Kaluza's Theory Research Articles

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

Null-Result Test for Effect on Weight from Large Electrostatic Charge

We report test results searching for an effect of electrostatic charge on weight. For conducting test objects of mass of order 1 kg, we found no effect on weight, for potentials ranging from 10 V to 200 kV, corresponding to charge states ranging from 10−9 to over 10−5 coulombs, and for both polarities, to within a measurement precision of 2 g. While such a result may not be unexpected, this is the first unipolar, high-voltage, meter-scale, static test for electro-gravitic effects reported in the literature. Our investigation was motivated by the search for possible coupling to a long-range scalar field that could surround the planet, yet go otherwise undetected. The large buoyancy force predicted within the classical Kaluza theory involving a long-range scalar field is falsified by our results, and this appears to be the first such experimental test of the classical Kaluza theory in the weak field regime, where it was otherwise thought identical with known physics. A parameterization is suggested to organize the variety of electro-gravitic experiment designs.

Theodor Kaluza's Theory of Everything: revisited

Theodor Kaluza's Theory of Everything: revisited

RELATIONAL LOOK ON THE PRINCIPLES OF THE GEOMETRIC PARADIGM

The article compares the descriptions of gravitational and electromagnetic interactions in two physical and theoretical paradigms: geometric and relational. On the one hand, the general theory of relativity and the 5-dimensional geometric theory of Kaluza and, on the other hand, the relational theory of electro-gravity are compared. The comparison describes the parallel manifestations of all the “four miracles” of Salam in two physical and theoretical approaches. Based on the relational concepts, it is shown that three types of the considered interactions - electromagnetic, scalar and gravitational - in the theory of electrogravity have a derivative character from electromagnetism. The idea is expressed that in the twentieth century, physics could develop mainly within the framework of the relational paradigm.

Field Equations and Lagrangian of the Kaluza Energy-Momentum Tensor

We provide an analysis and statement of the source term in the classical Kaluza field equations, by considering the 5-dimensional (5D) energy-momentum tensor corresponding to the 5D geodesic hypothesis that is typically presumed in the Kaluza theory. By providing the 5D matter Lagrangian, this work completes a Lagrangian analysis of the classical Kaluza theory that began by establishing the proper form of the unique Kaluza field Lagrangian. This work considers the transformation properties necessitated by general covariance of the Kaluza source terms, to establish the correct form for the source terms in the field equations, and to establish the 5D matter Lagrangian that corresponds to the 5D geodesic hypothesis. In addition to the effects of a scalar field expected from other scalar-tensor or scalar-electromagnetic theories, a peculiar Kaluza coupling coefficient arises for charged matter which acts to vary the source strengths in ways unknown to conventional physics. We briefly evaluate the implied modifications to source terms in the field equations. We find an ADM-like neutralization of gravity at high specific charge states and a saturation in field strength at high specific charge-to-mass ratios.

Kaluza theory with zero-length extra dimensions

A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the [Formula: see text]-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge bundle, and the other one to the metric of the fiber and giving the horizontal bundle of the connection. When combined, the two metrics give the Kaluza metric and its generalization to the non-Abelian case, justifying thus his choice. Considering the two metrics as fundamental rather than the Kaluza metric explains why Kaluza’s theory should not be regarded as five-dimensional (5D) vacuum gravity. This approach suggests that the only evidence of extra dimensions is given by the existence of the gauge forces, explaining thus why other kinds of evidence are not available. In addition, because the degenerate metric corresponding to the spacetime metric vanishes along the extra dimensions, the lengths in the extra dimensions is zero, preventing us to directly probe them. Therefore, this approach suggests that it is not justified to search for experimental evidence of the extra dimensions as if they are merely extra spacetime dimensions. On the other hand, the new approach uses a very general formalism, which can be applied to known and new generalizations of the Kaluza theory aiming to achieve more and make different experimental predictions.

Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.

Kitcher's Explanatory Unification, Kaluza–Klein Theories, and the Normative Aspect of Higher Dimensional Unification in Physics

I examine the relation between explanation and unification in both the original Kaluza–Klein theory, which originated in the works of Theodor Kaluza and Oskar Klein in the 1920s, and in the modern Kaluza–Klein theories which date back to the late 1970s and which are still considered by the majority of the physics community to be the best hope for a complete unified theory of all fundamental interactions. I use the conclusions of this case study to assess the merits of Philip Kitcher's account of explanation as unification. I also draw lessons about physicists’ pursuit of the higher dimensional unification of the fundamental forces of nature. 1 Introduction 2 Kitcher on Explanatory Unification 3 A Close Look at the Kaluza–Klein Theory 3.1 Kaluza's theory: unification of gravity and electromagnetism 3.2 Klein's theory: an elucidation and elaboration of Kaluza's theory 3.3 Klein's compactification of the fifth dimension: explaining the unobserved 4 A General Overview of the Emergence of the Modern Kaluza–Klein Theories 5 Kaluza–Klein Unification Examined by Kitcher's Standard of Unification 6 Concluding Remarks

Variational techniques in general relativity: A metric-affine approach to Kaluza’s theory

A new variational principle for General Relativity, based on an action functional $I\/(\Phi,\nabla)\/$ involving both the metric $\Phi\/$ and the connection $\nabla\/$ as independent, \emph{unconstrained\/} degrees of freedom is presented. The extremals of $I\/$ are seen to be pairs $\/(\Phi,\nabla)\/$ in which $\Phi\/$ is a Ricci flat metric, and $\nabla\/$ is the associated Riemannian connection. An application to Kaluza's theory of interacting gravitational and electromagnetic fields is discussed.

On the field equations of Kaluza's theory

The field equations of the original Kaluza's theory are analyzed and it is shown that they lead to modification of Einstein's equations. The appearing extra energy–momentum tensor is studied and an example is given where this extra energy–momentum tensor is shown to allow four-dimensional Schwarzschild geometry to accommodate electrostatics. Such deviation from Reissner–Nordström geometry can account for the interpretation of Schwarzschild geometry as resulting not from mass only, but from the combined effects of mass and electric charge, even electric charge alone.

Haunted Kaluza universe with four-dimensional Lorentzian flat, Kerr, and Taub–NUT slices

The duality between the original Kaluza's theory and Klein's subsequent modification is duality between slicing and threading decomposition of the five-dimensional spacetime. The field equations of the original Kaluza's theory lead to the interpretation of the four-dimensional Lorentzian Kerr and Taub–NUT solutions as resulting from static electric and magnetic charges and dipoles in the presence of ghost matter and constant dilaton, which models Newton's constant.

The fifth dimension: Theodor Kaluza's ground-breaking idea

Theodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space-time is followed by a discussion of the significance of Kaluza's five-dimensional unified theory in modern physics from the point of view of superstring and M-theory.

The fifth dimension: Theodor Kaluza's ground‐breaking idea

AbstractTheodor Kaluza (1885–1954) attracted the attention of the physical community since 1921 with his unified field theory of gravitation and electromagnetism in five dimensions. Despite Einstein's great interest in Kaluza's theory, 50 years elapsed before it contributed toward a paradigm shift in modern theoretical physics. The biography of this still unknown scientist is briefly presented along with an outline of his work in physics. A short history of the theories of unification and the dimensionality of space‐time is followed by a discussion of the significance of Kaluza's five‐dimensional unified theory in modern physics from the point of view of superstring and M‐theory.

Light deflection in Kaluza–Klein gravity

When general relativity is extended from four to five dimensions, as in the theory of Kaluza and Klein, the relations for the classical tests are modified. The light-deflection problem shows a particularly interesting modification. We derive the general expression for light deflection by a massive body in the five-dimensional theory, and show that it can lead to significantly reduced deflection angles.

Scalar field in a seven-dimensional manifold behaving as an SO(3)-covariant spinor field in space-time.

In a Kaluza theory with topology Minkowski-space\ifmmode\times\else\texttimes\fi{}three-sphere, a metrical field equivalent to the Pauli matrices introduces a natural spin structure. Other fields occurring naturally on this manifold behave then as spinor fields when viewed from their space-time projection.

Natural origin of SO3-spinors in an eight-dimensional Kaluza theory exhibiting an additional U1�SU2 internal symmetry

The higher-dimensional spaceM4×S1×S3 (M4 = Minkowski space) is assumed. The symmetry group ofS3 isSO4 ≃SU2×SU2 “Gravitational waves” produce a symmetry breaking so thatSO3, rotations inM4 are linked with one of theSU2. Certain components of the metrical tensor ofM4×S1×S3, appear then as spinor fields.

Geometry of N=1 Yang-Mills theory in curved superspace

Generalises the formalism of Ogievetsky and Sokatchev (1980) to describe the geometry of N=1 supersymmetric Yang-Mills theory (coupled in general to supergravity). This generalisation seems to be analogous to the Kaluza theory. The author's presentation uses recent developments in geometry of supergravity and exhibits some similarity with the construction of Atiyah and Ward (1977).

The Problem of Motion in the Kaluza Theory

It is shown that the equations of motion for a charged massive particle are consequences of the field equations in Kaluza unification theory of gravitation and electromagnetism, i.e., the equations of motion for the particle can be deduced from Kaluza field equations, just as that in Einstein's theory of motion of general relativity the equations of motion for a massive particle are consequences of the Einstein equations. Furthermore, the Lorentz equations for a particle moving in the Maxwell electromagnetic field on the Minkowskian space-time can also be obtained from the Maxwell equations by means of the Kaluze mechanism of the Maxwell theory.