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1. The Ehrenfest Paradox

After watching some of the posts here, I am not sure if I can conclude -

The circumference-radius ratio is INDEED not 2π, but with a factor γ (which means Euclidean geometry is not necessarily correct in relativity, and the radius 'cuts through the circumference' ?) , Or

The 'inelastic' radius 'shortens' to fulfill the Euclidean geometry (which is not correct, I supposed. The radius is perpendicular to the velocity, so it should not experience Lorentz contraction.)

2. The Twin Paradox

Time dilation tells us, in both of the frames of the twins, they 'believed' that the his brother is experiencing 'slower time' relative to himself, and both of their measurements of time must be correct, despite the results might seem to contradict to another.

Problem is -

When the twin travelling in spaceship with relativistic speed, gets back to earth to meet his brother, the contradiction arises. Who is older?

If one argues -

The 'relativistic' twin experiences a change of velocity and the direction of returning journey is opposite to the starting one. The calculation will not be that naive - substituting the speed to the equation of time dilation.

One could suggest a modified version of twin paradox -

The twin A travels at v~c, in a 'straight' path. But, the space is closed and curved. A gets back to earth. Same result arises in the original paradox.

It seems to be hard to combine the 'contradictory' results into one at their reunion. Can anyone get an explanation of non-inertial frame about the twin paradox? Is the modified one still involving in acceleration?

Thanks for answering.

After watching some of the posts here, I am not sure if I can conclude -

The circumference-radius ratio is INDEED not 2π, but with a factor γ (which means Euclidean geometry is not necessarily correct in relativity, and the radius 'cuts through the circumference' ?) , Or

The 'inelastic' radius 'shortens' to fulfill the Euclidean geometry (which is not correct, I supposed. The radius is perpendicular to the velocity, so it should not experience Lorentz contraction.)

2. The Twin Paradox

Time dilation tells us, in both of the frames of the twins, they 'believed' that the his brother is experiencing 'slower time' relative to himself, and both of their measurements of time must be correct, despite the results might seem to contradict to another.

Problem is -

When the twin travelling in spaceship with relativistic speed, gets back to earth to meet his brother, the contradiction arises. Who is older?

If one argues -

The 'relativistic' twin experiences a change of velocity and the direction of returning journey is opposite to the starting one. The calculation will not be that naive - substituting the speed to the equation of time dilation.

One could suggest a modified version of twin paradox -

The twin A travels at v~c, in a 'straight' path. But, the space is closed and curved. A gets back to earth. Same result arises in the original paradox.

It seems to be hard to combine the 'contradictory' results into one at their reunion. Can anyone get an explanation of non-inertial frame about the twin paradox? Is the modified one still involving in acceleration?

Thanks for answering.

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