In the Stanford linear collider, small bundles of electrons and positrons are fired at each other. In the laboratory’s frame of reference, each bundle is about 1 cm long and 10 μm in diameter. In the collision region, each particle has an energy of 50 GeV, and the electrons and positrons are moving in opposite directions.

(a) How long and how wide is each bundle in its own reference frame?

(b) What must be the minimum proper length of the accelerator for a bundle to have both its ends simultaneously in the accelerator in its own reference frame? (The actual length of the accelerator is less than 1000 m.)

(c) What is the length of a positron bundle in the reference frame of the electron bundle?