A New Interpretation of the Twin Paradox

The twins in the paradox are an attempt to frame the hypothetical in lay terms. AND by framing the hypothetical in lay terms including TWINS, there are practical conventions involving a common starting frame of reference that must be addressed.

There are many alternate constructions of the hypothetical that do not include twins or accellerations. Generally these were or are attempts to eliminate the GR time dilation that acceleration implies.

They are not the only way that the accelleration has been delt with.

Just what do you think the twins in the hypothetical are all about?

Since all you have been doing up to this point is linking to variations that do not address the issue, I hazard a guess that you did not know!

 

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So, you still think that the twins and "observers with clocks" are two different things?

Correct. This was my point all along, that acceleration is not germaine to the paradox. I can explain this in just two lines:

The proper time in SR is expressed as \(\tau=\int_0^T{\sqrt{1-(v/c)^2}dt} \)

For the "stay at home" twin \(v=0\) so \(\tau_1=T\)


For the "traveling" twin \(v \ne 0\) so \(\tau_2=\int_0^T{\sqrt{1-(v/c)^2}dt}<T=\tau_1 \)

Rubbish, there is no "GR time dilation" in the description of the problem.

So, you are too cheap to buy the Pauli book and learn? It would also help you with you misconceptions about the Doppler effect. Heck, probably you could finally learn physics in the time you have wasted trolling the forum.

 

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You are still deflecting Tach! Why were the twins introduced into the hypothetical, to begin with?

I really have a difficult time believing you are having this much trouble with something this simple! Hint: This paradox originated early in the history of SR.

Can you get to the correct answer from there? Or do you need more help?

Tach.., are you like in love with Pauli or something? It seems Pauli is your answer to everything, as if there were no other authority in the field.

 

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OK thanks for the source of your confusion but make no mistake: I have no misconceptions. You say these bizarre things like you have no grasp on events in the past. I was the first to say that the mirror moving parallel with its orientation would show no Doppler effects. You incorrectly extended that to mirrors of other orientations as well as matte objects. If Pauli makes the same mistakes that you have I'll eat my hat!

 

Nah, it is just a book that would keep you off the trolling for a while.

 

Start eating it.

 

OK, but before I get out the ketchup let me be sure I understand your claims:

Tach claims that a camera viewing light which has been reflected off of a matte object traveling between the camera and the light source would see precisely the frequency spectrum emitted by the light source regardless of the object's velocity. Fair statement?

Secondarily, and of lesser importance, Tach also claims that Pauli expressed this view in "Special Theory of Relativity". Fair statement?

If you need to adjust these statements please do. I want these goalposts anchored to the ground with cement bases. :thumbsup:

 

Nope, not a spectrum, a precise frequency tied to the speed of the object. You will need to think more about this. I'll give you a hint, if the speed is not the right value, the object appears black. Why?

You will need to buy the book in order to understand what Pauli says.

 

Tach, you have the book right?

And you understand it right?

Why can't you just explain it, in some comprehensible manner? Instead of continually just referring to it?

 

I already did, see post 62. Do you have difficulty with the two lines of simple math?

 

NEGATIVE. I'm not asking for hints about what silly business you believe, because I know the truth. You must make a claim and then I will inform you whether it's correct or not. Please adjust my statements so that they are in line with your beliefs, or bow out making the concession that you don't know what the hell you're talking about.

 

Another attempt at deflection. Your response in that post was not an answer then and it is not an answer now. Just more deflection.

 

You are just trolling. No amount of rational explanation will get through to you.

 

That's too bad, because it shows that you don't understand the physics of reflection.

 

I am not trolling here.

You asked a question which I answered in post 61. You did not like the answer but instead of sticking your neck out by saying what you thought, you began deflecting.

You never offered an answer to your own question.

Maybe you are the one trolling?

Or maybe you are just getting confused.

 

Well your noncommittal comments are understandable. I can see you've already changed your understanding regarding reflection off of matte moving objects, but you still have a way to go before you understand everything. I'm glad I've contributed to your education, though. And your maturity level will naturally improve with age.

BTW, You never gave me a "mainstream textbook reference" that made any claims about acceleration not being a component of SR. I'm fairly certain Pauli did not discuss the 3-twins paradox, did he?

 

Speaking of inability to comprehend, where did I claim that "acceleration is not being a component of SR"?
What exactly did I tell you in post 62?

Speaking about inability to comprehend, what did I tell you about page 72 in the Pauli book in post 59?

What in:


The proper time in SR is expressed as \(\tau=\int_0^T{\sqrt{1-(v/c)^2}dt} \)

For the "stay at home" twin \(v=0\) so \(\tau_1=T\)


For the "traveling" twin \(v \ne 0\) so \(\tau_2=\int_0^T{\sqrt{1-(v/c)^2}dt}<T=\tau_1 \)

did you fail to understand?

 

I'm happy to have helped, Tach. Your level of understanding has demonstrably grown over the past week, nice job. The next time you want a lesson in Physics, though, you should just ask rather than making silly pronouncements.

Also...not sure what to do about the 3-twin paradox misunderstanding you still harbor. Perhaps I'll spend some time explaining it to you. In the meantime, if you could, please find the mainstream physics reference that claims acceleration is "NOT key" to the twin's paradox so I can appreciate what exactly got your head all confused.

I hope you can appreciate that it's unusual for you to claim to be representing "mainstream Physics" when you're mistaken. Perhaps you should stop speaking for mainstream Physics until you graduate.

 

LOL, see here

"Twin Paradox Without Accelerations


In the above argument it is stated that Prime undergoes accelerations whereas Unprime does not, therefore, it is perhaps no surprise that the experience different things (in particular, a different duration for Prime's trip). Just in case the reader might decide that it must be the accelerations that cause the difference in duration for the twins, this section describes how it is possible to explain the paradox entirely without accelerations.

Instead of having Prime start at rest, next to Unprime, then accelerate to speed v, then stop at the distant station, then accelerate once again until moving at speed v back toward the initial station, etc., imagine the following demonstration. Unprime sits still at the original station. According to Unprime, Prime is moving along (and always has been) at the speed v, and passes Unprime at the moment that Unprime's and Prime's watches read t = t' = 0. Prime continues on, ultimately passing the distant station. At the moment he passes the distant station, Prime's watch reads t'=0.75 years (for reasons he understands, and were explained above). At that exact moment, Doubleprime (another person), passes the same distant station in another train heading back toward the original station at speed v. Both Prime and Doubleprime notice that the station clock reads t = 1.25 years. The also notice that both their watches display the time t' = t'' = 0.75 years (Doubleprime's watch is just coincidently equal to 0.75 years). According to Unprime (or his cohorts spread all over the place) Doubleprime has always been moving this way. Eventually Doubleprime passes the original station. As he passes, Doubleprime notices that his own watch reads 1.5 years, and that the watch on Unprime's wrist reads 2.5 years. Unprime notices the two watches also. Unprime's explanation is Time Dilation (just as in the above explanation). Doubleprime's explanation is that Unprime's clocks were running slowly and out of synchronization (again, just as in the above explanation).

The resulting difference between the reading on Unprime's watch and that on Doubleprime's watch is not the result of any accelerations experienced by anyone (nobody experienced any accelerations). But notice that the full duration measured by Unprime was, of course, measured in one reference frame; the duration for the full experiment recorded by Prime and Doubleprime required the combined results acquired in two different reference frames. That is the source of the asymmetry in the results. This explanation of the twin paradox (without accelerations) shows that it takes TWO different reference frames to keep track of the time duration experienced by the twin who actually takes the trip, while it take only one frame to keep track of the duration for the twin who stays at home. Their situations are fundamentally different, and the different time durations they experience are the result. "

You could benefit from going to school. Better use of your time than posting nonsense and trying to pass it as physics.