Related papers: Born Again
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
In a previous article [1] we presented an argument to obtain (or rather infer) Born's rule, based on a simple set of axioms named "Contexts, Systems and Modalities" (CSM). In this approach there is no "emergence", but the structure of…
Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it.
We introduce a two state vector formalism of quantum mechanics by generalizing Bell hidden variable model to higher dimensions and by attributing a physical significance, a state evolving backward in time, to the hidden variable. A simple…
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
We investigate the consistency of conditional quantum probabilities. This is whether there is compatibility between the Kolmogorov-Bayes conditional probabilities and the Born rule. We show that they are not compatible in the sense that…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
[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…
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 emergence of intrinsic probability has long been one of the most important and puzzling problems in quantum mechanics, and the law most directly related to this problem is the Born rule. For a century, there have been many attempts to…
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…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
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…
Generically the probabilities of observational results depend upon both the quantum state and the rules for extracting the probabilities from it. It is often argued that inflation may make our observations independent of the quantum state.…
Gleason's theorem is often cited as establishing the Born rule from the structure of Hilbert space, yet its original proof is mathematically sophisticated and rarely accessible to physicists. In this article we present a simple route to the…
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…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
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…
While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…