We know, from direct observation of the most distant visible objects in the universe, that the laws of physics and fundamental constants of nature are the same there as here on earth. Atoms of the same kind have the same spectra where ever they are in the universe. In 1915 Albert Einstein and David Hilbert asked Emmy Noether to investigate whether Einstein's theory of gravity obeyed the conservation of energy. Noether found a direct connection between conservation laws and continuous symmetry operations. Energy is conserved if one point in time in empty space is as good as any other. Momentum is conserved if one point in empty space is as good as any other. Angular momentum is conserved if one orientation of a system in empty space is as good as any other. In quantum physics, the momentum operator generates translation of a system in space, while the energy operator generates translation in time and the angular momentum operator generates space rotations.

Continuous symmetries such as described by Noether's theorem are (as far as we know) generated by quantities that are exactly conserved. However, in the first half of the 20th Century, physicists found an important new class of symmetries known as discrete symmetries. Discrete symmetries are like “on-off switches.” The most famous is the parity operator, P. This operator changes polar vectors (such as r) to their negative value, −r.  It does not affect axial vector operators such as angular momentum and spin.  It came as a huge shock to physicists in the 1950s to find that parity is conserved exactly in processes involving the electromagnetic and strong interactions, but is not conserved, by the maximum amount physically possible, in all weak interactions! Since there are two other very important discrete symmetry operators, charge conjugation C, which changes the sign of all additive quantum numbers, and time reversal T, which changes t to −t (and also complex conjugates!), physicists became immediately concerned about the corresponding conservation laws. They also became very suspicious of any quantity which appears to be conserved precisely in experiments, but is not the generator of any kind of symmetry.  Examples are baryon number B and lepton number L.