Non-Physics of Lorentz Transformation

This post directly connects to the previous post Physics Illusion: Lorentz Transformation to which we refer for clarifying figures. 

The basic postulate of Einstein's Special theory of Relativity SR is the Lorentz transformation connecting the coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ by 

• $x^\prime =\gamma (x-vt)$, $t^\prime =\gamma (t-vx)$          (L)

where $v$ with $\vert v\vert \lt 1$ is a given constant and $\gamma =\frac{1}{\sqrt{1-v^2}}$. This is a very simple linear transformation, which by the chain rule satisfies

• $\frac{\partial}{\partial x}=\gamma (\frac{\partial}{\partial x^\prime}-v\frac{1}{\partial t^\prime})$
• $\frac{\partial}{\partial t}= \gamma (\frac{\partial}{\partial t^\prime}-v\frac{\partial}{\partial x^\prime})$

which leaves a wave equation invariant in the sense that if the function $u(x,t)$ satisfies 

• $\frac{\partial u}{\partial t}-\frac{\partial u}{\partial x}=0$,         (1)

then the function $u^\prime (x^\prime ,t^\prime )=u(x,t)$ satisfies an equation of the same form:

• $\frac{\partial u^\prime}{\partial t^\prime}-\frac{\partial u^\prime}{\partial x^\prime}=0$.  (2)

This is very simple mathematics, of the same complexity as 1+1 = 2. Here $(x,t)$ may be viewed to represent Euclidean space-time coordinates with (1) expressing propagation of a wave with unit speed, while according to Lorentz $(x^\prime ,t^\prime )$ does not represent any physical reality.    

This is were Einstein stepped in with SR declaring:    

1. (L) connects the coordinates $(x,t)$ and $(x^\prime ,t^\prime )$ in two Euclidean coordinate  systems moving with respect to each other, both with the same physical meaning.
2. True physical laws must take same form in coordinate systems connected by Lorentz transformation (be Lorentz invariant)  = Principle of Relativity. 

Einstein then accepted the wave equation as a true physical law, but not Newton's 2nd Law because it is not Lorentz invariant, and so modified Newton's mechanics into a new form of relativistic mechanics with all sorts of strange effects including space contraction and time dilation by the coupling of space with time in (L).

In 2 Einstein decides over physics. In 1 Einstein contradicts Lorentz and so we ask who was right? 

An answer is given by recalling from the previous post the concept of coexistence or simultaneity, as the presence in space of a spatially extended body B represented by a range of coordinates $x$ like $0<x<1$ for which the time coordinate is the same e.g. $t=0$. If we plug in $t=0$ into (L) we get

•  $x^\prime =\gamma x$, $t^\prime =-\gamma vx$ or $x^\prime = -\frac{1}{v}t^\prime$ 

which represents a trajectory in the $(x^\prime ,t^\prime )$-system without coexistence. This is contradictory and so shows that SR is non-physics.

The bottom line is that SR does not make sense for extended bodies. But a Universe without extended bodies with coexistence is not a real Universe, only a fantasy. The consequences for modern physics based on SR are far-reaching.

Or is it possible to save SR by insisting that the Universe consists of bodies without spatial extension somehow interacting under Lorentz invariance? We are thne led to ask how different such point-like bodies may interact? So we image two point-like objects with space coordinates $x_1$ and $x_2$ in the $(x,t)$ system, and we ask about the corresponding time coordinates $t_1$ and $t_2$? With $t_1=t_2$ the interaction is instant as an expression of coexistence,  while if $t_1>t_2$ or $t_2>t_1$ there is delay excluding true interaction. We are thus led to expect that true interaction between bodies requires coexistence and so would not satisfy Lorentz invariance. 

The case for SR is weak.  

More on the non-physics of (L): Three Major Inconsistencies of the Lorentz Transformation.