Invariant speed

Abstract: We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the space- time construct are consistent with the existence of a dynamical 3-space, and "absolute motion". We illustrate this mapping first with the standard theory of sound, as vibra- tions of a medium, which itself may be undergoing fluid motion, and which is covari- ant under Galilean coordinate transformations. By introducing a di erent non-physical class of space and time coordinates it may be cast into a form that is covariant under "Lorentz transformations" wherein the speed of sound is now the "invariant speed". If this latter formalism were taken as fundamental and complete we would be lead to the introduction of a pseudo-Riemannian "spacetime" description of sound, with a metric characterised by an "invariant speed of sound". This analysis is an allegory for the development of 20th century physics, but where the Lorentz covariant Maxwell equa- tions were constructed first, and the Galilean form was later constructed by Hertz, but ignored. It is shown that the Lorentz covariance of the Maxwell equations only occurs because of the use of non-physical space and time coordinates. The use of this class of coordinates has confounded 20th century physics, and resulted in the existence of a "flowing" dynamical 3-space being overlooked. The discovery of the dynamics of this 3-space has lead to the derivation of an extended gravity theory as a quantum e ect, and confirmed by numerous experiments and observations. It is commonly argued that the manifest success of Lorentz covariance and the spacetime formalism in Special Relativ- ity (SR) is inconsistent with the anisotropy of the speed of light, and indeed the existence of absolute motion, that is, a detectable motion relative to an actual dynamical 3-space, de- spite the repeated experimental detection of such e ects over, as we now understand, more than 120 years. This apparent incompatibility between a preferred frame, viz a dynamical 3-space, and the spacetime formalism is explicitly resolved by the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates , showing that Lorentz covariance and the spacetime construct are indeed consistent with Galilean covariance, but that they suppress any account of an underlying dynamical 3-space. In the neo-Galilean formalism, known also as the Lo- rentzian interpretation of SR, length contraction and clock ef- fects are real e ects experienced by objects and clocks in mo- tion relative to an actual 3-space, whereas in the Minkowski- Einstein spacetime formalism these e ects are transferred to the metric of the mathematical spacetime, and then appear to be merely perspective e ects for di erent observers. Ex- periments, however, have shown that the Galilean space and time coordinates competently describe reality, whereas the Minkowski-Einstein spacetime construct is merely a mathe- See (1) and Damour (2) for discussion of Minkowski's work.