Can the Twin Paradox be simplified?

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"My contention" sounds awfully close to the way RJ sounds when he declares mainstream POV as flawed. The point that you continue to miss is the fact you keep talking about applying compensation contraptions to the traveling twin when I have pointed out to you that his being launched off a gravitating body negates the tenet of "the uniformly accelerated probe is located FAR AWAY from any gravitating body". Then you switch to applying goofy acceleration programs to the probe stationary in the UNIFORM gravitational field, thus destroying its "UNIFORM" concept. Then you throw your toys out of the pram when I point out these mistakes. After the toy throwing, you revert to the same high jinks with EEP.

See above. Why do you keep doing this to yourself? Look, you have wasted an enormous number of posts defending your posts but you are not any closer to writing the formalism that describes it, let alone solving it. On the other hand, I have already solved these exercises, so why are you wasting your energy trying to convince me when you are making zero progress in figuring out the solution to your own exercise? You claim that you are here to learn, at this rate you will never learn.

 

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This is not a time "dialation" problem, it is a problem of calculating the elapsed time, you are making the same error as RJ and OnlyMe. To make matters worse, the calculation isn't trivial at all, it requires that you understand the notion of geodesic deviation and this requires solving some very complicated equations. You could simplify things a little by using a variational method but you are still faced with some heavy duty math.

It isn't a "little" planning, it is quite complicated (unless you plan to cut corners in a massive and ugly way). Yes, the above is a simplified case of a more general problem but the math is still very complicated. Even more, constructing the formal description of the exercise is not easy, you need to know GR and EEP is of no use in solving. If you want to learn how to do it, you need to put your energy into it, not into other things.

 

Put the above into a coherent mathematical formalism and I will be able to tell you if it right or not. Dropping isolated formulas like \(a_{engine}+\omega^2r=9.81\) does not constitute a formalism by any stretch of imagination. Take it from launch, how long you accelerate, how long you coast, how do you decelerate and we'll see. Write down the equations for each section, what you have right now is unfalsifiable not because it is correct but because it is just a bunch of random things with no math.

 

I am not attempting to insult you, I am simply pointing out your many mistakes, if you think that that is an insult, then this is your problem. As an example look at the way you reacted when I pointed the errors in your recent exercise. You did not accept the correction until Trippy told you that you got it wrong. A a matter of fact, I can point to the many times you trolled my posts (and you were shown wrong) and the many personal attacks that you launched against me. If you do not like being proven wrong, check your facts before you post. That simple.

 

True, TS. But there are limits in terms of contentions, rewriting EEP with your additions inserted is way off limits, wouldn't you agree?

Yes, I followed, you presented a new exercise not realizing that solving it requires even more complicated formalism than before (see my comments on the issues with your new scenario). If you had a prayer at solving the old scenario, now you have none with the new one. I would be thrilled to see you proving me wrong by solving the scenario that you are proposing now.
In the meanwhile, you never admitted to butchering the EEP, as explained, you simply went on denying that you did anything wrong. You threw a fit over it and then you went on like you made no errors. What is more disturbing, is that you just repeated the same errors.

 

The post has been deleted as I said.

And that's enough said!

 

Ok,

This is a reasonable post, I think that we can agree on it. Now, how would you go about writing up the mathematical formalism that describes your newly suggested scenario above?

 

Tach, have you explained the error or just continued the claim? I could have missed it.

BTW This is really a good one, I think is goes into the Tach quotes of the day at least.

Not without a great deal more explaintion and supporting logic than I have noticed.

 

OK,


The point of contention was the misuse of EEP but this is beside the point now that you just claimed that you aren't using EEP anymore. Can you put all the above in a coherent formalism so we can talk about it? Like for all the sections of the trip?

 

Yes, many times, last time a few minutes ago. You don't miss it, you just deny it. Not the same thing. But this doesn't seem to matter since you now claim that your new solution doesn't use EEP anymore. So what is your solution to your exercise? Do you use the geodesic deviation? Accelerated motion in GR is very tricky, most applications use motion in the absence of external forces. It is even more tricky than the accelerated motion of a test particle in an em field of arbitrary \(\vec{B},\vec{E}\) and that one is very very tough. The accelerated motion in GR is much , much tougher, so what method are you using?

 

I'm thinking of an observer that remains in the stationary muon's frame...he would not claim that the muon's life has increased...what he would say is that the accelerated lab has experienced length contractions which make the muon's life APPEAR to be extended to those lab observers, right?

 

Tach, you must have edited the wrong post! I did not change anything, I can remember anyway, and have suggested no solution.

As for the question.., I admit it was phrased poorly, but I really did miss the explanation. I haven't even followed your link yet....

No, I just checked the link and I don't accept your interpretation as presented. As I have said the condition that the box be FAR AWAY from a gravitating body is essentially a test case for the hypothetical description.

Just as with the twin paradox question, about applying the solution to a twin that does not return home and being certain that he does still age, which you agreed with..., so it is with the EEP. If it applys FAR AWAY it applies in all cases. It would just not be the only effect acting on or potentially felt by an observer, if it is not FAR AWAY from other sources of gravitation.

As I said from your earlier quote, if it is a matter of experience, in the early 1900s then it is experienced NOT FAR AWAY from a gravitational field. You feel the same force when you accelerate in a car. It just is not the only force acting on you in that case.

The equivalence principle just says that the force you feel when accelerating is the same as an equivalent gravitational force in the same direction. Under most cases in experience, it is not a uniform acceleration and so is equivalent to changing gravitational force.

See, I can tweak it too!

 

No, the muons can be tracked over time and the lab can unambiguously clock their lifetimes from creation until decay, regardless of how far they actually travel in the lab frame (very routine in particle physics experiments, not just hypothetical). The extended lifetimes as measured in the lab frame are not merely appearance, but well-known, verifiable fact. From the muon's POV, the lab clock runs slower, but it also started ticking before the muon was created or stops after the muon decays, hence an observer in the muon's frame would still agree that the lab still clocks an extended lifetime. So again, how is time dilation distinguished in the case of an initial lab acceleration vs. an initial muon source acceleration?