17366038
Classical dynamics on triangleland
In Euclidean relational particle mechanics (ERPM) only relative times, relative angles and relative separations are meaningful, while in similarity relational particle mechanics (SRPM) only relative times, relative angles and ratios of relative separations are. These theories are clearly of interest in the absolute or relative motion debate. In this paper, ERPM and SRPM are provided in fully reduced form for three particles in 2D, i.e. the classical dynamics on triangleland in 2D with and without scale. Exact solutions to each of these are then found, and simple Newton?Coulomb-like and harmonic oscillator-like SRPM models are studied numerically. The mathematics one arrives at thus overlaps in many ways with that which arises in the absolutist approach. The ERPM gives standard mathematics, while the SRPM has standard small-relative-scale behaviour and an unexpected but in itself standard universal large-relative-scale behaviour. One way in which SRPM is unusual is that it is a model in which a symmetry principle underlies an unexpected departure from standard physical behaviour at sufficiently large relative scales (interpolation between the abovementioned two behaviours). ERPM and SRPM are also theoretically interesting at the quantum level, both on their own merit and as toy models for the development of various approaches to the problems of time and of observables in quantum general relativity.
119274399
Kerr–Newman black hole thermodynamical state space: blockwise coordinates
A coordinate system that blockwise-simplifies the Kerr–Newman black hole’s thermodynamical state space Ruppeiner metric geometry is constructed, with discussion of the limiting cases corresponding to simpler black holes. It is deduced that one of the three conformal Killing vectors of the Reissner–Nordström and Kerr cases (whose thermodynamical state space metrics are 2 by 2 and conformally flat) survives generalization to the Kerr–Newman case’s 3 by 3 thermodynamical state space metric.
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.
10694441
Strong-Coupled Relativity Without Relativity
GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and Ó'Murchadha, also permits the construction of a limited number of other theories of evolving 3-geometries, including conformal gravity and strong gravity. In this paper, we use the 3-space approach to construct a 1-parameter family of theories which generalize strong gravity. The usual strong gravity is the strong-coupled limit of GR, which is appropriate near singularities and is one of very few regimes of GR which is amenable to quantization. Our new strong gravity theories are similar limits of scalar-tensor theories such as Brans–Dicke theory, and are likewise appropriate near singularities. They represent an extension of the regime amenable to quantization, which furthermore spans two qualitatively different types of inner product.We find that these strong gravity theories permit coupling only to ultralocal matter fields and that they prevent gauge theory. Thus in the classical picture, gauge theory breaks down (rather than undergoing unification) as one approaches the GR initial singularity.
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.
120033764
Interpretation of Highly Intelastic Proton-Proton Interactions at 10, 20, and 30 BeV/c
118377935
Similarity renormalization group with novel generators
The choice of generator in the Similarity Renormalization Group (SRG) flow equation determines the evolution pattern of the Hamiltonian. The kinetic energy has been used in the generator for most prior applications to nuclear interactions, and other options have been largely unexplored. Here we show how variations of this standard choice can allow the evolution to proceed more efficiently without losing its advantages.
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.
121752579
Precision Lifetime Measurements on Positive and Negative Muons
An experiment to measure and compare the free decay rates of positive and negative muons is described. Muons from the Nevis synchrocyclotron were stopped in a liquid-hydrogen target containing less than 1 ppm ${\mathrm{D}}_{2}$ and less than 1 part in ${10}^{9}$ of other impurities. In this situation, the rate of ${\ensuremath{\mu}}^{\ensuremath{-}}$ capture in ${\mathrm{H}}_{2}$ was the only significant correction to the free decay rate of ${\ensuremath{\mu}}^{\ensuremath{-}}$ and was measured in a separate experiment. The lifetimes were monitored by measuring the time intervals between muon stops and decay electrons using a transistorized digitron of 30-nsec channel width. Electronic circuitry of the "interference remover" type was employed to eliminate time-dependent background. ${\ensuremath{\mu}}^{\ensuremath{-}}$ and ${\ensuremath{\mu}}^{+}$ lifetimes were measured with the same apparatus and under essentially the same conditions of rate and geometry. The ratio of the lifetimes is expected to be particularly insensitive to any systematic errors. We have obtained: ${\ensuremath{\tau}}_{{\ensuremath{\mu}}^{\ensuremath{-}}}=2.198\ifmmode\pm\else\textpm\fi{}0.002$ \ensuremath{\mu}sec (hydrogen correction made), ${\ensuremath{\tau}}_{{\ensuremath{\mu}}^{+}}=2.197\ifmmode\pm\else\textpm\fi{}0.002$ \ensuremath{\mu}sec, $R=\frac{{\ensuremath{\tau}}_{{\ensuremath{\mu}}^{\ensuremath{-}}}}{{\ensuremath{\tau}}_{{\ensuremath{\mu}}^{+}}}=1.000\ifmmode\pm\else\textpm\fi{}0.001$.
32865960
Recent advances in low level counting techniques.
Problems involving low level counting techniques are encountered in many diverse fields including biological and chemical tracer studies, archaeo­ logical and geological dating (I), investigations of natural and induced radio­ activities, and the study of fundamental particles. Such a host of methods and variations on methods have been reported that an exhaustive catalog would constitute little more than an annotated bibliography. We have, there­ fore, limited our attention to a few selected examples which seem to be of special interest because of their versatility or their extreme sensitivity. We prefer to organize our discussion around specific problems rather than around types of detectors since this permits a comparison of alternative methods and provides practical examples of various techniques in actual operation. Alpha counting is arbitrarily excluded. For a discussion of photographic methods (radioautographs) the reader is referred to Norris & Woodruff (2) and refer­ ences cited therein. We will discuss the methods developed for the measure­ ment of natural radiocarbon and tritium, cosmic ray produced Be7, and the K(O content of the human body. DOUble-beta decay experiments are consid­ ered since they seem to constitute one of the most difficult of the outstanding problems and because of their importance from the viewpoint of theoretical nuclear physics. Finally, an account is given of recent attempts to detect the neutrino, probably the most difficult low level counting problem of all and one which seems finally on the verge of successful solution. Principles.-The fundamental principles of low level counting are simple: maximize the number of detected events of the desired kind (signal) and minimize all others (background). The number of detected events is, of course, the product of sample size, over-all counting efficiency, and counting time. However, the striking importance of the net sample counting rate is not always fully appreciated. It can be shown (3) from elementary counting statistics, that if the sample rate is small compared with background (which is usually the case in a truly low level problem) and if counting statistics is the limiting source of error (also usually true), then the proper parameter for the comparison of counting methods is S2/B, the ratio of the square of the net sample rate to the background rate. (Any sample strength can be used in making the comparison so long as the same strength is used in testing all methods.) The method giving the maximum value of S2/B will yield the