The Twin Paradox: Triplets Edition

[Alain2.7183]

Can we use a GR explanation instead of a time-gap?

It's my understanding that the standard GR resolution also gives a time gap, and it is the SAME time gap that is given by gravitation-free (SR) analysis that uses the momentary co-moving inertial reference frames. See, for example, the Wikipedia page on the Twin Paradox, and in particular, their section on the traveler's perspective.

 

[ghwellsjr]

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.

Except that it's not the time gap that you spoke of earlier due to Jane turning around. This "time gap" is present all the time prior to her turning around and is equally observable by Joe as it is by Jane. But let's pursue this and see where it leads us. However, I want to go back to the scenario involving Adam and Charles because it will be easier to illustrate what I want to show you. After that I will pick up with Joe and Jane.

If you look back at post #65 at the top of page 5 you will see the third diagram showing Adam, in black, traveling at 0.6c away from Charles in blue for 12 months and then he turns around and returns in another 12 months to find that Charles has aged by 30 months. Please reread that post for background. I have redrawn the third diagram here with the axes in the more normal configuration for spacetime diagrams. They are not so wide this way. Note the monthly yellow signals sent by Charles and the monthly black signals sent by Adam:

Now if we focus on how Charles would actually measure the position of Adam as a function of time (as opposed to simply calculating his position based on his speed and the elapsed time), he would make use of the radar method. This works as follows. At some point in time, he sends a signal to Adam with the time the signal was sent. When Adam gets the signal, he sends a signal back, including the original time the signal was sent and the time on his clock when he sent the response. When Charles receives this signal, he takes the difference between the received time and the sent time and divides that by two and interprets that as a distance (because we are using c=1) and applies it to the midpoint (or the average) between the two times.

So let's see how that works on the diagram. At the first dot after Adam's departure, Charles sends a signal indicated by the yellow line which Adam receives at his clock time of 2. He sends the signal back to Charles who gets it at his time of 4. So Charles calculates (4-1)/2 = 1.5 light-months and applies that distance to the average of 1 and 4 which is 2.5 years. So we can see that at 2.5 years into the trip, Adam has traveled a distance of 1.5 light-months. (We can also verify that Adam's speed is 1.5/2.5 = 0.6c.) The "time gap" you spoke of is that Adam says that the time was 2 months when he received the signal from Charles and when he was 1.5 light-months away, not the 2.5 months that Charles calculates.

You can repeat this process for any point along the way of Charles's time line. It will correctly indicate the position of Adam, including the turn-around point and the trip back, according to Charles's IRF. I have made a list of all the points along Charles's time line that show signals going from Charles and with a response back from Adam. Each line shows a distance that Charles measures at the time it is applied:

0.00 @ 0.00
1.50 @ 2.50
3.00 @ 5.00
4.50 @ 7.50
6.00 @ 10.00
7.50 @ 12.50
9.00 @ 15.00
8.25 @ 16.25
7.50 @ 17.50
6.75 @ 18.75
6.00 @ 20.00
5.25 @ 21.25
4.50 @ 22.50
3.75 @ 23.75
3.00 @ 25.00
2.25 @ 26.25
1.50 @ 27.50
0.75 @ 28.75
0.00 @ 30.00

And you can repeat this process for Adam sending a similar signal to Charles and getting a response back from Charles. The situation between them is symmetrical, at least for the first four measurements (counting the one at zero) and they both see the other one as having a "time gap". However, the above diagram does not support Adam's measurements because he is not at rest in it. For that, we need to transform all the events in IRF displayed in the above diagram to an IRF moving at 0.6c to show Adam at rest. Here is the diagram depicting Adam's IRF for the outbound portion of his trip:

Notice that it correctly supports his first four measurements of the distance that Charles is moving away from him:

0.00 @ 0.00
1.50 @ 2.50
3.00 @ 5.00
4.50 @ 7.50

Adam receives the response back from Charles for this last measurement at the point he turns around so his measurement for the next one doesn't comport with the diagram.

So let's go to the IRF in which he is at rest for the return part of the trip to see how things work out there:

If we pick up the measurement he makes when he sends the signal at his turnaround point, we get the following list of distances and times for the last part of his trip. Please note that we are using his Proper Times signified by the black dots and not the Coordinate Time of the diagram. They go from 12 months to 24 months while he is at rest in this IRF. Here is the list of distance as a function of time that Adam measures for Charles at the end of his trip:

4.50 @ 16.50
3.75 @ 17.75
3.00 @ 19.00
2.25 @ 20.25
1.50 @ 21.50
0.75 @ 22.75
0.00 @ 24.00

Now if you look at what Adam measures for any of the times where a signal is sent while he is at rest in his first IRF and received from Charles while he is at rest in his second IRF we see that he always measures a distance of 4.50 light-months. It doesn't matter which one of the above three diagrams you use to trace out the signals, they all indicate the same measurement of distance but none of them support that distance in the diagrams. Since I am limited to three diagrams per post I will make a new diagram on the next post to correctly show this.

 

[ghwellsjr]

Here is the complete list of distances as a function of time that apply for the traveling twin measuring the distance to the home twin:

0.00 @ 0.00
1.50 @ 2.50
3.00 @ 5.00
4.50 @ 7.50
4.50 @ 8.50
4.50 @ 9.50
4.50 @ 10.50
4.50 @ 11.50
4.50 @ 12.50
4.50 @ 13.50
4.50 @ 14.50
4.50 @ 15.50
4.50 @ 16.50
3.75 @ 17.75
3.00 @ 19.00
2.25 @ 20.25
1.50 @ 21.50
0.75 @ 22.75
0.00 @ 24.00

Here is the diagram that correctly shows the measurements that Adam makes of Charles's distance and in which Adam is always at rest. Note that this is for a non-inertial reference frame but it does correctly show the propagation of all the signals (something which I had previously claimed would be impossible, such as in post #67):

Now this is a very satisfying composite diagram that takes portions from the two IRF's in which Adam is at rest and then fills in the details that covers the "time gap" that is apparent in other "marriages" of the two IRF's but without any time gap. Everything is as smooth as it is in any IRF. I like it, I hope you do too.

It might be helpful to understand how I arrived at this type of diagram. I was trying to see how to combine two "married" IRF's for a different scenario. Here is the first of those two diagrams:

Note that the above diagram showing the signals going from the home twin to the traveling twin is similar to the one that Dr Greg provided in post #39 of this thread.

And here is the other one that shows the signals going from the traveling twin to the home twin:

I printed both these diagrams out and laid the printouts one on top of the other and held them up to the light so I could see through both of them. I aligned the rest positions of the traveling twin and then marked the intersections of the blue and black signals that matched the "path" of the home twin on a normal IRF diagram. I was surprised to see that they formed a straight line between the last reasonable point on the first diagram with the first reasonable point on the second diagram. Here is the composite diagram:

I then took your suggestion for the traveling twin to keep track of the positions of the home twin as a function of time and rediscovered this type of composite non-inertial reference frame based on radar measurements of distance.

Finally I want to show you the similar non-inertial diagram for Joe and Jane:

Does this satisfy your desire for a diagram showing the traveling twin at rest? It does for me because it also maintains the correct depiction of the signals traveling between the twins.

 

[greswd]

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? Also, I think it would be better if you displayed the full images in your post. I'm used to viewing time as the horizontal axis too. Yeah, the high school method.



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.

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.


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.
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.


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


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

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.

 

[Dale]

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.

It is a bizarre diagram because it is a bizarre thing to do. Trying to draw the traveling twin's perspective is itself bizarre, the diagram is a correct representation of that bizarrness.

Secondly, in the original scenario John and Jane are never in the same frame, but in this case they are for some duration.

That is correct. There is a period of time in which radar pulses from the traveler are sent before the turnaround and received after the turnaround. All of those radar echoes take the same amount of time, as measured by the traveller's clock, so the distance is constant during that time.

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

Because the frame is non-inertial. Wierd things like that happen in non-inertial frames. You can consider it to be gravitational blueshift, as Einstein would.

 

[greswd]

It is a bizarre diagram because it is a bizarre thing to do. Trying to draw the traveling twin's perspective is itself bizarre, the diagram is a correct representation of that bizarrness.

Well, bizarre is it then.

That is correct. There is a period of time in which radar pulses from the traveler are sent before the turnaround and received after the turnaround. All of those radar echoes take the same amount of time, as measured by the traveller's clock, so the distance is constant during that time.

I don't know how both of you arrived at that conclusion, but I'm afraid to ask.

Because the frame is non-inertial. Wierd things like that happen in non-inertial frames. You can consider it to be gravitational blueshift, as Einstein would.

Would he? Oh well, I haven't learned GR yet.

 

[Dale]

I don't know how both of you arrived at that conclusion, but I'm afraid to ask.

It is actually pretty easy. Just start with the diagram for the inertial frame for the stay at home twin. Then you just draw radar pulses that go from the traveling twin, to the inertial twin, and back (here I have drawn a red, purple, and green one). Then count how many of the black dots there are from sending out the pulse to getting the echo back (9 months in each case). The radar distance is just 1/2 of the round trip time (4.5 light-months).

 

[ghwellsjr]

It is actually pretty easy. Just start with the diagram for the inertial frame for the stay at home twin. Then you just draw radar pulses that go from the traveling twin, to the inertial twin, and back (here I have drawn a red, purple, and green one). Then count how many of the black dots there are from sending out the pulse to getting the echo back (9 months in each case). The radar distance is just 1/2 of the round trip time (4.5 light-months).

Actually, you can start with any inertial frame and do the same thing. Not only that, but if you are careful to apply the distance at the midpoint of the dots, you can construct the entire rest frame for the non-inertial twin.

Furthermore, you can do the same thing for the inertial twin. You can start with any other inertial frame and construct the stay at home twin's rest frame. Not only that, but you can start with the traveling twin's non-inertial rest frame and reconstruct the stay at home twin's rest frame.

 

[greswd]

Actually, you can start with any inertial frame and do the same thing. Not only that, but if you are careful to apply the distance at the midpoint of the dots, you can construct the entire rest frame for the non-inertial twin.

Furthermore, you can do the same thing for the inertial twin. You can start with any other inertial frame and construct the stay at home twin's rest frame. Not only that, but you can start with the traveling twin's non-inertial rest frame and reconstruct the stay at home twin's rest frame.

Interesting, I'll experiment with that. What software do you guys use?

Also, I find it confusing because some have already acknowledged the time-gap explanation.

 

[Dale]

Interesting, I'll experiment with that. What software do you guys use?

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

Also, I find it confusing because some have already acknowledged the time-gap explanation.

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

 

[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.