Toward an Interpretation-Free Formulation of Quantum Theory: Fisher Statistics, Bayesian Statistics, Kalman Filtering, and Wigner's Friend in Observable System Theory
I have proposed OST (Observable System Theory) as a foundational theory of system theory.3 This theory adopts two principles, namely, the Born principle and the Causal principle, and furthermore explicitly uses the one-shot measurement principle as a rule of use. OST is one of the most fundamental scientific theories, alongside mathematics and physics, and it can provide a unified framework for discussing quantum mechanics (information), statistics (system theory), practical logic, epistemology (philosophy), statistical mechanics, and so on.In this paper, I clarify that Fisherian statistics, Bayesian statistics, and quantum mechanics share a common mathematical foundation, namely OST. In statistics, an OST-based understanding of the Kalman filter is presented. Moreover, the so-called “interpretation problem” of quantum mechanics after measurement is unnecessary, and the “Wigner’s friend paradox” is resolved within OST. In addition, the FR paradox (= Frauchiger–Renner paradox) is understood as a paradox arising from the violation of the one-shot measurement principle, and thus it suggests the validity of OST. Through these discussions, I claim the following two points:(i) OST-based statistics will, in the future, become the standard understanding of statistics.(ii) OST-based quantum mechanics is the final form of von Neumann-style quantum mechanics
I have proposed OST (Observable System Theory) as a foundational theory of system theory.3 This theory adopts two principles, namely, the Born principle and the Causal principle, and furthermore explicitly uses the one-shot measurement principle as a rule of use. OST is one of the most fundamental scientific theories, alongside mathematics and physics, and it can provide a unified framework for discussing quantum mechanics (information), statistics (system theory), practical logic, epistemology (philosophy), statistical mechanics, and so on.In this paper, I clarify that Fisherian statistics, Bayesian statistics, and quantum mechanics share a common mathematical foundation, namely OST. In statistics, an OST-based understanding of the Kalman filter is presented. Moreover, the so-called “interpretation problem” of quantum mechanics after measurement is unnecessary, and the “Wigner’s friend paradox” is resolved within OST. In addition, the FR paradox (= Frauchiger–Renner paradox) is understood as a paradox arising from the violation of the one-shot measurement principle, and thus it suggests the validity of OST. Through these discussions, I claim the following two points:(i) OST-based statistics will, in the future, become the standard understanding of statistics.(ii) OST-based quantum mechanics is the final form of von Neumann-style quantum mechanics
I have proposed OST (Observable System Theory) as a foundational theory of system theory. Roughly speaking, OST is a theory that unifies statistics and quantum mechanics. In comparison with ordinary statistics, its main advantage is that it possesses an explicit axiomatic structure. In this sense, I have claimed the following two points:(i): OST will, in the future, become the standard understanding of statistics.(ii): OST-based quantum mechanics is the final form of von Neumann-style quantum mechanics.Statistical mechanics, however, involves microscopic states, probability distributions, Gibbs states, coarse graining, time evolution, thermodynamic limits, and so on. For this reason, a complete axiomatization of statistical mechanics is generally regarded as difficult. In the present paper, we propose a different strategy: the system-theoretical part of statistical mechanics is formulated by means of the axiomatic structure of OST, while the remaining parts are treated in the conventional way, withoutforcing them into a single axiomatic system.The aim of this paper is to understand statistical mechanics in the language of OST. In other words, the parts of statistical mechanics in which statistics has traditionally been used are here reformulated by means of OST. Thus, statistical mechanics is examined from the viewpoint of the three-term structure: state, observable, measured value. Although this is only a partial axiomatization, it nevertheless allows us to make the following claim: (iii): OST-based statistical mechanics will, in the future, become the standard understanding of statistical mechanics.This should be regarded as a corollary of (i) above. At least from the foundational viewpoint of how statistical mechanics should be read as a descriptive specification, the author believes that the OST-based understanding of statistical mechanics is more natural than the conventional one.
Roughly a quarter of a century ago, the author proposed "Observable System Theory" (OST) as a foundational theory of systems theory. OST describes both statistics and quantum mechanics within a single framework of state–observable–measured value, governed by two explicitly formulated principles: the Born principle and the causal principle. This paper examines Bayesian networks (BNs) from the standpoint of OST, with particular attention to the following fundamental question: what, ultimately, do DAG calculations compute? The answer proposed here is that DAG calculations ultimately compute the probabilistic causality of measured values. Accordingly, OST admits two distinct notions of causality. The first is the causal evolution of states—equivalently, the causal evolution of observables in the Heisenberg picture—governed by OST's causal principle. The second is the probabilistic dependence structure among measured values, represented by a directed acyclic graph (DAG) together with local conditional probability distributions. The main result of this paper is the following fundamental theorem: for every finite Bayesian network specified by a DAG and local conditional probability distributions, there exists a corresponding measurement in OST whose outcome distribution coincides exactly with the joint probability distribution generated by the Bayesian network. We also aim to dispel the notion that theories involving multiple, distinct kinds of causal relation—such as Aristotle's doctrine of the four causes—are inherently untenable. Keywords: Observable System Theory; Bayesian network; directed acyclic graph; measurement; measured value; measurement probability.
Schrodinger's cat and Wigner's friend paradoxes are analyzed using the `wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' and are shown to be non-paradoxes within the quantum formalism. Then, the extended version of Wigner's friend thought experiment, proposed in a recent article titled, ``Quantum theory cannot consistently describe the use of itself '', Nature Communications {\bf 9}, 3711 (2018), by Frauchiger and Renner (FR) is considered. In quantum mechanics, it's well-known that, statistically observing a large number of identical quantum systems at some particular quantum state, which results in Born's probability, and merely inferring its presence in the same quantum state with the same probability yield distinct physical phenomena. If this fact is not taken care while interpreting any experimental outcomes, then FR type paradoxes pop up. ``What an astonishingly self-consistent the Quantum Theory is!' - is explicitly worked out in the case of FR gedankenexperiment. The present work shows the importance of single-quantum phenomenon for the non-paradoxical interpretation of statistically observed experimental outcomes.
This paper offers a comprehensive analysis of Wigner’s Friend paradox (1961), a foundational thought experiment in quantum mechanics that highlights the tension between the internal perspective of a measuring observer (who experiences a definite outcome) and the external perspective of a super-observer who treats the entire laboratory as a quantum system in superposition. It traces the historical lineage from Schrödinger’s cat and von Neumann’s measurement theory, provides a formal mathematical description of the state evolution and logical structure of the paradox, examines implications for major interpretations of quantum mechanics (Copenhagen, Everettian many-worlds, QBism, relational quantum mechanics, and objective collapse theories), and discusses modern extensions such as the Frauchiger–Renner paradox. The work explores profound philosophical and epistemological consequences for the nature of observation, objectivity, intersubjectivity, and the role of consciousness in quantum theory (2026).
By assuming (i) a universal, observer-independent quantum state, by considering (ii) measurement processes with wave function collapse as part of quantum mechanical time evolution (also within isolated systems), and by (iii) clearly distinguishing the state of a quantum system from the knowledge of conscious observers about this state, we suggest a modified Copenhagen interpretation of quantum mechanics that resolves Wigner's Friend and extended Wigner's Friend paradoxes. The suggested interpretation leads to differences in some outcome probabilities compared to previous analyses which, in principle, make it possible to falsify the suggested modifications or the previous analyses (or both). The fundamental problem of the incompleteness of quantum mechanics in the Copenhagen interpretation regarding the lack of a precise definition and a mechanistic description of the measurement process (including the collapse of the wave function) is not addressed in this study. However, the argumentation regarding the resolution of Wigner's Friend paradoxes also applies to attempts for such a mechanistic description using collapse models with stochastic extensions to the Schrödinger equation or trying to model wave function collapse with unitary time evolution and irreversibility of the measurement process resulting from quantum statistical mechanics.
Recently, we proposed measurement theory ( or. quantum language) as a linguistic turn of quantum mechanics (with the Copenhagen interpretation). This theory has a great power of scientific descriptions. In fact, we have continued asserting that even statistics can be described in terms of measurement theory. Thus, we believe that quantum language is future statistics (i.e., statistics will develop into quantum language). However, now we think that our arguments were too abstract and philosophical, that is, we should have presented concrete examples much more. Thus, in this paper, we show that the calculation of Kalman filter is more understandable in terms of quantum language than in terms of usual statistics. For this, we devote ourselves to statistical measurement theory, in which the Bertrand paradox is discussed.