Related papers: Quantum mechanics from an epistemic state space
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
This paper addresses the question why quantum mechanics is formulated in a unitary Hilbert space, i.e. in a manifestly complex setting. Investigating the linear dynamics of real quantum theory in a finite-dimensional Euclidean Hilbert space…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…
This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the…
In computational physics it is standard to approximate continuum systems with discretised representations. Here we consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics - a discretisation where…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
In the present paper I show how it is possible to derive the Hilbert space formulation of Quantum Mechanics from a comprehensive definition of "physical experiment" and assuming "experimental accessibility and simplicity" as specified by…
Recently there has been much interest in deriving the quantum formalism and the set of quantum correlations from simple axioms. In this paper, we provide a step-by-step derivation of the quantum formalism that tackles both these problems…