The Catch of Special Relativity

Modern physics is deeply troubled by in particular Einstein's Special Relativity SR based on the Lorentz transformation exhibiting strange effects of time dilation and space contraction including a wealth of contradictions. 

SR arises from an attempt to unify observations of the same physics in two different Euclidean coordinate systems moving with constant velocity with respect to each other. 

The set up is a human observer X equipped with a Euclidean one-dimensional $x$-axis with distance marked in terms of lightseconds according to the 2019 SI Standard specifying the speed of light to be exactly 299792458 meter/second with second measured by a standard caesium clock, thus with a speed of light equal to exactly 1 lightsecond/second. The observer X is stationary with respect the $x$-axis and makes observations assuming that light propagates with speed 1 along the $x$-axis independent of the motion of the source with receiver always stationary. 

X is thus stationary in a Euclidean $(x,t)$-system allowing observations of effects of both Newton's mechanics and Maxwell's electromagnetics following the 2019 SI Standard. This allows X to observe all of classical physics and there is no need to ask for anything more.  

But let us anyway introduce another fully similar observer X' stationary in a $x^\prime$-axis which moves with constant speed $v$ with respect to the $x$-axis and using the same standard caesium clock unaffected by inertial motion, with thus the following space coordinate connection:

• $x^\prime =x+vt$        (G)

Both space axes act as aethers for propagation of light with speed 1, and we thus have two aethers/space axes moving with respect to each other with speed $v$ expressing Galilean invariance by (G).

We thus have two observers X and X' both capable of surveying all of classical physics, but from different view points. One may ask to what extent X and X' can agree as a function of the size of $v$. This is the subject of Many-Minds Relativity. 

In SR the connection between observations by X in $(x,t)$-coordinates and by X' in a $(x^\prime ,t^\prime )$-coordinates is dictated by the Lorentz transformation:

• $x^\prime =\gamma (x-vt)$, $t^\prime =\gamma (t-vx)$,  $\gamma =\frac{1}{\sqrt{1-v^2}}$ (L) 

expressing Lorentz invariance. We see that $x=t$ (as the trajectory of a light signal emitted at $(0,0)$ in the view of X) if and only if $x^\prime =t^\prime$ (as the trajectory of a light signal emitted at $(0,0)$ in the view of X'). 

On the other hand, (G) states that if $x=t$ (as the trajectory of a light signal in the view of X) then $x^\prime =t+vt=(1+v)t$ appearing to correspond to a light speed of $1+v>1$ in the view of X'. 

Einstein was led to SR by dismissing (G) and favouring (L). 

The catch is now the following: A light signal emitted at $(0,0)$ in the view of X, and a light signal emitted at $(0,0)$ in the X' system, are distinct light signals propagated in distinct aethers/coordinate systems. The light signal emitted in the $x$-system at $t=0$ following the trajectory $x=t$ is not the same as the light signal emitted at $(0,0)$ in the $(x^\prime ,t^\prime )$ system. This is because a light signal has an extension in space and is not emitted from a point-like source as shown in the previous post.

This means that there is no mission of SR to explain how different inertial observers can agree on a common speed of light is, since there is no light signal propagating with the speed $1+v$ in the view of X', only a light signal with speed 1 in the view of X, and a light signal with speed 1 in the view of X'. 

SR seeks to describe the same physics in different coordinate systems in a case were the physics is not the same. In other words, SR has no mission after the 2019 SI Standard requiring each observer to be stationary in a coordinate system/aether of choice in which light propagates with speed 1. Einstein's SR of 1905 is thus not the same as SR after 2019 as a remarkable result of self-correction demanded by logic.

In particular, the null result of the Michelson-Morley experiment can be understood from the fact that both observers X and X' can be viewed to "drag along" their respective aether. Recall that Einstein interpreted the MM null result indicating that "there is no single unique aether", as "there is no aether at all", while I have followed the other possibility namely "there are many different aethers".