Related papers: Are All Probabilities Fundamentally Quantum Mechan…
How can quantum mechanics be (i) the fundamental theoretical framework of contemporary physics and (ii) a probability calculus that presupposes the events to which, and on the basis of which, it assigns probabilities? The question is…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
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…
Probability interference is a fundamental characteristic of quantum mechanics. In this paper we attempt to show with the help of some examples, where this fundamental trait of quantum physics can be found back in a social science…
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…
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of "classical" is often not…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical…
A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
In Mod. Phys. Lett. A 9, 3119 (1994), one of us (R.D.S) investigated a formulation of quantum mechanics as a generalized measure theory. Quantum mechanics computes probabilities from the absolute squares of complex amplitudes, and the…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
We present a fully local treatment of the double slit experiment in the formalism of quantum field theory. Our exposition is predominantly pedagogical in nature and exemplifies the fact that there is an entirely local description of the…
A new wave-particle non-dualistic interpretation for the quantum formalism is presented by proving that the Schr\"odinger wave function is an `{\it instantaneous resonant spatial mode}' in which the quantum particle moves. The probabilities…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…