Sunday, October 11, 2009

twins paradox

I don't understand the twins paradox. Or maybe I do understand it but don't understand the explanations for it.
Relativity is strange but I will accept it. If I lean out of a train travelling at 100 mph and throw a ball forwards at 30 mph then the ball will be travelling at 130 mph. If I throw it backwards at 30 mph then it will be travelling at 70mph. Simple.
Common sense would suggest that if I was on the same train (this is of course the new Tokyo vacuum train we're on) and shone a torch forwards out of the window the the beam of light generated would be travelling at 670 616 629 mph +100mph. whereas if I shone it backwards the beam of light would be travelling at 670 616 629 mph - 100mph. However apparently it doesn't. Apparently it travels at 670 616 629 mph whichever direction I point the bloody torch. When I am feeling sane none of this makes any sense. When my brain is racing it makes a kind of sense. I'm glad to say that these days I feel sane most of the time so I live in a world where it makes no sense at all, even with people talking about stretchy rulers and clocks running slow or fast.
However, I accept it. I accept that this how light, time, gravity etc works. Its been a minor accomplishment fro me to do it but I can accept that everything I believe about Newtonian physics is shite when we enter the realms of light particles.
I also accept that acceleration and gravity have identical effects on the speed of light - or maybe more accurately on the rate of time that we use to measure the speed of light (which is constant.) So time varies, but the speed of light doesn't.
Therefore a man at rest in the universe with negligible gravitational forces at play will measure a beam of light at exactly the same speed as a man flying past the same beam of light at a million miles an hour. To an onlooker this is of course nonsensical, but it happens because the clock on the spaceship is measuring time at a different rate to the one that the poor man floating in space has. I can't remember which clock is going faster.
Similarly a man standing on top of a mountain (or in orbit) has the same problem with his clock when he compares it to a man at sea level. They are measuring time at different speed because of the difference in gravity at altitude.
What this leads me to believe is that the effects of gravity and acceleration are identical on the measurement of time. A force of 1G caused by gravity is the same as a force of 1G caused by acceleration. And has the same effect on time used to measure the speed of light.
We've all see the planet of the apes. The spaceship goes out of control somewhere and returns to an Earth thousands of years in the future even though only a fraction of that time has passed on the spaceship. And the monkeys have got guns.
Apparently if one twin flies round the universe very very fast and returns to Earth he will be older than his twin who stayed here. Or was it younger? This is the bit that confuses me. Not the insult to the sensibilities and order of things confusion, more the "it doesn't make any sense"type confusion.
Suppose twin A stays on Earth subject to a gravitational force of 1G and all the effects that has on his time measuring equipment. Twin B (what unimaginative parents they've got) on the other hand jumps in his rocket with limitless fuel, food etc and heads out into the universe at a constant acceleration of 1G right up to (very nearly) the speed of light, he then flips the rocket around 180 degrees and decelerates at a constant 1G and eventually comes to a halt before ACCELERATING again at 1G back towards Earth. Halfway back he again flips the rocket round 180 degrees and again DECELERATES at 1G until he neatly parks his rocket next to his twin.
BOTH twins have been subject to the same force (1G) for the period of the journey. Relativity suggests that is impossible to determine which twin is moving away from the other one, and therefore which one was moving and which one was stationary.
Would one be older than the other? Which one would be older than the other? Why? And if you were a monkey which one would you want to shoot first?

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