118982450
Relational particle models: I. Reconciliation with standard classical and quantum theory
This paper concerns the absolute versus relative motion debate. The Barbour and Bertotti (1982) work may be viewed as an indirectly set up relational formulation of a portion of Newtonian mechanics. I consider further direct formulations of this and argue that the portion in question—universes with zero total angular momentum that are conservative and with kinetic terms that are (homogeneous) quadratic in their velocities—is capable of accommodating a wide range of classical physics phenomena. Furthermore, as I develop in paper II, this relational particle model is a useful toy model for canonical general relativity. I consider what happens if one quantizes relational rather than absolute mechanics, indeed whether the latter is misleading. By exploiting Jacobi coordinates, I show how to access many examples of quantized relational particle models and then interpret these from a relational perspective. By these means, previous suggestions of bad semiclassicality for such models can be eluded. I show how small (particle number) universe relational particle model examples display eigenspectrum truncation, gaps, energy interlocking and counterbalanced total angular momentum. These features mean that these small universe models make interesting toy models for some aspects of closed-universe quantum cosmology. Meanwhile, these features do not compromise the recovery of reality as regards the practicalities of experimentation in a large universe such as our own.
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.
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.
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.
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
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].
123045321
Evidence for local compensation of transverse momentum in pp collisions at 200 and 300 GeV/c
Evidence is presented for local compensation of transverse momentum in pp collisions at 200 and 300 GeV/c. The data are compared with a model which contains no dynamical transverse-momentum correlations. These data are used to determine a lower bound on the slope of the Pomeranchuk trajectory. (AIP)
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
125174279
Design and performance of the multiparticle argo spectrometer system
Abstract The Multiparticle Argo Spectrometer System, MASS, consists of a magnetic vertex spectrometer, two external trigger spectrometers, an on-line monitoring system and an off-line data analysis chain. The performance of MASS has been evaluated from physics data taken in a study of 28.5 GeV/ c pp collisions covering a large range of transverse momentum.
121141376
Charged Multiplicity Associated with Transverse Momentum of a Leading Proton in pp at 28.5 GEV/C
We have measured the mean charged multiplicity nCH as a function of transverse momentum p⊥ of the forward proton in the reaction p + p ⇒ p + MM for five intervals of missing mass MM using our Multiparticle Argo Spectrometer System. We observe an increase of nCH for p⊥ > 1 GeV/c.
139640917
Effects of Channel Failure Rates on the Jet Reconstruction Efficiencies an Resolutions in an Fe HF Calorimeter