Quantum mechanics explained

The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment

Derivation of the Rules of Quantum Mechanics from Information-Theoretic Axioms

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by Turing and von Neumann, in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for all dimensions.Comment: 20 pages, 6 figure

Mechanisms of Surviving Burial: Dune Grass Interspecific Differences Drive Resource Allocation After Sand Deposition

Sand dunes are important geomorphic formations of coastal ecosystems that are critical in protecting human populations that live in coastal areas. Dune formation is driven by ecomorphodynamic interactions between vegetation and sediment deposition. While there has been extensive research on responses of dune grasses to sand burial, there is a knowledge gap in understanding mechanisms of acclimation between similar, coexistent, dune-building grasses such as Ammophila breviligulata (C3), Spartina patens (C4), and Uniola paniculata (C4). Our goal was to determine how physiological mechanisms of acclimation to sand burial vary between species. We hypothesize that (1) in the presence of burial, resource allocation will be predicated on photosynthetic pathway and that we will be able to characterize the C3 species as a root allocator and the C4 species as leaf allocators. We also hypothesize that (2) despite similarities between these species in habitat, growth form, and life history, leaf, root, and whole plant traits will vary between species when burial is not present. Furthermore, when burial is present, the existing variability in physiological strategy will drive species-specific mechanisms of survival. In a greenhouse experiment, we exposed three dune grass species to different burial treatments: 0 cm (control) and a one-time 25-cm burial to mimic sediment deposition during a storm. At the conclusion of our study, we collected a suite of physiological and morphological functional traits. Results showed that Ammophila decreased allocation to aboveground biomass to maintain root biomass, preserving photosynthesis by allocating nitrogen (N) into light-exposed leaves. Conversely, Uniola and Spartina decreased allocation to belowground production to increase elongation and maintain aboveground biomass. Interestingly, we found that species were functionally distinct when burial was absent; however, all species became more similar when treated with burial. In the presence of burial, species utilized functional traits of rapid growth strategy, although mechanisms of change were interspecifically variable

Effects and Propositions

The quantum logical and quantum information-theoretic traditions have exerted an especially powerful influence on Bub's thinking about the conceptual foundations of quantum mechanics. This paper discusses both the quantum logical and information-theoretic traditions from the point of view of their representational frameworks. I argue that it is at this level, at the level of its framework, that the quantum logical tradition has retained its centrality to Bub's thought. It is further argued that there is implicit in the quantum information-theoretic tradition a set of ideas that mark a genuinely new alternative to the framework of quantum logic. These ideas are of considerable interest for the philosophy of quantum mechanics, a claim which I defend with an extended discussion of their application to our understanding of the philosophical significance of the no hidden variable theorem of Kochen and Specker.Comment: Presented to the 2007 conference, New Directions in the Foundations of Physic

Three dimensional quantum algebras: a Cartan-like point of view

A perturbative quantization procedure for Lie bialgebras is introduced and used to classify all three dimensional complex quantum algebras compatible with a given coproduct. The role of elements of the quantum universal enveloping algebra that, analogously to generators in Lie algebras, have a distinguished type of coproduct is discussed, and the relevance of a symmetrical basis in the universal enveloping algebra stressed. New quantizations of three dimensional solvable algebras, relevant for possible physical applications for their simplicity, are obtained and all already known related results recovered. Our results give a quantization of all existing three dimensional Lie algebras and reproduce, in the classical limit, the most relevant sector of the complete classification for real three dimensional Lie bialgebra structures given by X. Gomez in J. Math. Phys. Vol. 41. (2000) 4939.Comment: LaTeX, 15 page

Integrable potentials on spaces with curvature from quantum groups

A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson coalgebra. All these spaces have a non-constant curvature that depends on the deformation parameter z. As particular cases, the analogues of the harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed. Another deformed Hamiltonian is also shown to provide superintegrable systems on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant curvature that exactly coincides with z. According to each specific space, the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers. The non-deformed limit z=0 of all these Hamiltonians can then be regarded as the zero-curvature limit (contraction) which leads to the corresponding (super)integrable systems on the flat Euclidean and Minkowskian spaces.Comment: 19 pages, 1 figure. Two references adde

Partial Description of Quantum States

One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the question whether such a representation is complete has been debated since almost the early days of quantum mechanics. In this article, we develop an alternate way to formalize knowledge about the state of quantum systems, based solely on experimentally accessible elements, namely on outcomes of finite measurements. We introduce what we call partial description which, given a feasible measurement, indicates some outcomes which are known to be impossible (i.e. known to have a probability equal to 0 to occur) and hence have to be discarded. Then, we introduce partial states (which are partial descriptions providing as much information as possible) and compare this way to describe quantum states to the orthodox one, using vector rays. Finally, we show that partial states allow to describe quantum states in a strictly more expressive way that the orthodox description does

Quantum value indefiniteness

The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum alone. We discuss possible interpretations and consequences for quantum oracles.Comment: 19 pages, 2 tables, 2 figures; contribution to PC0

Finite precision measurement nullifies the Kochen-Specker theorem

Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden variable theories provided by Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-over-classical advantage for information processing can be derived from the Kochen-Specker theorem alone.Comment: 7 pages, plain TeX; minor corrections, interpretation clarified, references update

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure