Before moving on to consider momentum and energy, there is one other aspect of special relativity that I have so far neglected: the invariance of the interval. Given any two points, A and B, in ordinary Newtonian space, the distance between them is the same whatever coordinate system we use. This is almost obvious. In [...]
SOLUTIONS [problems] 5. (addition of velocities) Answer: A moves with velocity u = (v + v′)/(1 + v v′) in frame F. Take F and F′ to coincide at t = t′ = 0, and assume A leaves the origin of F′ at t=0. Then at t′ = 1 in the F′ frame, A reaches [...]
A few further elementary points, presented as straightforward problems: Problems 5. (addition of velocities) A moves with speed v′ along the x′-axis of frame F′, which in turn is moving at speed v along the x-axis of frame F. What is the speed of A in frame F? 6. (Doppler shift) (i) A moves towards [...]
The solutions to the last batch of problems. Solution 2 The labelled rectangular frame (the horizontal and vertical lines through point G) is the coordinate frame in the earth frame. Spaceship A is moving to the right at speed 0.6. The two axes (x and t) for its rest frame (the frame in which it [...]
For the moment, we stick to the lab frame F and deal with situations where we can ignore the coordinates y and z, so the coordinates are just (x, t). Suppose an observer X is sitting at the origin x = 0. The time t is the time that something happens in the frame F. [...]
