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 energy of 40×109 eV, and the electrons and positrons are moving in opposite directions.
1. How long and how wide is each bundle in its own reference frame?
2. 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).
3. What is the length of a positron bundle in the reference frame of the electron bundle?
4. What are the momentum and energy of the electrons in the rest frame of the positrons?