A map between Galilean relativity and 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...

Foundations of Physics, 2013

A recent paper suggested that if Galilean covariance was extended to signals and interactions, the resulting theory would contain such anomalies as would have impelled physicists towards special relativity even without empirical prompts. I analyze this claim. Some so-called anomalies turn out to be errors. Others have classical analogs, which suggests that classical physicists would not have viewed them as anomalous. Still others, finally, remain intact in special relativity, so that they serve as no impetus towards this theory. I conclude that Galilean covariance is insufficient to derive special relativity.

A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.

Foundations of Physics, 2009

Special relativity is based on the apparent contradiction between two postulates, namely, Galilean vs. c-invariance. We show that anomalies ensue by holding the former postulate alone. In order for Galilean invariance to be consistent, it must hold not only for bodies' motions, but also for the signals and forces they exchange. If the latter ones do not obey the Galilean version of the Velocities Addition Law, invariance is violated. If, however, they do, causal anomalies, information loss and conservation laws' violations are bound to occur. These anomalies are largely remedied by introducing waves and fields that disobey Galilean invariance. Therefore, from these inconsistencies within classical mechanics, electromagnetism could be predicted before experiment proved its existence. Special relativity, it might be argued, would then follow naturally, either as a resolution of the resulting conflict or as an extrapolation of the path between the theories. We conclude with a review of earlier attempts to base SR on a single postulate, and point out the originality of the present work.

2010

The General Theory of Relativity (GTR) is essentially a theory of gravitation. It is built on the Principle of Relativity. It is bonafide knowledge, known even to Einstein the founder, that the GTR violates the very principle upon which it is founded i.e., it violates the Principle of Relativity; because a central equation i.e., the geodesic law which emerges from the GTR, is well known to be in conflict with the Principle of Relativity because the geodesic law, must in complete violation of the Principle of Relativity, be formulated in special (or privileged) coordinate systems i.e., Gaussian coordinate systems. The Principle of Relativity clearly and strictly forbids the existence/use of special (or privileged) coordinate systems in the same way the Special Theory of Relativity forbids the existence of privileged and or special reference systems. In the pursuit of a more Generalized Theory of Relativity i.e., an all-encampusing unified field theory to include the Electromagnetic, Weak & the Strong force, Einstein and many other researchers, have successfully failed to resolve this problem. In this reading, we propose a solution to this dilemma faced by Einstein and many other researchers i.e., the dilemma of obtaining a more Generalized Theory of Relativity. Our solution brings together the Gravitational, Electromagnetic, Weak & the Strong force under a single roof via an extension of Riemann geometry to a new hybrid geometry that we have coined the Riemann-Hilbert Space (RHS). This geometry is a fusion of Riemann geometry and the Hilbert space. Unlike Riemann geometry, the RHS preserves both the length and the angle of a vector under parallel transport because the affine connection of this new geometry, is a tensor. This tensorial affine leads us to a geodesic law that truly upholds the Principle of Relativity. It is seen that the unified field equations derived herein are seen to reduce to the well known Maxwell-Procca equation, the non-Abelian nuclear force field equations, the Lorentz equation of motion for charged particles and the Dirac equation.

… e Outros Ensaios”, AS Alves, FJ …, 1998

We review the recent advances in the generally covariant and geometrically intrinsic formulation of Galilei relativistic quantum mechanics. The main concepts used are Galilei-Newton space-time, Newtonian gravity and electromagnetism, space-time connection and cosymplectic form, quantum line bundle and quantum connection, Schrodinger equation and Hilbert bundle, quantisable functions and quantum operators. The paper contains a number of improvements and simplifications with respect to the already published or announced results.

viXra, 2015

Using the concept of absolute time introduced in a previous work \cite{carvalho} we define two coordinate systems for spacetime, the Galilean and the Lorentzian systems. The relation between those systems allows us to develop a tensor calculus that transfer the Maxwell electrodynamics to the Galilean system. Then, by using a suitable Galilean limit, we show how this transformed Maxwell theory in the Galilei system results in the Galilei electrodynamics formulated by Levy Leblond and Le Bellac.

In an earlier contribution published two year ago [1], I tried to answer the question whether Einstein's Special Relativity Theory provided a complete description of reality. For it follows from what I have mentioned, that the velocity of light in vacuum was itself subjected to a modified Galilean velocity addition transformation which I have called, for its convenience, The Galilean-Lorentzian Transformation. I here return to this theme because I see that my claim (that light can itself obey a specialized velocity addition transformation property), has a verifiable consequence to the theory of relativity. I shall deduced in what follows that a homogenous gravitational coordinate system and a uniformly accelerated coordinate system contain certain relationship in much the same way that the principle of General covariance has subjected the electric and magnetic fields in Maxwell's theory. As the "Einstein's Equivalence Principle" is immaterial under electromagnetics but that electric or magnetic effect really depends on the observer's relative motion, just as we meet in any covariant theory, so too we have been led to the conclusion, which suggest itself, that the Equivalence Principle is also immaterial, in the theory of gravitation. The relations here deduced, will be valid only to a first approximation for simplicity.

Classical and Quantum Gravity, 1993

2010

Using post-Galilean space and time derivatives transformations and quantum mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation describing a spinless scalar particle. This new equation can also be obtained from Dirac's equation if $\beta=\gamma(1\pm\frac{v}{c})$. Biot-Savart law and additional continuity equations are obtained as a consequence of the invariance of Dirac's equation and Maxwell's equations under these transformations.