2019 SI Standard: Back to Classical Physics

Newton, forgive me! (Einstein)

The first step from classical to modern physics was taken by Einstein in 1905 in his Special Theory of Relativity SR replacing classical Galilean invariance satisfied by Newton's equations, by Lorentz invariance satisfied by Maxwell's wave equations for propagation of light. 

Einstein argued that laws of physics must be Lorentz invariant, which required a reformulation of Newton's mechanics into a new relativistic mechanics taking without gravitation the form of SR. 

In SR length and time were supposed to be measured with meter sticks and mechanical clocks, which by Lorentz invariance were subject to new strange effects of space contraction and time dilation.  

In 2019 (preceded in 1983) a new SI Standard was introduced with the length scale along any given $x$-coordinate axis measured in terms of travel time of light with a preset speed of light of 299792458 meter/second,  and time measured by a standard caesium atomic clock. This means that any given $x$-axis acts like an aether for propagation of light at given fixed speed. 

Consider a similar $x^\prime$-coordinate axis sliding on top of the $x$-axis with constant velocity $w$ as inertial motion with shared time $t$, like a different aether with shared time "carried along" with the sliding $x^\prime$-axis. Assuming that the origins of the axes coincide for $t=0$, the spatial coordinates will then following the 2019 SI Standard be connected by

• $x^\prime = x-wt$ 

which is a Galilean transformation. We can alternatively view the meter scale to be set by a meter-stick which does not change under inertial motion as if the meter stick is carried along by any given spatial axis without change of size. We are thus led to a many-aether theory, which in particular explains the null result of the Michelson-Morley experiment showing non-existence of a single unique aether. 

A basic feature is a connection established through resonance between emitter and absorber of light carried by an aether/coordinate system tied to the absorber, as explored in Computational Black Body Radiation.    

The 2019 SI Standard is in full agreement with Galilean invariant Newtonian mechanics. This means that after an interlude of 114 years Newtonian mechanics is back again, thus replacing relativistic mechanics with its strange space contraction and time dilation and Lorentz invariance. 

Light propagation is in the 2019 SI Standard carried by different aethers as different $x$-axes with basic question:

• To what extent is propagation of light Galilean invariant?  (Q) 

This question is addressed in Many-Minds Relativity as an observer version of a many-aethers theory.

Recall that the step from classical to modern physics was motivated by an argument claiming that Newtonian physics required an "absolute space" as a preferred Euclidean coordinate system, which however could not be identified. But Newtonian physics is Galilean invariant and so works equally well in all inertial systems and so does not need any absolute space. On the other hand, an absolute time rate can be set by a caesium clock unaffected by inertial motion. The rush to modernity thus was not founded on real physics.  

Summary: The 2019 SI Standard with the same preset speed of light in every inertial system effectively brings back classical Galilean invariance into physics, leaving Lorentz invariance/SR as a curiosity without physical meaning along with the original conception of Lorentz. This removes the main obstacle to a unified theory of mechanics and electromagnetics by letting real experimental physics/SI Standard take the lead before Einstein's ad hoc theory based on "thought experiments".

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".

Non-Physical Lorentz Transformation

This is a follow up of the previous post with another aspect of the non-physicality of the Lorentz transformation. 

Lorentz invariance is a holy feature of modern physics coming to expression for a wave equation:

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

with solution $u(x,t)$ depending on a 1d Euclidean coordinate $x$ and time coordinate $t$. As shown in this post, the function $u^\prime (x^\prime ,t^\prime )=u(x,t)$ expressed in the Lorentz transformed coordinates $(x^\prime ,t^\prime)$ stated in the previous post, satisfies the wave equation

$\frac{\partial u^\prime}{\partial t^\prime}-\frac{\partial u^\prime}{\partial x^\prime}=0$  (W'),

which is viewed to express Lorentz invariance: The function $u(x,t)$ satisfying the wave equation (W), in transformed coordinates $u^\prime (x^\prime ,t^\prime )$ satisfies the wave equation (W') which reads exactly the same way as (W). 

The current wisdom is thus to say that the wave equation being invariant under Lorentz transformation, expresses a physical law which takes the same form in different coordinate systems connected by the Lorentz transformation. Invariance!

After having noted that the wave equation is Lorentz invariant, Einstein bravely proclaimed that all (true) laws of physics are Lorentz invariant, which immediately forced him to throw out Newtonian mechanics since Newton's 2n Law is not Lorentz invariant, and proceed to form a new relativistic mechanics unfortunately creating lots of trouble for modern physicists.

To someone with a bit of schooling in mathematics the wave equation (W) needs a qualification into an initial value problem with $t>0$, and $u(x,0)$ as an initial value as a function with spatial extension for all $x$, thus as co-existence in space for $t=0$. 

Now comes the catch: The initial value is not Lorentz invariant, since $t=0$ and $t^\prime =0$ do not say the same. In fact, $u(x,0)=u^\prime (\gamma x, \gamma vx)$, which is not an initial value for $u^\prime (x^\prime ,0)$. 

Co-existence as extended existence in space at a specific time is fundamental. Without co-existence the world collapses into point-like isolated events in space without cohesion and meaning.  

In other words, not even the wave equation (W) is Lorentz invariant, and so the whole idea of modern physics to consider laws of physics which are Lorentz invariant, collapses. This should be a relief for all students of physics for which exams in relativistic mechanics appear as road-block.