Re: Twin Paradox - A new angle to the question itself.

The short answer is that whichever twin turns around to meet the other one (requiring acceleration) will age less. If they both accelerate equally they'll be the same age.

Now, often people will say that because you have to take the acceleration into account, you can't do this calculation in special relativity. That's actually not true; you can do it easily in special relativity so long as you allow instantaneous changes in velocity (or an infinite acceleration).

Here's how it works from A's perspective. A is on Earth the whole time. A sees B fly out in a rocketship for 20 years, and thinks that B only ages 5 years. Then he sees B change direction (infinitely fast), and B doesn't age at all during this very-short acceleration burst. Then B flies back for 20 more of A's years, and A thinks that B ages 5 more years on the way home. So when B gets back, B has only aged 10 years total, and A has aged 40.

That's the easy perspective. What happens from B's perspective? First B flies out for 5 of B's years, and sees A age only 1.25 years. (After all, it's A who appears to be moving, so A's clock looks slow.) But then B turns around infinitely fast. It turns out that when B changes direction like this, B's perception of simultaneousness (or "now") is shifted. An instant before B turns around, A has only aged 1.25 years. An instant after it now looks like A has aged 38.75 years! So it looks like A has aged instantly. For the 5 years B travels home, A ages the remaining 1.25 to make an even 40.

The reason for this instant aging is that B's idea of when "now" is at Earth is dependent on how fast B is moving (and in what direction). When B changes direction, the concept of "now" jumps into the future. Keep in mind that this is only true because B is far from Earth; if B were at Earth this effect wouldn't happen. Even stranger is that this aging of A is reversible! Right after B changes direction once, if B now accelerates the other way, changing direction again, B will again think that A has only aged a total of 1.25 years! B will think A had just gone back in time.

You'd think that if A appeared to go back in time you could make a paradox, but remember that B merely "thinking" that A went back in time is a far cry from actually "seeing" A go back in time, and it's an even father cry from "telling" A what will happen in the future. Turns out that taking into account that information only goes at lightspeed, there's no way to make a real paradox. (Unless you can go faster than light, of course. This turns out to be a proof that faster-than-light travel would make time-travel possible, which is why few physicists believe faster-than-light is possible.)

So, to sum up, the symmetry is broken by the acceleration. If both A and B accelerate, there will be no age difference. Here's an excellent FAQ for more info on this topic.