It is well-known that a classical point charge in 1+1 D hyperbolic motion in space and time is reaction-free. But this is a special case of a larger set of reaction-free trajectories that in general are curved paths through space, i.e. in 2+1 D. This
note catalogs the full family of reaction-free trajectories, giving a geometrical interpretation by which means the curved path possibility is easily related to the better known case of hyperbolic motion in 1+1 D. Motivated by the geometry, it is shown how the catalog of motions can be naturally extended to include the possibility of lossless reaction-free closed spatial orbits that turn out to be classical pair creation and destruction events. The extended theory can accommodate a vacuum plenum of classical current that could be regarded as a classical version of the Fermionic ZPF of QFT, reminiscent of the relationship between the Electromagnetic ZPF and the classical imitation that characterizes `Stochastic Electrodynamics.
An obstacle to the development of direct action version of electromagnetism was that in the end it failed to fulfill its initial promise of avoiding the problem of infinite Coulomb self-energy in the Maxwell theory of the classical point charge. This
paper suggests a small but significant modification of the traditional direct action theory which overcomes that obstacle. Self-action is retained but the associated energy is rendered finite and equal to zero in the special case of null motion.
The cosmological scale factor $a(t)$ of the flat-space Robertson-Walker geometry is examined from a Hamiltonian perspective wherein $a(t)$ is interpreted as an independent dynamical coordinate and the curvature density $sqrt {- g(a)} R({a,dot a,ddot
a})$ is regarded as an action density in Minkowski spacetime. The resulting Hamiltonian for $a(t)$ is just the first Friedmann equation of the traditional approach (i.e. the Robertson-Walker cosmology of General Relativity), as might be expected. The utility of this approach however stems from the fact that each of the terms matter, radiation, and vacuum, and including the kinetic / gravitational field term, are formally energy densities, and the equation as a whole becomes a formal statement of energy conservation. An advantage of this approach is that it facilitates an intuitive understanding of energy balance and exchange on the cosmological scale that is otherwise absent in the traditional presentation. Each coordinate system has its own internally consistent explanation for how energy balance is achieved. For example, in the spacetime with line element $ds^2 = dt^2 - a^2(t) d{bf{x}}^2$, cosmological red-shift emerges as due to a post-recombination interaction between the scalar field $a(t)$ and the EM fields in which the latter loose energy as if propagating through a homogeneous lossy medium, with the energy lost to the scale factor helping drive the cosmological expansion.
We sketch the derivation of a Newtonian gravity-like force emerging from a direct-action variant of classical electromagnetism. The binding energy is a consequence of maximal phase correlation of the sources mediated by approximately monochromatic di
rect-action fields. The resulting force then has the character of a strong version of the van der Waals force, whose superior strength can be attributed to relatively coherent primary fields (compared with the totally incoherent effects of the ZPF). The model also predicts the existence of a background having some of the character of dark energy.
All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not exhaustive and t
hat there exists another relatively less well known family of transformations with a different conformal factor in the particular case that K = -1. Simplified conformal factors are derived for the special case of maximally-symmetric spacetimes. The full set of all possible cosmologically-compatible conformal forms is presented as a comprehensive table. A product of the analysis is the determination of the set-theoretical relationships between the maximally symmetric spacetimes, the Robertson-Walker spacetimes, and functionally more general spacetimes. The analysis is preceded by a short historical review of the application of conformal metrics to Cosmology.
Advanced electromagnetic potentials are indigenous to the classical Maxwell theory. Generally however they are deemed undesirable and are forcibly excluded, destroying the theorys inherent time-symmetry. We investigate the reason for this, pointing o
ut that it is not necessary and in some cases is counter-productive. We then focus on the direct-action theory in which the advanced and retarded contributions are present symmetrically, with no opportunity to supplement the particular integral solution of the wave equation with an arbitrary complementary function. One then requires a plausible explanation for the observed broken symmetry that, commonly, is understood cannot be met by the Wheeler-Feynman mechanism because the necessary boundary condition cannot be satisfied in acceptable cosmologies. We take this opportunity to argue that the boundary condition is already met by all expanding cosmologies simply as a result of cosmological red-shift. A consequence is that the cosmological and thermodynamic arrows of time can be equated, the direct action version of EM is preferred, and that advanced potentials are ubiquitous.
We test the Yilmaz theory of gravitation by working out the corresponding Friedmann-type equations generated by assuming the Friedmann-Robertson-Walker cosmological metrics. In the case that space is flat the theory is consistent only with either a c
ompletely empty universe or a negative energy vacuum that decays to produce a constant density of matter. In both cases the total energy remains zero at all times, and in the latter case the acceleration of the expansion is always negative. To obtain a more flexible and potentially more realistic cosmology, the equation of state relating the pressure and energy density of the matter creation process must be different from the vacuum, as for example is the case in the steady-state models of Gold, Bondi, Hoyle and others. The theory does not support the cosmological principle for curved space K =/= 0 cosmological metrics.
This paper follows in the tradition of direct-acti
Some arguments in favour of the existence of tachyons and extensions of the Lorentz Group are presented. On the former, it is observed that with a slight modification to standard electromagnetic theory a single superluminal charge will bind to itself
in a self-sustaining circular orbit, suggestive of a (modified) electromagnetic interpretation of the strong force. Symmetries in that theory are used in the subsequent analysis as a starting point in the search for physically-motivated extensions of the Lorentz Group. There is some discussion of the validity of imaginary coordinates in superluminal transformations of frame. The article concludes with some speculation on the implications for faster-than light travel.
It is shown that only the maximally-symmetric spacetimes can be expressed in both the Robertson-Walker form and in static form - there are no other static forms of the Robertson-Walker spacetimes. All possible static forms of the metric of the maxima
lly-symmetric spacetimes are presented as a table. The findings are generalized to apply to functionally more general spacetimes: it is shown that the maximally symmetric spacetimes are also the only spacetimes that can be written in both orthogonal-time isotropic form and in static form.
