Related papers: Quantum mechanics from five physical assumptions
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
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…
We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…
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…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
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…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
The three major theoretical principles of quantum mechanics relevant to its interpretation are: (T1), linearity; (T2), invariance under certain groups; and (T3) the orthogonality and isolation of the different branches of the state vector.…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Relational quantum mechanics (RQM) proposes an ontology of relations between physical systems, where any system can serve as an `observer' and any physical interaction between systems counts as a `measurement'. Quantities take unique values…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space [not equal to] spacetime. II. The arena of observations and, more generally, of all events (i.e.…