Question

Special Relativity - Use space-time diagrams to propose a resolution to the runner on the train paradox.

Answer 1

The paradox: A train travels at a high speed, v, wrt the Earth. A runner on the train sprints toward the back of the train at velocity, v, wrt the train.
Clocks on the train should run slow compared to Earth clocks. The runner's clock should run slow compared to the train clock. Therefore the runner's clock should run doubly slow compared to the Earth clock. But the runner is not moving wrt the Earth!

Answer 2

@roadjester

Answer 3

My own professor never went in depth into space-time diagrams so i can't help you there. But I've got my own hw on quantum physics so I'll leave you with this:
http://www.physicsforums.com/showthread.php?t=186678
look at the explanation by "Janus".
Hope this helps.

Answer 4

What's wrt?

Answer 5

\(\LARGE \color {red} w\)ith \(\LARGE \color {red} r\)espect \(\LARGE \color {red} t\)o

Answer 6

help

Answer 7

DO you understand conceptually how the paradox is solved

Answer 8

@Mashy that's what I'm trying to understand

Answer 9

This is a blank spacetime diagram. The (x,t) coordinates are the reference frame of an observer on the ground, while the (x',t') coordinates are the reference frame of an observer sitting on the train.

Answer 10

The solid black line shown here is the worldline of an individual at rest in the unprimed reference frame (ground). Notice that his x-coordinate is constant.

As a reference, I've also drawn another dotted line, which would be the worldline of an individual at rest in the *primed* reference frame (train). It should be clear that while the individual's x-coordinate (i.e. position relative to the ground) is constant, the individual's x' - coordinate (the position relative to the train) is decreasing, getting closer and closer to the t' axis.