14,179 research outputs found
(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory
In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum
mechanics," Pascual Jordan (1927b,g) presented his version of what came to be
known as the Dirac-Jordan statistical transformation theory. As an alternative
that avoids the mathematical difficulties facing the approach of Jordan and
Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert
space formalism of quantum mechanics. In this paper, we focus on Jordan and von
Neumann. Central to the formalisms of both are expressions for conditional
probabilities of finding some value for one quantity given the value of
another. Beyond that Jordan and von Neumann had very different views about the
appropriate formulation of problems in quantum mechanics. For Jordan, unable to
let go of the analogy to classical mechanics, the solution of such problems
required the identication of sets of canonically conjugate variables, i.e., p's
and q's. For von Neumann, not constrained by the analogy to classical
mechanics, it required only the identication of a maximal set of commuting
operators with simultaneous eigenstates. He had no need for p's and q's. Jordan
and von Neumann also stated the characteristic new rules for probabilities in
quantum mechanics somewhat differently. Jordan (1927b) was the first to state
those rules in full generality. Von Neumann (1927a) rephrased them and, in a
subsequent paper (von Neumann, 1927b), sought to derive them from more basic
considerations. In this paper we reconstruct the central arguments of these
1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by
Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these
papers that bring out the gradual loosening of the ties between the new quantum
formalism and classical mechanics.Comment: New version. The main difference with the old version is that the
introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has
been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has
been accepted for publication in European Physical Journal
Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
Scalar-Tensor theories of gravity can be formulated in different frames, most
notably, the Einstein and the Jordan one. While some debate still persists in
the literature on the physical status of the different frames, a frame
transformation in Scalar-Tensor theories amounts to a local redefinition of the
metric, and then should not affect physical results. We analyze the issue in a
cosmological context. In particular, we define all the relevant observables
(redshift, distances, cross-sections, ...) in terms of frame-independent
quantities. Then, we give a frame-independent formulation of the Boltzmann
equation, and outline its use in relevant examples such as particle freeze-out
and the evolution of the CMB photon distribution function. Finally, we derive
the gravitational equations for the frame-independent quantities at first order
in perturbation theory. From a practical point of view, the present approach
allows the simultaneous implementation of the good aspects of the two frames in
a clear and straightforward way.Comment: 15 pages, matches version to be published on Phys. Rev.
Density perturbations in Kaluza--Klein theories during a de Sitter phase
In the context of Kaluza-Klein theories, we consider a model in which the
universe is filled with a perfect fluid described by a barotropic equation of
state. An analysis of density perturbations employing the synchronous gauge
shows that there are cases where these perturbations have an exponential growth
during a de Sitter phase evolution in the external space.Comment: LaTex file, 10 pages. To be published in Classical and Quantum
Gravit
Testing the equivalence principle: why and how?
Part of the theoretical motivation for improving the present level of testing
of the equivalence principle is reviewed. The general rationale for optimizing
the choice of pairs of materials to be tested is presented. One introduces a
simplified rationale based on a trichotomy of competing classes of theoretical
models.Comment: 11 pages, Latex, uses ioplppt.sty, submitted to Class. Quantum Gra
Interferometric weak value deflections: quantum and classical treatments
We derive the weak value deflection given in a paper by Dixon et al. (Phys.
Rev. Lett. 102, 173601 (2009)) both quantum mechanically and classically. This
paper is meant to cover some of the mathematical details omitted in that paper
owing to space constraints
An astronomical search for evidence of new physics: Limits on gravity-induced birefringence from the magnetic white dwarf RE J0317-853
The coupling of the electromagnetic field directly with gravitational gauge
fields leads to new physical effects that can be tested using astronomical
data. Here we consider a particular case for closer scrutiny, a specific
nonminimal coupling of torsion to electromagnetism, which enters into a
metric-affine geometry of space-time. We show that under the assumption of this
nonminimal coupling, spacetime is birefringent in the presence of such a
gravitational field. This leads to the depolarization of light emitted from
extended astrophysical sources. We use polarimetric data of the magnetic white
dwarf to set strong constraints on the essential coupling
constant for this effect, giving k^2 \lsim (19 {m})^2 .Comment: Statements about Moffat's NGT modified. Accepted for publication in
Phys.Rev.
A magnetic model for the incommensurate I phase of spin-Peierls systems
A magnetic model is proposed for describing the incommensurate I phase of
spin-Peierls systems. Based on the harmonicity of the lattice distortion, its
main ingredient is that the distortion of the lattice adjusts to the average
magnetization such that the system is always gapful. The presence of dynamical
incommensurabilities in the fluctuation spectra is also predicted. Recent
experimental results for CuGeO_3 obtained by NMR, ESR and light scattering
absorption are well understood within this model.Comment: 8 pages, 3 figures, Latex with EPL style files all include
Learning democracy in social work
In this contribution, we discuss the role of social work in processes of democracy. A key question in this discussion concerns the meaning of ‘the social’ in social work. This question has often been answered in a self-referential way, referring to a methodological identity of social work. This defines the educational role of social work as socialisation (be it socialisation into obedience or into an empowered citizen). However, the idea of democracy as ‘ongoing experiment’ and ‘beyond order’ challenges this methodological identity of social work. From the perspective of democracy as an ‘ongoing experiment’, the social is to be regarded as a platform for dissensus, for ongoing discussions on the relation between private and public issues in the light of human rights and social justice. Hence, the identity of social work cannot be defined in a methodological way; social work is a complex of (institutionalized) welfare practices, to be studied on their underlying views on the ‘social’ as a political and educational concept, and on the way they influence the situation of children, young people and adults in society
Electrostatics of ions inside the nanopores and trans-membrane channels
A model of a finite cylindrical ion channel through a phospholipid membrane
of width separating two electrolyte reservoirs is studied. Analytical
solution of the Poisson equation is obtained for an arbitrary distribution of
ions inside the trans-membrane pore. The solution is asymptotically exact in
the limit of large ionic strength of electrolyte on the two sides of membrane.
However, even for physiological concentrations of electrolyte, the
electrostatic barrier sizes found using the theory are in excellent agreement
with the numerical solution of the Poisson equation. The analytical solution is
used to calculate the electrostatic potential energy profiles for pores
containing charged protein residues. Availability of a semi-exact interionic
potential should greatly facilitate the study of ionic transport through
nanopores and ion channels
Generalized Symmetries of Impulsive Gravitational Waves
We generalize previous \cite{AiBa2} work on the classification of
() symmetries of plane-fronted waves with an impulsive profile. Due
to the specific form of the profile it is possible to extend the group of
normal-form-preserving diffeomorphisms to include non-smooth transformations.
This extension entails a richer structure of the symmetry algebra generated by
the (non-smooth) Killing vectors.Comment: 18 pages, latex2e, no figure
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