Related papers: Generalization of the Born rule
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
The problem of relating the mathematics of probability theory to the empirical world of experiments has been debated for centuries. One of the oldest solutions proposed for this problem is a principle that states that an event with…
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…
Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's…
Reichenbach's principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Typicality has always been in the minds of the founding fathers of probability theory when probabilistic reasoning is applied to the real world. However, the role of typicality is not always appreciated. An example is the paper "Foundations…
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…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…