Fake-edit: Ok got beaten on the twin paradox, no wonder with my incredibly long post, but:
The twins paradox stops being a paradox when acceleration (the change in direction) is taken into account. Acceleration speeds up the relatively traveling twin's time-flow (because of the direction of the acceleration), so they will be the same age when they get back together.
No. The one on earth will be older overall.
Anyway...
Anyway. I believe I asked this in one of the physics-related threads that popped up sometime in the past on this forums, but I don't recall getting a meaningfull answer.
So, is anyone able to explain to me the twins paradox? The guy who taught me physics relegated me to some book that I've never picked up, and I still can't wrap my head around it. Apparently it's somehow resolved during the actual acceleration, or maybe the reversing of movement direction that the ship would have to do at some point, to get back to the point of origin.
I can take some algebra, somewhat less of calculus, if you need to use it, but qualitative explanation would be enough.
Yeah, the twin paradox is a mean one because it seems to go against the whole spirit of relativity. To recapitulate, twin A stays on earth, twin B travels with his spaceship with nearly light speed to another planet, turns around, and comes back with nearly light speed. Now, apparently the theory says that the twin on earth will overall have aged more than the twin on the space ship.
From the viewpoint of earth this seems to make sense because from there it looked like time in the space ship was going slower throughout the journey because of time dilation. But, haven't we just just established that everything is relative? Because then, from the ship's point of view it was the earth that travelled away with almost c and then came back, so it should be the clocks on earth that should be going slower, i.e. people on earth should have stayed younger, not the other way around.
So that's the apparent paradox. Now, the short solution, and it definitely makes sense, is to say that the frame of references are
not symmetrical in this case, because one was undergoing acceleration, namely the twin on the spaceship as he turned around at the distant planet. Movement is relative, but acceleration is not: When I pass an object in my spaceship, I can't say if it's me that is 'really' moving while the object is stationary, or the other way around; that's all relative. However, when I accelerate towards an object, yes, it will still look as if the object accelerates towards me from my point of view, however, only one of us, namely me, will experience an inertial force, pushing me back into my seat. So acceleration is not just a matter of definition.
Thus, in the case of the twin paradox, the short solution is to say that the frames are not symmetrical or equivalent, and because one experiences acceleration, special relativity does not necessarily tell you what is actually happening from his point of view.
It gets more complicated if you actually do want to describe what exactly happens. I didn't remember too much either, so I just had a quick look at wikipedia, and while wikepedia is not always reliable with science explanations, the
article on the twin paradox seems reasonable, and I recognize one of the explanations from uni.
So here are two options of explaining what happens to the twin on the spaceship:
The first one is to think about what actually happened during the de- and acceleration at the distant planet. According to general relativity, experiencing acceleration and experiencing a gravitational pull are equivalent (or rather, the forces themselves might be equivalent). And we know that in a strong gravitational field, time will go slower (think of the astronaut approaching the event horizon of a black hole).
That means, as in terms of travelling at constant speed, the situation for both twins is equivalent, and both would observe time dilation in the respective other frame of reference. However, at the mid point of the journey, the spacefaring twin will experience an additional period of acceleration, which means that from his point of view the clocks in the outside world will go
faster. And apparently the math gives you that this period of faster clocks on earth is more than enough to make up for the slower clocks on earth during the legs to and from the distant planet, yielding an overall net effect of more time having passed on earth once the twin arrives back home.
The other explanation just uses special relativity, and I remember that one from uni. I think I didn't find it very convincing back then, but having read about it again now on wikipedia, it kind of makes sense. I'm just going to comment on what is written there.
Basically, the argument goes that the space twin arrives at the planet in one inertial frame of references, then de- and accelerates, and then travels back in another frame of reference. So he switches inertial frames (so far no argument to be had here). Now, the argument is that whatever happens during that acceleration (again, which SR doesn't describe per se), you ignore that for now, but you only compare the initial condition, i.e. the first frame of reference, and the outcome of the acceleration, i.e. the second frame of reference (you could assume an instant switch of velocities). You apparently then find than the simultaneity planes have shifted..
uh haha that sounds like bollocks, but I think it actually makes sense (and my theoretical physics prof thought so as well). So: The point is that for any frame of reference, you can draw a Minkowski diagram and see which events at what locations are happening simultaneously in your frame of reference. For example, as the space twin is just about the reach the point of instant re-acceleration, from his point of view his twin on earth is about to lift a cup of coffee at his 25th birthday. Then the space twin changes velocities arbitrarily fast. If we draw again a Minkowski diagram to find out what events are simultaneous in the new frame of reference to the "now" of the space twin (which, for him, is almost the same now as before), we will find that the corresponding events on earth happen much much later on their timescale (e.g., years). So the earth twin might just celebrate his 30th birthday now.
Thus, with these considerations, we could conclude that whatever happened during acceleration (which we cannot describe with SR), apparently the outcome was a shift in time on earth. And if we were to accelerate more smoothly instead of almost instantly, one would expect that during this time the clocks on earth would go faster from our point of view. Which is the same conclusion we draw in the other solution, but now without appealing to gravity and general relativity.
So. For me the second explanation kind of makes sense, but my feeling would be that a full explanation always would involve general relativity.
Hope that made some sense.
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