Crossing Symmetry

If a particle interaction

is observed to occur, then related interactions can be anticipated from the fact that any of the particles can be replaced by its antiparticle on the other side of the interaction. This is commonly known as "crossing symmetry". The observation of the above interaction implies the existence of the following interactions.

The overbar indicates the antiparticle. Crossing symmetry applies to all known particles, including the photon which is its own antiparticle. One example of the crossing principle is that of the relation between Compton scattering and electron-positron annihilation.

By examination, it can be seen that these two interactions are related by crossing symmetry. It could then be said that the observation of Compton scattering implies the existence of pair annihilation and predicts that it will produce a pair of photons.

Another example of crossing symmetry may have led Reines and Cowan to their experiment for the detection of the neutrino. If you take the electron product from the neutron decay reaction to the other side and convert it into a positron, then you have the reaction which they used.

Totalitarian Principle

From what we observe with massive particles, it would seem that any localized particle of finite mass should be unstable, since the decay into several smaller particles provides many more ways to distribute the energy, and thus would have higher entropy. Some have adopted the description "totalitarian principle" for this situation. It might be stated as "every process that is not forbidden must occur". From this point of view, any decay process which is expected but not observed must be prevented from occuring by some conservation law. This approach has been fruitful in helping to determine the rules for particle decay.

For example, with just conservation of energy and charge considered, one might expect a proton to decay into a positive pion plus a gamma ray to take away excess energy and conserve momentum:

The fact that neither this nor any other decay of the proton is observed suggests that the decay of the proton is forbidden by a strong conservation principle. This principle is called the conservation of baryon number, and no observed particle decays violate it. The proton does not decay because it is the least massive baryon, and has nowhere to go.

Another decay which was expected on energy and charge grounds was the decay of the neutron into a proton and an electron. The decay of the neutron is observed, but the fact that the electron does not have a definite energy implies that there is a third particle in the decay, the antineutrino.

The fact that the first of these decays did not occur suggested a prohibiting conservation law, which is called the conservation of lepton number.

Since the strengths of the interactions associated with particle decay descend in the order strong, electromagnetic and weak, it might be presumed that the strongest interaction would lead to the shortest lifetime, and that is what is observed. From experiments we can establish time regimes for the three types of interactions.

In the spirit of the "totalitarian principle", if you observed a decay in the 10^-16 s range you might guess that it is electromagnetic, and that some principle prevented it decay by the strong interaction. A 10^-10 s decay suggests that both strong and electromagnetic are somehow blocked.