Share this thread: 
#73
Jan1413, 11:57 AM

P: 147




#74
Jan1413, 03:55 PM

PF Gold
P: 4,696




#75
Jan1713, 12:27 PM

P: 147

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. 


#76
Jan1913, 02:31 AM

PF Gold
P: 4,696

(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 legexactly 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 turnaround 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? 


#77
Jan2213, 07:06 AM

P: 147

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.



#78
Jan2213, 07:30 AM

Mentor
P: 16,999




#79
Jan2213, 08:18 AM

PF Gold
P: 4,696

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? 


#80
Jan2213, 09:20 AM

P: 147

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? 


#81
Jan2213, 10:00 AM

PF Gold
P: 4,696

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


#82
Jan2213, 09:06 PM

P: 147

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. 


#83
Jan2213, 11:58 PM

PF Gold
P: 4,696

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


#84
Jan2313, 05:59 AM

P: 147

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: 


#85
Jan2313, 10:30 AM

PF Gold
P: 4,696

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. 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 itI 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"? 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? 


#86
Jan2313, 12:05 PM

Mentor
P: 16,999




#87
Jan3113, 03:28 PM

P: 147

The lack of automatic "quoteception" is making discussion a little long winded. Perhaps you could ask the IT guys to put it in? Based on the Doppler analysis, Jane sees Joe's signals as popups 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. 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. 


#88
Jan3113, 03:33 PM

P: 147

But I do remember John Baez using it. 


#90
Feb1613, 06:40 AM

Mentor
P: 16,999

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. 


Register to reply 
Related Discussions  
Triplet paradox: where's the error in my logic?  Special & General Relativity  18  
What is the Triplet state  Quantum Physics  24  
The Triplet Paradox?  Special & General Relativity  12 