Unification of Light Propagation and Mechanics

Summary of recent posts:

In modern physics Maxwell's electromagnetics including propagation of light and classical Newton's mechanics are viewed to be fundamentally different because Maxwell's equations are Lorentz invariant (take the same form under Lorentz transformation of Euclidean coordinates), while Newton's equations are Galilean invariant (take the same form under Galilean transformation). This has prevented the formation of a unified theory, which is a major element of the crisis of modern physics.

Einstein formed the Special Theory of Relativity SR in 1905 by declaring that laws of physics have to be Lorentz invariant, thus declaring Maxwell's equations to represent laws of physics, while dismissing Newton's equations as being Galilean but not Lorentz invariant. Einstein then replaced Newton's mechanics by a new form of relativistic mechanics as SR exhibiting new strange physics of space contraction and time dilation, which today is viewed to be a fundamental part of modern physics. 

But Einstein's frank declaration that laws of physics must be Lorentz invariant appears as an ad hoc requirement without any real physical basis, and so it may be reasonable to seek to give Newton's mechanics under Galilean invariance a new chance. 

Doing so, we then face the fact that Maxwell's equations are not Galilean invariant, which means that the choice of Euclidean coordinate system for the expression of the equations comes into play.

Maxwell's equations in particular describe propagation of light as wave between a light emitter A and a receiver B as two points in Euclidean coordinate system E. It is natural to assume that the receiver does not move in E, while the emitter A is allowed to move (creating Doppler effect). 

We thus consider propagation of light from A to B described by Maxwell's wave equations expressed in a spatial Euclidean coordinate system in which the receiver B is stationary. Maxwell's wave equations contain a coefficient $c$ representing the speed of light as speed of wave propagation. 

It is assumed that $c$ is a constant which does not change with choice of Euclidean coordinate system. This conforms with the 2019 SI Standard where the length scale in any Euclidean coordinate system is determined by travel time of light with a preset value of the speed of light  $c$ equal to 299792458 meter/second and time measured by a caesium atomic clock. 

The propagation of light from A to B is thus described by Maxwell's equations expressed in a Euclidean coordinate system E fixed to the receiver with a preset speed of light. 

We now compare with propagation of sound in still air represented by E described by a wave equation similar to Maxwell's. Alternatively, we may compare with elastic waves in an elastic bar. 

The fundamental aspect here is that fixing E to the receiver makes propagation of light fully analogous to propagation of sound in still air or elastic waves in an elastic bar represented by E, as if E in both cases serves as a medium for wave propagation. In the case of sound waves/elastic waves the medium is material in the form of still air/elastic bar represented by E, while in the case of light the medium/aether is immaterial in the form of E. 

We thus face a situation where the medium/aether for wave propagation in the form of a Euclidean coordinate system is tied to the spatial configuration, more precisely to the receiver as if the medium/aether is "dragged along" with motion of the receiver, just like the medium of an elastic bar in motion will be moving.

We reach so a unification of immaterial light propagation and material mechanics by always connecting the coordinate system for Maxwell's equations to the receiver. This is fully compatible with Newtonian mechanics and the 2019 SI Standard and there is no place for SR since no Lorentz transformation is involved. 

There are still issues if several receivers are involved moving with different velocities, which is the subject of Many-Minds Relativity.