Symmetries and Polarization

Abstract

In unpolarized cross sections constraints imposed by symmetries produce only quantitative changes which, in the absence of the precise knowledge of dynamics, cannot be used to test the validity of those symmetries. In polarization observables, in sharp contrast, imposition of symmetries produces qualitative changes, such as the vanishing of some observables or linear relationships among observables, which can be used to check the validity of symmetries without a detailed knowledge of dynamics. Such polarization observables can also separate the different constraints caused by different symmetries imposed simultaneously. This is illustrated for the two cases when Lorentz invariance and parity conservation, and Lorentz invariance and time reversal invariance, respectively, hold. It is also shown that it is impossible to construct, in any reaction in atomic, nuclear, or particle physics, a null experiment that would unambiguously test the validity of time-reversal invariance independently of dynamical assumptions. Finally, for a general quantum mechanical system undergoing a process, it is shown that one can tell from measurements on this system whether or not the system is characterized by quantum numbers the existence of which is unknown to the observer, even though the detection equipment used by the observer is unable to distinguish among the various possible values of the “secret” quantum number and hence always averages over them. This allows us to say whether the spin of a particle in a reaction is zero or not even if we can measure nothing about that particle’s polarization.