Related papers: Born's rule and permutation invariance
We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…
In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
The existence of precise particle trajectories in any quantum state is accounted for in a consistent way by allowing delocalization of the particle charge. The relativistic mass of the particle remains within a small volume surrounding a…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
A quantum version of the Lighthill equation that originated in the field of theoretical aeroacoustics is derived for the probability density of a superfluid starting from the time-dependent Gross-Pitaevskii equation. It involves a…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional $\Psi$, must be in quantum nonequilibrium with a probability distribution $P\neq\left\vert…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of…
We study a system in which the quantum dynamics of electrons depend on the particle density in their neighborhood. For any on-site repulsive interaction, we show that the exact two-body and three-body ground states are bound states. We also…
We introduce a permutationally invariant multipartite Bell inequality for many-body three-level systems and use it to investigate a connection between Bell nonlocality and (lack of) quantum chaos. An associated Bell operator is then defined…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…