Collisions and conservation laws
Collisions and conservation laws

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Collisions and conservation laws

7 Relativistic collisions

The high-energy collision experiments carried out at CERN, Brookhaven National Laboratory and other such facilities, involve particles that travel at speeds close to that of light. Under such circumstances the definitions of momentum and translational kinetic energy, that play such an important role in Newtonian mechanics, reveal certain shortcomings. It is still the case that translational kinetic energy is conserved in an elastic collision and that the momentum of an isolated system is always conserved, but the Newtonian expressions

bold p = m bold v and uppercase E sub trans = fraction 1 over 2 end m v squared

are now recognised as approximations, valid only at low speeds (i.e. at speeds much less than the speed of light), to more complicated expressions that work at any speed, up to the speed of light. The breakthrough that led to this realisation was the development of Einstein’s special theory of relativity in 1905. Here we shall quote a few of its well-established results concerning momentum and energy.

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