The Measurement Problem from the Perspective of an Information-Theoretic Interpretation of Quantum Mechanics

Abstract

The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems.

Situated observation in Bohmian mechanics

“…Even a theory that appeals to an implausible metaphysics may be useful in guiding one's application of quantum mechanics for predictive purposes. While clearly not the case with the 9 See Fuchs (2010), Healey (2012), andBub (2015) for diverse examples of the information-theoretic tradition. See Barrett (2020, 187-9) and Hagar and Hemmo (2006) for explanations of some of the limitations of information-theoretic formulations of quantum mechanics as even just predictive algorithms.…”

Von Neumann was not a Quantum Bayesian

“…A form of the idea is attributed to Democritus, 3 and Lucretius discussed it in verse. 4 Schrödinger commented, 'Quantum mechanics forbids statements about what really exists-statements about the object. Its statements deal only with the object-subject relation'.…”

“…A 'Quantum Bayesian' is one who interprets the probabilities arising in quantum physics according to some variety of the Bayesian view of probabilities. Given the profusion of schools of thought under the Bayesian umbrella, it should not be surprising that a variety of ways to be some kind of Bayesian about quantum theory has also arisen [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The most radical approach is QBism, which maintains that all quantum states are expressions of personalist Bayesian probabilities about potential future experiences [3,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

“…Democritus, fragment DK 68B9, which comes to us via Sextus Empiricus, Against the Mathematicians (ca 200), 7.136. The translation in K. Freeman's Ancilla to the Pre-Socratic Philosophers[65] is, 'We know nothing accurately in reality, but[only] as it changes according to the bodily condition, and the constitution of those things that flow upon [the body] and impinge upon it' 4. Lucretius, De Rerum Natura (ca 60-50 BCE), Book IV.…”

Quantum reaxiomatisations and information-theoretic interpretations of quantum theory

“…In particular, a research programme gradually developed of trying to reaxiomatise the theory in terms of broadly information-theoretic principles. That this programme might have implications for the traditional conceptual problems and for the interpretation of quantum theory is an idea which has been developed in stages by Jeff Bub, who has argued for what he calls an 'information-theoretic interpretation' of quantum theory (Bub [2000], Clifton et al [2003], Bub [2004Bub [ , 2005, Bub and Pitowsky [2010], Bub [2011Bub [ , 2014Bub [ , 2015). Throughout this work, Bub has been guided by an analogy with Einstein's use of postulates in special relativity.…”