THE PROBLEM IN A NUTSHELL CONCLUSION This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties. OVERVIEW Quantum collapse is a postulate in orthodox quantum mechanics, but it is poorly understood, though much has been written about it [1]. Here we point out that it also leads to a subtle internal tension in the theory when it is considered in conjunction with expressions that equate eigenstates with superposition states in a different basis because such expressions are consistent with a symmetry between states and observables under quantum superposition that is broken by quantum collapse. The tension can be relieved either by discarding the collapse postulate or by keeping it and considering pre-measurement and immediate post-measurement states to be of distinct kinds, in which case quantum collapse must be considered a transformation between two kinds of states. The basic strategy employed here is to convert a standard quantum mechanical relation into a logical equivalence, and then show that the imposition of the collapse postulate makes it possible to formulate an argument such that the truth value of the conclusion depends on which of the implications that are part of the equivalence is used, from which it is then possible to derive a contradiction.
THE PROBLEM IN A NUTSHELL CONCLUSION This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties. OVERVIEW Quantum collapse is a postulate in orthodox quantum mechanics, but it is poorly understood, though much has been written about it [1]. Here we point out that it also leads to a subtle internal tension in the theory when it is considered in conjunction with expressions that equate eigenstates with superposition states in a different basis because such expressions are consistent with a symmetry between states and observables under quantum superposition that is broken by quantum collapse. The tension can be relieved either by discarding the collapse postulate or by keeping it and considering pre-measurement and immediate post-measurement states to be of distinct kinds, in which case quantum collapse must be considered a transformation between two kinds of states. The basic strategy employed here is to convert a standard quantum mechanical relation into a logical equivalence, and then show that the imposition of the collapse postulate makes it possible to formulate an argument such that the truth value of the conclusion depends on which of the implications that are part of the equivalence is used, from which it is then possible to derive a contradiction.
The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.
Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are determinate, is unacceptably imprecise, and makes observation basic in fundamental physical theory, which looks like the wrong sort of process for the job. The problem of the interpretation of quantum mechanics is the problem of finding a more satisfactory understanding of the formalism in This project began in an independent study with Craig Callender, who provided much help in terms of direction, discussion, comments, and continuing support. Thanks also to Jerey Barrett for reading and commenting on an earlier draft of this paper, including helping me find some clearer and more economical way of putting some crucial points.
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the other). Hence, every time that a certain construal of reality encounters a problem, there is a choice between a modification to the mathematical formalism of the physical theory and a change in the model of reasoning. A case in point is negative construal of quantum superposition causing the problem of definite outcomes. To be sure, according to the said construal, it is not the case that a system being in a superposition of states is exclusively in one of the states constituting the superposition, which in turn implies that macroscopically differing outcomes of observation may appear all at once. The usual approach to the problem of definite outcomes is to modify the quantum mathematical formalism by adding to it some extra postulates (for instance, the postulate of wave function collapse). However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model of reasoning. This possibility is studied in the present paper.
Wave function collapse has long been regarded as a fundamental element of the quantum measurement process, providing a mechanism by which a superposed quantum state yields a single observed outcome. Despite its widespread use, the physical meaning of collapse remains conceptually controversial. In particular, it is often assumed that the quantities associated with a quantum state before measurement and the values obtained after measurement belong to the same conceptual category. This assumption leads naturally to the image of a discontinuous transition in which one value is selected from a superposition of possibilities. In the present work, we reexamine the concept of quantum collapse from the perspective of observability. We argue that pre-measurement quantities do not constitute observable values in the ordinary operational sense. Rather, they represent a structure of potential observability associated with possible measurement outcomes. By contrast, post-measurement outcomes correspond to operationally realized observability, in which a specific result becomes accessible through measurement. From this viewpoint, the apparent collapse does not represent a physical jump of an already existing value, but a transition from potential observability to operationally realized observability. Based on this distinction, we propose that many conceptual difficulties traditionally associated with wave function collapse arise from treating these two fundamentally different forms of observability as if they were physically equivalent. The apparent discontinuity of collapse may therefore originate not from a discontinuous change in reality itself, but from a conceptual conflation of potential observability and operationally realized observability. Within the Intrinsic Observability Framework (IOF), this interpretation naturally leads to the concept of accessibility transition, in which the emergence of a definite outcome is understood as a change in accessible structure rather than as a fundamental non-unitary state reduction. The present analysis suggests that wave function collapse may not be a fundamental physical phenomenon, but instead a consequence of the transition from potential observability to operationally realized observability. This perspective provides a conceptual reorganization of the measurement problem and clarifies the role of observability in the emergence of definite quantum outcomes.
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring system and a measured one. These properties result directly from the Schrödinger equation. They cannot be formulated in terms of observables, do not affect the wave functions themselves but express their history in an irreversible way. They carry a specific new kind of local probabilities, which evolve with a finite velocity under nonlinear wave equations. The second category of results extends these local properties to the case of a macroscopic system and its environment. Fluctuations in their interaction are predicted then and generate a specific incoherence in the quantum state of the system. These two kinds of effects act together when a macroscopic measuring system interacts with a measured system and with an environment. Their combination yields then an explicit and effective mechanism of collapse, with a random behavior resulting from random incoherence. Born's basic probability rule for the results of measurements turns out then simply a consequence of quantum dynamics. Some conjectures still enter into the derivation of these effects, which one may recognize to look hardly credible at first sight. They fit however so well together that one proposes a more thorough investigation of their approach as a promising strategy for a self-contained explanation of collapse.