Triplet Paradox

greswd

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

greswd

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

nitsuj

was kinda just poking fun at the triplets thing.

ghwellsjr

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

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

ghwellsjr

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

greswd

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

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?

Attached Thumbnails

 

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.

DaleSpam

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

ghwellsjr

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

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


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

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:
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

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

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 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:

ghwellsjr

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.
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.
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.
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.
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 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"?
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.
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?