arXiv subjects

R. Michael Jones

Publications and source records attributed to R. Michael Jones.

4 recordsLinked to original sources

arXiv2026

An approximate application of quantum gravity to the rotation problem

Arbitrary initial conditions allow solutions of Einstein's field equations for General Relativity to have arbitrarily large relative rotation of matter and inertial frames. The ``Rotation Problem'' is to explain why the measured relative rotation rate is so small. Nearly any reasonable theory of quantum gravity can solve the rotation problem by phase interference. Even as early as about a quarter of a second after the initial singularity, quantum cosmology would limit the cosmologies that contribute significantly to a path integral calculation to have relative rms rotation rates less than about $10^{-51}$ rad/year. Those calculations are based on using 50 e-foldings during inflation. For 55 or 60 e-foldings, the cosmologies contributing significantly to the path integral would have even smaller relative rotation rates. In addition, although inflation dominates the calculation, even if there had been no inflation, the cosmologies contributing significantly to the path integral would have relative rotation rates less than about $10^{-32}$ rad/year at about a quarter of a second after the initial singularity. These calculations are insensitive to the details of the theory of quantum gravity because the main factor depends only on the size of the visible universe, the Planck time, the free-space speed of light, the Hubble parameter, and the number of e-foldings during inflation. These calculations use the Einstein-Hilbert action in quantum gravity, including large-scale relative rotation of inertial frames and the matter distribution, in which each ``path'' is a cosmology with a different rms relative rotation rate. The calculation shows that the action is an extremum at zero rms relative rotation rate.

gr-qc↗

arXiv2020

The rotation problem

Any reasonable form of quantum gravity can explain (by phase interference) why on a large scale, inertial frames seem not to rotate relative to the average matter distribution in the universe without the need for absolute space, finely tuned initial conditions, or without giving up independent degrees of freedom for the gravitational field. A simple saddlepoint approximation to a path-integral calculation for a perfect fluid cosmology shows that only cosmologies with an average present relative rotation rate smaller than about $T^*H^2 \approx 10^{-71}$ radians per year could contribute significantly to a measurement of relative rotation rate in our universe, where $T^*\approx 10^{-51}$ years is the Planck time and $H \approx 10^{-10}$ yr$^{-1}$ is the present value of the Hubble parameter. A more detailed calculation (taking into account that with vorticity, flow lines are not normal to surfaces of constant global time, and approximating the action to second order in the mean square vorticity) shows that the saddlepoint at zero vorticity is isolated and that only cosmologies with an average present relative rotation rate smaller than about $T^*H^2 a_1^{1/2} \approx 10^{-73}$ radians per year could contribute significantly to a measurement of relative rotation rate in our universe, where $a_1 \approx 10^{-4}$ is the value of the cosmological scale factor at the time when matter became more significant than radiation in the cosmological expansion. This is consistent with measurements indicating a present relative rotation rate less than about $10^{-20}$ radians per year. The observed lack of relative rotation may be evidence for the existence of quantum gravity.

gr-qc↗

arXiv2002

The criteria for a solution of the field equations to be a classical limit of a quantum cosmology

If the gravitational field is quantized, then a solution of Einstein's field equations is a valid cosmological model only if it corresponds to a classical limit of a quantum cosmology. To determine which solutions are valid requires looking at quantum cosmology in a particular way. Because we infer the geometry by measurements on matter, we can represent the amplitude for any measurement in terms of the amplitude for the matter fields, allowing us to integrate out the gravitational degrees of freedom. Combining that result with a path-integral representation for quantum cosmology leads to an integration over 4-geometries. Even when a semiclassical approximation for the propagator is valid, the amplitude for any measurement includes an integral over the gravitational degrees of freedom. The conditions for a solution of the field equations to be a classical limit of a quantum cosmology are: (1) The effect of the classical action dominates the integration, (2) the action is stationary with respect to variation of the gravitational degrees of freedom, and (3) only one saddlepoint contributes significantly to each integration.

gr-qc↗

arXiv1999

The classical action for a Bianchi VI_h model

An estimate for the classical action for a Bianchi VI_h homogeneous spatially closed cosmology is presented as a function of b, a parameter of the model that is proportional to the relative rotation of the average inertial frame and the bulk of matter in the universe. It is assumed (through the equation of state) that a relativistic early universe is followed by a matter-dominated late universe. The action is used in a saddlepoint approximation to a semiclassical estimate for the wave function in quantum cosmology to explain why our inertial frame seems not to rotate relative to the stars. The saddlepoint is at b=0, as would be expected. Application of the saddlepoint approximation leads to the result that only those classical geometries whose action differs from the saddlepoint value for the action by an amount less than Planck's constant contribute significantly to the integration to give the present value of the wave function. Using estimates for our universe implies that only those classical geometries for which the present relative rotation rate of inertial frames and matter are less than about 10^(-130) radians per year contribute significantly to the integration. This is well below the limit set by experiment. The result depends on the ratio of the Hubble distance to the Planck length, but does not depend on the details of the theory of quantum gravity.

gr-qc↗