arXiv subjects

David L. Berkahn

Publications and source records attributed to David L. Berkahn.

4 recordsLinked to original sources

arXiv2024

Generalized Minkowski spacetime with geometric algebra

We begin from the generalised eight-dimensional Minkowski spacetime structure, previously developed in Clifford geometric algebra $ C\ell(\Re^3) $. We propose that this is the correct algebraic representation for physical three-dimensional space. We find that this representation incorporates spin and helicity directly into spacetime, in a Lorentz invariant manner. From this foundation, based on purely algebraic arguments, we derive Minkowski spacetime, the properties of electromagnetic radiation and Maxwell's equations. These results being achieved all without physical arguments, showing that these physical laws are actually purely geometric effects. This approach also leads to a generalization of complex mass and proper time. Several insight about time are produced, including an arrow of time, which ultimately becomes a five-dimensional property. We also provide a new argument explaining the non-existence of magnetic monopoles. We suggest that the rotational freedoms, inherent in three-dimensional physical space are an important aspect of nature, not properly addressed in physics, as they are not incorporated within the spacetime background, as achieved in this paper.

math-ph↗

arXiv2024

A new derivation of the Minkowski metric

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of physical three-dimensional space, if modeled with Clifford geometric algebra $ C\ell(\Re^3) $. We find that Minkowski spacetime can be embedded within a larger eight dimensional structure. This then allows a generalisation of the invariant interval and the Lorentz transformations. Also, with this geometric oriented approach the fixed speed of light, the laws of special relativity and a generalised form of Maxwell's equations, arise naturally from the intrinsic properties of the algebra without recourse to physical arguments. We also find new insights into the nature of time, which can be described as two-dimensional. Some philosophical implications of this approach as it relates to the foundations of physical theories are also discussed.

physics.gen-ph↗

arXiv2019

Hilbert's forgotten equation, the equivalence principle and velocity dependence of free fall

Referring to the behavior of accelerating objects in special relativity, and applying the principle of equivalence, one expects that the coordinate acceleration of point masses under gravity will be velocity dependent. Then, using the Schwarzschild solution, we analyze the similar case of masses moving on timelike geodesics, which reproduces a little known result by Hilbert from 1917, describing this dependence. We find that the relativistic correction term for the acceleration based on general relativity differs by a factor of two from the simpler acceleration arguments in flat space. As we might expect from the general theory, the velocity dependence can be removed by a suitable coordinate transformation, such as the Painlev{é}-Gullstrand coordinate system. The validity of this approach is supported by previous authors who have demonstrated vacuum solutions to general relativity producing true flat space metrics for uniform gravitational fields. We suggest explicit experiments could be undertaken to test the property of velocity dependence.

physics.gen-ph↗

arXiv2016

Generalizing the Lorentz transformations

In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed obtained. We then find with these generalized coordinate transformations acting on Maxwell's equations that the electromagnetic field transformations are nevertheless unchanged. We find further, that if we assume the absence of magnetic monopoles, in accordance with Maxwell's theory, our generalized transformations are then restricted to be the conventional ones. While the conventional Lorentz transformations are indeed recovered from our framework, we nevertheless provide a new perspective into why the Lorentz transformations are constrained to be the conventional ones. Also, this generalized framework may assist in explaining several unresolved questions in electromagnetism as well as to be able to describe quasi magnetic monopoles found in spin-ice systems.

physics.gen-ph↗