The Twin Paradox: Triplets Edition

[greswd]

Sorry for bumping this ol' thread, I was quite busy.

First up, do you guys recommended that I ignore the 3rd diagram I presented?

Also, how would we apply the Doppler shifts between Adam and Charles?

 

[ghwellsjr]

Ignore your 3rd diagram and follow the suggestions I made in post #38:

I agree, your third graph is implausible.

I have a suggestion: let's change the scenario to one that you can accurately draw graphs for. So let's change the speed of Adam to 0.6c. This will make the redshift Doppler factor be 0.5 and the blueshift Doppler factor be 2.

Adam will go for one year away according to his clock and one year returning. He will emit a flash of light every month for a total of 24, 12 on the way out and 12 on the way back. He will see the flashes coming from Charles at one half that rate on the way out for a total of 6 and for double that rate on the way back for a total of 24 more and a grand total of 30.

Charles will emit 30 flashes during the time that Adam is gone. Since he will be seeing Adam's flashes coming in at one half his rate and since he sees Adam turning around when he sees the 12th flash from Adam, he will be emitting his 24th flash at that moment. Then he sees the flashes coming in at double his rate for 12 more flashes from Adam while he is emitting 6 more. His total is again 30 while Adam's total is 24.

Please redraw your first two graphs using these numbers, make sure the slope of Adam's path is accurate for 0.6c and the rate of Adam's flashes are spaced farther apart by a factor of 1.25 compared to Charles's flashes to take into account his time dilation.

Then after you make those two graphs, make a third graph that is simply an overlay of the first two graphs. This is how you can show the Doppler effect and this one graph will show accurately the perspective of both Adam and Charles in terms of what they see compared to their own clocks.

 

[greswd]

Sorry I meant Adam and Bob. oops. Why is it that they both return having aged the same?

 

[ghwellsjr]

Sorry I meant Adam and Bob. oops. Why is it that they both return having aged the same?

You haven't done a correct set of graphs for Adam and Charles. If you do that and then add in a similar graph for Bob and Charles but flipped upside down, then you will be almost there. All you will need to do at that point is extend the light paths for Adam and Bob so that they go past Charles and reach all the way to the other person.

Or did you want to forget about graphs and pick up where we left off in the middle of page 2?

 

[greswd]

You haven't done a correct set of graphs for Adam and Charles. If you do that and then add in a similar graph for Bob and Charles but flipped upside down, then you will be almost there. All you will need to do at that point is extend the light paths for Adam and Bob so that they go past Charles and reach all the way to the other person.

Or did you want to forget about graphs and pick up where we left off in the middle of page 2?

graphs are very important, special relativity becomes very clear with a minkowski diagram. Plus as Einstein himself said, a geometric understanding is necessary to make sense of his general theory.

 

[ghwellsjr]

graphs are very important, special relativity becomes very clear with a minkowski diagram. Plus as Einstein himself said, a geometric understanding is necessary to make sense of his general theory.

If you're going to make a graph, it has to be done correctly. Your set of graphs haven't been done correctly. If you would do the graphs correctly for Adam and Charles, as I have suggested, and then add in Bob, as a flip side of Adam or a mirror image of Adam, then you will see how Adam and Bob have aged the same amount when they rejoin Charles.

If you don't want to make the graphs correctly, I will. And I will also explain the scenario without the use of graphs.

By the way, your graphs are not Minkowski diagrams, they are simply conventional position versus time graphs. And I'm not saying that simply because you are interchanging the time versus distance axes that is more common for a Minkowski diagram.

 

[Dale]

By the way, your graphs are not Minkowski diagrams, they are simply conventional position versus time graphs. And I'm not saying that simply because you are interchanging the time versus distance axes that is more common for a Minkowski diagram.

What is the difference?

 

[ghwellsjr]

Minkowski diagrams have at least two sets of axes to show how each event has two sets of coordinates for two different reference frames. All of the graphs that greswd presented have only one set of axes corresponding to the frame in which Charles remains at rest and in which Adam and Bob start out at rest and end up at rest.

People were drawing position versus time graphs long before Minkowski or Einstein or Lorentz or even Maxwell. I don't think Minkowski gets backwards credit for all those graphs just because they only have one set of axes.

 

[DrGreg]

Minkowski diagrams have at least two sets of axes

That's news to me. Do you have a textbook that uses that specific definition?

 

[ghwellsjr]

That's news to me. Do you have a textbook that uses that specific definition?

It's very hard to find a specific definition anywhere. Is there an official definition that you can point me to or that you want to provide even without reference?

If someone draws a graph of position versus time, does that automatically make it a Minkowski diagram? Would you call greswd's graphs on this thread Minkowski diagram's?

 

[DrGreg]

It's very hard to find a specific definition anywhere. Is there an official definition that you can point me to or that you want to provide even without reference?

If someone draws a graph of position versus time, does that automatically make it a Minkowski diagram? Would you call greswd's graphs on this thread Minkowski diagram's?

I don't have a formal definition either. But I've just looked in Rindler's book Relativity: Special, General, and Cosmological and found a diagram depicting Rindler coordinates against a single set of Minkowski axes which he calls a "Minkowski diagram" (2nd ed, p.269). So to my way of thinking any distance-versus-time diagram that is relativistically compatible (for an inertial frame, and therefore in Minkowski coordinates) is a "Minkowski diagram". Maybe some authors have a more restrictive interpretation but I've never seen that.

 

[ghwellsjr]

So then if Newton drew a distance-versus-time diagram but he did not show that a traveler's clock was running slower than the coordinate time, then it would not be a Minkowski diagram, correct? Or more specifically, if the diagram shows somehow that the traveler's clock is indicating a slower time than the coordinate time, then that makes it Minkowski? In other words, it doesn't have to explicitly use a second set of axes to show the slower time, it can just do it as points spaced further apart than the coordinate spacing, correct?

 

[greswd]

Technically, all displacement-time graphs look the same with reference to one particular frame.

The distinguishing factor is the transformation from one frame to another.
Now we've learned about two transformations, Galilean and Minkowskian.

Of course, we may come up with others, but they may not make physical sense.

When transforming between inertial frames, all transformations have to use the worldline as the time axis, and ensure that relative velocity between both frames is the same.

 

[phyti]

Minkowski diagrams replace the traditional time axis with ct (distance).
This results from transforming the equality for the invariant interval into a 4D expression, via t'=ict.
The benefit is twofold.
Unless one of the coordinates t or x is scaled, you could never graph it to scale!
It reveals what's really being compared. The object speed vs light speed, i.e. vt/ct=v/c.
It's the only variable in the gamma expression, which is the only factor distinguishing SR from pre-relativity physics.

 

[ghwellsjr]

How do we draw a graph to describe that from Adam's perspective? It is this graph
...
It shows a highly implausible scenario.

I agree, your third graph is implausible.

I have a suggestion: let's change the scenario to one that you can accurately draw graphs for. So let's change the speed of Adam to 0.6c. This will make the redshift Doppler factor be 0.5 and the blueshift Doppler factor be 2.

Adam will go for one year away according to his clock and one year returning. He will emit a flash of light every month for a total of 24, 12 on the way out and 12 on the way back. He will see the flashes coming from Charles at one half that rate on the way out for a total of 6 and for double that rate on the way back for a total of 24 more and a grand total of 30.

Charles will emit 30 flashes during the time that Adam is gone. Since he will be seeing Adam's flashes coming in at one half his rate and since he sees Adam turning around when he sees the 12th flash from Adam, he will be emitting his 24th flash at that moment. Then he sees the flashes coming in at double his rate for 12 more flashes from Adam while he is emitting 6 more. His total is again 30 while Adam's total is 24.

Please redraw your first two graphs using these numbers, make sure the slope of Adam's path is accurate for 0.6c and the rate of Adam's flashes are spaced farther apart by a factor of 1.25 compared to Charles's flashes to take into account his time dilation.

Then after you make those two graphs, make a third graph that is simply an overlay of the first two graphs. This is how you can show the Doppler effect and this one graph will show accurately the perspective of both Adam and Charles in terms of what they see compared to their own clocks.

As promised, here are the graphs that I suggested that you make. The first graph is similar to your first graph except I haven't shown dots along Adam's path (black) to show where he receives signals from Charles (blue with yellow signals) because they are uncalibrated:

Similarly, I haven't shown dots along Charles's path (blue) to show where he receives signals from Adam (black):

Finally, I suggested that you overlay these two graphs to get a correct third graph that shows everything, including Adam's perspective:

Note that we can now see Adam's time dilation. Since his speed is 0.6c, gamma is 1.25 and his tick marks are spaced at 1.25 of the coordinate grid. This illustrates that his Proper Time is equal to gamma multiplied by the coordinate time. You can also see that he sends a signal to Charles at every tick but during the outbound portion of his trip, he receives the signals from Charles every other month corresponding to a redshift Doppler factor of 0.5.

Charles is also sending out a signal every month to Adam but since he is stationary in this frame, his Proper Time is coincident with the coordinate time. Still, you can see that he receives signals from Adam every other month at the beginning. His redshift Doppler factor during this time is also 0.5.

Charles continues to see Adam' clock running at 1/2 the rate of his own until he sees Adam turn around when Adam's clock reaches 12 months. This occurs when Charles's clock is at 24 months. From then on, he sees Adam's clock running at twice the rate of his own for a blueshift Doppler factor of 2 so that in 6 more months of his own time, he sees Adam's clock adanvce by 12 months. At the end, he has seen Adam's clock advance 12 months in slow motion and 12 months in fast motion for a total of 24 months.

Meanwhile, Adam has been watching Charles's clock advance at 1/2 his own rate (redshift Doppler) so that after one year of his own time, Charles has advanced by 6 months. When he turns around, he sees Charles's clock advancing at double the rate of his own (blueshift Doppler) so that in the one year that it takes him to return, he sees Charles advance by 2 years for a total of 30 months.

 

[greswd]

Sorry for taking such a long hiatus. I was very busy with other matters. Anyway, I understand the diagrams well.

With regards with my rejected 3rd diagram. I found this from UNSW that looks very similar.

http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm

 

[ghwellsjr]

Sorry for taking such a long hiatus. I was very busy with other matters. Anyway, I understand the diagrams well.

With regards with my rejected 3rd diagram. I found this from UNSW that looks very similar.

http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm

Their first diagram looks very similar to my third diagram above because we both combined the signals from both twins to show how they were received by the other twin. That's what I was trying to get you to do but you never did, not even in your third diagram so how can you say yours is similar to theirs?

They did a better job on their first diagram compared to the one shown in post #34 from wikipedia but it's still not perfect. Here's what it should look like:

They show Joe 7 after he receives the signal from Jane 3 but he should be slightly before. Note also how they show Jane 5 receiving the signal from Joe 6 at the same time but she should be slightly earlier. In fact these two situations should show the same relationship because it is a reciprocal Doppler shift.

And their second diagram is wrong, not to mention ridiculous. They should show Joe 2 on the bottom diagonal and they should show Joe 6 on the top diagonal. Here is the diagram for the frame in which Jane is at rest during the outbound portion of her trip:

And here is the diagram for the frame in which Jane is at rest during the inbound portion of her trip:

What they were trying to do is combine the bottom part of the outbound portion of the trip with the top part of the inbound portion of the trip while showing in dotted lines the signals coming from Joe. They did a fairly good job of that but why don't they correctly show the signals going to Joe from Jane? They do show all five of Jane's signals but if they had shown Joe 6 at the correct location he would have received the signal from Jane 2 after the correct position for Joe 6 and it should be coming between Joe 4 and Joe 5 as they indicate in their first diagram.

It is impossible to combine the two parts of the outbound and inbound portions of Jane's two rest frames into one like this. If you're going to do it correctly, you need a much more complicated diagram. You need to show the correct Doppler signals for both twins throughout the diagram, just like all three of my diagrams show. It's so easy to do in an Inertial Reference Frame, why do you feel the need to do it in a non-inertial frame?

 

[nitsuj]

Is this all true if it were two twins and an older unrelated person?

 

[greswd]

Is this all true if it were two twins and an older unrelated person?

The same amount of aging still applies, if it actually does apply.

 

[greswd]

@ghwellsjr so are you saying that UNSW got it wrong?

 

[nitsuj]

The same amount of aging still applies, if it actually does apply.

was kinda just poking fun at the triplets thing.

 

[ghwellsjr]

@ghwellsjr so are you saying that UNSW got it wrong?

Yes, that's what I said, wrong and ridiculous. Don't forget the ridiculous part.

I said their first diagram is close to being right but their second diagram is wrong.

If they had used their second diagram to show just the messages coming from Joe to Jane they would have made a diagram that was more like the one DrGreg made in post #39. Note that he is only showing the messages going from the inertial twin to the traveling twin. That part of the diagram, as I already stated, is fairly good.

But the part that is completely wrong is where they also try to show the messages going from Jane to Joe. If you look at their first diagram, you can see that Joe receives these messages at two different rates. The first three messages take over two years each for him to receive, then in his last year he receives all the rest of them. They show this pretty close to being right and it's important that a diagram show that the inertial twin receives half of the messages at a slow rate and half of the messages at a fast rate and it's important to show that the time interval over which he receives those message is not evenly spaced. He spends way more of his time receiving the low rate messages and only a short time near the end receiving the high rate messages.

It's also important that a diagram show that the traveling twin spends exactly half her time receiving the low rate messages during the outbound portion of her trip and the other half of her time receiving the high rate messages during the inbound portion of her trip. They do a good job of showing this aspect in both diagrams.

However, if you look at their second diagram, you see that Joe does not receive any messages until half way through the diagram at which point he receives all the messages from Jane equally spaced in time. It's the correct spacing in time for the last messages but not for the first three. It's faster than it should be. This is wrong and it's a ridiculous concept to try to show on a combined diagram like this. In fact, I have no idea how to correctly show Joe receiving the messages from Jane at the correct rates and to show the transmission of the signals traveling at c between the two twins. I'm not saying it can't be done, just that I don't know how to do it.

And again, I ask you, why do you feel compelled to combine portions of two perfectly good Inertial Reference Frames into one ridiculous monstrosity? Why not just show everything in each one of the Inertial Reference Frames like I did in post #67?

 

[greswd]

Yes, that's what I said, wrong and ridiculous. Don't forget the ridiculous part.

I said their first diagram is close to being right but their second diagram is wrong.

If they had used their second diagram to show just the messages coming from Joe to Jane they would have made a diagram that was more like the one DrGreg made in post #39. Note that he is only showing the messages going from the inertial twin to the traveling twin. That part of the diagram, as I already stated, is fairly good.

But the part that is completely wrong is where they also try to show the messages going from Jane to Joe. If you look at their first diagram, you can see that Joe receives these messages at two different rates. The first three messages take over two years each for him to receive, then in his last year he receives all the rest of them. They show this pretty close to being right and it's important that a diagram show that the inertial twin receives half of the messages at a slow rate and half of the messages at a fast rate and it's important to show that the time interval over which he receives those message is not evenly spaced. He spends way more of his time receiving the low rate messages and only a short time near the end receiving the high rate messages.

It's also important that a diagram show that the traveling twin spends exactly half her time receiving the low rate messages during the outbound portion of her trip and the other half of her time receiving the high rate messages during the inbound portion of her trip. They do a good job of showing this aspect in both diagrams.

However, if you look at their second diagram, you see that Joe does not receive any messages until half way through the diagram at which point he receives all the messages from Jane equally spaced in time. It's the correct spacing in time for the last messages but not for the first three. It's faster than it should be. This is wrong and it's a ridiculous concept to try to show on a combined diagram like this. In fact, I have no idea how to correctly show Joe receiving the messages from Jane at the correct rates and to show the transmission of the signals traveling at c between the two twins. I'm not saying it can't be done, just that I don't know how to do it.

And again, I ask you, why do you feel compelled to combine portions of two perfectly good Inertial Reference Frames into one ridiculous monstrosity? Why not just show everything in each one of the Inertial Reference Frames like I did in post #67?

Just an attempt to visualize it from the space twin's perspective. Guess you could take it up with them Aussie bastards.

 

[ghwellsjr]

Just an attempt to visualize it from the space twin's perspective. Guess you could take it up with them Aussie bastards.

What more can the space twin visualize beyond what any other IRF already tells us?

 

[greswd]

What more can the space twin visualize beyond what any other IRF already tells us?

He can visualize that "ridiculous" diagram. Doesn't that explain the time gap objection, and also the visual description that you gave earlier on?

Another interesting fact is that if your three diagrams are transformed using Galilean methods, they produce something that looks somewhat similar to the "ridiculous" diagram.

 

[ghwellsjr]

What more can the space twin visualize beyond what any other IRF already tells us?

He can visualize that "ridiculous" diagram. Doesn't that explain the time gap objection, and also the visual description that you gave earlier on?

Yes, it does explain the visual description that I gave earlier on but it's exactly the same visual description. I asked you "what more can the space twin visualize".

(Keep in mind, I only applied the term "ridiculous" to the part of the second diagram that is supposed to illustrate what Joe visualizes. I said they did a fairly good job of showing what Jane visualizes. With that in mind, let's continue.)

Look at the diagram from the website:

Look at the diagram on the left. You will see that Jane only sees one message from Joe during the outbound leg of her trip shortly after her second anniversary. Then during the inbound leg, she sees the remaining seven messages equally spaced in time.

Now because the webpage does not show you complete IRF's I want to take you to my diagrams in post #67. The first one is virtually identical to theirs that we just looked at. But now look at my second diagram. During the outbound leg, Jane sees one message from Joe slightly after her second anniversary and then all the rest of them equally spaced during the return leg--exactly like in the first IRF. Same for the third diagram. And notice that none of these diagrams have any time gaps in them.

So now we get to the webpage's second diagram. They say in the text that this is the combination of two IRF's, the two that I show completely that we just considered. Now they chop up those two IRF's and combine them on one diagram and in the course of doing that, they introduce a time gap which they duly explain. But note that this time gap is not anything that Jane can see or visualize. I'm just asking the question, why create the problem in the first place?

It makes as much sense to me as if I took my first diagram and cut it in half horizontally at the turn-around point and then rotated each half so that Jane's path was in a straight vertical line. Then I would have introduced a huge triangular shaped gap which I would need to explain and if I succeeded in doing that, do I deserve extra credit? Does it have any bearing on what Jane visualizes? If you think so, please tell me what it is.

Are you interested in continuing the analysis to include the other triplet? If so, I need you to drop this issue of the combined IRF's. Are you willing to do that?

 

[greswd]

I think the time gap is something that Jane can visualize. And since it matches your visual description, it does have bearing on what she sees. For instance, if Jane backtracks she can find out that some photons popped out from nowhere.

 

[Dale]

For instance, if Jane backtracks she can find out that some photons popped out from nowhere.

Which is a rather strong indication that something is terribly wrong with the proposed "perspective".

 

[ghwellsjr]

I think the time gap is something that Jane can visualize. And since it matches your visual description, it does have bearing on what she sees. For instance, if Jane backtracks she can find out that some photons popped out from nowhere.

I can certainly see why you believe this based on your third graph from post #30 and #37 buy you are the only one that believes this. You point me to a link in post #66 that you claim supports your graph but if you read the text, you will see that they go to great lengths to show that the Doppler explanation is correct and any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong. Did you carefully read the text with regard to what Jane sees and experiences and concludes?

Furthermore, if you want to hang on to your chopped up graph for Adam and Charles, what are you going to do for a graph that also includes Bob?

 

[greswd]

Which is a rather strong indication that something is terribly wrong with the proposed "perspective".

Why is it wrong? Its a time gap after all. I pulled that diagram from UNSW.

but if you read the text, you will see that they go to great lengths to show that the Doppler explanation is correct and any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong. Did you carefully read the text with regard to what Jane sees and experiences and concludes?

There's nothing wrong with your Doppler explanation.

But I can't find the part where they say that any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong (what a mouthful ) , could you highlight it?

 

[ghwellsjr]

but if you read the text, you will see that they go to great lengths to show that the Doppler explanation is correct and any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong. Did you carefully read the text with regard to what Jane sees and experiences and concludes?

There's nothing wrong with your Doppler explanation.

But I can't find the part where they say that any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong (what a mouthful ) , could you highlight it?

What I'm trying to say is that they don't support your notion of a time gap in their text. They consistently are showing that you can get into trouble by trying to marry two IRF's together. You have to understand when they say Jane is in an inertial frame they mean she is at rest in an inertial frame. They don't mean that she is not also in one inertial frame during her entire trip. She's in every IRF, including the one in which Joe is at rest as they show in their first diagram. Here are two quotes:

The naive interpretation--the reason why the situation is called a paradox--is to assume that the situation is competely symmetrical. If that were the case, Jane's diagram would simply be a mirror image of Joe's. But Special Relativity applies only to the relations between inertial frames of reference. In this regard, the situations of the twins are definitely not symmetrical. Joe is [at rest] in one inertial frame throughout. (We discuss the partial symmetry below.)

In these diagrams, we have resolved the paradox by pointing out that the problem is not symmetrical: Jane actually has two different inertial frames of reference [in which she is at rest], the outgoing voyage and the return. Two different clock synchronisation events are required, and the easist examples of these are at their separation (for the outward journey) and their reunion (for the return).

So they are affirming that we could analyze Jane's experience from any IRF.

Now I have to ask you where they even mention anything about a time gap?

 

[greswd]

They consistently are showing that you can get into trouble by trying to marry two IRF's together.


Now I have to ask you where they even mention anything about a time gap?

Hmm..I don't think they're showing that because they erm...married two IRF's together?


They didn't use that specific term, but I think the diagram definitely shows that.

 

[ghwellsjr]

Hmm..I don't think they're showing that because they erm...married two IRF's together?

They didn't use that specific term, but I think the diagram definitely shows that.

They go to great lengths to show that what Jane actually sees as indicated by the marriage of her two rest IRF's is exactly what she sees as indicated by Joe's rest IRF. But you don't agree with that. You claim that she can see a time gap. That's the problem. And you haven't given any indication of what she is seeing differently in her two rest IRF's compared to Joe's IRF.

I guess I should ask you this question: Can Joe see the time gap that you claim that Jane can see?

 

[greswd]

They go to great lengths to show that what Jane actually sees as indicated by the marriage of her two rest IRF's is exactly what she sees as indicated by Joe's rest IRF. But you don't agree with that. You claim that she can see a time gap. That's the problem. And you haven't given any indication of what she is seeing differently in her two rest IRF's compared to Joe's IRF.

I guess I should ask you this question: Can Joe see the time gap that you claim that Jane can see?

They have shown that what Jane sees tallies with Joe (in terms of signals received). I do agree with that, if there is a time gap it doesn't mean I disagree.

On a side note, I don't think they have strongly asserted that any idea that Jane sees things differently based on the "marriage" is wrong. If they did they probably wouldn't have drawn the 2nd diagram in the first place.


You have also enquired about Jane being able to see anything beyond or differently than Joe's IRF, and I believe the time gap is that difference.

Other than that, the two diagrams can be considered different sides of the same events (sending signals to one another), and as mentioned above, they should tally.

The time gap is quite clearly illustrated in their diagram.


Joe doesn't notice the time gap because he is always in an IRF and from his point view Jane just ages slower due to time dilation. There is a time gap for Jane, because as mentioned in the passage, when she undergoes infinite acceleration, or switches frames:

The causes of this asymmetry are the fact that Jane reverses direction and Joe does not, and the finite time that light takes to transmit this information to Joe means that Joe doesn't get the news immediately. Jane leaves one inertial frame and joins another, and she has the effect of that change immediately. Joe, on the other hand, doesn't notice the effects of Jane being in a different inertial frame until much later because she is a long way away from him when it happens. The asymmetry is as simple as that.

 

[ghwellsjr]

They have shown that what Jane sees tallies with Joe (in terms of signals received). I do agree with that, if there is a time gap it doesn't mean I disagree.

OK, good, we're making progress because back in post #23 when I presented exactly the same Doppler explanation that you just quoted from the webpage at the end of your previous post, you disagreed and thought I was brilliantly and cleverly making an incorrect argument.

On a side note, I don't think they have strongly asserted that any idea that Jane sees things differently based on the "marriage" is wrong. If they did they probably wouldn't have drawn the 2nd diagram in the first place.

Yes, I agreed with that over and over again. Their two diagrams agree with what Jane sees and they agree with what Jane sees in all three of the "unmarried" IRF's that I drew in post #67.

You have also enquired about Jane being able to see anything beyond or differently than Joe's IRF, and I believe the time gap is that difference.

Only if Jane looks at the "married" diagram will she can see the time gap in the diagram. If Joe looks at the "married" diagram, then he can see the time gap in the diagram. The time gap exists in that "married" diagram, not in the first diagram, and not in the three IRF diagrams that I drew. Nobody ever sees any time gaps in any IRF diagram. It's only when you take one part of one IRF diagram and marry it to another part of another IRF diagram that you have to be concerned about a time gap.

Other than that, the two diagrams can be considered different sides of the same events (sending signals to one another), and as mentioned above, they should tally.

They only tally for Jane. They don't tally for Joe. I explained this over and over again. Here, let's look at their two diagrams again (or you can look at their animation):

Focus on the diagonal lines going upwards to the left like this \. Do you see how in the first diagram, Joe receives the first three spaced far apart and the last three spaced much closer together? Do you see how in the second "married" diagram, Joe receives all six with exactly the same spacing? Both diagrams can't be right. The second "married" diagram does not tally for Joe and that is why I'm trying to get you to forget about "married" diagrams. They can only work in limited situations. Unmarried IRF diagrams work in all situations.

The time gap is quite clearly illustrated in their diagram.

Yes, and only in their second diagram. Jane won't actually see any time gap with her eyes looking at her own clocks or looking into space at any remote clocks. Just because someone draws a diagram of an IRF like the first one or a "married" diagram like the second one will have no bearing on what she actually sees.

Joe doesn't notice the time gap because he is always in an IRF and from his point view Jane just ages slower due to time dilation.

Joe doesn't notice a time gap for the same reason that Jane doesn't notice a time gap. They can only notice a time gap if they take two legitimately drawn IRF diagrams in which no time gap appears and chop them up and glue them together.

Furthermore, it's incorrect to imply that Joe is always in an IRF and Jane is not, contrary to what your website implies. Joe is at rest in what we euphemistically call "Joe's IRF" and Jane is moving in that same IRF. Since he is at rest in that IRF, he and his clock tick at the same rate as the coordinate time of the IRF but because Jane is moving, she and her clock are time dilated meaning that one year according to her clock takes longer than one year of coordinate time. Please look back at the first IRF diagram in post #67 to see how this is indicated in Joe's rest IRF.

But in either of Jane's two rest IRF's, Joe is not at rest and so he and his clock are time dilated in the same way that Jane's was in his rest IRF. Time dilation is no more observable by the twins than is a time gap. These are only evident when you assign an IRF to a scenario and describe what happens to clocks in relation to the coordinate time of the IRF. No observer in a scenario is ever aware of or can have any knowledge of the IRF that we arbitrarily select to describe that scenario. Think about it--I drew three IRF diagrams that all have different time dilations for the two twins, each one being just as legitimate as the others, none of them being preferred, not even an observer's rest IRF, so how could any observer determine which time dilation was "in force"?

There is a time gap for Jane, because as mentioned in the passage, when she undergoes infinite acceleration, or switches frames:

Again, this euphemistic terminology only means that she does not remain at rest in any IRF because she is not inertial. But it doesn't mean that we must analyze what happens to Jane or Joe or what each one can see by using only their rest frames. We can use any IRF we want, even one in which none of them is ever at rest. No IRF is preferred, not even an observer's rest IRF.

The causes of this asymmetry are the fact that Jane reverses direction and Joe does not, and the finite time that light takes to transmit this information to Joe means that Joe doesn't get the news immediately. Jane leaves one inertial frame and joins another, and she has the effect of that change immediately. Joe, on the other hand, doesn't notice the effects of Jane being in a different inertial frame until much later because she is a long way away from him when it happens. The asymmetry is as simple as that.

This quote is not an explanation of time dilation or of at time gap. As I said before, it is a description of the Doppler analysis that I presented to you back in post #23 and which you disagreed with in post #24 so I'm glad you are now firmly in agreement with the Doppler analysis.

I know this has been a long post but the crux of the issue is that you asked about a triplet scenario which I want to continue explaining but I cannot do it unless you are willing to accept that any single IRF is legitimate and adequate to explain everything and there is never a need to combine portions of two or more IRF's. If we can continue without regard to "married" IRF's and I can explain the triplet scenario in the same way that I explain the twin scenario, then maybe you can try to see how you would marry two or more IRF's to explain the triplet scenario.

Are you willing to concede that time dilation and time gaps appear only in diagrams and are not observable by any of the observers in any scenario?

 

[Dale]

if Jane backtracks she can find out that some photons popped out from nowhere.

Which is a rather strong indication that something is terribly wrong with the proposed "perspective".

Why is it wrong? Its a time gap after all.

It is wrong precisely because it introduces time gaps and it has photons popping out from nowhere. So far, no one has been able to write the laws of physics in a way that is compatible with it. If you can figure out a way then you should publish it.

 

[greswd]

OK, good, we're making progress because back in post #23 -- you disagreed and thought I was brilliantly and cleverly making an incorrect argument.

Did I? I didn't say you were incorrect, what I meant was the explanation was smooth and slick (as snake oil, nah just kidding ) before careful consideration.

Yes, I agreed with that over and over again. Their two diagrams agree with what Jane sees and they agree with what Jane sees in all three of the "unmarried" IRF's that I drew in post #67.

Hmm, I thought you brought up that point in the first place?

... if you read the text, you will see that they go to great lengths to show that the Doppler explanation is correct and any idea that Jane sees anything differently because of an analysis based on jumping between her two inertial frames is wrong.

The lack of automatic "quoteception" is making discussion a little long winded. Perhaps you could ask the IT guys to put it in?

They only tally for Jane. They don't tally for Joe.
Do you see how in the first diagram, Joe receives the first three spaced far apart and the last three spaced much closer together? Do you see how in the second "married" diagram, Joe receives all six with exactly the same spacing? Both diagrams can't be right.

I believe that's an error on their part. The world line of a photon "fired" by Jane is not continuous after she switches frames.

Jane won't actually see any time gap with her eyes looking at her own clocks or looking into space at any remote clocks. Just because someone draws a diagram of an IRF like the first one or a "married" diagram like the second one will have no bearing on what she actually sees.

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.

Furthermore, it's incorrect to imply that Joe is always in an IRF and Jane is not, contrary to what your website implies. Joe is at rest in what we euphemistically call "Joe's IRF" and Jane is moving in that same IRF. Since he is at rest in that IRF, he and his clock tick at the same rate as the coordinate time of the IRF but because Jane is moving, she and her clock are time dilated meaning that one year according to her clock takes longer than one year of coordinate time. Please look back at the first IRF diagram in post #67 to see how this is indicated in Joe's rest IRF.

But in either of Jane's two rest IRF's, Joe is not at rest and so he and his clock are time dilated in the same way that Jane's was in his rest IRF. Time dilation is no more observable by the twins than is a time gap. These are only evident when you assign an IRF to a scenario and describe what happens to clocks in relation to the coordinate time of the IRF. No observer in a scenario is ever aware of or can have any knowledge of the IRF that we arbitrarily select to describe that scenario. Think about it--I drew three IRF diagrams that all have different time dilations for the two twins, each one being just as legitimate as the others, none of them being preferred, not even an observer's rest IRF, so how could any observer determine which time dilation was "in force"?

Again, this euphemistic terminology only means that she does not remain at rest in any IRF because she is not inertial. But it doesn't mean that we must analyze what happens to Jane or Joe or what each one can see by using only their rest frames. We can use any IRF we want, even one in which none of them is ever at rest. No IRF is preferred, not even an observer's rest IRF.

There isn't any time dilation "in force", what I meant was due to John always being in a single inertial frame he did not notice any time gap.

This quote is not an explanation of time dilation or of at time gap. As I said before, it is a description of the Doppler analysis that I presented to you back in post #23 and which you disagreed with in post #24 so I'm glad you are now firmly in agreement with the Doppler analysis.

Well, I still consider it an explanation of a time gap that is also in line with the Doppler analysis. But since the passage has been ambiguous so be it.

I know this has been a long post but the crux of the issue is
that you asked about a triplet scenario which I want to continue explaining but I cannot do it unless you are willing to accept that any single IRF is legitimate and adequate to explain everything and there is never a need to combine portions of two or more IRF's. If we can continue without regard to "married" IRF's and I can explain the triplet scenario in the same way that I explain the twin scenario, then maybe you can try to see how you would marry two or more IRF's to explain the triplet scenario.

Are you willing to concede that time dilation and time gaps appear only in diagrams and are not observable by any of the observers in any scenario?

Now you sound quite forceful but at least we can iron out all the confusion.
If you've read through and don't have anything to add then we can proceed and all this time gap stuff won't form part of the discussion.

 

[greswd]

It is wrong precisely because it introduces time gaps and it has photons popping out from nowhere. So far, no one has been able to write the laws of physics in a way that is compatible with it.

Yeah that was my initial argument. lol

But I do remember John Baez using it.

 

[greswd]

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

 

[Dale]

You don't need GR unless there is significant gravitation involved, which is traditionally not considered part of the twins scnario.

All you need is to make sure that you always use legitimate coordinate systems.

 

[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.