An Abstract Theory of Physical Measurements

Bas C. van Fraassen

Abstract This chapter explores measurement ‘from above’: that is, looking for a view that we can have after the measurement procedures, concepts, and theories have stabilized. This resting point in the conceptual and scientific development is fleeting and momentary — yet marking a context in which some things can be taken for granted pro tem, where it makes sense to ask about the world-picture of currently accepted physical theory. The physical conditions of possibility for measurement, the general theory of measurement, and what cannot count as measurement in a theoretical context are discussed, drawing on general lessons derived from 20th-century foundations of physics.

Wolfgang Ernst Friederich Pauli

John F. Cyranski

O. Tapia

Beginning in abstract space and dislodging the representational form paves a way to formulate a version of a quantum physical measurement scheme. With materiality playing sustainment roles with respect to q-states, these latter control system response towards external probes. Sustainment concerns all possible q-states. The particle character usually assigned to eigenstates and eigenvalues dies out, while energy gaps relate to possible energy quanta exchanges; the occupancy concept no longer required. Abstract and laboratory spaces are incommensurate, linking them leads to a possible physical q-measurement theory. Connectors (links) are referred to as gangplanks and/or gangways, they perform in frontiers arbitrating quantum to classical regions. Inertial frames facilitate linking q-state domains via projection to wave function space. A physical quantum measurement theory obtains grounded on these elements including quantum information concepts.

Roger Balian

Carlo Maria Scandolo, G Chiribella

This is an extended abstract based on the preprint arXiv:1608.04459. We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms 'Causality, Purity Preservation, Pure Sharpness, and Purification' identify purity as a fundamental ingredient for every sensible theory of thermodynamics. Indeed, in physical theories satisfying these axioms, called sharp theories with purification, every mixed state can be modelled as the marginal of a pure entangled state, and every unsharp measurement can be modelled as a sharp measurement on a composite system. We show that these theories support a well-behaved notion of entropy and of Gibbs states, by which one can derive Landauer's principle. We show that in sharp theories with purification some bipartite states can have negative conditional entropy, and we construct an operational protocol exploiting this feature to overcome Landauer's principle