h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I need some advice to settle a pub argument. Talking about time dilation, a friend came up with a proposition that I couldn't counter (well, not without looking stupid anyway).

Normally it goes like this. There are two twins; twin A stays on Earth and twin B goes on a very fast spacecraft and orbits the Earth a few times. In theory, time for twin B should slow down as he is travelling faster relative to twin A, so when he returns to Earth he is a little younger than twin A. Fine so far, and this phenomenon has been demonstrated several times, but...

As friend correctly pointed out, although twin B is travelling faster than twin A from twin A's point of view, from twin B's frame of reference twin A has been travelling at exactly the same speed in the opposite direction. And relativity is all about relative frames of reference. So, how does the universe decide who gets to age faster? What am I missing?

Valuable drinking time postulating me thinks
HF

Nope - had plenty of that too.

Perhaps A is moving fast relative to B from the point of view of someone outside both inertial reference frames...?

Yes, but someone in yet another frame might see B moving faster than A. Who, or what, decides?

You know when you are being accelerated.

Is it not that the orbiting twin returns to the earthbound one, wheras if the earthbound one returned to the orbiting one then it would be him who you would be younger? Until later...
BCNU - Crescent

that would make sense, since if A and B are moving apart, then for A to catch up with the aging of B, they would first have equal the velocity of B, to become stationary relative to B (at which point they would still be older, but not getting any more progressivly so) and then they would have increase velocity, realtive to B in order to catch them up. Once their velocity relative to B increases, then they are in the higher time frame so they ap[pear to age slower so B ages faster and then when A meets B and matches velocity their ages and aging rate would then be the same again.
?

JB - acceleration may come into somewhere, can you expand on that? (In words of one syllable please

Crescent - I see your point but again who decides who is returning to who? Relative to what?

Ictoan - sorry, didn't understand a word of that!

This is the kind of question I as an astrophysics student should be able to answer. But I still don't quite get those theories. It just seems that if everything is relative, a lot of these phenomena of space dilation should not occur. And if you throw in "spooky action at a distance", the idea of there being no time instant also seems wrong.

A couple of semi-armchair guesses (I'm first year science in uni). It's a little late, so I might not be very coherent.

1: Since velocity is a vector quantity, A would see B moving in the opposite direction and hence the time dilation would be reversed. Many relativistic equations depend on the factor sqrt[1-(v^2)/(c^2)], where v is the relative velocity and c is the speed of light. Relative to B, this factor is less than 1, and so time expands and length shrinks. However, from A's point of view, B is moving in the opposite direction, and so v has a minus sign...I was going to say that this makes the factor greater than 1, but I just realized that a perfect square cannot be negative unless i is involved, which it isn't. Disregard this statement.

2: One of the two fundamental postulates of relativity is that everyone in the Universe observes light to move at a constant velocity, c, in a vacuum, no matter what the observer's velocity or acceleration. Thus A sees himself moving at a certain velocity relative to a beam of light passing by his spaceship, but B sees him moving at a different relative velocity. For example, suppose he's going at 0.5c. A sees that after he crosses a certain distance X in time t, the light has crossed another distance and has gone a distance of c*t further ahead. However, from B's point of view, the beam of light has moved a distance of 2X. In the same time (measured by an independant clock), A perceives himself to have gone a shorter distance than B measures him to have gone. Thus when A measured the time than B has just measured, he will have gone further - an effect of time dilation as predicted by special relativity.

me neither!

better yet, read

http://www.phys.vt.edu/~jhs/faq/twins.html

which covers this better than I ever could!

Although it does warn that
" You may need to consult an elementary text on Special Relativity for explanations of the Time Dilation, Lorentz Contraction, and Relativity of Simultaneity effects that I will use without explanation."

It's all relative...no really!

If twin B leaves the Earth and orbits at relativistic speed when s/he returns s/he will have aged more slowly than twin A. Twin A in this set-up is at rest with respect to twin B and not travelling backwards.

The whole point of Relativity is that it is relative to the observer. Time for twin B does not alter in any way. The clock on the spaceship behaves entirely as you would expect it to on Earth *for twin B*. If you can imagine two clocks in this experiment, one on the wall and a screen next to it showing the one on the spaceship, then to twin A the image of the spaceship clock would slow down with respect to the clock on the wall as B travelled closer to the speed of light. If B could achieve the speed of light then clock in the image on the screen in front of A would stop.

Some other things would also happen. The transmission arriving at the screen would fade out as the frequency of the carrier wave got longer and longer (this is the Doppler effect that leads to red-shift of starlight as objects get further away).

The mass of the spaceship and everything in it would reach Infinity.

The energy required to achieve this state would also reach Infinity.

Remember E=mc^2 (energy = mass times the speed of light squared)

Getting back to the twins, if you as an observer were truly at rest in space relative to the whole shooting match you would see twin A age more slowly than you and twin B age more slowly than twin A.

Hope this helps?

turvy

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

"the definition of invariant mass is much preferred over the definition of relativistic mass. These days, when physicists talk about mass in their research, they always mean invariant mass".

Thanks guys - Ictoan's link answers it. Too for a Monday morning, but if I interpret it correctly, both twins observe each others' clocks slowing down, so the assumption I was alluding to in post 1 that one is moving "faster" than the other is false. The difference is that (as Cresent stated) the travelling twin also makes the return trip, and by doing so changes his frame of reference:

"This explanation of the twin paradox (without accelerations) shows that it takes TWO different reference frames to keep track of the time duration experienced by the twin who actually takes the trip, while it take only one frame to keep track of the duration for the twin who stays at home. Their situations are fundamentally different, and the different time durations they experience are the result."

I just borrowed "Space Time Physics" by John Wheeler from the library. I'll get back to you.

did my link make any sense to you as a science student, Xanatic?

I haven't had a chance to look yet.

Had a quick look through it. I had some problems with the idea of acceleration if speed is relative. I'll have a better look later.

OK, ta, I'd be interested in your take on it!