Can the Twin Paradox be simplified?

That's exactly what proper time is. It's the 'distance' as the time experienced along a wordline.

You seem to believe it's something else. So, let me quote Roger Penrose:

"The Minkowski 'length' s of the [wordline] segment OP has a direct physical interpretation. It is the time interval actually experienced by the particle between the events O and P!
That is to say, if there were a very sturdy and accurate clock attached to the particle, then the difference between the times it registers at O and P is precisely s. Contrary to expectations, the coordinate quantity t does not itself describe the time as measured by an accurate clock unless it is at rest in our coordinate system ..."

Your claim that proper time measured in one frame is "the same in all frames" is bollocks.

 

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The question did not have anything to do with my earlier statement.

I never claimed that accelerometers were to be used to replace clocks in determining time dilation. I compared the use of clocks in determining time dilation and the potential for accelerometers to be used to provide information about acceleration and velocities that could be used in a similar way, when addressing distances.

Normally in a discussion of SR these are not necessary distinctions. Usually everyone agrees on a rest frame, flat spacetime and the abscence of gravitational influences. Even so, in most "mainstream" credible sources even the assumed conditions are, at least sometimes included, when defining the hypothetical.

Normally, in a standard or even alternate twin paradox hypothetical, the issue of the simutaneity of relativity should never become an issue, unless it is the subject of discussion, since in most if not all of these hypotheticals, the frame of reference of the stay at home twin or observer, is assumed to represent, "the at rest" frame of reference for the hypothetical. From that all twins and/or observers "know" who is is motion. No one should be actually confused as to that point. All observers having knowledge of the agreed upon at rest frame of reference are then able to make the appropriate transformations to reconcile any differences in their POV, and fully understand what the other(s) "see" from their POV.

CptBork's introduction of the issues involving the simutaneity of relativity, were completely acceptable, as that is an issue and POV that is often misunderstood. It just does not normally require as much depth of discussion, within the hypothetical, as when it is the subject of discussion.

The "can of worms" I was referring to, is the confusion that often arises between, those two separate aspects of SR. The simutaneity of relativity issue during the traveling twin's journey and the difference in their ages when they are reunited.

 

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funkstar: I said this:

Then you said this:

But I was commenting on this, which is what Tach actually posted:

Notice how he is also contradicting what you posted?

 

No. First of all, the line of simultaneity would NOT make the meeting of Unprime/Doubleprime simultaneous with the meeting of Prime/Tripleprime from ANY brother's frame! I have no idea why you would even think that nonsense. Do the math and you will find you are gravely mistaken.

I'll make up some convenient numbers here for clarification: Unprime uses LOGIC, not an elapsed proper time calculation, to determine how old Prime is. Let's say Prime leaves Unprime at 12:00, headed East at 50kph; then, two hours later, Doubleprime cruises in at 50kph headed West. Doubleprime confirms that he passed Prime 1/2 hour ago and both of their watches read 12:30 at the time of passing. Unprime then uses LOGIC to deduce that Prime's watch reads 1:00 "right now". There is no elapsed proper time calculation made!

Seriously, you're the one touting the Three Brother scenario, you'd think you would understand the application of it.

 

You have hit the nail on the head here. Proper time invariance is irrelevant when the brothers aren't analyzing the same world line segments! The world line segments being analyzed differ due to the concept of relative simultaneity, and the segments are actually determined by the logic I just previously posted. Tach making pronouncements about T>T'>T"' FOR ALL FRAMES is trivally true and IRRELEVANT because those particular world line segments don't necessarily have a meaning for all brothers. Prime would be calculating different proper times because he would be measuring DIFFERENT SEGMENTS of the brothers' world lines.

I've said the same thing so many times in so many ways I'm not sure there are many permutations left if I stick with English.

 

I can see how it might be read that way, but I don't think it is the most obvious reading, nor do I think that is what Tach meant: I was stating what it means for proper time to be invariant. Tach was pointing out that because it is invariant, he can do the calculation in any frame he choses, and know that a similar calculation would yield the same result in all other frames. That doesn't seem contradictory to me.

 

No, I don't, on the other hand, your posts on the subject are clearly wrong as pointed out by me and funkstar.

So, you don't know what frame - invariance means. And you reaffirm it. Good show!

 

That's bad , since this is not how problems of this type get solved. You have messed up the math and now you are trying to turn this problem in a "logic" problem.

Maybe in your nick of the woods, in mainstream physics it goes like this:

Unprime sees that on hiw own watch T seconds elapsed for Prime's trip.
Unprime calculates that the proper time elapsed on Prime's clock is \(\tau'=\int_0^T{\sqrt{1-(v/c)^2}dt}\) where \(v\) is Prime's speed wrt Unprime. If \(v=const\), then the integral reduces to \(\tau'=T \sqrt{1-(v/c)^2}\). All these have been explained to you hundreds of posts ago, when I explained to you the notion of proper time along with all the mistakes that you've done in your calculations.

Yep, the scenario that was developed by Max von Laue 100 years ago still stands, shows that only fringers still believe that acceleration is necessary in explaining the twin paradox. If you invest a few bucks in a book, you could read the same explanation by other professors (Morin, Mermin, Simonetti). Seriously, don't you think that you should invest a little in your education?

 

Firstly, I don't think that Trippy is that uneducated to repeat your incorrect statements, I think that he understands proper time invariance (while you clearly don't).
Secondly, and more importantly, do you see that "T" upper limit in the calculations of the integrals that define the proper time? The limit in:

\(\Delta \tau'= \int_0^T {\sqrt{1-(v'/c)^2}dt}\)
\(\Delta \tau'"= \int_0^T {\sqrt{1-(v'"/c)^2}dt}\) ?

Well, that common upper limit represents the line of simultaneity that you keep asking for. In the case of your silly exercise, T is obtained solving the chasing equation \(v'"T=v'(T+1.25)\). I have explained that to you several different ways since post 136.

You mean trivially true, right? This means true. Period. End of story.

I think that you have just demonstrated that you don't understand the term "wordline" either. Each twin has his own wordline, so there is no there is no reason why his own wordline would mean anything for the other twins. On the other hand, the proper times to the "meeting" of Prime and Tripleprime are key in solving your trivial exercise.

Bzzt, wrong. Whether one uses Unprime or Prime as a reference, one should get the same result, the upper limit for the integrals I showed you above is the coordinate time elapsed until Prime and Tripleprime meet. If you do the calculations correctly, you should get the same exact result as if you did the calculations from Unprime's perspective. I recommend that you have a look at exercise 11.19 in Morin's book, I recommended the same exercise to OnlyMe, perhaps it will clear away some of your misconceptions. You do not even have to solve the exercise, it gives you the solution ready made so you too, can learn how to calculate proper times correctly for the twin paradox.

On the other hand, if you don't know what you are doing, you end up contradicting von Laue, Simonetti, Morin, Mermin and who knows how many more professors, a great performance, RJ!

 

But the proper time is dependent on the geodesic; it is the geodesic according to Penrose.

Everyone else is good with this one? In that case, I give up.

 

It is unlikely that Penrose made the mistake of confusing the geodesic ( a curve) with its arclength, more likely that you don't understand what you are reading and you treat physics as literature. On the other hand, it is quite clear that you still haven't tried to learn what "invariants" are, the stuff at the core of your misconceptions.

Yes, time for you to give up. Physics is about math, not about literature, so you need to learn what "frame-invariant" means. Here is a hint:

\((cdt)^2-dx^2\) is the best known example of invariants (see Einstein's 1905 paper). Now, try connecting the dots to the definition for proper time interval, \(d \tau\). Do you think that you can do this all by yourself or do you still need someone else to do the calculations for you?

 

You don't really need any math to understand proper time. All proper time is, is time as measure by an accurate clock in the frame of reference of that clock.

To put this in context of the twins, each has their own accurate clock. The two clocks do not agree on the elapsed time but they are both measuring the proper time of the twin that is holding the clock.

Frame invariance just means that as the traveling twin changes frames of reference his/her clock continues to measure proper time relative to his/her and the cocks, frame of reference. It does not matter whether the twin and clock are at rest, moving inertially or accelerating, thier clock will always measure proper time for their frame of reference.

The stay at home twin's clock measures the proper time of the stay at home twin. The traveling twin's clock measures the proper time of the traveling twin.

 

Tach...you're about 100 posts invested into your errors. It's clearly too late for you to admit that you're full of shit, even if you were to see it. I tell you what, if you can find a SINGLE OTHER MEMBER that completely understands the source of our disagreement and nevertheless claims that you are right, I will acquiesce. To be clear, you cannot simply find someone that disagrees with my conclusion, but must agree with your logic for disagreeing with my conclusion. How's that?

 

Nope, proof is that my corrections are in line with mainstream science while you cling desperately to your fringe misconceptions.

No, please don't do that! I like you when you post fresh errors in your desperate attempts at covering the older ones. Once you admit to error (not that you ever will) all the sources of entertainment dry out.
I mean, we went over your not understanding the equations of closing speed, on to not knowing what proper time is, we spent a long time getting you to understand what invariants are, took a long detour through your not accepting the Clock Hypothesis and declaring the Bailey and the Vessot experiments as "flawed", then we spent a loong time on your denial of the texts by professors like Max von Laue, Simonetti, Morin, Mermin that culminated with your "four twin" fake counterexample to the above mentioned professors' texts , took a detour through your misconceptions about how GR treats the same problem (the rate change of the clocks is a function of speed and NOT a function of acceleration, contrary to your beliefs). I mean, look at the wealth of hilarious errors you posted, if you admit now that it was all wrong, the entertainment will stop. Tell you what, why don't you think about a fresh excuse for your fringe ideas. I mean, how could all these mainstream scientists be right while you are wrong? Can't be.

 

I was wrong to criticize your closing speed calculation; I knew SOMETHING was wrong but it took a second try to identify your actual mistake (which was to treat Unprime's 0.0 and Tripleprime's 0.0 as simultaneous even though their clocks were also synced at 1.25 and they were moving relative to each other). The rest of the word salad that you're tossing in the air is a mixture of obfuscation, delusion and misinterpretation on your part.

Surely, with all of these apparent problems with my stance it should be easy as pie to convince another forum member of your veracity?

 

Tach is full of shit. That is one thing I can acquiesce to.

I posted a direct quote by Roger Penrose after stating proper time is "the 'distance' as the time experienced along a wordline", and Tach fires back this:

funkstar appears to be a more accomplished translator of Tach's meaning than I am.

Then he says this:

I don't think it's too much of a stretch for "the geodesic" to be taken to mean its length, given that I was referring to Penrose's quote at the time.

But hey, if it gives Tach the opportunity to paper over the cracks, I say it's a win-win!

 

Err, you are admitting to one mistake? How about the 15 other ones?

Yeah, I forgot to add to your list of mistakes that you couldn't understand the meaning of the "encounter" equation \(v'"T=v'(T+1.25)\) and that you thought that I was using Newtonian addition of velocities when I wrote the result as \(T=\frac{1.25v}{v'"-v'}\). My fault, I missed this one from the list of your errors, so it isn't 15 errors, it is 16. Since you mentioned it, I am adding it to the list. Happy now?

I am not trying to convince anyone else, I am just exposing your errors.

 

Uhh, yes, I misidentified your mistake on my first try, I have no problem admitting that; I located your actual error a few minutes later. So you're critiquing my critique of your critique of my original analysis. If you want to declare that a victory then...congratulations?

There's been a lot of talk in here. So, do you believe the Third Brother shows proof of absolute time dilation?

 

Nah, I am just adding to the laundry list of your errors.

First off, you need to learn proper terminology, there is no such thing as "absolute time dilation". If you want to talk physics you need to stop making up your own fringe terms and learn how to use the terms used by the mainstream.

Second off, it is totally unimportant what I think. What is important is that mainstream physicists, starting with Max von Laue, continuing with Simonetti, Morin, Mermin and countless others have proven that acceleration is not the cause of the differences measured in elapsed proper time. The "three twin" formulation proves it beyond any doubt. That is, for people that know physics, I cannot vouch for the anti-mainstream fringers who have their own ideas and agendas. If you still think that you contradicted the mainstream view, I suggest that you submit your "discovery" tto some peer reviewed journals. If you fail to publish in mainstream (as you will), I can recommend a few fringe journals that would be more than happy to publish your "refutation" of the mainstream view.