The Einstein field equations have no known and acceptable interior solution that can be matched to an exterior Kerr field. In particular, there are no interior solutions that could represent objects like the Earth or other rigidly rotating astronomical bodies. It is shown here that there exist closed surfaces upon which the frame-dragging angular velocity and the red-shift factor for the Kerr metric are constant. These surfaces could serve as a boundary between rigidly rotating sources for the Kerr metric and the Kerr external field.

## A NUCLEAR BOMB WORTH MORE THAN ITS WEIGHT IN GOLD

In the December 2013 issue of *Physics Today* David Kramer tells us—in an article titled A nuclear bomb worth more than its weight in gold?—that “some critics of the B-61 life extension program question whether the program is necessary.” And, “Representative John Garamendi (D-CA) questioned why the B-83, a newer bomb that officials acknowledge won’t need a life extension for at least 10 years, shouldn’t replace the B-61”. Strangely enough the article omits the principal reason why the administration may think the B-61 is worth more than its weight in gold.

The article appears in *Physics & Society* 6 Feb 2014. The link is:

The MS with better quality figures and equations is available here: P&S-EPW-nid

## DOES GOD PLAY DICE? CONCEPTUAL QUANTUM PHYSICS FOR THE PERPLEXED

The late 19th century and the beginning of the 20th brought with it a revolution in the scientific understanding of the universe around us, one whose effects are still being felt around the world as it forces people to change their ideas about the universe and the place of human beings within it. Even a conceptual understanding of the early origin of the universe requires an introductory knowledge of quantum mechanics. Unfortunately, the attempt to reconcile quantum mechanics with concepts brought over from classical mechanics has led to much confusion especially among non-physicists and students of physics. This essay is an attempt to address some of this wide spread confusion.

## GROUPS: NATURE’S “INVISIBLE HAND”: AN ESSAY ON THE STANDARD MODEL

It is the purpose of this essay to take the reader from some elementary ideas about groups to the essence of the Standard Model of particle physics along a relatively straight and intuitive path. The idea is to give an Olympian view of this evolution, one that is often missing when absorbing the detailed subject matter of the Standard Model as presented in an historical approach to the subject.

Groups Natures Hidden Symmetry

Errata:

p.58: First equation should read

p. 59: Line after 2nd equation from the bottom of the page should read, “This corresponds to a right-handed spinor and, for spin 1/2 is designated (1/2, 0).”

The end of the last line should read, ” . . . is designated by (0, 1/2).”

## Dark Matter and Charged Exotic Dust

The density profiles of dark matter halos are often modeled by an approximate solution to the isothermal Lane-Emden equation with suitable boundary conditions at the origin. It is shown here that such a model corresponds to an exact solution of the Einstein-Maxwell equations for exotic charged dust. It is also shown that, because of its necessarily very small charge to mass ratio, the fact that the particles are charged does not necessarily rule out such material as a candidate for dark matter.

Dark Matter-Charged Exotic Dust

Version published in Journal of Physics and Astronomy, Volume 2, Issue 3 (2013):

## Electromagnetic and Gravitational Waves: the Third Dimension

Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by use of the Hamilton-Jacobi equation and the gravitational by a transformation to a local inertial frame. Here, the covariant Lorentz force equation and the second order equation of geodesic deviation followed by the introduction of a local inertial frame are respectively used. It is often said that there is an analogy between the motion of charged particles in the field of an electromagnetic wave and the motion of test particles in the field of a gravitational wave. This analogy is examined and found to be rather limited. It is also shown that a simple special relativistic relation leads to an integral of the motion, characteristic of plane waves, that is satisfied in both cases.

*Canadian Journal of Physics* **89**, 1187-1194 (2011).

Electromagnetic and Gravitational Waves: The Third Dimension

## Quantum Mechanics and Motion: A Modern Perspective

Physics Essays Vol. 23, pp. 242-247 (2010)

This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum, yields a world-line. If a force acts on the particle, its probability distribution is accordingly modified. This must also be true for macroscopic objects, although now the description is far more complicated by the structure of matter and associated surface physics.

## The Demystification of Emergent Behavior

Emergent behavior that appears at a given level of organization may be characterized as arising from an organizationally lower level in such a way that it transcends a mere increase in the behavioral degree of complexity. It is therefore to be distinguished from systems exhibiting chaotic behavior, for example, which are deterministic but unpredictable because of an exponential dependence on initial conditions. In emergent phenomena, higher levels of organization are not determined by lowerlevels of organization; or, more colloquially, emergent behavior is often said to be “greater than the sum of the parts”. The concept plays an especially important but contentious role in the biological sciences. This essay is intended to demystify at least some aspects of the mystery of emergence.

(This is an updated and expanded version of the original post with some portions rewritten to enhance clarity.)

## Charge, geometry, and effective mass in the Kerr-Newman solution to the Einstein field equations

Foundations of Physics Vol. 38, pp. 959-968 (2008)

The original publication is available at www.springerlink.com

http://dx.doi.org/10.1007/s10701-008-9245-x

It has been shown that for the Reissner-Nordstrom solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature [*Found. Phys*. **38**, 293-300 (2008)]. The presence of charge results in a negative curvature. This work, which includes a discussion of effective mass, is extended here to the Kerr-Newman solution.

## Negative Energies and Field Theory

The assumption that the vacuum is the minimum energy state, invariant under unitary transformations, is fundamental to quantum field theory. However, the assertion that the conservation of charge implies that the equal time commutator of the charge density and its time derivative vanish for two spatially separated points is inconsistent with the requirement that the vacuum be the lowest energy state. Yet, for quantum field theory to be gauge invariant, this commutator *must* vanish. This essay explores how this conundrum is resolved in quantum electrodynamics.

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