Related papers: Born's rule from almost nothing
An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this…
We prove an analogue of the classical ballot theorem that holds for any random walk in the range of attraction of the normal distribution. Our result is best possible: we exhibit examples demonstrating that if any of our hypotheses are…
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…
Many structures in nature are invariant under the transformation (p,r)->(br,-p/b), where b is some scale factor. Born's reciprocity hypothesis affirms that this invariance extends to the entire Hamiltonian and equations of motion. We…
In recent papers, Zurek has objected to the decision-theoretic approach of Deutsch and Wallace to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds…
The paper discuss the structure of quantum mechanics and uniqueness of its postulates. The Born rule for quantum probabilities is fixed by requirement of nonexistence of quantum telepathy. Von Neumann projection postulate describes the…
We show that quantum probabilities can be derived from statistical mechanics of classical fields. We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
Quantum mechanics has lacked a widely recognized interpretation since its birth. Many of these are still under consideration because interpretations are tough or impossible to disprove experimentally. We show how to distinguish…
We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a…
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…
This work is an attempt to justify Born's rule within the framework of the many-minds interpretation seen as a development of the many-worlds interpretation of Everett. More precisely, here we develop a unitary model of many-minds based on…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
According to Born's rule quantum probabilities are given by the overlap between the system state and measurement states in a quite symmetrical way. This means that both contribute to any observed nonclassical effect that is usually…
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
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…
It is shown that the probability density satisfies a hyperbolic equation of motion with the unique characteristic that in its many-particle form it contains derivatives acting at spatially remote regions. Based on this feature we explore…
I argue that various derivations of the Born probability rule within strictly unitary quantum mechanics implicitly use anthropic constraints on the properties of the probabilities, but without proposing an ensemble from which those…
Sufficient conditions are given for a function $F(p)$ to be the Laplace transform of a function $f(t)$ or a distribution $f$. No assumption on $f$ is given a priori. It is not even assumed that $f=0$ for $t<0$.
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…