Can the Twin Paradox be simplified?

That is because:

a. RJ messed up his calculations
b. RJ does not understand closing speed
c. RJ does not understand the notion of proper time , let alone the invariance of proper time

None of the above stops him from piling new errors on top of the older ones.

 

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I don't know about all that. I think he is rightfully claiming that either of the first two twins can end up younger or older, depending on which one accelerates into the reference frame of the other. I think (or hope) that he now understands that acceleration is not the "cause" of time dilation.

 

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based on what he's posting it is clear that he doesn't. That would amount to him admitting that he was wrong all along. I like him better this way, he keeps everybody entertained with making new mistakes in his attempts at covering the older ones. I hope that he never admits he's wrong.

 

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I believe I can answer Janus58's and Neddy Bate's questions with a reminder of what started this whole thing:

First, a definition:

An example of absolute time dilation is in the traditional Twin Paradox, whereby all observers can mutually conclude that absolute time dilation occurred for one of the twins due to the fact that he has physically aged less as they stand side-by-side. Note that this involves multiple co-location events (i.e. starting and ending together). It also necessitates acceleration.

Here's the point of the 4th Twin:

Now, when I say "contradict" what I mean is that the two groups of twins do not concur. This is not claiming some sort of problem with a Relativistic universe, as Janus may be thinking I am claiming. I'm simply pointing out that the Third Twin scenario fails as an example of absolute time dilation that occurs without acceleration, and my Fourth Twin was used to hammer that point home.

In other words, there isn't a scenario yet been provided in which absolute time dilation occurs devoid of acceleration, therefore I maintain that acceleration is a necessary causal component of it by definition.

 

I think that's a fair statement.

But do you still think "acceleration" is more analogous to "interest rate" in the savings account analogy? Or do you now understand why I said that "relative velocity" is more analogous to "interest rate"?

 

@Trippy: hahaha, I totally agree! I think it was originally called the "third brother". This is actually why the first few times I wrote it out I put quotes around the word "twin", in an almost ironic sense. Regarding whether or not the Twin Scenario is a paradox depends upon which definition you use.

From here:

You are offended by the term because you're using the 2nd definition, while the first definition is more apropos. The Twin Paradox is a "seemingly absurd" scenario which, when properly analyzed is true. The fact that you understand it doesn't mean that the average Joe who first heard the details would agree that it is not "seemingly absurd".

@Neddy Bate: Yes, I agree with you. Interest rate is more analogous to relative velocity, while acceleration is akin to changing that interest rate. If we want to establish "absolute account growth rate differences" in this analogy and have it remain true to our discussion we would need to necessitate that both accounts began with the same rate, and that one of them must undergo a change in that rate.

 

Sounds good to me!!!

 

I seem to remember an early hypothetical that involved a spaceship in orbit around a planet. In this hypothetical the GR time dilation associated with location within a gravity well was excluded. The GR time dilation associated with acceleration is not involved since the spaceship is in free fall and experiences no acceleration.

In this case the twins would be able to see each other once each orbit through telescopes and over time the twin in the spaceship would appear to age differently than the one on the planet.

I think it was actually Einstein who came up with the original of this hypothetical, but I don't remember the exact details off hand.

The point is and has been that if twins are involved, acceleration is required to make the hypothetical approximate real conditions. The three twin, or triplet scenario was an alternate hypothetical that was intended to resolve the acceleration issue. BTW it did not involve triplets. Instead it used a planet, two space ships and observer's with clocks. In the end it only compared elapsed time on the clocks and no aging of twins or triplets.

All.., or most of these hypotheticals are set up in an attempt to limit the time dilation to SR effects alone. There is no practical way to do that in practice. Even GPS satellites experience a greater dilation due to GR, than those involving SR.

However, since the SR effects are small at classical velocities, there really is no practical test of the hypotheticals that actually excludes GR effects. We cannot avoid the affect of gravitation on clocks and most accelerations will have a similar affect on clocks, via the equivalence principle.

Today with atomic clocks and super computers to handle the calculations we can account for both the GR and SR time dilation affects experienced by satellites. It is acomplished with a significant degree of accuracy everyday by the GPS system.

 

You keep repeating this mistake as if it were the scientific truth. Actually experiment says exactly the opposite that acceleration plays no role in time dilation, speed does. You have been shown the Clock Hypothesis several times now and the fact that it disproves your and RJBeery's claims on the subject.

That much is true. Now, here is an interesting tidbit that refutes RJBeery's claims 9and yours), the clocks used by GPS undergo tremendous acceleration at launch. Nevertheless, the launch acceleration does not affect the rate of said clocks. Why? You guessed it: "The Clock Hypothesis".

 

I agree on the importance of using three inertial frames of reference but it would be counterproductive to not use the Lorentz transformation. If you want to see how the twin paradox asymmetries and clock synchronizations are properly eliminated from this famous riddle, see The Quintessence of Axiomatized Special Relativity Theory.

 

Ever tired of self-promoting your crank piece?

 

Err...the rocket's firing notwithstanding, those clocks are under "acceleration" the entire time they reside on the surface of the Earth. Speaking of which, let's keep that rocket moving out to a point where the clock is essentially unaffected by Earth's gravity. Hell, let's stop the Earth's rotation while we're at it, just to keep things simple. Now their clock rates differ but their relative velocity is zero. Oh, "relative velocity isn't valid for non-inertial frames", you say? Well what is it that exists in the non-inertial frame of gravitation, in which absolute and measurable time dilation occurs, and relative velocity either does not exist or is not defined?

 

Actually, Eugene reminded me about the OP which was another claimant that the Triplet version of the Twin Paradox eliminated acceleration (#1 from the list). I hope the OP author has been following this thread.

 

I agree that's a simplification. It's easy to conceptualize enriching ordinary spacetime with an absolute frame of reference. Since an absolute frame of reference doesn't alter any of the predictions of the standard theory, then there's no harm in assuming the simpler view.

 

Different acceleration. Nice try. Still having trouble understanding the "Clock Hypothesis", I presume?

 

I just produced a scenario where absolute time dilation occurs without relative velocity. Can you produce a scenario where absolute time dilation occurs without acceleration?

No? Then I guess we're left with two choices: either mainstream Physics is wrong, or Tach is full of shit and doesn't speak for mainstream Physics. I'm voting for the latter! :bagpuss:

 

You "produced" just a bunch of errors.

 

Tach, your link to the clock hypothesis did not involve experiments where acceleration under GR was involved, so it proves nothing about the affect of acceleration on time dilation. I addressed this in an earlier post.

And just what effect would you expect tremendous acceleration to have on clock rate? It would be the same as moving a clock deeper into a gravity well. The clocks slow down under acceleration and speed up under free fall conditions.

Just what do you consider tremendous acceleration anyway?

The whole twin paradox issue is an SR thought experiment anyway and even when it is known that there are GR effects they are generally set aside and ignored. No one is actually sending twins on trips to some distant star and back to test it anyway.

Acceleration affects clock rates the same way an equal gravitational field would. Orbital acceleration excluded since while in orbit you are in free fall and only position in the planetary gravitational field is involved.