General Relativity Question

Your first example is basically the twin paradox and your second example is a more compliecated example of same.The basic explanation is that accelerating ruins the inertial reference frame for a moment.Lets say, from earth's point of view, it takes the rocket 50 years to fly from Earth and back.
I'll call the turning point, Point P.The rocket takes of at 80% of the speed of light and travels to point P.
From Earth's point of view, this took 25 years, but it looks like (people on Earth are looking through a telescope) people on the rocket only aged 15 years.From the rocket's point of view it only took 15 years, but it looks like people on earth only aged 9 years.So in getting from Earth to point P we have the following information.
Earth's point of view:
It took 25 years but the rocket only aged 15.Rocket's point of view:
It took 15 years but Earth only 9.Then the rocket accelerates so that it is heading at the same speed back to Earth. This acceleration causes Earth to jump from 9 years to 41 years from the rockets point of view.
It takes 15 years for the rocket to return home, from the rockets point of view, in which time Earth ages 9 years.So from the rockets point of view, the rocket has experienced 15 + 15 = 30 years of travel and Earth has experienced 9 + 9 + 32 (from the acceleration) years.From Earth's point of view it took 50 years for Earth and the rocket aged only 30 years.So both agree it took 50 for Earth and 30 for the rocket.It's a lot to take in, but that essentially is the explanation.This message has been edited by Son Goku, 12-17-2005 05:45 PM

Thanks, I was wondering how clear it was. I love the paradox because when you understand it, it pulls one of the final Newtonian concepts from your mind, the notion of absolute simultaneity.To jmrozi1: This kind of "paradox" usually comes from thinking about relativistic time dilation, but keeping Newtonian concepts of simultaneity.As you can see at point P (before the acceleration) Earth aged 25 and the spaceship aged 15 are simultaneous from Earth's perspective.From the rocket perspective, Earth aged 9 and the rocket aged 15 are simultaneous.

A rather mundane answer, but an inertial reference frame is one with constant velocity, when you accelerate you aren't keeping your velocity constant. Everything else.We have nine pieces of information here:
The aging and speed of the Earth with respect to Earth
The aging and speed of the Ball with respect to Earth
The aging and speed of the Rocket with respect to Earth
The aging and speed of the Earth with respect to Rocket
The aging and speed of the Ball with respect to Rocket
The aging and speed of the Rocket with respect to Rocket
The aging and speed of the Earth with respect to Ball
The aging and speed of the Ball with respect to Ball
The aging and speed of the Rocket with respect to BallA few of these will agree. This is the answer to your question. There can be a variety of answers to the question, "What is the speed of the ball?", depending on which one of the observers you ask, same for the other two.As a side note, what your discussing here is actually Special Relativity, which isn't half as wierd or complicated as General Relativity.

Yes, pretty much. There is a way you can make Special Relativity treat it, but in reality it is a GR question. It's entirely handwaving. Essentially a way of putting a balck box around the point of acceleration.Here is the explanation using the barest hint of General Relatiivty, because I really don't want to use the acceleration metric.I'm going to go as far as I can with Special Relativity first.
Before acceleration the ship is in frame O' and after acceleration the ship is in frame O''.
We will also say that t(P' or P'') is the age of Earth as viewed from that frame.
The velocities of the frames relative to Earth are v'= 4/5 c and v''= -4/5 c respectively.
However lets see what their velocity are with respect to eachother.
From the relativistic velocity addition law we find this velocity to be 40/41 c.
And the respective gamma factor is g = 41/9.
This means that the time dilation effect between the O' and O'' frames is such that a time interval of t(P') = 9 years in O' is viewed as t(P'') = gt(P') = 41 years in the O'' frame.The General Relativistic reason for this effect basically comes from the equivalence principle.
So the acceleration a point P from frame O' to O'' is basically the same as an object falling from one height above a giant planet to another height and the effect comes from gravitational time dilation between these two heights.
I'll go into more detail if you want. I know what you mean. In fact one of my biggest issues when people teach SR is that they downplay or don't deal with proper time.
Which is unusual given its importance in GR.
To be honest I always thought the "pole in the barn" paradox should be introduced first, if you going to bother with paradoxes at all.

I suspected you would say something.
You are of course right, SR does deal with this perfectly well.
Its just the way I seperate GR and SR in my head.This message has been edited by Son Goku, 12-21-2005 01:58 PM

I'm glad to be on a forum where somebody will pull me up on it.As a side question for myself, thats related to Quantising GR, what do you think of Loop Quantum Gravity?
I don't know much about it or String, so I'd be happy to hear your opinion.

Your basically asking a foundational question that relates to a thing called background independance. (And one that a lot of people miss)
There is quite a bit to it and several side issues that'll take more than one post.
I'd be happy to explain, but would you prefer here or in a new thread?