17480703
Interacting vector fields in relativity without relativity
Barbour, Foster and O Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics. Neither time nor a locally Minkowskian structure of spacetime are presupposed. Both arise as emergent features of the world from geodesic-type dynamics on a space of three-dimensional metric–matter configurations. In fact gravity, the universal light-cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism. It yields relativity—and more—without presupposing relativity. This paper completes the recovery of the presently known bosonic sector within the 3-space approach. We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang–Mills fields minimally coupled to gravity.
17821899
Records Theory
In quantum gravity, one seeks to combine quantum mechanics and general relativity. In attempting to do so, one comes across the ‘problem of time’ impasse: the notion of time is conceptually different in each of these theories. In this paper, I consider the timeless records approach toward resolving this. Records are localized, information-containing subconfigurations of a single instant. Records theory is the study of these and of how science (or history) is to be abstracted from correlations between them. I critically evaluate motivations for this approach that have previously appeared in the literature. I provide a ground-level structure for records theory and discuss what kind of further tools are needed, illustrated with some toy models: ordinary mechanics, relatonal particle dynamics, detector models and inhomogeneous perturbations about homogeneous cosmology. PACS numbers 04.60-m, 04.60.Ds
119109018
Approaching the problem of time with a combined semiclassical-records-histories scheme
I approach the problem of time and other foundations of quantum (QM) cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle mechanics (RPMs). If there is also commutation with Lin—the Kuchař observables condition—the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchař observables is explicitly resolved for 1D and 2D RPMs. Then as a first route to Halliwell’s approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchař observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group averaging and Barbour’s best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewise-improved softened case of Halliwell 2009 for a subsequent paper II. Finally, I provide comments on Halliwell’s approach and how well it fares as regards the various facets of the problem of time and as an implementation of QM propositions.
17420273
Seminar on Records Theory
In quantum gravity, one seeks to combine quantum mechanics and general relativity. In attempting to do so, one comes across the `problem of time' impasse: the notion of time is conceptually different in each of these theories. In this seminar, I consider the timeless records approach toward resolving this. Records are localized, information-containing subconfigurations of a single instant. Records theory is the study of these and of how science (or history) is to be abstracted from correlations between them. I explain how to motivate this approach, provide a ground-level structure for it and discuss what kind of further tools are needed. For a more comprehensive account with many more references, see [1].
118832557
Geometrodynamics: Spacetime or Space ?
This thesis concerns the split of Einstein's field equations (EFE's) with respect to nowhere null hypersurfaces. Areas covered include A) the foundations of relativity, deriving geometrodynamics from relational first principles and showing that this form accommodates a sufficient set of fundamental matter fields to be classically realistic, alternative theories of gravity that arise from similar use of conformal mathematics. B) GR Initial value problem (IVP) methods, the badness of timelike splits of the EFE's and studying braneworlds under guidance from GR IVP and Cauchy problem methods.
14733645
The Campbell--Magaard Theorem is inadequate and inappropriate as a protective theorem for relativistic field equations
Given a particular prescription for the Einstein field equations (EFE's), it is important to have general protective theorems that lend support to it. The prescription of data on a timelike hypersurface for the (n + 1)-d EFE's arises in `noncompact Kaluza--Klein theory', and in certain kinds of braneworlds and low-energy string theory. The Campbell--Magaard (CM) theorem, which asserts local existence (and, with extra conditions, uniqueness) of analytic embeddings of completely general n-d manifolds into vacuum (n + 1)-d manifolds, has often recently been invoked as a protective theorem for such prescriptions. But in this paper I argue that there are problems with loosening the CM thoerem of restrictive meanings in its statement, which is worthwhile thing to do in pursuit of the proposed applications. While I remedy some problems by identifying the required topology, delineating what `local' can be taken to mean, and offering a new, more robust and covariant proof, other problems remain unsurmountable. The theorem lends only inadequate support, both because it offers no guarantee of continuous dependence on the data and because it disregards causality. Furthermore, the theorem is only for the analytic functions which renders it inappropriate for the study of the relativistic equations of modern physics. Unfortunately, there are no known general theorems that offer adequate protection to the proposed applications' prescription. I conclude by making some suggestions for more modest progress.
117822599
Muon Capture in (pmud)+ Molecules
124078930
Muon Capture in Hydrogen
Abstract : An experiment to measure the muon capture rate in liquid hydrogen was carried out using scintillation counter techniques. The experiment tests muon-electron universality in interaction with a proton at a momentum transfer of 100 MeV/c. The use of ultra-pure liquid hydrogen, a purified muon beam, neutron-gamma ray discriminating detectors and oscilloscope photography made possible the detection of the 5.2 MeV neutron from the relatively improbable capture reaction (mu + p yields n + nu). The muon molecular formation rate was measured in an independent experiment, but the present result is relatively insensitive to it. The stability of the muon molecular ortho state against transitions to the para ground state for times comparable to the free muon life-time is confirmed. The experimental result of the capture rate measurement, 464 + or - 42 per second is compared with 562 + or - 60 per second, the rate expected on the basis of the conserved vector current theory, muon-electron universality and the accepted value of the "induced pseudo scalar" coupling constant.
46298471
Differential Rotation and Dynamics of the Solar Interior
Splitting of the sun's global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.
119158624
Block Diagonalization using SRG Flow Equations
Here s is a flow parameter and the flow operator Gs specifies the type of SRG [4]. Decoupling between low-energy and high-energy matrix elements is naturally achieved in a momentum basis by choosing a momentum-diagonal flow operator such as the kinetic energy Trel or the diagonal of Hs; either drives the Hamiltonian toward banddiagonal form. This decoupling leads to dramatically improved variational convergence in few-body nuclear systems compared to unevolved phenomenological or chiral EFT potentials [5, 6]. Renormalization Group (RG) methods that evolve NN interactions with a sharp or smooth cutoff in relative momentum, known generically as Vlow k, rely on the invariance of the two-nucleon T matrix [7, 8]. These approaches achieve a block-diagonal form characterized by a cutoff Λ (see left plots in Figs. 1 and 2). As usually implemented they set the high-momentum matrix elements to zero but this is not required. Block-diagonal decoupling of the sharp Vlow k form can
22980504
The Solar Acoustic Spectrum and Eigenmode Parameters
The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10−5. For a 3-year data set, the fractional error is expected to be 3 × 10−6. The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.