Postby kroner » Wed Mar 17, 2004 4:38 am
Oh, now you've put me on the spot to explain special relativity... Ok, let's see if I can do this...
The speed of light is constant in all reference frames. This is the most importnat point.
Consider the following situation: You are in a very fast box car going at speed v, while I am standing next to the train watching.
Alright, so the first point is time dialation. A flaslight shines some light from the cieling of the train car straight down. To you, the light goes at the speed of light c and reaches the floor in h/c time where h is the height of the car.
Now to me, the light also goes at the speed of light c, but the light goes a different distance. While its going down, the car has also moved forward a distance of v*t. By the pythagorian theorem, the distance i see it go is not h, but sqr(h^2 + (v*t)^2). So if the distnce per time was the same but the distance traveled is different, the time for the same event has to be different. The time I experience must be longer.
While the for you the event takes t = h/c, for me, t = sqr(h^2 + (v*t)^2)/c. solve for t to get t = (h/c)*(1/sqr(1- (v/c)^2)). in other words, time goes faster for you by a factor of γ = 1/sqr(1- (v/c)^2).
Now comes the concept of there being no definition of simultaneous events. You shine two flashlights from the middle of the car towards each end. to you, both beams travel the same distance d and hit the ends of the car in the same amount of time t = d/c, but to me, the back end of the car comes up to meet the one light beam so that it only has to travel a distance of d - v*t1 in time t1 = d/(c + v), and the front end of the car moves away from the light and so it has to travel distance d + v*t2 in time t2 = d/(c - v). now obviously if the events started at the same time but took different amounts of time to complete, they didn't finish at the same time. to me the difference in time between the events at distance 2d apart is 2d*v/(c^2-v^2), even though to you they were simultaneous. from this we see that simultaneous events at different locations are not simultaneous from other reference frames.
I hope with these two principals, it becomes a bit more clear how relativity works and the speed of light can be constant in all reference frames. There is also length contraction and mass dialation but I won't get into that.
Last edited by
kroner on Wed Mar 17, 2004 4:40 am, edited 1 time in total.
DOOM!