Related papers: Quantum Theory of Probability and Decisions
What are quantum entities? Is the quantum domain deterministic or probabilistic? Orthodox quantum theory (OQT) fails to answer these two fundamental questions. As a result of failing to answer the first question, OQT is very seriously…
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
The review presents the basics of quantum decision theory, with the emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. The difference of an operationally testable rational choice…
It is shown that the Pauli equation and the concept of spin naturally emerge from logical inference applied to experiments on a charged particle under the conditions that (i) space is homogeneous (ii) the observed events are logically…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
Core quantum postulates including the superposition principle and the unitarity of evolutions are natural and strikingly simple. I show that -- when supplemented with a limited version of predictability (captured in the textbook accounts by…
In this paper one generalizes the classical probability and imprecise probability to the notion of "neutrosophic probability" in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior, Schr"dinger's Cat…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Quantum mechanics has enjoyed a multitude of successes since its formulation in the early twentieth century. At the same time, it has generated puzzles that persist to this day. These puzzles have inspired a large literature in physics and…
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…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalisation is possible by reducing the number of quantum postulates used by Busch.…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual…
The familiar "modulus squared" form of all quantum mechanical probabilities is derived from an assumption of equal a priori probabilities concerning the final states available.
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…