Related papers: Logical Structure of Physical Probability Assertio…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
Quantum mechanics is reformulated using Hartle's definition of the state of an individual physical system and a variant of von Neumann's propositional calculus. An elementary set of quantum postulates lead inductively to the familiar…
Most quantum logics do not allow for a reasonable calculus of conditional probability. However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics as well as…
We show that when the thermal wavelength is comparable to the spatial size of a system, thermodynamic observables like Pressure and Volume have quantum fluctuations that cannot be ignored. They are now represented by operators; conventional…
We put forward a new take on the logic of quantum mechanics, following Schroedinger's point of view that it is composition which makes quantum theory what it is, rather than its particular propositional structure due to the existence of…
Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical…
It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the…
Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Probability theory as extended logic is completed such that essentially any probability may be determined. This is done by considering propositional logic (as opposed to predicate logic) as syntactically suffcient and imposing a symmetry…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
This paper proposes a basic theory on physical reality, and a new foundation for quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization procedure, but…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…