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 Robertson's 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. (shrink)

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational (...) contribution.Nonlinear field equations for the torsion result. In a “low-energy” approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector. (shrink)

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion Ωμ of spacetime. This conjecture is made feasible by the natural separation of the connection ω μ v into “gravitational” and “electromagnetic” parts α μ v and β μ v , respectively, related to the metric and to the torsion. When α μ v is neglected in front of β μ v , the affine geodesics are shown to become the equations of motion of charged (...) particles with Lorentz force, for an appropriate choice of Ωμ. Since β μ v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if Ωμ were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when β μ v 《 α μ v ).In addition to the factor q/m, the velocity of the test particle appears in Ωμ. This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor. (shrink)

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 Newton's 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. (shrink)

Most Latin American scholars treat Latin American nations as a simple study object with similar characteristics. The purpose of this essay is to analyze some myths, stereotypes, realities, and challenges given to one of the most important regions of the world, knowing as Latin America. Latin Americ..

In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation (...) is not geometric.In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis.Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric. (shrink)

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line elements (...) that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

En los últimos años, la importancia del rol del Estado en la formulación de políticas económicas ha sufrido transformaciones considerables. En México, ha sido impuesto el modelo neoliberal en reemplazo de las políticas proteccionistas y estatistas de los regímenes populistas. Los resultados han ..

The electrodynamics consistent with the para-Lorentzian mechanics developed in previous papers is obtained. The transformation law for the fields, Maxwell's 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.

The issue of whether teleparallel nonlinear connections exist is resolved by their explicit construction on Finslerian metrics that arise in the Robertson test theory of special relativity (RTTSR), and on the Minkowski metric in particular. The method is an adaptation to the Finsler bundle of a similar construction for teleparallel linear connections. It suggests the existence of a concept of metric compatibility alternative toω μλ +ω λμ = 0 for teleparallel nonlinear connections. A sophisticated system of partial differential equations whose (...) solutions have been discussed in the computing literature is interpreted in geometric terms. The characteristics of the solutions are checked against compliance with the conditionω μλ +ω λμ = 0, an issue whose relevance for this theory derives from the fact that nonantisymmetric connections repeatedly appear in teleparallel geometry. (shrink)

It is shown that relativistic spacetimes can be viewed as Finslerian spaces endowed with a positive definite distance (ω0, mod ωi) rather than as pariah, pseudo-Riemannian spaces. Since the pursuit of better implementations of “Euclidicity in the small” advocates absolute parallelism, teleparallel nonlinear Euclidean (i.e., Finslerian) connections are scrutinized. The fact that (ωμ, ω0 i) is the set of horizontal fundamental 1-forms in the Finslerian fibration implies that it can be used in principle for obtainingcompatible new structures. If the connection (...) is teleparallel, a Kaluza-Klein space (KKS) indeed emerges from (ωμ, ω0 i), endowed ab initio with intertwined tangent and cotangent Clifford algebras. A deeper level of Kähler calculus, i.e., the language of Dirac equations, thus emerges. This makes the existance of an intimate relationship between classical differential geometry and quantum theory become ever more plausible. The issue of a geometric canonical Dirac equation is also raised. (shrink)

In 1960–1962, E. Kähler enriched É. Cartan’s exterior calculus, making it suitable for quantum mechanics (QM) and not only classical physics. His “Kähler-Dirac” (KD) equation reproduces the fine structure of the hydrogen atom. Its positron solutions correspond to the same sign of the energy as electrons.The Cartan-Kähler view of some basic concepts of differential geometry is presented, as it explains why the components of Kähler’s tensor-valued differential forms have three series of indices. We demonstrate the power of his calculus by (...) developing for the electron’s and positron’s large components their standard Hamiltonian beyond the Pauli approximation, but without resort to Foldy-Wouthuysen transformations or ad hoc alternatives (positrons are not identified with small components in K ähler’s work). The emergence of negative energies for positrons in the Dirac theory is interpreted from the perspective of the KD equation. Hamiltonians in closed form (i.e. exact through a finite number of terms) are obtained for both large and small components when the potential is time-independent.A new but as yet modest new interpretation of QM starts to emerge from that calculus’ peculiarities, which are present even when the input differential form in the Kähler equation is scalar-valued. Examples are the presence of an extra spin term, the greater number of components of “wave functions” and the non-association of small components with antiparticles. Contact with geometry is made through a Kähler type equation pertaining to Clifford-valued differential forms. (shrink)

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 Einstein's 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 Maxwell's electrodynamics. (shrink)

The revised Robertson's test theory of special relativity (SR) has been constructed upon a family of sets of passive coordinate transformations in flat space-time [J. G. Vargas and D. G. Torr,Found. Phys., 16, 1089 (1986)]. In the same paper, it has also been shown that the boosts depend in general on the velocities of the two frames involved and not only on their relative velocity. The only exception to this is SR, if one has previously used an appropriate constraint to (...) remove the other relativities—like Galilean relativity—from the family.In this paper we look at these coordinate transformations in the only way there is to do so, namely as transformations in a seven-dimensional “Cartan Space” (Cartan first considered this in his dealings with Newtonian kinematics). In this space, the boosts only depend on the relative velocity of the frames. The passive coordinate transformations in each set are shown to have a nonlinear group structure isomorphic to that of the Poincaré group.The existence of a preferred frame, except in SR, makes the active transformations inequivalent to the passive ones. It is shown that the composite active-passive transformations act on a ten-dimensional space and that each member set of the family also has a group structure. As a result, one ends up with a family of mutually isomorphic 9-parameter (homogeneous) supergroups and a family of mutually isomorphic (9 + 4)-parameter (inhomogeneous) supergroups. The presence of extra parameters could be looked upon as “internal” degrees of freedom, which are, however, an offshoot of the Robertson space-time. (shrink)

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one (...) free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant “Robertson's subfamilies.” It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory. (shrink)

It has recently been shown by Vargas, (4) that the passive coordinate transformations that enter the Robertson test theory of special relativity have to be considered as coordinate transformations in a seven-dimensional space with degenerate metric. It has also been shown by Vargas that the corresponding active coordinate transformations are not equal in general to the passive ones and that the composite active-passive transformations act on a space whose number of dimensions is ten (one-particle case) or larger (more than one (...) particle).In this paper, two different (families of) electrodynamics are constructed in ten-dimensional space upon the coordinate free form of the Maxwell and Lorentz equations. The two possibilities arise from the two different assumptions that one can naturally make with respect to the acceleration fields of charges, when these fields are related to their relativistic counterparts. Both theories present unattractive features, which indicates that the Maxwell-Lorentz framework is unsuitable for the construction of an electrodynamics for the Robertson test theory of the Lorentz transformations. It is argued that this construction would first require the formulation of Maxwell-Lorentz electrodynamics in the form of a connection in Finsler space. If such formulation is possible, the sought generalization would consist in simply changing bases in the tangent spaces of the manifold that supports the connection. In addition, the number of dimensions of the space of the Robertson transformations would be ten, but not greater than ten. (shrink)

Cavalleri and Spinelli have criticized previous work, connected with synchronization procedures, by the present author. This reply discusses their criticisms.