Related papers: Probability in two deterministic universes
Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary…
We revisit the vexed question of how unpredictability can arise in a deterministic universe, focusing on unitary quantum theory. We discuss why quantum unpredictability is irrelevant for the possibility of what some people call `free-will',…
A new class of stochastic variables, governed by a specifice set of rules, is introduced. These rules force them to loose some properties usually assumed for this kind of variables. We demonstrate that stochastic processes driven by these…
In quantum logic, i.e., within the structure of the Hilbert lattice imposed on all closed linear subspaces of a Hilbert space, the assignment of truth values to quantum propositions (i.e., experimentally verifiable propositions relating to…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
It is argued that a realistic interpretation of quantum mechanics is possible and useful. Current interpretations, from Copenhagen to many worlds are critically revisited. The difficulties for intuitive models of quantum physics are pointed…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
In a recent paper (quant-ph/9906015), Deutsch claims to derive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." We show…
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly…
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…
QBism is currently one of the most widely discussed 'subjective' interpretations of quantum mechanics. Its key move is to say that quantum probabilities are personalist Bayesian probabilities and that the quantum state represents subjective…
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within…
I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…
Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…