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The Quantum Measure -- And How To Measure It

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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, acts as an $E$-pass filter. This raises the question whether in certain circumstances we can claim to know that the event $E$ actually did occur.


Alvaro Mozota Frauca and Rafael Dolnick Sorkin, How to Measure the Quantum Measure, Int J Theor Phys 56: 232-258 (2017), arxiv:1610.02087