Can the Twin Paradox be simplified?

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First off, thank you for being more civil this time and not hurling insults. Second off, the above is insufficient as a proof because anyone can content that the acceleration effects simply canceled each other , so you cannot conclude that acceleration played no role.

On the other hand, my approach conclusively proves that acceleration plays no role since there is no way that the acceleration effects canceled each other. This is a big difference and a standard procedure in setting up experiments, you cannot allow any suspicion that the effect that you want to test is zeroed out by the methodology. Your methodology zeroes out the acceleration effect right off the bat.

Asymmetry only STRENGTHENS the proof. The more the experiment is tilted in FAVOR of acceleration causing havok (and finding out that it doesn't) , the STRONGER the proof that it REALLY has no effect. The setup for your experiment is suspect, mine , by exacerbating the conditions, is not.

 

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This is precisely where your logic lacks, you are only proving that difference in velocity results into differences of elapsed proper time, the fact that you took away the acceleration you can not prove that acceleration plays no role.
By canceling the acceleration off the bat, you fail to prove that acceleration plays no role.
Do you understand your error in logic? Do you understand how your setup lacks?

 

If one twin experiences 1g and no velocity, i.e. remains at rest on Earth (the stay at home twin), the other twin (the traveling twin) constantly experiences 1g of acceleration for the entire time he is traveling, and when they are reunited the traveling twin has aged less, it cannot be in anyway attributed to the acceleration, which remains the same for both twins throughout the traveling twin's journey.., and must be the result of the traveling twin's "rms velocity" relative to the stay at home twin.

What is wrong with this logic?

 

I'm sorry Trippy but even with that distinction I don't see how we can claim displacement (aka distance with direction) over time occurs for either the twins in different gravity wells or the twins at different ends of an accelerating rocket ship.

I personally think it's more natural to say that you must accelerate a body in order to give it a velocity, but I'm not convinced we can say either one truly "comes first".

First of all, perhaps you should just formally define relative velocity. The reason is that I can define acceleration in ways that do not involve relative velocity.

Point being: On one hand, we have relative velocity without acceleration (in the Third Brother scenario, for example). We'll just accept the notion that it's possible without worrying about how they got that velocity in the first place. On the other hand, we also have acceleration without relative velocity in the two scenarios currently being discussed. In the velocity-without-acceleration scenario we cannot conclude unambiguous time dilation; in the latter two acceleration-without-relative-velocity we can conclude unambiguous time dilation.

While I don't ask you to agree, would you consider admitting that my logic is not completely faulty?

 

That doesn't make much physical sense.
Changes in velocity = accelerations; all velocities are relative.

I don't see how you can physically accelerate a frame of reference without changing its relative velocity. Should I be paying more attention? Is there a difference between accelerating a frame and defining its relative velocity?

 

Nope, you are missing the point, in order to demonstrate that acceleration plays no role, you cannot cancel out the acceleration. The point of the experiment/exercise is to prove that the aging differential is a function of velocity differential and not a function of acceleration, remember? By canceling out the acceleration effects, you fail to prove what you've been trying to prove.

Precisely, see above.

Incomplete statement, this is where your error lies. The correct statement is:
" if both twins are subjected to the same acceleration for the same amount of time IN THE ABSENCE OF ANY OTHER DIFFERENCES (aka DIFFERENCE IN SPEED) they should age by the same amount.

But you are applying a DIFFERENCE IN SPEED IN ADDITION to the acceleration. Therefore, any person versed in physics will immediately point out that your problem statement is violated in the very experiment you are attempting to set up.

And your "setup" violates your (incomplete) problem statement, thus disproving your conclusion.

 

Yes, Arfa Brane, we're discussing how EEP relates to the problem.

1) Clock A on a large, unrotating mass while clock B resides in the dead of space.
2) Clock A at the nose of a constantly-accelerating rocket ship while clock B resides in the tail.

Both scenarios involve unambiguous time dilation, as well as "acceleration" via EEP, but the displacement between clocks does not change; therefore I am claiming it is difficult to make the case that relative velocity is required for unambiguous time dilation.

 

This is the correct experimental setup that completely refutes RJBeery's ideas.

 

The falsity of your claims has been proven multiple times in this thread. Read again here. Learn a new mantra: "acceleration plays no role, it is all in the speed".

 

Please remember I cannot read Tach's posts. Also, on first blush I'm not sure what the point of this would be. In order to establish unambiguous time dilation you would need 2 co-location events and that is not possible if their acceleration was all in the same direction. Even so...I still don't see what we think it might show us.

 

Could you tell me what those things might be, specifically? Because this runs contrary to my beliefs. I have to say though...it's nice to finally have some debaters with enough balls to put substance in their posts.

 

Yes, you can. You can also read this.

The point is to show that your fringe ideas are easily refuted by simple application of basic physics.

You sure about that ?

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It will show that you have been wrong for about 400 posts.

Physics ain't religion. There is no place for "beliefs" in physics.

 

Tach, just for information purposes. I just checked out the ignore function and RJ if he has put your name in his ignore list cannot see any of your posts past or current.

The post numbers remain the same but some are missing.....

BTW I don't put anyone on ignore. I was just confirming his statement.

So unless someone else quotes you he can't see what you post.

 

This is a very good example where sticking to a single construction of a hypothetical is of value, at least up to the point where some consensus can be established.