement that this "must" match, this is just a requirement you have invented for no good reason that I can see.

 

[Dale]

There is no point beyond me giving you something to ponder. Speaking of arbitrary, I find it arbitrary to NOT correct for SR-related length contraction when we DO correct for size at a distance, width at an angle, sound pitch of an engine speeding by, color for binary rotating stars, and Doppler effects of Gendanken space-walkers with clocks. I'm just seeking some logical consistency really, but the convention itself bears no consequences on Science one way or the other.

We do that correction, and call the corrected value the "rest length". And you didn't answer the question:

Given that the concept you label "true length" is exactly the SAME as the concept everyone else labels "rest length", why do you feel the need to CHANGE the term from "rest length" to "true length"?

 

[bobc2]

ghwellsjr and bobc2: Holy crap, you guys win by attrition I guess. I don't know where you find the time to write all that...

I don't know that there are any winners here. But, here's just one more offering on behalf of shortcuts. The lower right depicts red and blue moving together at relativistic speed (relative to the black rest system). They start together at point A, then at point B they are still together, but the red guy heads for point C.

Now, tell me, when they are side by side at point B, which guy is closer to point C? Does changing direction make the red guy somehow closer than the blue guy?

 

[rjbeery]

Now, tell me, when they are side by side at point B, which guy is closer to point C? Does changing direction make the red guy somehow closer than the blue guy?

I had considered myself done with this thread but...I don't get your point here. What are you saying?

 

[bobc2]

I had considered myself done with this thread but...I don't get your point here. What are you saying?

I'm saying that it is a 4-dimensional universe. The 4-D distance from point B to point C in this 4-D space is the same for the blue guy and the red guy. Then, the blue guy keeps going in the same direction and the red guy changes direction in 4-D space. Just because the red guy changes direction does not change the 4-D distance from point B to point A.

It's the path that red takes in 4-D space that determines the total 4-D distance traveled from point A to point B to point C. And he moves along the 4-D path at the speed of light.

Thus, it is the path through 4-D space that determines the age of the red guy when he arrives at point C. Sure, he had to accelerate to change direction at point B, but that had nothing to do with the 4-D distance from B to C--the chosen path determined his age.

 

[bobc2]

rjbeery, you are probably bothered by the seemingly instantaneous acceleration at the turnaround. It is not instantaneous at all (see sketch below). You just can't see the small path length of curved world line on the astronomic scale of the sketch. If you have questions about proper distance, time, world lines and hyperbolic calibration curves, etc., I'm sure someone on the forum could probably explain it better than I have. Nevertheless, the aging inequality as shown below clearly explains the twin paradox as a result of two different world line paths taken through spacetime. The acceleration is not relevant to the aging, other than providing the means for the traveler to change direction of motion in 4-D space.