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ES, I just had a quick look. The broker's reference frame cannot be used in this way, because the twins themselves are non inertial. You can only use the Lorentz transformations to transform from one intertial frame to another.
To solve the twin paradox using Lorentz transformations you have to allow for discontinuities when the velocities of the reference frame canges. Failing to do that leads to an eror. In the twin paradox, if one of the twins is inertial, then evaluting things in that reference frame will give the correct result, while evaluting thinks in the reference frame of the other will give incorrect results.
The twin Paradox is essentially just looking at the two calculations and then seeing that they don't agree. What you have done is evaluting things in another reference frame in which you spread that error evenly over the two twins, making the difference go away.
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Originally posted by Count Iblis II:
What you have done is evaluting things in another reference frame in which you spread that error evenly over the two twins, making the difference go away. Hi, Look, what you are actually saying, is that there is no MATH error, but sort of lack of understanding of the problem on my part. Is this fair assessment ? ES
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Originally posted by extrasense: Originally posted by Count Iblis II:
What you have done is evaluting things in another reference frame in which you spread that error evenly over the two twins, making the difference go away.
Look, what you are actually saying, is that there is no MATH error, but sort of lack of understanding of the problem on my part.
Is this fair assessment ?
ES Yes, I would agree wit that. I didn't see any math problems, I didn't check in detail. The point is that you can, using correct maths, arrive at your result. My favorite way to explain this is to forget about Lorentz transformations and start from the formula for the invariant space-time interval: ds? = c? dt? - dx? You just apply this to the two twins and the paradox is solved!
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Originally posted by Count Iblis II: Originally posted by extrasense:
Look, what you are actually saying, is that there is no MATH error, but sort of lack of understanding of the problem on my part Yes, I would agree wit that. [/QB] I wanted to address this point of yours that I disagree with: """"The broker's reference frame cannot be used in this way, because the twins themselves are non inertial."""" But they are inertial in this article. How the twins arrived at those inertial systems, should not matter, unless you suggest that the prior history of the twins must be taken into account ???? e  s
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Originally posted by extrasense: Originally posted by Count Iblis II: Originally posted by extrasense:
Look, what you are actually saying, is that there is no MATH error, but sort of lack of understanding of the problem on my part Yes, I would agree wit that.
But they are inertial in this article.
How the twins arrived at those inertial systems, should not matter, unless you suggest that the prior history of the twins must be taken into account ????
e s [/QB]Es, yes I see now. There is no acceleration at all in the case you look at. In that case you can indeed get rid of the paradox by expressing everything in terms of coordinates of a fixed inertial frame.
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