Strange Twins Paradox: A Crackpot Physics Mystery | Discover the Solution Here!

[JohnWisp]

Not exactly a problem. As I said, it is a notational confusion. When you say x=vt you are writing the equation of a worldline. So x and t are no longer general coordinates, but only points on a worldline. So I prefer to use the parametric representation of the line with a clearly distinct parameter for each worldline (see post 11).

When you make the substitution you are no longer talking about general t or t', but only specific ones on that line. So the first equation gives you the relationship between t and t' on one worldline and the second equation gives you the relationship between t and t' on a completely different worldline. So there is no contradiction in the fact that different relationships hold on different lines. The only place where both relationships must hold is where the lines intersect. And that is correct since both hold at t=t'=0.

Yes, this is false. There is no clock comparison issue. You haven't used the proper time equation yet, so you haven't shown what the clocks actually read. Whenever you specify when a reading is taken on a clock then you will get one answer independent of the frame.

1) As far as x-vt or x=-vt', you may consult section 4 of Einstein's paper. I am only adhering to his standard.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

2) As far as the clock comparison and your claim it is false, you need to show why it is false to back your claim. All of my claims are backed with the specific math or I do not make claims. I expect you will do the same.

 

[JohnWisp]

I have no problem with that, but the fact remains that steps 2 and 4 are non constant accelerations so the symmetry for a constant acceleration is not applicable. Your assertion of symmetry is unwarranted.

This is false.

Einstein wrote the following,

if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize

The two clocks stated in the same frame exactly as this experiment.

So, the OP did exactly the same as Einstein suggested. This is therefore, mainstream and not subject to contradiction.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Then, someone wanted to see another interpretation. So, I brought up constant acceleration.

This is absolutely not necessary since Einstein did not include any acceleration factors in his paper.

 

[JohnWisp]

Oops, I goofed. Somehow my mind interpreted the phrase "they have exact time values" as meaning they were exactly the same. I apologize and to make peace, I offer you some diagrams to illustrate your scenario for the case where v=0.6c and t=12 months. First, a diagram showing the only frame you mentioned in your first post, that of the original rest state of the two twins:

The dots represent one-month intervals of Proper Time for each twin. Please note how both twins are time dilated after they both acquire a speed of 0.6c.

I have shown the synchronization process that twin 2 carries out at his Proper Time of 8 months. His signal travels over to twin 1 at his Proper Time of 14 months and he returns the signal. This return signal arrives at twin 2 at his Proper Time of 26 months. One-half of the round trip signal time is 9 months so he adds 9 months to 8 months and determines that twin 1's clock read 14 months when his own clock read 17 months. This is a difference of 3 months.

We can easily determine this difference if we realize in this scenario that gamma is the ratio of the Coordinate Time to the Proper Time for twin 1 at the moment he accelerates. Since the Coordinate Time is the same as the Proper Time for twin 2, we can say;

γ = CT/PT1
CT = PT2
γ = PT2/PT1
γ-1 = PT2/PT1 - PT1/PT1
γ-1 = (PT2-PT1)/PT1

Now we note that t = PT1 so:

t(γ-1) = PT2-PT1

Now I'm going to transform the above frame into one in which both twins are at rest after they both accelerate:

Now you can clearly see that the Proper Time of 17 months which is also the Coordinate Time is equal to the Proper Time of 14 months for twin 1.

Your drawings are wrong.

Acceleration is absolute under and not subject to worldlines.

I already gave the acceleration equations and I suggest you refute the mainstream to prove your case since my equations are nothing more than mainstream.

 

[Nugatory]

This is false.

Einstein wrote the following: "If the clock at A is moved with the velocity v..."

Einstein did not write that; it was written by whoever translated the German that Einstein did write into English. This process introduces enough ambiguity that you cannot take the English translations completely literally, and you are reading much more into that word "moved" than can be justified.

Instead, you really have to understand the math, which is way more precise and language-independent.

 

[JohnWisp]

Both twins think the other's clock is dilated, only during the period between the first's acceleration and the second's acceleration. But they can not use clock synchronization during that time.

After the second's acceleration, both think their clocks are running at the same rate. And they can measure the difference in their readings.

That difference will match the difference that the first twin thinks accumulated between their accelerations, not what the second twin thinks. This is because before and after the acceleration, the second twin will have a different definition of "now" for locations other than his own.

The very act of acceleration will appear to cause a shift in time, a redefinition of "now" at all distant locations. Locations in the direction of the acceleration will seem to shift into the future, the further away they are the bigger the shift. And likewise locations in the other direction will seem to shift into the past.

So in this specific setup the twin accelerating second will think this for the other's clock: it starts to run slow, but when he suddenly launches it jumps forward in time, and not only makes up the difference but reverses it. Then they both agree, the second twin's clock is behind.

EDIT: This describes the setup with instant acceleration. I didn't read other replies in detail and am not sure why references to constant acceleration were made in some of them, or if the OP is interested in discussing such an alternative scenario.

1) The acceleration shift in time is absolute under special relativity. In fact, it is slowed. So, any accelerated frame will appear to shift into the past. And, the distance it no important unless you have specific acceleration equations that prove your statement.

2) The rest of your post does not matter until you understand accelerating frame tick slower.

The clock postulate generalizes this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, it only depends on v, and does not depend on any derivatives of v, such as acceleration. So this says that an accelerating clock will count out its time in such a way that at anyone moment, its timing has slowed by a factor (γ) that only depends on its current speed; its acceleration has no effect at all.

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

 

[JohnWisp]

Einstein did not write that; it was written by whoever translated the German that Einstein did write into English. This process introduces enough ambiguity that you cannot take the English translations completely literally, and you are reading much more into that word "moved" than can be justified.

Instead, you really have to understand the math, which is way more precise and language-independent.

I understand the math.

I also understand German. It is hard to translate motion incorrectly between the two languages.

Now, if you have the original German and can show the problem you suggest, then please post your proof.

 

[Passionflower]

Einstein did not write that; it was written by whoever translated the German that Einstein did write into English. This process introduces enough ambiguity that you cannot take the English translations completely literally, and you are reading much more into that word "moved" than can be justified.

Sorry but I think you are talking nonsense, do you actually speak German?

From the Urtext:

... und bewegt man die Uhr in A mit der Geschwindigkeit v auf der Verbindungslinie nach B, so gehen nach Ankunft dieser Uhr in B die beiden Uhren nicht mehr synchron, ...


There is nothing ambiguous about it: the clock in A is moved with a velocity of v and arrives at B.

 

[Dale]

1) As far as x-vt or x=-vt', you may consult section 4 of Einstein's paper. I am only adhering to his standard.

Often the seminal works are full of confusing notation, particularly since the notation was not standardized. One of the things that makes the great minds so great is that they were able to understand despite the poor notation of the time. Einstein was smart enough to use the confusing notation without becoming confused, you apparently are no Einstein.

If you are done trying to deflect the issue, you may want to go back and address the substantive criticism of post 28.

2) As far as the clock comparison and your claim it is false, you need to show why it is false to back your claim. All of my claims are backed with the specific math or I do not make claims. I expect you will do the same.

Exactly what math do you think backs up your claim? You have only demonstrated that the relationship between the t and t' coordinates on one worldline is different from the relationship between the t and t' coordinates on a different line. You have not demonstrated anything at all about the actual numbers read on the clocks, let alone that there is some contradiction among them.

 

[Dale]

This is false.

Einstein wrote the following,

if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize

So what? Nowhere in Einstein's quote does he say that the acceleration was constant. The quote is irrelevant.

The acceleration described in the OP is not constant and the symmetry you assert does not exist. My statements are 100% true.

 

[Passionflower]

I thought of that too, but both experience the same instantaneous acceleration, in other words, the acceleration is symmetric between the frames.

Identical acceleration profiles of two observers at different x values is not a symmetric situation. Think in this respect about Bell's spaceship paradox.

 

[georgir]

I don't know what you mean by adding two lines of simultaneity. On either of my two graphs, every horizontal line is a line of simultaneity and there are no jumps in the clocks of either twin.

Yes, every horizontal line is a line of simultanety for the observer that is considered at rest in the particular graph. That is, before the acceleration on graph 1, and after the acceleration on graph 2.

Now transform the horizontal lines from graph 2 to graph 1. For example, through the red point marked "14" on your graph, it will be a line connecting red "14" and blue "17". That is what the red twin thinks is his "now" at that moment, not the horizontal line.

The interesting lines of simultanety are through red point "12". Before acceleration, it is the horizontal line. After acceleration, it is the line connecting red "12" and blue "15".

There is no standard definition of "now" for accelerating observers. There is only a standard definition of "now" in Special Relativity for Inertial Reference Frames (IRF) and by extension for an inertial observer at rest presumably at the origin of an IRF but if an observer accelerates, then there are many different definitions of "now" for a non-inertial rest frame of an observer. Just because you like one doesn't mean it is any more a fact than the ones you don't like. They are all "facts" according to their different definitions. Those definitions are no more a fact than Einstein's second postulate that light propagates at c in all directions in an IRF.

We are not interested in "now" for accelerating observers in this setup. There is no accelerating reference frames. There is only instant acceleration, and inertial reference frames for before and after the acceleration, which are completely well defined.

 

[georgir]

1) The acceleration shift in time is absolute under special relativity. In fact, it is slowed. So, any accelerated frame will appear to shift into the past. And, the distance it no important unless you have specific acceleration equations that prove your statement.

2) The rest of your post does not matter until you understand accelerating frame tick slower.
The clock postulate generalizes this to say that even when the moving clock accelerates, the ratio of the rate of our clocks compared to its rate is still the above quantity. That is, it only depends on v, and does not depend on any derivatives of v, such as acceleration. So this says that an accelerating clock will count out its time in such a way that at anyone moment, its timing has slowed by a factor (γ) that only depends on its current speed; its acceleration has no effect at all.

http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html

You are missing the point... What you are talking about is how an accelerated clock looks to an inertial observer. What I am talking about is how things look to an accelerating observer... And not even during the acceleration itself, just right before it and right after it, both completely inertial cases. Re-read my posts.

 

[pervect]

Some quick comments: the only space-time diagrams posted to this thread have been dismissed as "wrong", but the OP has not responded with a "correct" space-time diagram.

Alas, the verbal descriptions of the "paradox" seem rather ambiguous (having seen a few "paradoxes", I would guess it likely that this ambiguity is at the heart of the paradox.

I would place the burden on the OP to supply such a space-time diagram, as the alternative is to watch the thread spin around i circles forever.

I don't see how anybody else other than the original poster will feel motivated to go to the effort of creating and posting a space-time diagram to simply see it dismissed as "wrong" by the OP in a few lines of text, without apparent thought.

So if a space-time diagram is needed (and I think it is), it is pretty much up to the OP to step forwards and do one.

 

[ghwellsjr]

I don't know what you mean by adding two lines of simultaneity. On either of my two graphs, every horizontal line is a line of simultaneity and there are no jumps in the clocks of either twin. Maybe you could copy one of my graphs and mark it up to show what you mean because it is not clear what you are talking about.

Yes, every horizontal line is a line of simultanety for the observer that is considered at rest in the particular graph. That is, before the acceleration on graph 1, and after the acceleration on graph 2.

Now transform the horizontal lines from graph 2 to graph 1. For example, through the red point marked "14" on your graph, it will be a line connecting red "14" and blue "17". That is what the red twin thinks is his "now" at that moment, not the horizontal line.

The interesting lines of simultanety are through red point "12". Before acceleration, it is the horizontal line. After acceleration, it is the line connecting red "12" and blue "15".

OK, is this what you mean?

And yes, that line of simultaneity through red point "12" is very interesting. Do you want to explain what happened to blue points "10" through "14"? Do you want to show how signals between red and blue propagate at the speed of light in the diagram as they cross the seam between the two frames?

There is no standard definition of "now" for accelerating observers. There is only a standard definition of "now" in Special Relativity for Inertial Reference Frames (IRF) and by extension for an inertial observer at rest presumably at the origin of an IRF but if an observer accelerates, then there are many different definitions of "now" for a non-inertial rest frame of an observer. Just because you like one doesn't mean it is any more a fact than the ones you don't like. They are all "facts" according to their different definitions. Those definitions are no more a fact than Einstein's second postulate that light propagates at c in all directions in an IRF.

We are not interested in "now" for accelerating observers in this setup. There is no accelerating reference frames. There is only instant acceleration, and inertial reference frames for before and after the acceleration, which are completely well defined.

I don't want to get hung up on terminology, I just want to show you something that you seem to be unaware of and that is the radar method of establishing an observer's rest frame. I'm going to repost the second diagram in which blue remains at rest (after his acceleration) because I have already put in the radar method for him to measure how far away the red twin is at blue's time 17.

He can't establish that distance in real time, he has to be making measurements all during his trip. Every month he sends a radar signal to the red twin which propagates on a 45-degree angle and the red twin reflects it back toward the blue twin along with his current time. So at blue's time 8 he sends a radar signal to red which arrives at red's time 14 and is received back at blue time 26. Blue then calculates one half of the delta between 8 and 26 which is 9 and applies that as a distance at the time which is the average of 8 and 26 which is 17. So he says that when his time was 17, red was 9 light-months away and the time on red's clock was 14 (blue reads this at his time 26 or else red sends him the information along with the radar echo).

Once you understand this process, you can verify it for every month along blue's path. And since blue was already at rest in this IRF, the radar method will exactly agree with the IRF.

I have redrawn the first diagram from earlier making it taller and removed the blue's radar measurement:

Please copy this diagram to your computer and print it or open it in Paint and use it to make a table of how red will calculate how far away blue is at every one of red's months. Also keep track of the corresponding times on blue's clock, just like I showed you earlier. When you get all done, you can sketch out the results on the same diagram and post it for us to see. Can you do that? I promise you, you will find it interesting, maybe even more interesting than what you said about red's point 12.

 

[georgir]

OK, is this what you mean?

No, and since it is such a simple thing I am now sure you are just trolling me.
Regardless, here is the diagram, and I am out of this thread.

 

[JohnWisp]

Sorry but I think you are talking nonsense, do you actually speak German?

From the Urtext:

... und bewegt man die Uhr in A mit der Geschwindigkeit v auf der Verbindungslinie nach B, so gehen nach Ankunft dieser Uhr in B die beiden Uhren nicht mehr synchron, ...


There is nothing ambiguous about it: the clock in A is moved with a velocity of v and arrives at B.

Why are you attacking me?

My point was that Einstein assumed instantaneous acceleration or his conclusions may be false with his statement.

So, the translation does assume this.

That mean's instantaneous acceleration (moved from a rest state to v) is ignored in the calculations for Einstein's teachings on time dilation.

that is exactly what I was saying.

 

[JohnWisp]

Often the seminal works are full of confusing notation, particularly since the notation was not standardized. One of the things that makes the great minds so great is that they were able to understand despite the poor notation of the time. Einstein was smart enough to use the confusing notation without becoming confused, you apparently are no Einstein.

If you are done trying to deflect the issue, you may want to go back and address the substantive criticism of post 28.

Exactly what math do you think backs up your claim? You have only demonstrated that the relationship between the t and t' coordinates on one worldline is different from the relationship between the t and t' coordinates on a different line. You have not demonstrated anything at all about the actual numbers read on the clocks, let alone that there is some contradiction among them.

I am confused by your post.

Are you claiming my assertions

1) x =vt
2) x'=-vt'

is not the appropriate logic for translation between the two frames?

Next, I do not know the actual times on the clocks at the Einstein clock sync method and never claimed I did.

I am claiming based on time dilation, once the clock values are determined, relativity can't be consistent since it claims one clock is less than the other and vice versa.

As far as drawing the wordlines, I do not know how to do it for this problem.

If I did, then there would be a solution everyone could agree on.

 

[JohnWisp]

So what? Nowhere in Einstein's quote does he say that the acceleration was constant. The quote is irrelevant.

The acceleration described in the OP is not constant and the symmetry you assert does not exist. My statements are 100% true.

You are right. Einstein never claimed anything about acceleration calculations in his quote.

In fact, he did not include the effects in his conclusions and that is what the OP did.

But, some asked about the acceleration phase and I tried to provide the mainstream calculations for those questions.

The OP however is perfectly consistent with Einstein ignoring the acceleration effects.

So that is allowed unless you can show otherwise.

 

[JohnWisp]

Identical acceleration profiles of two observers at different x values is not a symmetric situation. Think in this respect about Bell's spaceship paradox.

This is not applicable.

The Bell problem showed identical accelerations at different x values x1, x2.

Under non-relativity, the string would not break.

Under relativity, it does break.

So, this problem is not applicable given the different x values.

 

[JohnWisp]

Some quick comments: the only space-time diagrams posted to this thread have been dismissed as "wrong", but the OP has not responded with a "correct" space-time diagram.

Alas, the verbal descriptions of the "paradox" seem rather ambiguous (having seen a few "paradoxes", I would guess it likely that this ambiguity is at the heart of the paradox.

I would place the burden on the OP to supply such a space-time diagram, as the alternative is to watch the thread spin around i circles forever.

I don't see how anybody else other than the original poster will feel motivated to go to the effort of creating and posting a space-time diagram to simply see it dismissed as "wrong" by the OP in a few lines of text, without apparent thought.

So if a space-time diagram is needed (and I think it is), it is pretty much up to the OP to step forwards and do one.

I do not have a world line solution.

If I did, then I would provide a solution to this problem which I have already confessed I do not have.

So, you are asking me to solve a problem I already confessed I cannot solve.

 

[JohnWisp]

I want to post this link since it is the standard on differential aging given constant acceleration.

Perhaps someone can use this to solve the problem.

http://arxiv.org/pdf/physics/0411233v1.pdf

 

[pervect]

I do not have a world line solution.

If I did, then I would provide a solution to this problem which I have already confessed I do not have.

So, you are asking me to solve a problem I already confessed I cannot solve.

Let's review and recap and rephrase a bit:

1) Assume T1 and T2 are in the same frame.

2) T2 instantly acquires some v.

3) Both remain in relative motion for some time

4) After t elapses in the T1 frame, T1 also acquires the same v.

Can you draw a space-time diagram for this much?
Can you interpret the space-time diagram given in

https://www.physicsforums.com/attachment.php?attachmentid=57752&stc=1&d=1365671314

I don't think I'll be able to help much if you can't get at least this far on your own.

Then, to complete the paradox, I would add the following:

"At some event, T2 stops moving"

q: what is the time of this event in the T2 frame - i.e. the proper time
q: what is the time of the event in the T1 frame - (we need to know this to place it on the diagram).
q: what is the position of the event in the T1 frame (this follows from the velocity and the answer to the previous question).

At this point, we can proceed with the "paradox" - if it still exists.

This is considerably less complicated than a lot of the references you've been using. Some familiarity with the Lorentz transform would be helpful in converting from the T1 frame to the T2 frame.

 

[Dale]

Are you claiming my assertions

1) x =vt
2) x'=-vt'

is not the appropriate logic for translation between the two frames?

Correct, the transform of x=vt is x'=0. In other words, x=vt is the same worldline as x'=0, while x'=-vt' is a completely different worldline.

Next, I do not know the actual times on the clocks at the Einstein clock sync method and never claimed I did.

I am claiming based on time dilation, once the clock values are determined, relativity can't be consistent since it claims one clock is less than the other and vice versa.

Such claims are not permitted here. Thread closed.

PS. You may open a new thread to ask your questions, but leave off the anti-relativity commentary. It is against the forum rules, and factually incorrect. The framework of Minkowski geometry guarantees that SR is self consistent. Furthermore, it is absurd for you to think that you have found an inconsistency when you, by your own admission, don't even know how to calculate the very numbers which you claim are inconsistent.

 

[Fredrik]

I'm unlocking this thread at the request of ghwellsjr, because he wants to post some stuff he had already prepared when the thread got locked. We will probably lock the thread again tomorrow, so I don't encourage anyone else to continue the discussion. Note that the OP isn't even here anymore.

 

[ghwellsjr]

Thanks Fredrik.

This is a continuation from post #49 on this thread.

In that post I described how to calculate the coordinates of a non-inertial rest frame for the red twin. The first step is to draw in radar signals sent from the red twin every month and reflecting off the blue twin:

Now we have to compile a list of information that the red twin collects.

In the first column are the Proper Times when he sent each signal and when he received the echo separated by commas.

The second column contains his calculations of the distance the blue twin was away from him and his Proper Time when the blue twin was there. The first calculation is one half of the difference between the two numbers in the first column and the second calculation is one half of the sum of those two numbers.

The third column is the Proper Time the red twin sees on the Blue Twin's clock whenever he receives an echo.

0,0	0.0 @ 0.0	0
1,4	1.5 @ 2.5	2
2,8	3.0 @ 5.0	4
3,12	4.5 @ 7.5	6
4,14	5.0 @ 9.0	8
5,16	5.5 @ 10.5	10
6,18	6.0 @ 12.0	12
7,20	6.5 @ 13.5	14
8,22	7.0 @ 15.0	16
9,24	7.5 @ 16.5	18
10,26	8.0 @ 18.0	20
11,28	8.5 @ 19.5	22
12,30	9.0 @ 21.0	24
13,31	9.0 @ 22.0	25
14,32	9.0 @ 23.0	26
15,33	9.0 @ 24.0	27
16,34	9.0 @ 25.0	28
17,35	9.0 @ 26.0	29

Now we plot the information in the second column and label the Proper Times for the third column, interpolating any that are missing:

The advantage of this type of non-inertial frame is that the light signals continue to propagate at c and there are no discontinuities in the times on either twin.

Furthermore, we can reverse the process by having the blue twin perform the same radar measurements of red twin's positions as a function of his own Proper Time and recreate the second diagram shown on post #49. In other words, it continues to show, like Inertial Reference Frames what each observer actually sees and measures.

After you have done a few of these non-inertial frames, you can take some short cuts and only do the calculations where the discontinuities occur. Of course, real observers can't do this because they can't see the discontinuities until after they happen.