Related papers: Probability in two deterministic universes
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…
In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
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…
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
Quantum Darwinism posits that the emergence of a classical reality relies on the spreading of classical information from a quantum system to many parts of its environment. But what are the essential physical principles of quantum theory…
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should…
We develop a new formalism for constructing probabilities associated to the causal ordering of events in quantum theory, where by an event we mean the emergence of a measurement record on a detector. We start with constructing probabilities…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
This essay is a two-step reflection on the question 'Which events (can be said to) occur in quantum phenomena?' The first step regiments the ontological category of "statistical phenomena" and studies the adequacy of "probabilistic event…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…
I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as…
An intelligent agent will often be uncertain about various properties of its environment, and when acting in that environment it will frequently need to quantify its uncertainty. For example, if the agent wishes to employ the…
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 Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…