Related papers: Possibilities for Probabilities
The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|\psi\rangle$ is determined by $P(a)=|\langle a|\psi\rangle|^{2}$. Despite its great success in…
The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…
The transition from the quantum to the classical is governed by randomizing devices (RD), i.e., dynamical systems that are very sensitive to the environment. We show that, in the presence of RDs, the usual arguments based on the linearity…
The reason why orthodox quantum theory necessarily invokes consciousness is explained. Several procedures whereby the Born probability rule can be introduced are discussed, and reasons are given for prefering one in which consciousness…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of {\it non-local box}. The concept has been introduced from the principle of non-locality…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the…
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…
We formalize the hidden measurement approach within the very general notion of an interactive probability model. We narrow down the model by assuming the state space of a physical entity is a complex Hilbert space and introduce the…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum…
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…
In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…
We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability…
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…
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…
When a conscious observer is part of a quantum mechanical system, rule (4) cuts off solutions to the Schrodinger equation. It is important to show that this interruption of the Hamiltonian dynamics does not effect the statistical…
The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement…