This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called “Epistemic Constraint.” Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called “Epistemic Constraint.” Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called "Epistemic Constraint." Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid's fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory tells the story of a conceptual protagonist I have called “Epistemic Constraint.” Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive epistemic constraints from within quantum mechanics, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, this dissertation develops the Bohrian Program, which has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. The approach therefore slightly expands the list of what is considered primitive in the foundations of quantum theory.
This doctoral dissertation on the foundations of quantum theory isolates and formalizes physical knowability constraints, understood here as constraints on what any conceivable observer can know about the physical world; I henceforth call these “epistemic constraints” for terseness. Here, epistemic constraints concern the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
This doctoral dissertation on the foundations of quantum theory isolates and formalizes physical knowability constraints, understood here as constraints on what any conceivable observer can know about the physical world; I henceforth call these “epistemic constraints” for terseness. Here, epistemic constraints concern the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid’s fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical values to them. In an epistemic process, the accessible variables are just ideal observations as observed by an actor or by some communicating actors. Group actions are defined on these variables, and using group representation theory this is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible conceptual variables are derived as a result of the formalism, and in the discrete case it is argued that the possible physical values are the eigenvalues of these operators. The Born formula is derived under specific assumptions. The whole discussion here is a supplement to the author's book [1]. The interpretation of quantum states (or eigenvector spaces) implied by this approach is as focused questions to nature together with sharp answers to those questions. Resolutions if the identity are then connected to the questions themselves; these may be complementary in the sense defined by Bohr. This interpretation may be called a general epistemic interpretation of quantum theory. It is similar to Zwirn's recent Convival Solipsism, and also to QBism, and more generally, can be seen as a concrete implementation of Rovelli's Relational Quantum Mechanics. The focus in the present paper is, however, as much on foundation as on interpretation. But the simple consequences of an epistemic interpretation for some so called quantum paradoxes are discussed. Connections to statistical inference theory are discussed in a preliminary way, both through an example and through a brief discussion of quantum measurement theory.
The measurement problem in quantum mechanics (QM) is related to the inability to include learning about the properties of a quantum system by an agent in the formalism of quantum theory. It includes questions about the physical processes behind the measurement, uniqueness, and randomness of obtained outcomes and an ontic or epistemic role of the state. These issues have triggered various interpretations of quantum theory. They vary from refusing any connection between physical reality and a measurement process to insisting that a collapse of the wave-function is real and possibly involves consciousness. On the other hand, the actual mechanism of a measurement is not extensively discussed in these interpretations. This essay attempts to investigate the quantum measurement problem from the position of the scientific consensus. We begin with a short overview of the development of sensing in living organisms. This is performed for the purpose of stressing the relation between reality and our experience. We then briefly present different approaches to the measurement problem in chosen interpretations. We then state three philosophical assumptions for further consideration and present a decomposition of the measurement act into four stages: transformation, conversion, amplification and broadcasting, and, finally, perception. Each of these stages provides an intuition about the physical processes contributing to it. These conclusions are then used in a discussion about, e.g., objectivity, the implausibility of reversing a measurement, or the epistemic status of the wave-function. Finally, we argue that those in favor of some of the most popular interpretations can find an overlap between their beliefs and the consequences of considerations presented here.