The Quantum Measure -- And How To Measure It


Sorkin, R. (2017). The Quantum Measure -- And How To Measure It. Perimeter Institute. https://pirsa.org/17030047


Sorkin, Rafael. The Quantum Measure -- And How To Measure It. Perimeter Institute, Mar. 07, 2017, https://pirsa.org/17030047


          @misc{ pirsa_PIRSA:17030047,
            doi = {10.48660/17030047},
            url = {https://pirsa.org/17030047},
            author = {Sorkin, Rafael},
            keywords = {Quantum Foundations},
            language = {en},
            title = {The Quantum Measure -- And How To Measure It},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {mar},
            note = {PIRSA:17030047 see, \url{https://pirsa.org}}

Rafael Sorkin Perimeter Institute for Theoretical Physics


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