Related papers: Quantum Mechanics with Extended Probabilities
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is…
According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be…
A formulation of quantum mechanics based on an operational definition of state is presented. This formulation, which includes explicitly the macroscopic systems, assumes the probabilistic interpretation and is nevertheless objective. The…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…
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…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
A quantum theory of the universe consists of a theory of its quantum dynamics and a theory of its quantum state The theory predicts quantum multiverses in the form of decoherent sets of alternative histories describing the evolution of the…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
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…
By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…
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…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
I review the decoherent (or consistent) histories approach to quantum mechanics, due to Griffiths, to Gell-Mann and Hartle, and to Omnes. This is an approach to standard quantum theory specifically designed to apply to genuinely closed…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
According to quantum theory, the outcomes of future measurements cannot (in general) be predicted with certainty. In some cases, even with a complete physical description of the system to be measured and the measurement apparatus, the…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
We introduce a condition for the strong decoherence of a set of alternative histories of a closed quantum-mechanical system such as the universe. The condition applies, for a pure initial state, to sets of homogeneous histories that are…