So once again, I'm trying to wrap my head around the asymmetry in the twin paradox problem. Here's my setup. The two twins start on a very massive but small planet such that they always have an unobstructed view of each other.(adsbygoogle = window.adsbygoogle || []).push({});

1. They each attach a beacon to themselves that will briefly flash every month based on their individual clocks.

2. One twin goes in orbit around the planet at a distance to obtain a circular orbit with a period of 1 month and a velocity with a Lorentz factor of 30.

[Given the constraint of a circular orbit with the specified period and Lorentz factor (and neglecting GR), this places the orbit at 1.24e14 meters about a planet with mass 1.67e41 kg].

3. Neglecting the 12 hour delay that is approximately takes light to travel the distance between the twins, the twin on the planet will see the twin in orbit's flash in the same place in the sky, but by the stationary twins clock, this will only happen every 30 months.

4.Once again, neglecting the same 12 hour delay for light to make its journey, the twin in the ship will see the stationary twin flash his beacon 30 times for every orbit he makes.

Now the question - if we treat the orbiting twin as the "stationary" observer, then shouldn't he observe the other twin's beacon (originally the twin on the planet) to be flashing very slowly? The best explanation someone has given me in the past is that because one of the twins is accelerated, there is an asymmetry. But then, that suggests there's some preferred reference frame relative to accelerated observer.

The only argument I can think of to support some type of preferred frame would be if I had super strength and pushed off against the earth with enough force to accelerate myself beyond the planet's escape velocity.

In the planet's frame, the kinetic energy of this two body system is 0.5* my mass * v^2

(assuming I'm not moving at speeds near c)

In my frame, the kinetic energy of the two body system is 0.5 * Earth's mass * v^2

Clearly the product of the force I applied over with whatever distance that I applied it over isn't equal to the energy in the latter of the two frames.

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# Twin Paradox With A Beacon

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