Can the Twin Paradox be simplified?

That is my contention! Tach's insistence that the Three Twins somehow determines absolute time dilation is mistaken because, as I attempted to show, an additional brother can produce conflicting conclusions.

 

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Took you about half a second to reply to that, Tach.

Which tells me you just jerked your knee.

And in your typical manner, your reply is, 'Look at something else'.

Come on Tach. In your own words, explain how two frames, moving with respect to each other, can be brought into a state of zero relative velocity without one or the other undergoing acceleration.

 

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Nope, it cannot but your many mistakes on the subject have combined in convincing you that you have refuted mainstream physics.

 

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No, it just tells that I know what I am talking about while you obviously don't.

This is what one does when confronted with incorrect or fringe views, one points to mainstream books, texts, websites, etc.

have you read the paragraph? It is very short and easy to understand. Besides, it is written by a very good professor. Additionally, it is well known in mainstream physics.

PS: You joined this thread late, you would benefit from reading it, I already went over many of the issues puzzling you with RJ already. It would also be a good idea if you also read on the "Clock Hypothesis". Should clear a lot of your misconceptions.

 

Ahh, got it! I have to admit it was bugging me that your math did not concur with mine while I KNEW mine was right. I have located your final error:

Above you are neglecting to add 1.25 to Unprime's watch (because that is Tripleprime's starting point). 5.69 + 1.25 = 6.94

\(T' = T \sqrt{1-0.64} = 6.94*(.6) = 4.166\)

This finally agrees with my original (and correct) calculations. I repeat:

When Prime and Tripleprime meet up, Prime's watch reads 4.166 yr and Tripleprime's reads 2.5 yr. Tripleprime and Prime conclude that Unprime is aging more slowly than Prime, while Unprime and Doubleprime conclude that Prime is aging more slowly than Unprime.

Conflicting conclusions means no absolute statement can be made. Q.E.D.

 

Nope, the 1.25 time differential is accounted for in the equation:

\(v'"T=v'(T+1.25)\)

Nice try. Next.

 

No, the 1.25 there represents the headstart of Prime, NOT Unprime's watch. You are calculating "how long" it will take Tripleprime to catch Unprime with your equation from their point of passing. On to this you must add Unprime's original watch reading in order to declare what time his watch would read.

 

You're not ever going to be an instructor of any kind, are you Tach?

You haven't answered, but replied as expected.

 

This is why it is multiplied by \(v'\).

Nope, I am calculating exactly what you tried to calculate and you missed, how long it takes Tripleprime to catch Prime. Come on, time to give up, don't you think?

 

Physics? No. I am a ski instructor.

You are starting to sound a lot like OnlyMe. The website explains the approach quite clearly, RJ understood it and used it in his unsuccessful attempt at disproving it. It is very simple really, the second twin is replaced by two twins flying at equal and opposite speeds, each covering half the distance separating them initially. This removes the "midpoint turnaround" acceleration. Very clever, you can find it in quite a few textbooks. If you are willing to invest a few dollars, David Mermin has a beautifully detailed treatment using 3 twins and NO acceleration in his "Space and Time in Special Relativity" pages 187-194.

 

I understand you would prefer that I "gave up" before making your error crystal clear, but let's start Unprime's watch at 100 rather than 0. Now, Tripleprime passes him at 101.25. Then, we calculate how long it will take Tripleprime to reach Prime...again we get 5.69. Shall we conclude that Unprime's watch reads 5.69 or 106.94?

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I repeat for the fifth time, my original calculations are correct as is my conclusion. Shall I presume that an admission from you is not forthcoming?

 

Yep, but you set it to 0 in your "scenario". Your attempt at moving the goalposts a little will not change anything, see below.

You are piling up the errors, T represents the time necessary for Tripleprime to catch up with Prime. What their initial watches were set to is irrelevant, you will need to add the 5.69 to it.

Every time you post, you unveil either another one of your errors or, at least, another one of your misconceptions. So, please continue posting, by all means.

 

Fine, but on the very next calculation you use T to calculate Prime's WATCH READING. In order to do this you must add the initial reading of 1.25 (or 101.25 in my second example) to T.

 

OK, Tach, I'm going to bed. It's 10:54 Central Time, which gives you about 10 hours to drum up the courage to admit that my original analysis was correct...

 

Nope, read again:

T' and T'" are just the proper time intervals for the time to "catchup" expressed respectively in Prime's frame and Tripleprime's frame respectively. They are the transformed of the interval T, calculated initially in Unprime's frame , into their respective frames (this is why they are proper times).

Now, if you insist on deriving the "total elapsed times", then:

\(\tau=5.69\) (contrary to your claims, no time gets added to him since he starts at 0)
\(\tau'=3.412+0.75=4.1662\) (he is the one who started earlier by 1.25 measured in Unprimed frame, i.e. by 1.25 \sqrt{1-0.64} in his own frame)
\(\tau'"=1.2518\) (he also starts at 0)

Contrast the above with your festival of mistakes:

So, contrary to your repeated claims, the situation is : \(\tau'"<\tau'<\tau\). That is, the twin moving the fastest wrt a common reference frame has always the least elapsed time. Of course, you can only compare only the readings of Tripleprime and Prime for your silly attempt at disproving mainstream view of the issue since they are the only ones that are co-located at the end. You can only infer the reading for Unprime. I explained the same principle many different ways to you in this thread. I think funkstar tried to explain this long ago. Fell on deaf ears.
Either way, your "counter-example" to mainstream physics comes up short, as expected, the fastest moving twin CONSISTENTLY exhibits the least elapsed time. So, contrary to your claims, there is never any "contradiction".

Sweet dreams. Next morning you'll start fresh, with new and ever more interesting mistakes.
May I recommend that you invest into David Mermin's book "Space and Time in Special Relativity" and that you read his excellent treatment on the subject?

 

Listen, this is MY analysis. You cannot analyze proper times from a single reference frame of your choosing (which differs from mine) and then declare mine as wrong when the numbers don't match. I already said the times listed are what the respective local watches would read because the analysis is centered around what each brother would conclude about the others. You're only focusing on what Unprime would conclude about the others and then making the leap that this establishes something absolute...which is precisely what my analysis contradicts. Tripleprime and Prime would come to a contradictory conclusion about whether Unprime or Prime were aging slower, that's the whole point.

By the way, you have another error:

T''' = 1.2518 shouldn't even pass the smell test, as T''' = 1.25 at the co-location event of Tripleprime and Unprime. What you meant was 1.25 + the initial watch reading of 1.25, which would give 2.5 on Tripleprime's watch when he meets up with Prime, which is correct (surely you don't contend that it only takes him .0018 yrs to catch Prime?!)

This is all a purposeful distraction anyway. You've already admitted that nothing can be absolutely concluded, but you're burying it in this deluge of words:

So which brother is absolutely moving the fastest then?

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You mistakenly thought that the Third Brother helped establish an "absolute" frame of reference, and you were mistaken. This is why you didn't, won't and can't answer the following (because you NOW know the answer):

 

Trouble is with your "analysis" that you are jumping frames, you are trying to "analyze" the problem in Prime's frame while you give the speeds for both Prime and , worse, for Tripleprime with respect to Unprime. This is one of the several sources of your erroneous results. To make matters worse, you fail to calculate the proper times correctly. This is another source for your erroneous results. The reason you get contradictory results is that your calculations are wrong, not because you have magically managed to disprove mainstream science.

I did not "declare", I proved.

Err, nope, I have been simply trying to teach you how to calculate proper time as a function of coordinate time. While I failed to teach you since you are repeating the same mistakes over and over, at least I managed to teach you to use the correct term, i.e. "proper time", instead of your "absolute time dilation" nonsense.

Correct calculations and basic mainstream textbooks say that you are wrong.

Nope, you are wrong, you still do not understand the notion of proper time.

Nope, it takes Tripleprime exactly 1.2518 yrs on his watch to catch up with Prime. You see, you still do not understand the meaning of proper time. "2.5 on Tripletime watch" is just the same error that you are repeating over and over. You cannot even add 1.25 to Tripletime's time, do you know why?

Err, wrong, what in \(\tau'"<\tau'<\tau\) did you not understand?

Nope, you failed to follow the simplest calculations but thank you for the fresh mistakes that illustrate that you still haven't grasped the notion of proper time. With respect to the chosen reference frame (Unprime) the meeting twins move at different speeds. Since Tripleprime moves faster than Prime (both wrt Unprime), his proper time is less. This is what funkstar attempted to teach you in the other thread. Since you seem not to believe either of us, may I suggest that you consult Taylor and Wheeler's "Spacetime Physics", they have a very good treatment on this subject.

 

Turns out that I can. Not only that I can but this is standard in mainstream relativity. Well, trouble is that proper time is an invariant in relativity*. That means that regardless of the frame used for calculating it , you need to get the same result if you do the calculations correctly. This is why it is called proper time, because it is frame independent. The mere fact that you obtained different results depending on the frame you used and then declaring that you found a "contradiction" in mainstream relativity shows without any doubt that your calculations are wrong. I am very disappointed to see that you will not be able to have yet another entertaining comeback from this fiasco, I truly enjoyed our interaction.

*See any textbook on the subject.

 

Of course; this is why I used the term "absolute time dilation". Since the participants are not co-located, proper times are meaningless in any absolute sense because you must choose a particular frame from which to compare simultaneity. "Absolute time dilation" means that all frames would concur that one twin aged less than the other...which necessitates that the twins were co-located twice, requiring acceleration. I would normally say that you are simply unable to understand my analysis but what you AREN'T saying is proof that you do, in fact, understand it just fine.

[Extensive analysis given]

That's six times you've literally ignored the question, as if you never even read it. Why might that be?