Related papers: Classical Logic in Quantum Context
Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
I give a review of the conceptual issues that arise in theories of quantum cosmology. I start by emphasising some features of ordinary quantum theory that also play a crucial role in understanding quantum cosmology. I then give motivations…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
The old cosmological-constant (CC) problem indicates an inconsistency of the usual formulation of semiclassical gravity. The usual formulation of semiclassical gravity also seems to be inconsistent with the conventional interpretation of…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
In order to arrive at Bohmian mechanics from standard nonrelativistic quantum mechanics one need do almost nothing! One need only complete the usual quantum description in what is really the most obvious way: by simply including the…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
An extended analysis is made of the Gell-Mann and Hartle axioms for a generalised `histories' approach to quantum theory. Emphasis is placed on finding equivalents of the lattice structure that is employed in standard quantum logic.…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…
Recently, three experiments have been proposed in order to show that the standard and Bohmian quantum mechanics can have different predictions at the individual level of particles. However, these thought experiments have encountered some…
A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic…