Unravelling Lorentz Covariance and the Spacetime Formalism

Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein's theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2016

have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties-that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity-are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invariance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein's theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and unidirectional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.

Physics International, 2013

The major extant relativity theories-Galileo's Relativity (GaR), Lorentz's Relativity (LR) and Einstein's Special Relativity (SR), with the latter much celebrated, while the LR is essentially ignored. Indeed it is often incorrectly claimed that SR and LR are experimentally indistinguishable. Here we show that (i) SR and LR are experimentally distinguishable, (ii) that comparison of gas-mode Michelson interferometer experiments with spacecraft earth-flyby Doppler shift data demonstrate that it is LR that is consistent with the data, while SR is in conflict with the data, (iii) SR is exactly derivable from GaR by means of a mere linear change of space and time coordinates that mixes the Galilean space and time coordinates. So it is GaR and SR that are equivalent. Hence the well known SR relativistic effects are purely coordinate effects and cannot correspond to the observed relativistic effects. The connections between these three relativity theories has become apparent following the discovery that space is an observable dynamical textured system and that space and time are distinct phenomena, leading to a neo-Lorentz Relativity (nLR). The observed relativistic effects are dynamical consequences of nLR and 3-space. In particular a proper derivation of the Dirac equation from nLR is given, which entails the derivation of the rest mass energy mc 2 .

2015

The four dimensional spacetime continuum, as originally conceived by Minkowski, has become the default framework within which to describe physical laws. Due to its fundamental nature, there have been various attempts to derive this structure from more fundamental physical principles. In this paper, we show how the Minkowski spacetime structure arises directly from the geometrical properties of three dimensional space when modeled by Clifford geometric algebra of three dimensions Cℓ(ℜ 3). We find that a time-like dimension, as well as three spatial dimensions, arise naturally, as well as four additional degrees of freedom that we identify with spin. Within this expanded eightdimensional arena of spacetime, we find a generalisation of the invariant interval and the Lorentz transformations, with standard results returned as special cases. The power of this geometric approach is shown by the derivation of the fixed speed of light, the laws of special relativity and the form of Maxwell's equations, without any recourse to physical arguments. We also produce a unified treatment of energy-momentum and spin, as well as predicting a new class of physical effects and interactions.

This is a reprint of a paper, that I co-authored with Prof. Frank Meyer from the University of Wisconsin, published in the quarterly journal, RECIPROCITY, of the International Society of Unified Science. We members all espoused the breakthrough in theoretical physics, originated by Dewey B. Larson of Portland,, Oregon

2015

Following Minkowski's formulation of special relativity, it is generally accepted that we live in a four-dimensional world consisting of three space and one time dimension. Due to its fundamental importance, a variety of arguments have been proposed over the years attempting to derive this spacetime structure from underlying physical principles. In our approach, we show how Minkowski spacetime arises from the geometrical properties of three dimensional space. We demonstrate this through modeling physical space with Clifford's geometric algebra of three dimensions. We indeed find using this representation that a time-like dimension arises naturally within this space but also extends spacetime to eight dimensions through incorporating four spin degrees of freedom. This expanded arena of spacetime produces a generalized group of Lorentz transformations and provides a natural description of fundamental particles. Nearly all standard results are returned in this expanded structur...

A map is discussed that connects, in 1+1 dimensions, Galilei's relativity to Einstein's special relativity. By means of this map it is possible to derive special-relativistic formulas from the corresponding Galilean ones. Beyond being interesting on its own, this map is also significant with respect to a recent debate on the extension of relativistic symmetries to the Planck scale (especially in the framework of the so-called doubly special relativity). The map in fact provides an explicit example of how can be misleading to interpret a mathematical correspondence between two relativity schemes as an argument in favor of their physical equivalence.

Foundations of Physics, 1981

GaliIean space-time plays the same role in nonrelativistic physics that Minkowski space-time does in relativistic physics. In this paper, the fundamental concepts (velocity, momentum, kinetic energy, etc.) and principles (laws of motion and conservation laws) of classical physics are formulated in the language of Galilean space-time. Much of the development closely parallels the development of similar concepts and principles in the theory of special relativity.

ISRN Mathematical Physics, 2013

We present two models combining some aspects of the Galilei and the Special relativities that lead to a unification of both relativities. This unification is founded on a reinterpretation of the absolute time of the Galilei relativity that is considered as a quantity in its own and not as mere reinterpretation of the time of the Special relativity in the limit of low velocity. In the first model, the Galilei relativity plays a prominent role in the sense that the basic kinematical laws of Special relativity, for example, the Lorentz transformation and the velocity law, follow from the corresponding Galilei transformations for the position and velocity. This first model also provides a new way of conceiving the nature of relativistic spacetime where the Lorentz transformation is induced by the Galilei transformation through an embedding of 3-dimensional Euclidean space into hyperplanes of 4-dimensional Euclidean space. This idea provides the starting point for the development of a se...

In support of their contention that it is the absence of a subsisting medium that imbues the speed of light with fundamentality, Bryan Cheng and James Read discuss certain "…shbowl universes"in which physical in-‡uences evolve, not at the speed of light, but that of sound. The Lorentz transformation simulated in these sonic universes, which the authors cite from the literature of analogue gravity, is not that of Einstein, for whom an aether was "super ‡uous", but that of the earlier relativity of Lorentz and Poincaré, which did suppose such a medium. The authors'intention is not to argue analogically, but simply to contrast the situation of light with that of sound. However, I argue that these universes are too successful as analogues to support the authors'case. By reducing Lorentzian relativity to its bare essentials, they provide a compelling demonstration of the viability and explanatory strengths of the earlier theory. They show how a thoroughly wave-theoretic treatment of the Lorentz transformation would explain why all aspects of matter transform in like manner, thereby avoiding a di¢ culty that was a signi…cant reason for the demise of Lorentzian relativity after 1905. Importantly, these sonic universes also suggest a unifying explanation, not only of the Lorentz transformation and de Broglie wave, but of the principle of relativity, which was merely postulated, rather than explained, by Einstein in 1905.