Electrocusionist

2011-May-23, 09:32 AM

I've been reading wikis and very simple papers on introductions to Special Relativity.

On the 9th episode of Astronomy Cast, titled 'Einstein's Theory of Special Relativity', Dr. Gay gave an example with a common-to-SR moving train theme: A is inside the moving train with two mirrors placed perpendicular to A's body, one next to the crown of her head, one next to her feet. B is outside the train, on a field, with a similar mirror setup.

SR continues with respect time dilation with 'a moving clock ticks more slowly than when it is at rest with respect to the observer'.

Now, my dilemma. I wanted to convince myself with a little math, so I used one of the few equations I can handle comfortably: v = d/t

Since speed of light is the same for all observers, I gave v a meager 10 m/s for the sake of my calculating prowess. Let's say for B light travels 20 m in 2 s. So,

B: 10 m/s = 20 m / 2 s

Near A, light has to travel the extra distance because the train is moving so I gave it 25 m (correct me if this 'assumption', or all assumptions so far such as using 'sub-standard' formulas, is baseless).

Since v (= 10 m/s) shall remain the same, it's a matter of finding out the time light took to travel 25 m, which in this case is: t = 25m / 10 m/s = 2.5 s

The final time measurements read, A = 2.5 s, B = 2 s.

For the life of me, I can't understand how the moving clock, at A's position, is slower in this case.

I know I'm missing something and I'd be grateful if someone pointed out the error of my ways. Also, I'm terrible at keeping things concise, so apologies there.

Thank you, once more, for your time!

On the 9th episode of Astronomy Cast, titled 'Einstein's Theory of Special Relativity', Dr. Gay gave an example with a common-to-SR moving train theme: A is inside the moving train with two mirrors placed perpendicular to A's body, one next to the crown of her head, one next to her feet. B is outside the train, on a field, with a similar mirror setup.

SR continues with respect time dilation with 'a moving clock ticks more slowly than when it is at rest with respect to the observer'.

Now, my dilemma. I wanted to convince myself with a little math, so I used one of the few equations I can handle comfortably: v = d/t

Since speed of light is the same for all observers, I gave v a meager 10 m/s for the sake of my calculating prowess. Let's say for B light travels 20 m in 2 s. So,

B: 10 m/s = 20 m / 2 s

Near A, light has to travel the extra distance because the train is moving so I gave it 25 m (correct me if this 'assumption', or all assumptions so far such as using 'sub-standard' formulas, is baseless).

Since v (= 10 m/s) shall remain the same, it's a matter of finding out the time light took to travel 25 m, which in this case is: t = 25m / 10 m/s = 2.5 s

The final time measurements read, A = 2.5 s, B = 2 s.

For the life of me, I can't understand how the moving clock, at A's position, is slower in this case.

I know I'm missing something and I'd be grateful if someone pointed out the error of my ways. Also, I'm terrible at keeping things concise, so apologies there.

Thank you, once more, for your time!