The Twin Paradox: Triplets Edition

[greswd]

I use Mathematica for calculations and plots directly based on calculations, but I typically use PowerPoint or Paint for drawing.

Cool, time for me to get my free copy of Mathematica.

"Some" will also tell you that the world is flat.

Haha, no one will ever tell me that the world is flat.

Cranks have progressed to higher stuff these days. There's this guy who claims to be the Flat Earth Society president but he's most probably trolling.

However, I have met some bible thumpers who told me that evolution cannot be true because the world is only 6000 years old.

 

[PeterDonis]

There's this guy who claims to be the Flat Earth Society president but he's most probably trolling.

Can't say about that specific guy, but the Flat Earth Society actually exists and has for decades. Here's their website:

http://theflatEarth'society.org/cms/

 

[ghwellsjr]

As usual, I was busy with work, hence I've taken a long time to reply. Sorry bout that.

Anyway, what software did you use to draw those diagrams?

I wrote my own program using a general purpose language called LabVIEW. I did this last November after you posted some graphs that I thought were quite interesting, not the normal kind of spacetime diagram, so I thank you for providing me the inspiration and motivation to do it.

Also, I think it would be better if you displayed the full images in your post.

I don't know what you mean by this. I thought I was displaying the full images.

I'm used to viewing time as the horizontal axis too. Yeah, the high school method.

Me too, but showing them rotated does have the advantage that they don't get too wide which otherwise makes the whole page wide and makes reading other posts difficult if you don't have a wide monitor.

http://img600.imageshack.us/img600/6065/triplets10.png
Thanks for taking the time to come up with this creative and somewhat bizarre diagram. I admit that I've never seen something like that before.

You're welcome. I have never seen one that looks just like mine before either.

Firstly, for some duration of time Jane is an inertial frame moving away from John. (or Adam-Charles for that matter)
In that inertial frame, which occupies half of the above diagram, the closely spaced photon world lines do not exist. So marrying the frames would look like the original time-gap diagram.
What you've done is to try to make the world lines continuous, I do understand how your diagram ended up like that.

The time-gap is an artifact caused by insisting the Jane is always at rest in an Inertial Reference Frame and that after she accelerates, she has to jump to a new IRF. If you will simply realize that both Jane and Joe (not John) are always in all IRF's and use just one IRF for the whole scenario, then there won't be any time-gaps. But even if you want to use the very common time-gap explanation, the time-gap is never observable by Jane or Jim. It's merely a calculation based on an arbitrary definition of an IRF.

I'm glad you understand how I produced the diagram.

Secondly, in the original scenario John and Jane are never in the same frame, but in this case they are for some duration. I don't think that's what I meant when I spoke of a time-gap.
Using my suggested method for Jane to figure out John's position, it can't produce your diagram.

No, but it won't produce any diagram you provided either. My diagram is based on actual measurements that Jane makes, not on speculation about what Jim must be doing. If you can produce a diagram according to your suggested method, I'd like to see it. The diagram I produced was inspired by your request and I appreciate your motivating and inspiring me to produce it.

Your method works fine, initially you posted (4+7=) 11 sets of data. But I'm not sure how you managed to produce the other 8 sets.

I'm lost here, can you point me to the post number where I did this?

Lastly, if John and Jane are in the same frame, why is John sending out pulses at a much higher frequency?

No matter what inertial or non-inertial frame or even if you don't want to analyze this scenario according to a frame, Jane will see Jim sending out pulses out a higher frequency during the last half of her trip and a lower frequency during the first half of her trip. If your diagram doesn't show that, then it is either wrong or incomplete.

Furthermore, Jim will see Jane sending out pulses at that same higher frequency during a shorter portion of the end of the scenario and at that same lower frequency during a longer portion of the beginning of the scenario. All my diagrams show exactly the same thing in this regard. If you produce a diagram that doesn't show this, then it is either wrong or incomplete.

I also found this on Wikibooks, which clearly talks about a time gap. (not written by me LOL )

Yes, they do talk about a time gap, but it's not clearly talked about. Maybe you can explain what they mean when they talk about the 4.5 secs and 8 secs interval. Where did those numbers come from, what do they mean, and why is this so different from the other explanations of the time gap?

_____________________________________________________________________________

A bit of history:

By the time I read your Doppler explanation in this thread, it was the 4th time I had come across this.

The first was in an online exercise. It said that Jane starts receiving signals at a higher frequency when she turns around.
I thought to myself this, "When I left, my twin was the same age. When I returned, he was older. What happened in between?"

So I drew a diagram and arrived at the time-gap explanation.

The second and third times were identical, one was from some guy on another forum, one was from Paul Hewitt's Conceptual Physics.

Anyway, some people have already acknowledged this time-gap explanation too.

Yes, in an attempt to provide the traveling twin with a rest frame, the time-gap explanation (or objection) is very popular. However, now that I know how to provide the traveling twin with a rest frame that doesn't have a time-gap, I plan to show this in the future when the subject comes up again.

 

[greswd]

"Some" will also tell you that the world is flat.

But who should I follow? Everyone online has got about equal standing.

Last time you were a golden boy, but now you've gone green, so I guess that ups your standing. Anyway, congrats on being made a mentor.


EDIT: Your diagram looks very similar to ghwellsjr's, as though they came from the same program. Coincidence?

I wrote my own program using a general purpose language called LabVIEW. I did this last November after you posted some graphs that I thought were quite interesting, not the normal kind of spacetime diagram, so I thank you for providing me the inspiration and motivation to do it.

You're welcome, though I'm far from inspiring.

LabVIEW is mainly for professionals right? I'm curious, are you guys currently students, educators etc?


Anyway, I'm still busy so it'll be a while before I reply.

 

[ghwellsjr]

But who should I follow? Everyone online has got about equal standing.

I decided who I should follow by examining how effective they were in convincing others and how I could understand their arguments. Until you understand the subject matter, you cannot tell who to believe. That's why I avoid discussions about gravity and GR. I'm just glad that you don't have to understand GR in order to understand SR. SR is simple, GR is complex. SR only requires a little bit of high school algebra. GR requires an understanding of tensors which stops me right in my tracks. I'm content to help others with SR. I'll leave the GR tutoring to others.

Last time you were a golden boy, but now you've gone green, so I guess that ups your standing. Anyway, congrats on being made a mentor.


EDIT: Your diagram looks very similar to ghwellsjr's, as though they came from the same program. Coincidence?

DaleSpam just copied my diagram, opened it in Paint, added some extra lines of different colors, and then uploaded them to his post. He didn't start from scratch.

You're welcome, though I'm far from inspiring.

LabVIEW is mainly for professionals right? I'm curious, are you guys currently students, educators etc?

If you want to buy it, you'd probably only do that as a professional since it's quite expensive. However, you can try it for awhile if you are interested. I'm a professional engineer. Didn't learn much as a student. Learned most of what I know about SR right here on this forum (mainly from DaleSpam and JesseM years ago) by reading the long threads before ever even joining.

Anyway, I'm still busy so it'll be a while before I reply.

 

[ghwellsjr]

I want to revisit your statement that my non-inertial diagram doesn't follow your suggested method:

http://img600.imageshack.us/img600/6065/triplets10.png

Using my suggested method for Jane to figure out John's position, it can't produce your diagram.

I agree that I wasn't following your suggested method when I created the above diagram but let's take another look at your suggested method:

Let's say Jane keeps time and she knows the relative velocity between her and Joe, thus she knows the distance between them.

Based on the Doppler analysis, Jane sees Joe's signals as pop-ups on her computer screen, telling her how old Joe is and all the cool stuff he did on his birthday like getting wasted.

Considering everything from her frame, be it inertial or not, and knowing that Joe's signals always approach at the speed of light, Jane can thereby conclude that she received signals that contradict with Joe's known positions. Sort of figuring out there's a time gap.

When you talk about Joe's known positions, you have to realize that positions are a function of time and since we're talking about two different times (Joe's and Jane's) we can also be talking about two different positions. As long as the relative speed between Jane and Joe remains the same (which is the case as long as they both remain inertial), Jane's radar measurements of Joe's positions will show that he is traveling at the speed that Jane knows is their relative velocity (as you say). However, the information that Jane receives from Joe's signals assumed to be traveling at the speed of light don't contradict Joe's known positions, they "contradict" Joe's "known times". But this is nothing more than a demonstration of Time Dilation. It's not what is known as a time-gap caused by Jane turning around. And as I stated before, Joe can make the exact same measurements of Jane's positions as a function of his time and conclude that she is traveling away from him at the same speed but that her clock is Time Dilated.

But at the point where Jane turns around, the relative velocity between them changes and so her radar measurements of Joe's positions are affected. Fortunately, if she continues to follow the same process that she did before she turned around, she will get consistent results, just like Joe does when he observes her turning around.

Consider what would happen if Jane didn't know whether or not Joe remained at rest during the whole scenario. Wouldn't her continued radar measurements of his positions and her observations of his times applied at the midpoint of when those measurements were made follow your suggested method of making a diagram? It turns out that this method always works for all scenarios for any number of observers no matter what trajectory they follow.

So I think I did follow your suggested method, even though I didn't realize it at the time I did it.

 

[greswd]

Sorry, I'm still too busy to read through what you wrote.

I'm a professional engineer. Didn't learn much as a student. Learned most of what I know about SR right here on this forum (mainly from DaleSpam and JesseM years ago) by reading the long threads before ever even joining.

Wow, you must have a lot of patience to read through all those long threads. Right now I'm even finding your posts too long. I prefer to K.I.S.S.

I don't mean to be a busybody, but I'm always curious about other members and I always wonder what it would be like to discuss science with them IRL.

Right now, I have literally no one to discuss science with. The forums are my only avenue.

 

[ghwellsjr]

Sorry, I'm still too busy to read through what you wrote.

Wow, you must have a lot of patience to read through all those long threads. Right now I'm even finding your posts too long. I prefer to K.I.S.S.

That's one reason why DaleSpam is so good at this. He forced me to work things out on my own. But I enjoy cranking out all the details as I'm aware that other people may be reading my posts. I would never do this in a private format for just one person. It also helps me to formalize my thinking and I'm still learning as you can see.

I don't mean to be a busybody, but I'm always curious about other members and I always wonder what it would be like to discuss science with them IRL.

Right now, I have literally no one to discuss science with. The forums are my only avenue.

Most people, even scientifically astute people, do not want to spend a lot of time discussing one on one and you never know when they have time. This thread has already spanned six months and it works because we can come and go as time permits.

EDIT: And we still haven't gotten to the point of your thread--triplets!

 

[greswd]

That's one reason why DaleSpam is so good at this. He forced me to work things out on my own. But I enjoy cranking out all the details as I'm aware that other people may be reading my posts. I would never do this in a private format for just one person. It also helps me to formalize my thinking and I'm still learning as you can see.

So am I. But sometimes I feel that the descriptions are really long-winded. And 90% of discussion on PF is like that. It is more conducive for confusion than learning.

The only time when I'm willing to read long descriptions is when following some online tutorial.

Most people, even scientifically astute people, do not want to spend a lot of time discussing one on one and you never know when they have time.

But for me, there are no scientifically astute people around IRL. Maybe it'll improve once I get into college.

This thread has already spanned six months and it works because we can come and go as time permits.

EDIT: And we still haven't gotten to the point of your thread--triplets!

We're practically pen pals now.

Don't worry, this thread will have to end at some point in time. During this period, I think I have learned quite a lot about scientific discussions. There's been some personal growth for me, in a weird way.

So what kind of engineering do you do? Also, is your custom software available for download? :D

 

[Dale]

But who should I follow? Everyone online has got about equal standing.

Me, of course, because I am more equal than everyone else

Seriously, don't follow anyone. Learn the math and work stuff out on your own. If you can work it out on your own then you will know who is right and who is wrong, or you will understand that both sides are right and just having difficulty translating from math to English.

EDIT: Your diagram looks very similar to ghwellsjr's, as though they came from the same program. Coincidence?

No coincidence. I shamelessly appropriated his drawing and then took it to Microsoft Paint to color a few lines. It is his drawing, with some minor highlighting.

However, you can see the original on which ghwellsjr based his here (Fig 9): http://arxiv.org/abs/gr-qc/0104077

 

[greswd]

Me, of course, because I am more equal than everyone else

Seriously, don't follow anyone. Learn the math and work stuff out on your own. If you can work it out on your own then you will know who is right and who is wrong, or you will understand that both sides are right and just having difficulty translating from math to English.

That I shall.

No coincidence. I shamelessly appropriated his drawing and then took it to Microsoft Paint to color a few lines. It is his drawing, with some minor highlighting.

However, you can see the original on which ghwellsjr based his here (Fig 9): http://arxiv.org/abs/gr-qc/0104077

I see. I've already obtained my free copy of Mathematica , currently figuring out how to draw some graphs.

 

[ghwellsjr]

This thread has already spanned six months and it works because we can come and go as time permits.

EDIT: And we still haven't gotten to the point of your thread--triplets!

We're practically pen pals now.

Don't worry, this thread will have to end at some point in time. During this period, I think I have learned quite a lot about scientific discussions. There's been some personal growth for me, in a weird way.

So what kind of engineering do you do? Also, is your custom software available for download? :D

I'm an electronics engineer but I spend most of my time programming test fixtures in LabVIEW.

When we finish with this thread, I'll send you a copy of my software.

 

[greswd]

I'm an electronics engineer but I spend most of my time programming test fixtures in LabVIEW.

When we finish with this thread, I'll send you a copy of my software.

I'm thinking about going into either electronics or computer science. But I'm not quite sure what each has to offer.

Yup, I'd like to finish the thread soon. Thanks.

 

[ghwellsjr]

I'm thinking about going into either electronics or computer science. But I'm not quite sure what each has to offer.

Computer science has a lot of competition to offer in the job market. Electronics engineering does too but if you know LabVIEW, you will have no problem getting a job. If you want to go that route, look for a college that teaches LabVIEW in their electronics major

Yup, I'd like to finish the thread soon. Thanks.

Well then, study my posts. They're really very simple. Special Relativity is very easy to understand. If you think it's difficult, it's only because you're trying to make it more difficult than it is. You need to understand the concept of an Inertial Reference Frame and how to use the Lorentz Transformation process to convert all the coordinates of one frame into the coordinates of another frame moving with respect to the first one. It's tedious but simple. That's why I wrote a program to do all the tedious work for me.

 

[greswd]

Computer science has a lot of competition to offer in the job market. Electronics engineering does too but if you know LabVIEW, you will have no problem getting a job. If you want to go that route, look for a college that teaches LabVIEW in their electronics major

Thanks for the advice. I'll get acquainted with LabVIEW.

Well then, study my posts. They're really very simple. Special Relativity is very easy to understand. If you think it's difficult, it's only because you're trying to make it more difficult than it is. You need to understand the concept of an Inertial Reference Frame and how to use the Lorentz Transformation process to convert all the coordinates of one frame into the coordinates of another frame moving with respect to the first one. It's tedious but simple. That's why I wrote a program to do all the tedious work for me.

Yeah, I'm so troublesome, always thinking too hard; arguing too much. And always taking such a long time to reply.

Yes, in an attempt to provide the traveling twin with a rest frame, the time-gap explanation (or objection) is very popular. However, now that I know how to provide the traveling twin with a rest frame that doesn't have a time-gap, I plan to show this in the future when the subject comes up again.

Actually, both the Doppler and Length Contraction explanations are always used. The time gap is usually left out. I have only seen it in John Baez and that Wikibook article.

I'm not fine with the time-gap, but some of the posters in this thread are totally fine with it. I thought you'd try to justify the time-gap lol.

You probably won't meet someone as troublesome as me again.

 

[greswd]

I don't know what you mean by this. I thought I was displaying the full images.

They appear as tiny little X-es instead of full images. Like the server was unable to retrieve the image or something.

Me too, but showing them rotated does have the advantage that they don't get too wide which otherwise makes the whole page wide and makes reading other posts difficult if you don't have a wide monitor.

Not if you've got a Mighty Mouse. But I don't want to sprain my neck.

The time-gap is an artifact caused by insisting the Jane is always at rest in an Inertial Reference Frame and that after she accelerates, she has to jump to a new IRF. If you will simply realize that both Jane and Joe (not John) are always in all IRF's and use just one IRF for the whole scenario, then there won't be any time-gaps. But even if you want to use the very common time-gap explanation, the time-gap is never observable by Jane or Jim. It's merely a calculation based on an arbitrary definition of an IRF.

Jane is an inertial frame for some duration, but you've introduced some worldlines which previously did not exist in that frame. In the time-gap explanation, this leads to "broken" worldlines. Either that or a trapezoid worldline for Joe. Both weird, but as the wise guru DaleSpam said:

It is a bizarre diagram because it is a bizarre thing to do.

I'm lost here, can you point me to the post number where I did this?

#92 Pg 6
But I think DaleSpam explained it.

No matter what inertial or non-inertial frame or even if you don't want to analyze this scenario according to a frame, Jane will see Jim sending out pulses out a higher frequency during the last half of her trip and a lower frequency during the first half of her trip. If your diagram doesn't show that, then it is either wrong or incomplete.

Furthermore, Jim will see Jane sending out pulses at that same higher frequency during a shorter portion of the end of the scenario and at that same lower frequency during a longer portion of the beginning of the scenario. All my diagrams show exactly the same thing in this regard. If you produce a diagram that doesn't show this, then it is either wrong or incomplete.

DaleSpam called it gravitational blueshift. But if Jane only accelerates for almost zero duration, why would grav blueshift last for a long period of time?
Unfortunately I'm not well versed in GR and I'm not going to pretend that I am. :shy:

Yes, they do talk about a time gap, but it's not clearly talked about. Maybe you can explain what they mean when they talk about the 4.5 secs and 8 secs interval. Where did those numbers come from, what do they mean, and why is this so different from the other explanations of the time gap?

It's based on the values they chose. It's the same as my explanation.

When you talk about Joe's known positions, you have to realize that positions are a function of time and since we're talking about two different times (Joe's and Jane's) we can also be talking about two different positions. As long as the relative speed between Jane and Joe remains the same (which is the case as long as they both remain inertial), Jane's radar measurements of Joe's positions will show that he is traveling at the speed that Jane knows is their relative velocity (as you say). However, the information that Jane receives from Joe's signals assumed to be traveling at the speed of light don't contradict Joe's known positions, they "contradict" Joe's "known times". But this is nothing more than a demonstration of Time Dilation. It's not what is known as a time-gap caused by Jane turning around. And as I stated before, Joe can make the exact same measurements of Jane's positions as a function of his time and conclude that she is traveling away from him at the same speed but that her clock is Time Dilated.

But at the point where Jane turns around, the relative velocity between them changes and so her radar measurements of Joe's positions are affected. Fortunately, if she continues to follow the same process that she did before she turned around, she will get consistent results, just like Joe does when he observes her turning around.

Consider what would happen if Jane didn't know whether or not Joe remained at rest during the whole scenario. Wouldn't her continued radar measurements of his positions and her observations of his times applied at the midpoint of when those measurements were made follow your suggested method of making a diagram? It turns out that this method always works for all scenarios for any number of observers no matter what trajectory they follow.

So I think I did follow your suggested method, even though I didn't realize it at the time I did it.

Hmm, I thought my statement was pretty straightforward. If Jane undergoes infinite acceleration for an infinitesimally short duration, then Joe's worldline will be a V-shape. Not a trapezoid. Yeah.


Consider the original time-gap diagram; let's say Jane extrapolates the worldlines of the signals sent to her. Info on Joe's b-day is encoded within each signal.
Jane calculates Joe's positions and takes into account time dilation. She finds the worldline of the first signal does coincide with her calculation of Joe's first b-day.

Then she does it for all the other signals. She will find some inconsistencies, such as the signal for Joe's 11th b-day sent in between his 5th and 6th b-days.
However, Joe is a nice boy and would never troll her like that. After extrapolating everything, Jane reaches the conclusion that Joe somehow rapidly aged when she made the turnaround halfway into her trip...

 

[ghwellsjr]

I don't know what you mean by this. I thought I was displaying the full images.

They appear as tiny little X-es instead of full images. Like the server the server was unable to retrieve the image or something.

This happens to my diagrams when you are not logged in. Just log in again, and everything will be fine.

Consider the original time-gap diagram; let's say Jane extrapolates the worldlines of the signals sent to her. Info on John's b-day is encoded within each signal.
Jane calculates John's positions and takes into account time dilation. She finds the worldline of the first signal does coincide with her calculation of John's first b-day.

Then she does it for all the other signals. She will find some inconsistencies, such as the signal for John's 11th b-day sent in between his 5th and 6th b-days.
However, John is a nice boy and would never troll her like that. After extrapolating everything, Jane reaches the conclusion that John somehow rapidly aged when she made the turnaround halfway into her trip...

You've got me all confused. Earlier you pointed to a website that discussed Joe and Jane (not John and Jane), but Joe only aged 8 years (to Jane's 6) so I don't know how to consider the original time-gap diagram. Can you provide the post number or link where it is displayed?

Also, I don't know how Jane could ever get confused about Joe's (or John's) accumulated years, she watches them progress in an orderly manner, first at one-half her own aging rate and then after she turns around at twice her own aging rate. If you have a diagram that shows something different than that, then it is wrong.

 

[greswd]

You've got me all confused. Earlier you pointed to a website that discussed Joe and Jane (not John and Jane), but Joe only aged 8 years (to Jane's 6) so I don't know how to consider the original time-gap diagram. Can you provide the post number or link where it is displayed?

Also, I don't know how Jane could ever get confused about Joe's (or John's) accumulated years, she watches them progress in an orderly manner, first at one-half her own aging rate and then after she turns around at twice her own aging rate. If you have a diagram that shows something different than that, then it is wrong.

Oh, I got the names mixed up. My bad. I mentioned John Baez and maybe I confused myself.

I was talking about a generic time-gap diagram, not a specific scenario. I made up those numbers but it still illustrates my point.

In a time-gap diagram Jane does receive Joe's signals in order. However if she tries to extrapolate signal worldlines to her calculated positions of Joe (based on relative velocity and elapsed time) , she finds inconsistencies as I described in my previous post.

 

[ghwellsjr]

Oh, I got the names mixed up. My bad. I mentioned John Baez and maybe I confused myself.

I was talking about a generic time-gap diagram, not a specific scenario. I made up those numbers but it still illustrates my point.

In a time-gap diagram Jane does receive Joe's signals in order. However if she tries to extrapolate signal worldlines to her calculated positions of Joe (based on relative velocity and elapsed time) , she finds inconsistencies as I described in my previous post.

But you were talking about a specific scenario. In fact, I see that you have edited your post to change the name back to Joe:

Consider the original time-gap diagram; let's say Jane extrapolates the worldlines of the signals sent to her. Info on Joe's b-day is encoded within each signal.
Jane calculates Joe's positions and takes into account time dilation. She finds the worldline of the first signal does coincide with her calculation of Joe's first b-day.

Then she does it for all the other signals. She will find some inconsistencies, such as the signal for Joe's 11th b-day sent in between his 5th and 6th b-days.
However, Joe is a nice boy and would never troll her like that. After extrapolating everything, Jane reaches the conclusion that Joe somehow rapidly aged when she made the turnaround halfway into her trip...

And here is the diagram for Joe and Jane from this website that you linked to:

But Joe ages by only 8 years and Jane ages by 6 years so I can't make any sense of your statement about his 11th b-day. So if you are thinking of a different scenario, I need to know how fast Jane is traveling and how old she is when she turns around. It would also be helpful if you would provide a correctly drawn diagram illustrating the worldlines of the signals that you talked about.

 

[greswd]

But you were talking about a specific scenario. In fact, I see that you have edited your post to change the name back to Joe:

And here is the diagram for Joe and Jane from this website that you linked to:

But Joe ages by only 8 years and Jane ages by 6 years so I can't make any sense of your statement about his 11th b-day. So if you are thinking of a different scenario, I need to know how fast Jane is traveling and how old she is when she turns around. It would also be helpful if you would provide a correctly drawn diagram illustrating the worldlines of the signals that you talked about.

Nah, just a rough, generic example with numbers I made up.
Jane or Joe are just names for the traveling and homebound twins. I wasn't specifically referring to the UNSW diagram.

Here's my original diagram.

http://img826.imageshack.us/img826/1289/vvvvvi.png

Now I'm just going to use the names Jane and Joe.

After extrapolating, Jane calculates that the 9th signal was sent in between Joe's 7th and 8th b-days. Extrapolating for the 7th and 8th signals, Jane wonders why one was sent before schedule and another sent behind schedule.

 

[Dale]

DaleSpam called it gravitational blueshift. But if Jane only accelerates for almost zero duration, why would grav blueshift last for a long period of time?
Unfortunately I'm not well versed in GR and I'm not going to pretend that I am. :shy:

If you go to the Dolby and Gull paper and look at figure 9 you can see the answer, although they did not describe it much in the text.

The instantaneous acceleration of the traveling twin (Barbara for Dolby and Gull) causes a "shock like scale discontinuity" that travels away from the twin in a future-directed light cone and also a past directed light cone.

Those "shocks" are what cause the turning of the stay at home twin's worldline (Alex for Dolby and Gull), one shock brings Alex to rest in the non-inertial frame and the other accelerates him towards Barbara. Those shocks also cause light to undergo gravitational red/blueshift. It redshifts as it goes from region P to region I and blueshifts as it goes from region I to region F.

 

[greswd]

If you go to the Dolby and Gull paper and look at figure 9 you can see the answer, although they did not describe it much in the text.

The instantaneous acceleration of the traveling twin (Barbara for Dolby and Gull) causes a "shock like scale discontinuity" that travels away from the twin in a future-directed light cone and also a past directed light cone.

Those "shocks" are what cause the turning of the stay at home twin's worldline (Alex for Dolby and Gull), one shock brings Alex to rest in the non-inertial frame and the other accelerates him towards Barbara. Those shocks also cause light to undergo gravitational red/blueshift. It redshifts as it goes from region P to region I and blueshifts as it goes from region I to region F.

Hmm, they wrote this:

It is often said of the twin paradox that[4] “a complete explanation of the problem can only be given
within the framework of general relativity”. However, as we have just shown, Barbara’s hypersurfaces
of simultaneity depend only on the kinematics involved, and can be fully understood without resorting
to general relativity

 

[Dale]

Hmm, they wrote this:

Yes, they did write that, and it is correct, there is no tidal gravity in this scenario so no need for GR.

 

[greswd]

Yes, they did write that, and it is correct, there is no tidal gravity in this scenario so no need for GR.

I see. Anyway I can't say anything otherwise for the time being; till I've learned GR. Thanks Dale.

 

[ghwellsjr]

Here's my original diagram.

http://img826.imageshack.us/img826/1289/vvvvvi.png

Now I'm just going to use the names Jane and Joe.

After extrapolating, Jane calculates that the 9th signal was sent in between Joe's 7th and 8th b-days. Extrapolating for the 7th and 8th signals, Jane wonders why one was sent before schedule and another sent behind schedule.

I know you don't like my long explanations so I made a bunch of diagrams for you to look at. First is the rest frame for Joe:

I drew this one upside-down so that I could transform it to the next two diagrams that show Jane's two inertial rest frames:

Please note that all three of the above diagrams correctly show Jane receiving the signals from Joe.

I need to start a new post since there is a limit of three images uploaded per post.

 

[ghwellsjr]

Now I've copied the last part of Jane's IRF and pasted it on to her first IRF to get a correct diagram of your image in the previous post:

Now you observe that the signals that Joe sends after his 6th one, get changed when they hit the interface between the two IRFs. For example, Joe's 7th signal suddenly changes to his 10th signal. But this merely shows that you cannot just connect the two IRFs along a vertical line. Instead, you could have at least drawn it like this:

But why not draw it like Dr Greg did in his last diagram in post #39 or like your referenced website did as shown in post #119?

Now between these last two diagrams, we can see that the problem is not a time gap but a distance gap. How is Jane to know if the 6th signal that she receives from Joe was sent when he was 4.5 light years away or 18 light years away? Same thing with all the rest of his signals up to his 24th signal.

One way she can know is to measure how far away he was when he sent each signal. I'll go into this in the next post.

 

[ghwellsjr]

I've already explained the radar method of determining how far away an object is but I'll go into more detail now. I've gone back to Jane's first IRF and added in several radar signals shown in different colors:

The first one is shown in blue and was sent when Jane's clock read 3 and the echo was received when her clock read 12. The return echo is aligned with Joe's 6th signal. She measures his distance by calculating how long it took for the radar signal to make its round trip and dividing that in half. Since it took 9 years, she divides that in half to get 4.5 years and so she concludes that Joe was 4.5 light years away at 4.5 years before she received the echo which puts it at 7.5 years. This agrees with the closer of the two distances making up the gap in the previous post.

She can repeat the process every year as shown by the different colored radar signals. For example, the next one was sent at year 4 and received at year 13 for a difference of 9 years. So again, she determines that Joe was 4.5 light years away. In fact, she will conclude this for all the signals sent up to the time when she changed directions at 12 years. But she can continue this process all the way to the end and when she gets done, she can make a diagram that will look like this:

Don't you agree that this is one possible way for Jane to solve the problem of how far away Joe is when he sent each signal?

 

[greswd]

I know you don't like my long explanations so I made a bunch of diagrams for you to look at.

Thanks for taking my needs into consideration.
You must've spent a lot of time and effort on these diagrams and I really appreciate it.

If the image is too wide I just use [MB3 + Drag]

Don't you agree that this is one possible way for Jane to solve the problem of how far away Joe is when he sent each signal?

I agree it's possible. I had a whole bunch of questions but Dale seems to have answered them using a so-called "non-tidal GR".

 

[ghwellsjr]

Thanks for taking my needs into consideration.
You must've spent a lot of time and effort on these diagrams and I really appreciate it.

If the image is too wide I just use [MB3 + Drag]

Fortunately, this new PF software adjusts each post to the proper width instead of the entire page--very nice.

Don't you agree that this is one possible way for Jane to solve the problem of how far away Joe is when he sent each signal?

I agree it's possible. I had a whole bunch of questions but Dale seems to have answered them using a so-called "non-tidal GR".

Now I'm hoping you will be convinced that you can take the above diagram of Jane's non-IRF rest frame and have Joe use the same radar method that she used and construct his own IRF rest frame:

So the same technique applies to both IRF and non-IRF frames.

One further thing I want to make sure you understand is that the Doppler method works correctly on both these rest frames. In other words, they both show what Jane sees of Joe's clock and provide the same Doppler ratios. If we wanted to, we could make two more diagrams showing the signals going from Jane to Joe and show how the Doppler method would also apply to Joe looking at Jane's signals. Does this all make sense to you or should I draw those diagrams?

 

[tade]

Where is the time gap?

 

[greswd]

Where is the time gap?

ghwellsjr was trying to show that there is none.


@ghwellsjr

Ok, I understand it now.
Except for Dale's explanations, but that's because I haven't learned GR.

 

[ghwellsjr]

I think we are ready to go back and pick up the triplet scenario. Back at post #19 I had asked you about what Adam and Bob would see of each others clocks when they each turn around. In your subsequent answer we got diverted on to this long discussion that focused on just the Twin Paradox relationship between Charles and Adam and we have pretty well covered that. I have re-read all the posts leading up to #19 and I would suggest that you do the same and then please answer my questions again:

Excellent.

I said in post #11 that Adam and Bob are going to age (about) a couple years so let's say they travel away for exactly one year according to their own clocks and then turn around and get back to Charles in exactly one more year. We'll first deal with what happens between Adam and Bob and when we get done with that we'll figure out what goes on between each of them and Charles.

Now according to the Doppler Analysis, Adam and Bob will each see the other ones clock running slower than their own by the factor of 5.00250125×10^-4 (which is 1/1999). So the first question we want to answer is what time will each of them see on the other ones clock when they reach the point of turnaround? The answer is simple--we multiply 1 year by 5.00250125×10^-4 (or divide it by 1999), which is just a little over four and a half hours.

The next question is what Doppler Factor will apply at the moment of turn around? How fast will they each see the other ones clock ticking immediately after they each turn around? What do you think?

 

[greswd]

I think we are ready to go back and pick up the triplet scenario. Back at post #19 I had asked you about what Adam and Bob would see of each others clocks when they each turn around. In your subsequent answer we got diverted on to this long discussion that focused on just the Twin Paradox relationship between Charles and Adam and we have pretty well covered that. I have re-read all the posts leading up to #19 and I would suggest that you do the same and then please answer my questions again:

I really don't know how to answer it. I suppose you could tell me everything you have on your mind, otherwise we'll take another hundred posts to resolve this.By the way, could you simplify Dale's GR explanations?

 

[ghwellsjr]

I really don't know how to answer it.

I suppose you could tell me everything you have on your mind, otherwise we'll take another hundred posts to resolve this.

Study this thread and see if you can get some hints.

By the way, could you simplify Dale's GR explanations?

No, I don't know GR so you'll have to ask him for more help.

 

[greswd]

Study this thread and see if you can get some hints.

Not really. It seems to be more confusing .

 

[ghwellsjr]

Study this thread and see if you can get some hints.

Not really. It seems to be more confusing .

Back on post #65 (page 5) I showed you several diagrams including this one:

and in the next post you said:

I understand the diagrams well.

Now that diagram is the same as this one from post #92 (page 6):

except this one is rotated 90 degrees and flipped so that it is like a conventional spacetime diagram. So I'm sure you're not having a problem with that.

Now here is the first diagram from the other thread:

Can you see that the right half of this diagram is identical to the diagram above it? And can you see that the left half of the diagram is a mirror image of the right half? Does this have anything to do with your confusion?

 

[greswd]

Will the solution involve another trapezoid?

 

[ghwellsjr]

Will the solution involve another trapezoid?

The non-IRF diagram using the radar method for each of the outside triplets calculating the path of the inside triplet will produce the same trapezoid as in the Twin Paradox "solution" but the shape they each calculate for the other outside triplet will be a more complicated.

But before we get to the complicated non-IRF diagram, I think you need to resolve your confusion over the simple IRF solutions. Can you provide specifics on what you are confused about?

 

[greswd]

The non-IRF diagram using the radar method for each of the outside triplets calculating the path of the inside triplet will produce the same trapezoid as in the Twin Paradox "solution" but the shape they each calculate for the other outside triplet will be a more complicated.

But before we get to the complicated non-IRF diagram, I think you need to resolve your confusion over the simple IRF solutions. Can you provide specifics on what you are confused about?

I understand your previous trapezoid diagram well.

Will the shape both calculate for the other outside triplet be a trapezoid as well?

 

[ghwellsjr]

I understand your previous trapezoid diagram well.

Then you should have no problem calculating the non-inertial rest frame for one of the outside triplets using the radar method. I have changed the scenario slightly to make it easier for you to do this. The only difference is that the traveling triplets go out for 16 months and 16 months coming back instead of just 12 each way, and the inertial triplet ages by 40 months:

Will the shape both calculate for the other outside triplet be a trapezoid as well?

No. Work it out and you'll see what it is.

 

[greswd]

Dayum, I got to do this manually.

Why provide the LabVIEW graphing software only after we're done?

 

[ghwellsjr]

Dayum, I got to do this manually.

It's not that hard. Start by making a table like I did in post #92 and #93 (page 6).

Why provide the LabVIEW graphing software only after we're done?

Yes, otherwise, you won't appreciate it. But my software doesn't do non-inertial frames. It allows you to define a triplet scenario (speed and length of time for the traveling triplets) and draws the diagram in the inertial triplet's rest frame and then it uses the Lorentz Transformation to redraw it at whatever speed you want the new IRF to be moving relative to the original IRF.

When I did the non-inertial rest frames, it was all done by cut-and-paste in Paint and I have only done this one on graph paper.

 

[greswd]

I will appreciate it

 

[ghwellsjr]

Here is a diagram repeating the one from post #140 but showing just a pair of radar signals emitted by Red as he measures the distance to Blue:

Now he can make the following table to summarize his findings:

Radar   Radar   Calculated   Calculated    Blue's
Sent    Rcvd      Time        Distance      Time
  0       0        0             0            0
  4      16       10             6            8
 16      28       22             6           32
 32      32       32             0           40

Remember that the Calculated Time is determined by adding the Radar Sent and Rcvd times together and dividing by two and the Calculated Distance is determined by subtracting the Radar Rcvd time from the Radar Sent time and dividing by two. If you want, you can include as many more samples from post #140 as you want. For completeness, I have included the readings at the beginning and at the ending (even though those radar signals are instantaneous).

Now here is another diagram repeating the one from post #140 but showing just a few of the radar signals emitted by Red as he measures the distance to Black:

And here is a table showing these findings (including the ones at the beginning and ending):

Radar   Radar   Calculated   Calculated   Black's
Sent    Rcvd      Time        Distance     Time
  0       0        0             0           0
  1      16        8.5           7.5         4
  4      28       16            12          16
 16      31       23.5           7.5        28
 32      32       32             0          32

Now we are ready to construct the non-inertial rest frame for red as he determines the distances to Blue and Black:

You can confirm that this diagram represents the findings from the two tables and any additional samples you want to include.

If you want, you can download the diagram and draw in radar and/or Doppler signals (along 45-degree diagonals) for all three observers and confirm that this diagram conforms to all my other diagrams in terms of what each observer sees of the other observers. All the diagrams that I have drawn are equivalent and contain the same exact information.

Any questions?