- #1

In the section about converting between different frames of reference, the author explains that the coordinates for measuring position are x for east-west direction, y for north-south, z for up-down and t for time. He then gives coordinates for three measurements made from two different frames of reference, Emmy’s and Nero’s:

Emmy:

(t = -1s; x = -10m; y = -10m; z = 0m)

(t = 0; x = 0m; y = -10m; z = 0m)

(t = +1s; x = +10m; y = -10m; z = 0m)

Nero:

(t = -1s; x = +10m; y = +10m; z = 0m)

(t = 0; x = 0m; y = +10m; z = 0m)

(t = +1s; x = -10m; y = +10m; z = 0m)

He goes on to say:

“If you play around with these numbers a little, you can come up with a simple recipe for converting between Nero’s measurements and Emmy’s: you simply take the east-west coordinate measured by Nero, and subtract his speed (10 m/s) multiplied by the time. A little more fiddling around will show you that getting from Emmy’s measurement to Nero’s involves just the reverse: you take the east-west coordinate measured by Emmy, and add to it Nero’s speed multiplied by the time. In this way, you can take any measurement made by Nero and convert it into a measurement that will make sense to Emmy, and vice versa.”

No matter how much I try, I can’t get from one frame of reference to the other by following these directions. I’m clearly missing something very obvious! Could anyone shed some light?