I haven't seen the twin problem configured this way before. But it seems to me it should lay to rest the argument that SR can't account for the age difference.(adsbygoogle = window.adsbygoogle || []).push({});

Instead of going from the earthtothe star and back, the traveler goes from the earth in a big circlearoundthe star and back. The star is the center of the circle and the earth is a point on the circle. The traveler then experiences a continuous acceleration throughout his trip. If the star is 100LY from earth and the traveler's speed is .99c then his acceleration (v^2/r) works out to about 8m/sec/sec. That's less than the 9.8m/sec/sec that his twin experiences staying on the earth! So, when he returns (2pi*100 years later), if he has aged any less than his twin, it can't be because of acceleration.

Now all you have to do is a relativistic doppler calculation for an object moving in a big circle. I haven't done it, but it shouldn't be hard. The distance between the twins is r*sin(theta/2) where theta is the angle at the star. So their relative speed is just 1/2*r*cos(theta/2), or about 50*cos(t/200), where t is in years. The total number of ticks on the traveler's clock should be an integral of his tick rate doppler adjusted for this speed.

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# The twins in a big circle

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