guy incognito
Well-Known Member
Your first question:Two cars are traveling towards each other on a road. One car has a speed of 30 MPH along the road, the other car has a speed of 70 MPH along the road. The distance between them is closing at the rate of 100 MPH. Each driver observes the distance between them as closing at that rate. According to SR, does each driver see the same number of meter sticks between them at every point in time? What I'm getting at is, if the distance between the cars in the road frame is 100 miles, and each driver sees that distance closing at the rate of 100 MPH, then all the frames (road, driver a, and driver b) see that distance as 100 miles, and they also see the time elapsing at the same rate, correct?
Yes, both drivers see the same number of meter sticks between them. A person standing at the burger king DOES NOT. At relative speeds of 100mph the lorentz factor approaches 1. "sqrt(1-(v/c)^2)" = 1 when v <<< c
Say that instead of 30mph and and 70mph they are going .31c and .71c (as measured from the ground). The person at the burger king (in the same frame as the ground) measures them at 0.31c and 0.71c. He calculates their closing speed to be 1.02c, FASTER than the speed of light! thats insane! But what does the driver see? When they measure the other drivers speed he measures some value slightly less than the speed of light.
Say that the burger king measures each of the cars speeds to be .99c. He then measures their closing speed to be 1.98c. Each driver still perceives the other driving to be driving at LESS than the speed of light. This is the reason your box diagram does not make sense. I can measure a closing speed between the light and the sensors from MY point of view and calculated the speed you are moving RELATIVE to me. Inside the cube though you will measure the speed of light to be exactly c REGARDLESS of your direction or speed or the light sources direction or speed.
I know it seems crazy and counter intuitive, but that is simply how it works. No matter where or when you measure the speed of light, even if you are moving, or if the light source is moving, you WILL measure it to be exactly c, and that has been proven by experiment after experiment.