Q. Why is the Twin Paradox of Relativity Not Symmetrical?

"The Twin Paradox: If a twin on a rocket travels at high speed for a while, and then returns to the Earth, the Earth-twin would have aged much more than the space-twin. But isn't it just as valid to say that the Earth is moving away from the rocket? Then the situation would be switched. Why would the astronaut return to find the Earth-twin aged far more, and not the Earth-twin find the astronaut aged much more?"

A. While in relativity, all inertial frame of reference are equivalent, the eqiuvalence is broken because the astronaut, unlike the stay-at-home twin has to accelerate to return to the Earth. Unlike relative motion, absolute acceleration is easily determined (in the absence of gravity) due to the pseudo-forces that the acceleration creates in the accelerated frame of reference. An example of a pseudo force is the apparent force that pushes you forward aginst your seatbelt when your car brakes suddenly. The equations of special relativity do not deal with acceleration (although it is easy to calculate the twin paradox effects in special relativity assuming an instantaneous turn around) - that is the province of general relativity. The equations of GR are more complex, but an accelerating clock will run slow - so as the clock accelerates into its return trip, it runs very slowly and the earth bound clock races ahead according to both twins.