PAllen said:
I think of muons surviving a long time in an accelerator ring a perfect demonstration of the twin paradox. Gravity is constant over this scale, you have a round trip (literally).
Also, I consider any comparison of two different paths through spacetime as examples of the twin paradox in GR context. Some of the airplane experiments have entailed round trips. To make an accurate prediction, both gravity changes and speed had to be factored in, with the results agreeing with prediction to within experimental error.
If you want to insist on a 100% pure SR verification, with no GR component, you have the silly requirement that the universe must be empty. The total geometric structure of the universe is inconsistent with the flat Minkowski metric. What one can say is the SR effects within the context of GR are well verified, including the 'combined' twin paradox. And that the pure SR case does not exist in our universe.
I am actually saying that for both effects of importance for the twin paradox, time dilation due to gravitational potential and time dilation due to high velocities, you must take the locally dominant gravitational field into account. You cannot really explain the time dilation due to high velocities in a way that is consistent with measurement within the framework of special relativity where you totally ignore gravitation.
DaleSpam said:
Citing from the above provided link:
"The so-called “twin paradox” occurs when two clocks are synchronized, separated, and rejoined. If one clock remains in an inertial frame, then the other must be accelerated sometime during its journey, and it displays less elapsed proper time than the inertial clock."
Is is the explanation that the difference in time elapsed is because one of the twins have undergone acceleration and not the other that I think is very troublesome... All experimental evidence (if you can, show me otherwise) points in the direction that what matter for an atomic clock is what speed it has in relation to the locally dominant gravitational field and how deep it is in the gravitational potential of that field, and has nothing to do with who has undergone acceleration. Example:
Two twins take off in spacecraft s both going at 100 km/s radially outwards from the sun. One twin keeps going outwards at the same speed, he stays in the inertial reference frame. The other twins accelerate by 100 km/s towards the sun so that he is at rest relative to the sun, he is the accelerated twin.
1. Whose clock do think will run faster, the accelerated twin that is at rest with respect to the sun or the twin that stays in the inertial frame moving at 100 km/s outwards from the sun?
2. When the twin that stays in his inertial frame reaches the radial distance from the sun of Pluto he decides to accelerate with a 100 km/s towards the sun, so that both twins now are at rest with respect to the sun. If the two twins send their time by light signals to each other, which twin do think will have experienced more elapsed time according to his atomic clock?
3a. The twin at Pluto moves infinitely slow back to the first twin. They compare their clocks. Who will show more elapsed time?
3b. The twin closest to the sun moves infinitely slow to the twin at the radial distance of Pluto. They compare their clocks. Who will show more elapsed time.
(I am a bit unsure what I would answer to 3a and 3b)
For the sake of argument let us ignore the fact that they have been spending time at different gravitational potential and only consider the time dilation due to velocity.
I could make a lot of other examples but if you stay with the assumption that on Earth it is basically speed in relation to the centre of the Earth that matters and in the solar system, far from any planet, it is basically the speed in relation to the sun that matters you tend to get the right result.