The quantum measure - and how to measure it
Abstract:
When utilized appropriately, the path-integral offers an alternative to the ordinary quantum formalism of state-vectors, selfadjoint operators, and external observers - an alternative that seems closer to the underlying reality and more in tune with quantum gravity. The basic dynamical relationships are then expressed, not by a propagator, but by the *quantum measure*, a set-function mu that assigns to every (suitably regular) set E of histories its generalized measure mu(E). (The idea is that mu is to quantum mechanics what Wiener-measure is to Brownian motion.) Except in special cases, mu(E) cannot be interpreted as a probability, as it is neither additive nor bounded above by unity. Nor, in general, can it be interpreted as the expectation value of a projection operator (or POVM). Nevertheless, I will describe how one can ascertain mu(E) experimentally for any specified E, by means of an arrangement which, in a well-defined sense, filters out the histories that do not belong to E. This raises the question whether in certain circumstances we can claim to know that the event E actually did occur.