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I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep…
One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are the multi-time probability distributions estimated from the results of…
By probabilistic logic I mean a normative theory of belief that explains how a body of evidence affects one's degree of belief in a possible hypothesis. A new axiomatization of such a theory is presented which avoids a finite additivity…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default…
Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…