Time-reversal asymmetry and state-vector collapse

A sentence in the Search and Discovery story “Time-reversal asymmetry in particle physics has finally been clearly seen” (Physics Today, November 2012, page 16 ) has me somewhat puzzled. Bertram Schwarzschild writes, “If the first decay of a daughter reveals it to have been in a specific flavor or CP eigenstate, her still undecayed sister must—at that instant—be in the opposite state.” What is implicit in this sentence is that state-vector collapse takes place at the decay of the first B meson, so that the second meson is instantaneously projected onto the opposite state.

I have two objections to this sentence. First, it is not relativistically invariant: Because the two events—decay of the first meson and “transformation” of the second—have spacelike separation, their time ordering is not defined. Second, the decay is governed by a relativistic version of the Schrödinger equation, which is reversible, whereas state-vector collapse is, by nature, irreversible.

It is instructive to make a comparison with the analysis of a Bell-type experiment, in which a two-particle observable is measured via two detectors that are far apart, with each measuring the spin of one of the two particles. The quantum mechanical result is given by applying Born’s rule to the two-particle observable.

The two experimentalists, Alice and Bob, then compare their results by exchanging them at a speed less than that of light, and they notice the results are correlated, in conformity with the theoretical predictions of nonlocal correlations. The same theoretical results may be derived from state-vector collapse: When Alice measures the first spin, Bob’s spin is projected instantaneously onto a well-defined polarization state; correlations may be easily computed and are, of course, in agreement with those derived from Born’s rule.

State-vector collapse is strictly equivalent to Born’s rule in a nonrelativistic context, but I think it is safer to use Born’s rule when special relativity comes into play. Indeed, to the best of my knowledge, there is no satisfactory relativistic generalization of state-vector collapse, which is understandable since simultaneity is not defined for two spacelike separated events. Therefore, a full justification of the argument used in the Physics Today report should begin with state-vector collapse taking place in a well-defined reference frame at the instant when the decay products of the B mesons reach the detectors. Then, from the correlations observed between the results of the detectors, it should be possible to reconstruct the decays and show that they can be interpreted as an effective state-vector collapse.

Such an analysis would likely vindicate that of the BaBar experiment, but as the use of Einstein-Podolsky-Rosen correlations goes far beyond the usual one, it should be fully justified.