So what does special relativity tell us about the example of someone (Karen) traveling in space vs someone (Susan) standing still on earth
- nothing can travel faster than the speed of light (in a vacuum), and nothing can ever reach the speed of light
- Karen is in a spaceship moving with velocity v, Susan is stationary, watching the ship with Karen and a lamp in it --> if you observe anyone or anything moving by you at a speed close to the speed of light, you will conclude that time runs more slowly for that person (in space) - they age more slowly, clock moving by ticks more slowly than your clock.
- if you observe 2 events simultaneously (flashes of light in 2 different places at the same time), the two events will not appear to be simultaneous if one is moving close to the speed of light --> light goes off in spaceship, travels in a straight line, directly across the spaceship. (Travels at a distance d, at velocity c, and takes an amount of time - time
_{karen} = c/d) to get there).
- In classical physics (WRONG), the velocity of light, c, would be added with the velocity of the spaceship, to find the total velocity of light. So the principle of relativity says - the speed of light is the same for all observers (even ones moving at different velocities) - WRONG
- - Implies - time flows at a different rate for observers moving at different velocities
- t_{s} = t_{k} / √(1 - (v/c)2)
- thus, when susan looks at Karen, it looks like time on the spaceship is flowing more slowly - karen herself is moving slower. But to Karen, its susan who appears to be moving slower.
if you measure the size of something moving by you at close to the speed of light, you will find that its length (in the direction of its motion) is shorter than it would be if the object were not moving, mass would be greater than if it were stationary