It has been proved1 that there exists no null test of time-reversal invariance (TRI) in nuclear and particle physics in any reaction with two particles in and two particles out. That is, there is no single experimental observable that is required to be zero by TRI. This follows from the fact that TRI equates a reaction observable to an observable in the inverse reaction, so the difference (or sum) of the two is zero. Even in elastic scattering, which is its own inverse reaction, two different observables are related by TRI; e.g., polarization and analyzing power, so that Ay − Py = 0. Because of this requirement to compare two experimental observables, one of which is often difficult to measure with precision (say 1%), it is easy to understand why such tests of T-symmetry have rarely attained the 1% level of experimental accuracy. In strong contrast, since null tests of parity conservation are available, e.g. Az = 0 from P-symmetry, the weak-interaction parity non-conserving contribution to Az in pp scattering has been determined to the truly remarkable accuracy of 2.2 × 10−8 (ref. 2). Thus, it is clear that a comparable null test of T-symmetry would permit an improvement in experimental precision of several orders of magnitude.