Space traveler and time dilation

[ExecNight]

Hello,

Theoretically speaking, if we get a clock that ticks a red light every 1 second on the spaceship or whatever. And it has a quantum entangled pair on earth.

So how would the Twin on the spaceship actually see the Earth clock ticking throughout the journey?

That would be interesting to know maybe explains how this works better in a way.

 

[Al68]

The critical point to understand (which is elaborated in detail in the paper), is that the traveler CAN ADOPT NO OTHER CONCLUSION, IF HE WISHES TO AVOID CONTRADICTING HIS OWN ELEMENTARY (AND CORRECT) MEASUREMENTS. It is in that sense that I use the phrase "real and meaningful". If elementary, correct measurements are not "real and meaningful", how can anyone ever hope to do any physics?

The traveler can certainly recognize that the coordinates he correctly assigns (using Einstein's simultaneity convention) in his frame to events on Earth do not represent a "real and meaningful" sequence of events requiring causality to be explained.

I might even use the word "fictional" in the same way that fictional forces are used to explain the motions of objects when using a non-inertial reference frame. (The traveler must also assign fictional forces to account for Earth's motion). These forces are not "real and meaningful", either, yet physics thrived for hundreds of years using fictional forces.

And those fictional forces arise for the same reason that bizarre time coordinates get assigned to events on earth, so why not call them fictional?

 

[Ich]

CAN ADOPT NO OTHER CONCLUSION, IF HE WISHES TO AVOID CONTRADICTING HIS OWN ELEMENTARY (AND CORRECT) MEASUREMENTS.

Sorry, that's nonsense. Go back one step to the operational meaning of the respective coordinates.

If elementary, correct measurements are not "real and meaningful", how can anyone ever hope to do any physics?

Which measurements? (This is a rhetorical question).
Describe how you take the "measurement" of something going back in time.

There is none.

What you see at this locus will preserve causality.

 

[Mike_Fontenot]

Describe how you take the "measurement" of something going back in time.

If an unaccelerated object (the "home" twin) is periodically transmitting her current age, then an inertial observer (the traveling twin), who is moving at a constant velocity with respect to her, can receive those messages. He knows that, when he receives a message, that the age being reported in the message is not her current age (because she has aged while the message was in transit). From first principles, and elementary calculations, and without knowing anything about special relativity, the traveler can compute what his twin's current age is (by properly allowing for her ageing during the transit of the message).

That calculation, although elementary, is very easy to do incorrectly. The proper way to do it is detailed in my paper. If that process is done correctly, the result is precisely what is given (much more quickly and easily) by my CADO equation.

If you want to know more, you'll have to dig up my paper...most university libraries either have it, or can obtain it from another library.

(And the reason why the above process, which assumes the traveler is also unaccelerated, is of any value in determining the conclusions of an accelerating traveler, about the current age of the home twin, is also detailed in the paper).

Mike Fontenot

 

[yogi]

I agree that if the problem was presented and explained as two one way trips, most of the confusion would be completely eliminated. But the ship is still non-inertial for an (entire) one way trip.

Why would the reason be wrong? The reason for the aging difference is exactly the same in Einstein's 1918 paper as in standard resolutions. The only difference is he uses realistic acceleration (with Earth clock running fast in ship frame) instead of an instantaneous turnaround (earth clock "jumps ahead").

Why is the ship non-inertial?


Yes as to your second comment - it is like many of the standard solutions - those based upon resolving the problem via GR - Max Born and others who thought a reason for the age diffeence other than SR was needed to resolve the clock paradox - that is why after 1918, some authors of repute began saying flatout the problem can only be solved with GR - that is properly refuted by most others - but it all started with the the subtrifuge introduced by the 1918 paper.

 

[yogi]

OK, but in the GR case where you're dealing with non-inertial frames either way, depending on the frame you choose it may not be the twin that "travels with respect to space" who ages less, it could be the other twin.

So, if we hang the satellite clock on a sky hook, and call it a coordinate frame - then rotate the Earth beneath at the speed necessary to eliminate the affects of gravity acting upon the clock at the top of the tower, then it is the tower clock that does the traveling wrt the fixed frame of the satellite clock - so the two clocks are no longer in sync when they meet after one revolution - I guess that is what you are saying - or did I miss your point.

 

[Al68]

I agree that if the problem was presented and explained as two one way trips, most of the confusion would be completely eliminated. But the ship is still non-inertial for an (entire) one way trip.

Why would the reason be wrong? The reason for the aging difference is exactly the same in Einstein's 1918 paper as in standard resolutions. The only difference is he uses realistic acceleration (with Earth clock running fast in ship frame) instead of an instantaneous turnaround (earth clock "jumps ahead").

Why is the ship non-inertial?

Because the ship can't get half way through the twins paradox scenario without accelerating. At the half way point, the ship is at rest with earth.

And if we make that the end of a one-way trip, the ship twin is younger than the Earth twin unambiguously, since both are at rest in the same inertial frame.

As far as Einstein's 1918 paper, he never claimed GR was necessary to resolve the twins paradox. He just showed that it could also be analyzed from the accelerated frame of the ship with the same result for the same reason as the standard SR resolutions.

 

[yogi]

Because the ship can't get half way through the twins paradox scenario without accelerating. At the half way point, the ship is at rest with earth.

And if we make that the end of a one-way trip, the ship twin is younger than the Earth twin unambiguously, since both are at rest in the same inertial frame.

As far as Einstein's 1918 paper, he never claimed GR was necessary to resolve the twins paradox. He just showed that it could also be analyzed from the accelerated frame of the ship with the same result for the same reason as the standard SR resolutions.

Although Einstein started with two clocks at rest in the same frame in his 1905 description -it is not necessary. The one way trip I always thought we had in mind was that of a twin initially accelerated to crusing speed thereafter passing the stay put twin at a close distance at which instant both clocks are set to zero, and the voyage begins. Same thing upon reaching the target -the flyby twin notes the time on a local clock (which we can stipulate to be in the fame of the stay put twin) and the observer at the target notes the time on the flyby clock. This eliminates any acceleration - the voyage from stay-put twin to destination is inertial all the way.

I will agree that Einstein didn't promulgate the 1918 paper as exclusive - but others have taken the position that only GR is the correct reasoning - but this may be a subjective bias of mine - perhaps the issue is at some level, simply a distinction without a difference. - GR deals with potentiall energy, SR with KE differences between moving frames - and we know one can be derived from the other - so maybe I will stop campaigning this issue

 

[stevmg]

JesseM gave an example using SR why the "moving" twin ages less quickly than the earthbound twin. He does it both ways - using the Earth as the inertial frame and then the spaceship as the inertial frame. In both ways the Earth twin aged more than the traveling twin. Here is the post:

https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

I repeat, here is JesseM's post. It is short, sweet and simple.

https://www.physicsforums.com/showpost.php?p=2610219&postcount=63

The GPS satellites that were sent up thirty years ago confirm this.

 

[JDługosz]

If you have two circular orbiting satellites at the same height traveling in opposite directions and set both clocks to zero as they pass, when they meet again, both clocks will read the same

So I would think. The question is why? Each sees the other running slow as they pass (a SR effect). How does GR resolve this?

 

[Mike_Fontenot]

The one way trip I always thought we had in mind was that of a twin initially accelerated to crusing speed thereafter passing the stay put twin at a close distance at which instant both clocks are set to zero, and the voyage begins. Same thing upon reaching the target -the flyby twin notes the time on a local clock (which we can stipulate to be in the frame of the stay put twin) and the observer at the target notes the time on the flyby clock. This eliminates any acceleration - the voyage from stay-put twin to destination is inertial all the way.

You didn't say what you thought the two twins would conclude about the home twin's age at that instant when the traveler flys by the target (without changing his speed).

The answer (which perhaps you already know) is that the traveler will conclude that the home twin is younger at that instant, whereas the home twin will conclude that she (the home twin) is older that the traveler at that instant. I.e., you just get the simple time-dilation result in that case, where each twin concludes that the other twin is younger...they disagree about their corresponding ages.

And the target inertial observer (at rest relative to the home twin) will agree with the home twin. Suppose the target observer happens to be the same age as the home twin, according to both of THEM. Then the traveler WON'T regard the target observer and the home twin to be the same age.

This example can be generalized in a very enlightening way. Suppose that, when the traveler is flying by the target, that there just happen to be lots of inertial observers passing the target at that same instant...with those observers all having different constant velocities wrt the home twin. I.e., thay are all momentarily co-located at the target at that instant, but they are all moving at different constant velocities wrt one-another. In that case, those inertial observers will all come to DIFFERENT conclusions about the home twin's age at that instant.

Equivalently, you can imagine that the traveler himself, while momentarily located at the target, repeatedly makes a sequence of instantaneous velocity changes. But suppose he doesn't maintain any of those velocities long enough for his age, or for the separation between the two twins, to change. I.e., he is doing a bunch of velocity changes, but they are all packed into essentially a negligible total amount of time. (It is also necessary to say that the essentially constant separation referred to above is the separation ACCORDING TO THE HOME TWIN, at the instant when the traveler is doing all his instantaneous speed changes (whereas the traveler will conclude that their separation is instantaneously changing whenever he instantaneously changes his velocity, and that's NOT what we want to use in the CADO equation)).

In the above scenario, the traveler will be constantly CHANGING his conclusion about the home twin's current age. This is trivial to see from the structure of the CADO equation:

CADO_T = CADO_H - L*v,

where for brevity I have not shown the dependence of all the quantities in this equation on the traveler's age t, and I have omitted the factor of c*c needed in the second term on the RHS for dimensional consistency (so we must use the equation as written only with units where c = 1). Recall that, in this equation, the separation L is taken as positive, and v is taken as positive when the twins' separation is increasing.

In that equation, at the instant when the traveler is doing all his repeated instantaneous velocity changes at the target, the ONLY quantity on the RHS that changes is the velocity v. The first term on the RHS is the current age of the home twin ACCORDING TO THE HOME TWIN, at the instant of all those velocity changes by the traveler. Since the traveler is making the entire sequence of all these velocity changes in essentially zero time, the home twin will conclude that neither of them is ageing during that entire sequence of velocity changes. Likewise, the home twin will conclude that their separation doesn't change at all during the entire sequence of those velocity changes, because the total time which elapses during the entire sequence of velocity changes is infinitesimal.

So it's easy to see from the equation that the quantity on the LHS (which is the current age of the home twin, ACCORDING TO THE TRAVELER), will be going through a sequence of instantaneous changes. And it is clear that the larger the separation L is, the larger those swings in the age of the home twin will be. [ADDENDUM2]: Since the velocity v must be in the range -1 < v < 1, the CADO equation shows that the current age of the home twin, according to the traveler, can suddenly change by up to 2L years. So, for example, if the twins are 20 lightyears apart when the traveler instantaneously changes his velocity, the home twin's age can change by up to 40 years. [END ADDENDUM2]

And, as already pointed out earlier in this thread, note that any time the velocity is suddenly increased (made more positive, or less negative), the age of the home twin will suddenly DECREASE, ACCORDING TO THE TRAVELER.

With finite accelerations, the behavior is qualitatively similar, if the separation is large enough. I give a numerical example on my previously referenced webpage that provides a fairly dramatic illustration.

Mike Fontenot

 

[Al68]

Although Einstein started with two clocks at rest in the same frame in his 1905 description -it is not necessary. The one way trip I always thought we had in mind was that of a twin initially accelerated to crusing speed thereafter passing the stay put twin at a close distance at which instant both clocks are set to zero, and the voyage begins. Same thing upon reaching the target -the flyby twin notes the time on a local clock (which we can stipulate to be in the fame of the stay put twin) and the observer at the target notes the time on the flyby clock. This eliminates any acceleration - the voyage from stay-put twin to destination is inertial all the way.

Of course that works, but with your one way trip, the ship twin ages less between "events" only because you arbitrarily chose Earth's frame as the one to measure proper distance in by defining the "target" as a location at rest with earth. That's just asking for the objection: "Why don't we look at it from the ship's frame"? If you instead chose the ship's frame to measure proper distance in, for example by defining the target as a hypothetical object (buoy) trailing (at rest with) the ship, you would get the opposite result. And both twins would then agree that less time elapsed for the Earth twin between "events", if the second event is the buoy reaching earth.

So for an inertial trip, time dilation is symmetrical, and the symmetry is only broken by arbitrarily picking a frame for the proper distance between events to be measured in. That's perfectly valid, but understandably inadequate as an explanation to many.

But if the twins are at rest with each other at the end of the trip, the choice of frame to measure the proper distance in between events isn't arbitrary, so the solution is more satisfying to many.

 

[matheinste]

There are of course many alternative scenarios for this problem, many of them are aimed at removing acceleration so that it is not considered to be the cause of the differential ageing. However, they are open to the criricism of being a little complicated and not really making the point.

They often boil down to A passes B and sets clocks. A meets C and reads clocks, C meets B and compares clocks. This is often interpreted as, two people who have never met before, meet, and compare ages. I know it is a little more complicated than that and does make a point, but that is how it looks at first sight. Uninteresting.

The original, A leaves B when they are the same age. A returns to B, their ages are compared and are found to differ from each other. The point being that they are the SAME objects, be it clocks or twins or whatever, at parting and reuniting. Simple and highly thought provoking as shown by the continuing number of threads on the subject although the resolutions to the problem are well known.

Matheinste.

 

[yogi]

You didn't say what you thought the two twins would conclude about the home twin's age at that instant when the traveler flys by the target (without changing his speed).

The answer (which perhaps you already know) is that the traveler will conclude that the home twin is younger at that instant, whereas the home twin will conclude that she (the home twin) is older that the traveler at that instant. I.e., you just get the simple time-dilation result in that case, where each twin concludes that the other twin is younger...they disagree about their corresponding ages.

Mike Fontenot

No that is not the result to expect - The distance should be measured in the proper frame defined by the separation between the Earth and target - there is no motion between these two clocks and there is no time difference between them - The traveler has moved a distance relative to this length in the Earth target frame - the only spacetime distance traveled by the stay at home twin consists of a temporal increment - so 3 of the factors for the two spacetime points are known, namely the fixed twins time read by the target clock as the traveler flies over: the distance traveled by the stay put twin (which equals zero), and the proper distance traveled by the traveling twin (the separation between the start and target in the earth-target frame). All that is left to calculate is the time lapsed on the traveling twins clock - it will always be less than the reading of the stay put twin's clock and the target clock - there is no ambiguity as to which twin aged the most - this is a simple application of the principle of interval invariance.

Einstein got the same result by sync both clocks in the same frame - then accelerating one clock to crusing speed until it reached the other clock (first example in part 4 of the 1905 paper under peculiar results) All that has been done is to start and stop the travelers clock on the fly - no new physics, and no ambiguity

The situation is different if the circumstances are different - two clocks passing each other at relalive velocity v will always measure the other clock to be running slow without more information- here you have a third clock that defines that defines a proper length - and when that bases is used as the length the time difference is real, not apparent. To carry it further - once we have calculated the traveling twins time, ithen you plug back into the equation and you get the apparent distance that the traveler beleives he has traveled to the target -

A similar analogy is the hi speed laboratory generated pion that reaches top speed in a fraction of inch - then continues unabated until disintegration - start the lab clock a fraction of an instant after emission - the pion travels a few feet and disintegrates - the trip as measured from the time the pion reaches crusing speed to disintegration is a one way inertial voyage - all the clocks in the lab read the same - there is no issue about whether the pion aged less than the lab personnel

 

[yogi]

Of course that works, but with your one way trip, the ship twin ages less between "events" only because you arbitrarily chose Earth's frame as the one to measure proper distance in by defining the "target" as a location at rest with earth. That's just asking for the objection: "Why don't we look at it from the ship's frame"? If you instead chose the ship's frame to measure proper distance in, for example by defining the target as a hypothetical object (buoy) trailing (at rest with) the ship, you would get the opposite result. And both twins would then agree that less time elapsed for the Earth twin between "events", if the second event is the buoy reaching earth.

So for an inertial trip, time dilation is symmetrical, and the symmetry is only broken by arbitrarily picking a frame for the proper distance between events to be measured in. That's perfectly valid, but understandably inadequate as an explanation to many.

But if the twins are at rest with each other at the end of the trip, the choice of frame to measure the proper distance in between events isn't arbitrary, so the solution is more satisfying to many.

You can look at it from the traveling twins frame - but the target is moving toward the traveling twins clock so the traveling twin's measure of distance will not be a proper one because the target is not fixed - so immediately, the traveling twin views the distance shorter and therefore since the relative velocity is v, he will necessarily conclude that his clock logged less time because t = d/v and since his measurement of the shorter distance, is in his own frame he will also measure a shorter time - so again we know which twin aged the most and there is no ambiguity - both twins agree on the one way trip just as they agree upon the round trip

 

[yogi]

There are of course many alternative scenarios for this problem, many of them are aimed at removing acceleration so that it is not considered to be the cause of the differential ageing. However, they are open to the criricism of being a little complicated and not really making the point.

They often boil down to A passes B and sets clocks. A meets C and reads clocks, C meets B and compares clocks. This is often interpreted as, two people who have never met before, meet, and compare ages. I know it is a little more complicated than that and does make a point, but that is how it looks at first sight. Uninteresting.

The original, A leaves B when they are the same age. A returns to B, their ages are compared and are found to differ from each other. The point being that they are the SAME objects, be it clocks or twins or whatever, at parting and reuniting. Simple and highly thought provoking as shown by the continuing number of threads on the subject although the resolutions to the problem are well known.

Matheinste.

Some good observations

My idea behind proposing experiments that are "acceleration-free" is to eliminate a factor which is not excluded in Einstein's original description which involved statically sychronized clocks. To put one clock in motion , some acceleration is involved and therefore the question as to the influence of acceleration on clocks lingered. As to whether it played a part in the process - I am convinced it does not - although this has not always been my position - but while all accepted solutions give the same result - they are sometimes not satisfying if one is really trying to get a physical picture of what is happening - Its easy to be left perplexed as to "where the time has gone" and how does the clock that runs fast wind up that way without some physics at play - Lorentz worried most of his life about the problem - conjurred up many theoretical reasons that would bring about physical results, but in the end they do not seem to meet our modern understanding For my own peace of mind, i found an answer that was useful for me ... using only Minkowsky unification, i.e, the invariance of the spacetime interval. I now no longer think of clocks running slow in other frames - rather I view the spacetime distance (interval) between two points in spacetime is always the same - it then turns out to be a simple matter to decide the coordinates of the endpoints of the interval in each frame - in other words, the clock can be thought of as not running slow per se, but rather not running for as long a distance in time because it has to do some of its running in the space direction.

 

[Aaron_Shaw]

But there's no such things as slowing clocks, contracting metersticks, or planets jumping forward in time. SR is about relations of objects, not changes happening to them.

Does anyone have any references i can read through regarding the above statement? I was under the impression that time dilation and length contractions etc were REAL physical phenomena, rather than illusions or optical effects?

Thanks.

 

[Ich]

I was under the impression that time dilation and length contractions etc were REAL physical phenomena, rather than illusions or optical effects?

I'm not saying they are illusions. The classification as "real physical phenomena" is misleading as well.
In a spacetime diagram, a meterstick is two-dimensional, not one-dimensional. Rather than "the length" changing with velocity, you're talking about different lengths derived from an unchanged two-dimensional object.

"Spacetime Physics" by Taylor & Wheeler should be good for a start.
Or try "Geometry of the Theory of Relativity" from http://www.itp.uni-hannover.de/~dragon/".

 

[yuiop]

... But there's no such things as slowing clocks, contracting metersticks, or planets jumping forward in time. SR is about relations of objects, not changes happening to them...

As Galileo might have muttered if he was around when relativity was introduced "... and yet one twin biologically ages less than other."

That is a direct contradiction to teaching that "there's no such things as slowing clocks" and bound to be confusing to students. If it was carefully explained that clocks with relative motion really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other, then I think there would be a lot less confusion.

 

[matheinste]

As Galileo might have muttered if he was around when relativity was introduced "... and yet one twin biologically ages less than other."

That is a direct contradiction to teaching that "there's no such things as slowing clocks" and bound to be confusing to students. If it was carefully explained that clocks with relative motion really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other, then I think there would be a lot less confusion.

I believe that although saying that moving clocks run slow has its place in the teaching of SR and only causes confusion initially, it does not explain the reciprocal effect of time dilation very well. But anyway, differential ageing is not relly about time dilation.

The whole twin scenario is a victim of its own popular appeal. It is introduced in popular books to whet the reader's taste for relativity and make it interesting. After all, to non physicists, it is the counterintutive aspect of relativity which is its appeal. You do not need the twin scenario to explain the concept of differrent proper time being recorded along different spacetime paths, but once the twin sceanario is seen there is no escaping it.

As for clocks appearing to run at different rates for different observers, pehaps it is better to remove the emphasis from the clock and focus on the observer. If we say that for a given clock, the time it records is the projection of its spacetime path onto the time coordinate axis of the coordinate system in which the observer of the clock is at rest, it gives a better picture, is easier to visualise and does not use the mistaken and even meaningless concept of ideal clocks, similar by defintion, running physically at differtent rates. Unfortunately the spacetime geometry concepts are not always introduced at the necessarily early stage at which time dilation is introduced.


Matheinste.

 

[Al68]

The distance should be measured in the proper frame defined by the separation between the Earth and target - there is no motion between these two clocks and there is no time difference between them

That's only true in Earth's frame. In the ship's frame, Earth's clock reads less time than the target clock when the ship reaches the target. In the ship's frame, when the ship reaches the target, the Earth twin is much "younger" than the target observer and the Earth twin is also younger than the ship twin.

You can look at it from the traveling twins frame - but the target is moving toward the traveling twins clock so the traveling twin's measure of distance will not be a proper one because the target is not fixed...

I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Again, your way is perfectly valid, but many people have questions that it simply doesn't address. Like why did we arbitrarily choose to define the distance in Earth's frame instead of defining it in the ship's frame? Isn't the ship's inertial frame just as valid, and wouldn't it be just as correct to define the distance traveled in the proper frame of the ship, resulting in less elapsed time for the Earth twin?

 

[Ich]

That is a direct contradiction to teaching that "there's no such things as slowing clocks" and bound to be confusing to students.

Where's the contradiction?
How does it confuse?

Clocks are doing fine, but the elapsed time differs for different paths. That's the explanation, nothing else.

it was carefully explained that clocks with relative motion really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other,

then I think we'd have managed to introduce completely unnecessary quantum-like uncertainty paradoxes into relativity. Just read again: "really do physically run at different rates, but we can not tell which clock is really running slower until both clocks are brought to rest with respect to each other".
You're claiming that such statements are good teaching praxis to explain that the sum of two sides of a triangle is different from the length of the remaining side?
That it's necessary for a student to "understand" how a number, clock rate, belonging to an object, can be really physically different from the corresponding number of a second object, but that in order to decide which one really really really was larger you have to bring the objects together afterwards?
Come on.

 

[yogi]

That's only true in Earth's frame. In the ship's frame, Earth's clock reads less time than the target clock when the ship reaches the target. In the ship's frame, when the ship reaches the target, the Earth twin is much "younger" than the target observer and the Earth twin is also younger than the ship twin.I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Again, your way is perfectly valid, but many people have questions that it simply doesn't address. Like why did we arbitrarily choose to define the distance in Earth's frame instead of defining it in the ship's frame? Isn't the ship's inertial frame just as valid, and wouldn't it be just as correct to define the distance traveled in the proper frame of the ship, resulting in less elapsed time for the Earth twin?

You have raised some good points AI68 - I am not sure I can clarify anything - but I will try The experiment is analogous to the one way trip of a pion. The traveling twin will reach the target clock and the target clock will be read by the traveling twin, and the traveling twin's clock (hereinafter TTC) will be read by the operator at the target. The traveling twin will observe that his clock has logged less time than the target clock, and since the target clock will be in sync with the stay at home twin's clock, there is no disagreement. The TT will justify the difference by using his time to compute the distance he has traveled in his own frame - it will be less than the proper distance between the target clock and Stay at home twin distance. Now, the TT is going to be still perplexed, because if he has not set up a 4th clock in his own frame - so he will be justified in saying that when two clocks pass each other at relative velocity, each will observe the other clock to be running slow. That is where the paradox starts because there is simply not enough information to resolve the root cause of the diffeence ...until the proper space factor is introduced along with the measurement made at the location of the target clock The twin scenario is a measuration problem, not a physical affect. I know you know all of this, but for those who have not dropped from the thread and are still reading the posts, here are a couple of quotes:

For a pion the journey is one way - Resnick had this to say

"The proper time ...is the time interval measured by a clock attached to a pion that is at one place in the rest frame of the pion. In the lab frame the pions are moving at hi speed and the time interval there is an improper one...Thus depending on which frame we choose to make measurements in, this example illustrates the physical reality of either the time dilation or the length contraction predictions of relativity... The moving pion sees the lab distances contracted and in its proper decay time it can cover lab distances greater than those measured in its own frame."


And at page 77 "There are many shorthand expressions in relativity which can easily be misunderstood by the uninitiated Thus the phrase "moving clocks run slow" means that a clock moving at a constant velocity relative to an inertial frame containing synchronized clocks will be found to run slow when timed by those clocks. We compare one moving clock with two synchronised clocks. Those who assume that the phrase means anything else often encounter difficulties."

Again, I know you are fully knowledgeable in these matters - but the point that seems in need of clarification is that the pion's clock (our traveling twin) will always run slower than the lab clock (the stay at home twin clock) if the result is a physical reality - no matter where you anchor the reference frame the same time difference must follow if you account for the non-proper distance in the relatively moving frame in relation to the fame selected to be stationary

 

[yogi]

I was referring to choosing a second "target" that was at rest with the ship. So the distance between that second target and the ship would be the proper distance in the ship frame, while length contracted in Earth's frame. Then instead of only having a target at rest with Earth and local to the ship at the end, we would also have a target at rest with the ship and local to Earth at the end. And if the second target reaches Earth at the same time (in ship frame) as the ship reaches the first target, the Earth clock will show less elapsed time than the clock on the second target (synched with ship's clock) when the second target reaches earth.

Cont of Post 73 - To further clarify - if you placed two clocks in the frame of the traveling twin and moved the frame containing the stay put twin and target clock relative thereto at constant velocity v, you of course we get the opposite result. The Earth and target clocks would accumulate less time during the experiment than the clocks in the TT frame. Adding a second clock to the TT fame will define a proper distance and sync time in the TT frame, a different result is to be expected than the case where the same experiment is worked from the point of view of the TT fame without the addition of any other measuring help in the TT frame.

 

[JesseM]

Again, I know you are fully knowledgeable in these matters - but the point that seems in need of clarification is that the pion's clock (our traveling twin) will always run slower than the lab clock (the stay at home twin clock) if the result is a physical reality - no matter where you anchor the reference frame the same time difference must follow if you account for the non-proper distance in the relatively moving frame in relation to the fame selected to be stationary

But to measure the time in the lab frame you have to use two different clocks at different locations to make local measurements of the time t₀ when the pion is created and the time t₁ when it decays. And since you're making local measurements, the synchronization convention makes all the difference. If you synchronize the two lab clocks according to the definition of simultaneity in the lab frame, then (t₁ - t₀) is greater than the time as measured by the pion's clock (i.e. the pion's clock is running slow), but if you synchronize them according to the definition of simultaneity in the pion frame, then even though the two clocks are still running at a normal rate in the lab frame, (t₁ - t₀) will be less than the time measured by the pion's clock.

 

[Al68]

Cont of Post 73 - To further clarify - if you placed two clocks in the frame of the traveling twin and moved the frame containing the stay put twin and target clock relative thereto at constant velocity v, you of course we get the opposite result. The Earth and target clocks would accumulate less time during the experiment than the clocks in the TT frame. Adding a second clock to the TT fame will define a proper distance and sync time in the TT frame, a different result is to be expected than the case where the same experiment is worked from the point of view of the TT fame without the addition of any other measuring help in the TT frame.

This is why a one way inertial trip doesn't go very far to explain anything. Adding a second clock at rest with the ship wouldn't change the result we got using the other clocks. All that did was provide a means to better measure the complete results that already existed in reality. Regardless of whether there is a second clock in either frame, the fact remains that at any given time in Earth's frame (including any target being reached), the ship's clock reads less than Earth's clock. And at any given time in the ship's frame (including any target being reached) Earth's clock reads less than the ship's clock.

Sure we can hypothesize "targets" at rest in either frame, and accordingly measure proper distance in whichever frame we choose, but such targets (and proper distances) are irrelevant if nothing happens at them.

But if a target happens to be the location at which the ship changes velocity relative to earth, then it becomes relevant to the situation.

 

[yogi]

But to measure the time in the lab frame you have to use two different clocks at different locations to make local measurements of the time t₀ when the pion is created and the time t₁ when it decays. And since you're making local measurements, the synchronization convention makes all the difference. If you synchronize the two lab clocks according to the definition of simultaneity in the lab frame, then (t₁ - t₀) is greater than the time as measured by the pion's clock (i.e. the pion's clock is running slow), but if you synchronize them according to the definition of simultaneity in the pion frame, then even though the two clocks are still running at a normal rate in the lab frame, (t₁ - t₀) will be less than the time measured by the pion's clock.

Quite right Jesse. I have been trying to avoid the initial sync problem to eliminate acceleration from the reasoning - so I think you could do the thought experiment by having the high speed pion already up to speed when it enters the room carrying within its velocity frame a second clock - the pion frame now becomes the proper frame and the lab is making a one way journey between thye two clocks in the pion frame - in this arrangement the lab clock will appear slower - since these measurments are local in the sense of all being carried out in the space of the lab, then because the reciprocal experiment first discussed considers the lab at rest leads to the apparent result that the pion clock runs slow, its easy to conclude the affect is not real nor objective. I think we talked about this before - anyway, perhaps we can agree that all clocks run at the same rate but log different times depending upon which frame is selected for the proper distance (i.e., the two clock frame).

 

[yogi]

Let me embellish upon post 77 - as far as Special Relativity is concerned, there does not appear to be any reason why clocks should run at differnt rates - so if a clock on a one way trip reads different than another clock to which it was initially synchronized - the differnce must be due to the spatial part of the interval - so if t* measures time in the pion frame and t measures time in the lab frame - then if the lab is taken as the rest frame the pion will have traveled a distance vt in the lab, whereas if the pion frame is considered stationary, the lab will have traveled a distance vt* in the pion frame - so the spatial part of the spacetime interval determines which clock appears to run slow

 

[Mike_Fontenot]

One of the central tenets of special relativity is that there is NO privileged inertial frame. If neither twin ever accelerates, they are each essentially a clock in a (different) inertial frame. There's no way either one of those clocks can be privileged, in any absolute or invariant sense.

Mike Fontenot

 

[yogi]

One of the central tenets of special relativity is that there is NO privileged inertial frame. If neither twin ever accelerates, they are each essentially a clock in a (different) inertial frame. There's no way either one of those clocks can be privileged, in any absolute or invariant sense.

Mike Fontenot

True - in all of the above there is no distinction as to which frame is moving and which is at rest - in SR there will be no true rest frame involved in any event.. at best a true rest frame might be definable in connection with a point where the CBM is isotropic, but this appears to no better than any other arbitrary inertial frame for SR problems. In SR only relative motion is significant, and in Einstein's world, acceleration is also relative - the reationary force felt by masses should be the same irrespective of whether an object is accelerated relative to the universe, or the universe is accelerated relative to the object.