Ok, now consider this: Instead of a 4 l.y. distant star, the travel is to a 40 l.y. star. Accelerations and decelerations of B can last exactly the same as in the previous 4 l.y. travel, but, now, they end up with an age difference of 100years - 60years = 40 years, not 4. So, how can accelerations and decelerations have to do with it?

I thought you'd got me on that one! But . . . .

As far as each twin is concerned, in my very simple model, there is no 'fixed ' earth or distant star. In fact we have no fixed grid in space for our measurements, at all.

They are both in a deserted part of deep space. I am not allowing you to have any more in your experiment than this.

They could both be going at

**any** speed you like at the start of the experiment. The only things they can see or measure are each other and their ships and their relative motion.

Apart from the fact that one has used his engines (which must play a part in resolving the paradox), when they start to move apart, their relative motions are equal and opposite.

Now take up my previous argument. Neither twin knows which of them has actually 'moved', only that they have changed position, relative to each other.

The actual distances they each observe the other one to have traveled is not really relevant. What

**is** relevant is the fact that, when they finally meet (when their space time vectors coincide again) they will have different lengths of beard!

SR tells us that when the traveling one (the one who uses his rockets) returns to the original spot will have aged less because of time dilation and he will appear younger.

But, from his point of view, it was the

**other** one who went off at speed and then returned. So the other one will appear younger to him.

How can there not be a paradox there? if A>B, you can't say B>A.

But, if you allow for the effect of acceleration on one of them (which one of them could feel as a 'weight force' on him), to alter the rate of progress of time on his ship. That is a GR effect. As has been said previously, effects on the passage of time have been observed, due both to high speeds ( the muon observations - SR) and due to gravitational fields (the Mossbauer effect - GR).

I think this answers your question at the beginning of this post.

It is the initial impulse / change of speed and the subsequent changes as he turns round and comes to a halt that affects his 'aging' rate. Clearly, on a longer journey, he would end up with a different actual age difference.

In a more straightforward situation, there is NO paradox, of course, if two ships pass each other and observe the one-second bleeps that they are each generating. Each ship will see the other one's bleeps at slower than the one second rate of his own clock. That's simple (?!?!) S.R..

As far as I remember, having read the Einstein monograph some time ago, as a posy undergraduate, he used the notion of two clocks and not twins, but, of course, the same applies. Personalising it , makes the phenomenon slightly more 'creepy'. He frequently used models or pictures first and then sorted out the maths later. There have certainly been lots of discussions of these effects on more than just light photons and electrons, socratus. And, in any case, if it's good enough for an electron, it's good enough for me and my brother.