The twin paradox is the popular thought experiment involving twins, one of whom makes a journey to a nearby star in a high-speed rocket (travelling at a velocity close to the speed of light) and when he reaches the star, changes direction and returns home at the same speed. When he gets home, he finds that time has slowed down during his journey and that his twin who has remained on Earth has aged more. (The paradox being that because both twins have travelled at the same speed with respect to each other, why has one aged faster than the other?)
My understanding is that the solution is as follows. When he arrives at the star and changes direction, the travelling twin switches from a reference frame travelling away from Earth at a velocity near the speed of light to another reference frame travelling towards Earth with a velocity of the same magnitude but in the opposite direction. In contrast the non-travelling twin stays in the same reference frame. It is often pointed out that the travelling twin experiences an acceleration when he switches from one reference frame to another, whereas the non-travelling twin does not experience an acceleration. (This acceleration could be a Dirac delta function i.e. an instantaneous switch of direction)
My first question is what is the travelling twin’s acceleration with respect to? Since in special relativity there are no absolute reference frames. I assume it is the Earth??
Secondly, and this is the question which is intriguing me the most, suppose hypothetically there were only two objects in the Universe namely the two twins. If, in this hypothetical universe, one twin travelled on a rocket for a distance of say ten light years and then returned back to meet the original twin. Would the travelling twin’s clock still run slow with respect to the other twin? since there would be no distant background stars/galaxies in this hypothetical universe to measure the acceleration against? Is it just as valid to say that the “stationary twin” is the one in motion? Additional comment
In a various replies to this question, it has been mentioned that the moving twin feels an acceleration and the stationary one does not, but in this hypothetical Universe containing only the two twins I cannot see how this can be the case