Related papers: Constructor Theory of Probability
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
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…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected…
The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion…
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (``cat" measurements) cannot make reliable predictions on the results of…
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for…
The Born rule asserts the probability distribution of eigenstates observed in unbiased quantum measurements, but the reason it holds remains elusive. This manuscript discusses how the Born rule might be explained by Schrodinger equation…
Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If…
How should we model an observer within quantum mechanics or quantum field theory? How can classical physics emerge from a quantum model, and why should classical probability be useful? How can we model a selective measurement entirely…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…
Quantum theory encounters a difficulty when attempting to describe recording devices. If the recording is of events in which quantum uncertainty plays a role, such as an experiment on a quantum system, quantum theory is unable to correctly…
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…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
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…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…