In the past, most experiments in particle physics involved stationary targets: one parti...

In the past, most experiments in particle physics involved stationary targets: one particle (usually a proton or an electron) was accelerated to a high energy E, and collided with a target particle at rest (Fig. 12.29a). Far higher relative energies are obtainable (with the same accelerator) if you accelerate both particles to energy E, and fire them at each other (Fig. 12.29b). Classically, the energy of one particle, relative to the other, is just 4E (why?) . . . not much of a gain (only a factor of 4). But relativistically the gain can be enormous. Assuming the two particles have the same mass, m, show that

Suppose you use protons (mc² = 1 GeV) with E = 30 GeV. What do you get? What multiple of E does this amount to? (1 GeV=10⁹ electron volts.) [Because of this relativistic enhancement, most modern elementary particle experiments involve colliding beams, instead of fixed targets.]