14,343 research outputs found
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
Yang-Mills gravity in biconformal space
We write a gravity theory with Yang-Mills type action using the biconformal
gauging of the conformal group. We show that the resulting biconformal
Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity
in the case of slowly changing fields. In addition, we systematically extend
arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena
for studying flat space Yang-Mills theories. By applying the biconformal
extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we
establish a 1-1, onto mapping between a set of gravitational gauge theories and
4-dim, flat space gauge theories.Comment: 27 pages; paper emphasis shifted to focus on gravity; references
adde
The existence of time
Of those gauge theories of gravity known to be equivalent to general
relativity, only the biconformal gauging introduces new structures - the
quotient of the conformal group of any pseudo-Euclidean space by its Weyl
subgroup always has natural symplectic and metric structures. Using this metric
and symplectic form, we show that there exist canonically conjugate,
orthogonal, metric submanifolds if and only if the original gauged space is
Euclidean or signature 0. In the Euclidean cases, the resultant configuration
space must be Lorentzian. Therefore, in this context, time may be viewed as a
derived property of general relativity.Comment: 21 pages (Reduced to clarify and focus on central argument; some
calculations condensed; typos corrected
String Without Strings
Scale invariance provides a principled reason for the physical importance of Hilbert space, the Virasoro algebra, the string mode expansion, canonical commutators and Schroedinger evolution of states, independent of the assumptions of string theory and quantum theory. The usual properties of dimensionful fields imply an infinite, projective tower of conformal weights associated with the tangent space to scale-invariant spacetimes. Convergence and measurability on this tangent tower are guaranteed using a scale-invariant norm, restricted to conformally self-dual vectors. Maps on the resulting Hilbert space are correspondingly restricted to semi-definite conformal weight. We find the maximally- and minimally-commuting, complete Lie algebras of definite-weight operators. The projective symmetry of the tower gives these algebras central charges, giving the canonical commutator and quantum Virasoro algebras, respectively. Using a continuous, m-parameter representation for rank-m tower tensors, we show that the parallel transport equation for the momentum vector of a particle is the Schroedinger equation, while the associated definite-weight operators obey canonical commutation relations. Generalizing to the set of integral curves of general timelike, self-dual vector-valued weight maps gives a lifting such that the action of the curves parallel transports arbitrary tower vectors. We prove that the full set of Schroedinger-lifted integral curves of a general self-dual map gives an immersion of its 2-dim parameter space into spacetime, inducing a Lorentzian metric on the parameter space. The immersion is shown to satisfy the variational equations of open string
Toward a Background Independent Quantum Theory of Gravity
Any canonical quantum theory can be understood to arise from the
compatibility of the statistical geometry of distinguishable observations with
the canonical Poisson structure of Hamiltonian dynamics. This geometric
perspective offers a novel, background independent non-perturbative formulation
of quantum gravity. We invoke a quantum version of the equivalence principle,
which requires both the statistical and symplectic geometries of canonical
quantum theory to be fully dynamical quantities. Our approach sheds new light
on such basic issues of quantum gravity as the nature of observables, the
problem of time, and the physics of the vacuum. In particular, the observed
numerical smallness of the cosmological constant can be rationalized in this
approach.Comment: Awarded Honorable Mention, 2004 Gravity Research Foundation Essay
Competition; 8 pages, LaTe
Statistical computation of tolerance limits
Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes
Reliability growth modeling analysis of the space shuttle main engines based upon the Weibull process
The Weibull process, identified as the inhomogeneous Poisson process with the Weibull intensity function, is used to model the reliability growth assessment of the space shuttle main engine test and flight failure data. Additional tables of percentage-point probabilities for several different values of the confidence coefficient have been generated for setting (1-alpha)100-percent two sided confidence interval estimates on the mean time between failures. The tabled data pertain to two cases: (1) time-terminated testing, and (2) failure-terminated testing. The critical values of the three test statistics, namely Cramer-von Mises, Kolmogorov-Smirnov, and chi-square, were calculated and tabled for use in the goodness of fit tests for the engine reliability data. Numerical results are presented for five different groupings of the engine data that reflect the actual response to the failures
Field Theory as Free Fall
It is shown that the classical field equations pertaining to gravity coupled
to other bosonic fields are equivalent to a single geodesic equation,
describing the free fall of a point particle in superspace. Some implications
for quantum gravity are discussed.Comment: 18 pages, plain late
Quantum Gravitational Contributions to the CMB Anisotropy Spectrum
We derive the primordial power spectrum of density fluctuations in the
framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer
approximation to the Wheeler-DeWitt equation for an inflationary universe with
a scalar field. In this way we first recover the scale-invariant power spectrum
that is found as an approximation in the simplest inflationary models. We then
obtain quantum gravitational corrections to this spectrum and discuss whether
they lead to measurable signatures in the CMB anisotropy spectrum. The
non-observation so far of such corrections translates into an upper bound on
the energy scale of inflation.Comment: 4 pages, v3: sign error in Eq. (5) and its consequences correcte
- …