Related papers: Born Again
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inflation. It has recently been argued that when identical copies of a quantum measurement system exist,…
Proponents of the Everett interpretation of Quantum Theory have made efforts to show that to an observer in a branch, everything happens as if the projection postulate were true without postulating it. In this paper, we will indicate that…
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the…
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…
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 Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
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…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
Without Niels Bohr, QBism would be nothing. But QBism is not Bohr. This paper attempts to show that, despite a popular misconception, QBism is no minor tweak to Bohr's interpretation of quantum mechanics. It is something quite distinct.…
In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function.…
We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
In the modern quantum mechanics of cosmology observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third person probabilities of what occurs. However,…
We show that the quadratic measure need not be postulated, but follows from the compatibility of two structural features of physical processes: linear reversible evolution prior to the formation of persistent records, and multiplicative…
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…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…