Jose G. Vargas

Revised Robertson's test theory of special relativity

The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson [Rev. Mod. Phys.21, 378 (1949)] of the Lorentz transformations from the results of the experimental evidence. Some researchers would argue that the proof contains an unwarranted assumption disguised as a convention about synchronization procedures. Others would say that alternative conventions are possible. In the present paper, no convention is used, but the Lorentz transformations are still obtained using only the results of the experiments in Robertsons proof, namely the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments. Thus the revised proof is a valid test theory which is independent of any conventions, since one appeals only to the experimental evidence. The analysis of that evidence shows the directions in which efforts to test special relativity should go. Finally it is shown how the resulting test theory still has to be improved for consistency in the analysis of experiments with complicated experimental setups, how it can be simplified for expediency as to what should be tested, and how it should be completed for a missing step not considered by Robertson.

The Cartan-Einstein Unification with Teleparallelism and the Discrepant Measurements of Newton's Constant G

We show that in 1929 Cartan and Einstein almost produced a theory in which the electromagnetic (EM) field constitutes the time-like 2-form part of the torsion of Finslerian teleparallel connections on pseudo-Riemannian metrics. The primitive state of the theory of these connections would not, and did not, permit Cartan and Einstein to realize how their torsion field equations contained the Maxwell system and how the Finslerian torsion contains the EM field. Cartan and Einstein discussed curvature field equations, though failing to focus on the fact that teleparallelism automatically implies gravitational field equations with torsion terms as source, both in first and second order. We further show that the first-order contribution of the EM field to the source of the gravitational field may play havoc with the remeasurement of Newtons gravitational constant, even if the experiment is electrically grounded. These results are also used as support for the thesis that there is an alternative to the present way of dealing with the great theoretical questions of physics. On the practical side, the inconveniences faced in measuring G may be greatly compensated by the possibility of manipulating spacetime with electric fields at the first-order level.

Teleparallel Kähler Calculus for Spacetime

In a recent paper [J. G. Vargas and D. G. Torr, Found. Phys. 27, 599 (1997)], we have shown that a subset of the differential invariants that define teleparallel connections in spacetime generates a teleparallel Kaluza-Klein space (KKS) endowed with a very rich Clifford structure. A canonical Dirac equation hidden in this structure might be uncovered with the help of a teleparallel Kähler calculus in KKS. To bridge the gap to such a calculus from the existing Riemannian Kähler calculus in spacetime, we commence the construction of a teleparallel Kähler calculus in spacetime. In the process, we notice: (a) Unknown to him, one of Einsteins equations in his attempt at unification with teleparallelism states that the interior covariant derivative of the torsion is zero. (b) A mechanism exists in the tangent bundle of teleparallel spaces for producing confinement (in the applicable cases, one would have to show why nonconfinement also occurs, rather than the other way around). (c) When the torsion is not zero, the interior covariant derivative in the sense of Kähler, δF, does not coincide with *d*F. The system (dF = 0, δF = j) rather than (dF = 0, *d*F = j) should then be used for generalizations of Maxwells electrodynamics.

Nonrelativistic para-Maxwellian electrodynamics with preferred reference frame in the universe

The electrodynamics consistent with the para-Lorentzian mechanics developed in previous papers is obtained. The transformation law for the fields, Maxwells equations, and the potentials are the main topics considered. One then obtains the gauge transformation and the electromagnetic action with a view to further develop the para-Lorentzian theory of the electron.

Is Electromagnetic Gravity Control Possible

We study the interplay of Einstein’s Gravitation (GR) and Maxwell’s Electromagnetism, where the distribution of energy‐momentum is not presently known (The Feynman Lectures, Vol 2, Chapter 27, section 4). As Feynman himself stated, one might in principle use Einstein’s equations of GR to find such a distribution. GR (born in 1915) presently uses the Levi‐Civita connection, LCC (the LCC was born two years after GR as a new concept, and not just as the pre‐existing Christoffel symbols that represent it). Around 1927, Einstein proposed for physics an alternative to the LCC that constitutes a far more sensible and powerful affine enrichment of metric Riemannian geometry. It is called teleparallelism (TP). Its Finslerian version (i.e. in the space‐time‐velocity arena) permits an unequivocal identification of the EM field as a geometric quantity. This in turn permits one to identify a completely geometric set of Einstein equations from curvature equations. From their right hand side, one may obtain the actual d...

The Theory of Acceleration Within Its Context of Differential Invariants: The Root of the Problem with Cosmological Models?

Acceleration is an almost-sterile concept. However, since four-velocity is a four-dimensional (thus reduced) tangent vector field over geometric phase-spacetime (t, xi, ui), it yields a very rich concept of acceleration as a vector-valued 1-form. As in general relativity, the usual concept of acceleration comes out in the wash. By virtue of their nature, constants such as mass and charge are absent from this theory, though there is room for the concept of mass in the “renormalization” of the metric. Since, modulo these constants, force and acceleration become synonymous, the theory of acceleration (TOA) becomes a theory of “shadow” interactions: gravitational, electromagnetic (EM), and a third interaction that we refer to as “Third.” The TOA constitutes part of the theory of all the invariants associated with the above frames, namely, classical differential phase-space time geometry (PSTG). That is its context. The TOA connects with the remainder of PSTG through terms which appear in the acceleration 1-form but which fail to reach the equations of the motion. This absence splits the torsion into one part that we call “electromagnetic + Third” and another part, “Fourth,” which cannot manifest itself as a classical interaction. “Fourth,” which appears to shadow the weak interaction, nevertheless has gravitational effects through its contribution to the source side of Einsteins equations. It is, therefore, dark matter. Cosmological energy appears to be nothing but the energy of this particular type of dark matter, accounting for three quarters of the total. A cosmological term more sophisticated than the one involving the cosmological constant thus results.