Einstein Obsessed by the Speed of Light

Einstein founded his Special Theory of Relativity SR on two Postulates: 

1. The speed of light (denoted by c) is the same in all inertial systems.
2. Physical laws literally take the same form in all inertial systems.  

We have seen that since 2019 Postulate 1 is simply an agreement to define the length unit of meter in terms of the distance traveled by a light signal over a certain time interval, or equivalently an agreement to define the length unit of light-second as the distance traveled by light during 1 second. This is the new SI standard to be valid in all inertial coordinates system moving at different velocities. In other words, the unit of length in each coordinate system is simply adjusted so as to make the speed of light = c. 

The real question is to what extent different observers using different inertial systems, can agree. They agree on the speed of light but everything else is up to comparison.

Maybe this was understood by Einstein as an anticipation of the 2019 standard, or Einstein did not understand the difference between an agreement to use a certain standard as compared to actual physics not asking for any agreement as a physical fact. The fact that that the Sun rises every morning is not the result of an agreement but simply a physical fact.

In any case Einstein elevated the speed of light to have a fundamental significance. Einstein supported this idea by a claim that no physical effect can propagate faster than light (in vacuum), which gave light a special prominence in particular through the "equivalence of energy $E$ and mass $m$ mediated by  $E=mc^2$.  

But what is then the significance of the speed of light? Would the World be different if the speed of light was only half of current standard? Would the World be different if the speed of sound was only half of current estimate? What is the physical meaning of $E=mc^2$, if any at all?

It appears that Einstein in his 1905 patent office became obsessed with an idea that the speed of light $c$ has a universal significance, which he supported in "thought experiments" imagining himself riding on the crest of a light wave at the speed of light.  

We experience sound and light reaching our ears and eyes, but we rarely ask about the speed of sound or light, since it has no significance except as a nuisance in communication over large distances. 

Making something insignificant to something completely fundamental, will ruin any theory. Einstein was a master of such delusions. 

Speed of Light vs Speed of Gravity: Maxwell vs Newton vs Aether

Propagation of light in vacuum is described by Maxwell's equations expressed in terms of an electric field $E(x,t)$ and a magnetic field $B(x,t)$ where $x=(x_1,x_2,x_3)$ is the coordinate of an Euclidean spatial coordinate system $X$ and $t$ is a time coordinate, with dot representing differentiation with respect to time:

• $\dot B + \nabla\times E =0$  and $\dot E - \nabla\times B =0$    (1)   

where $\nabla =(\frac{\partial}{\partial x_1},\frac{\partial}{\partial x_2},\frac{\partial}{\partial x_3})$, and the speed of light $c$ is normalised to 1. Observation of the speed of light in the system $X$ by an observer $O$, thus gives the value 1. Since today the meter is defined in terms of light second, $c=1$ is an agreement and not a law of physics. 

So far so good, but what about the speed of the $X$? Relative to what? 

Suppose a different observer $O^\prime$ relies on the same Maxwell's equations (1) expressed in a different coordinate system $X^\prime$ moving with relative constant speed $v$ vs $X$, as a so called inertial system. Analysis in Many-Minds Relativity Chap 18 shows that $O$ and $O^\prime$ will agree up to a precision scaling with $v^2$. For human observers this means a precision of $10^{-9}$, which may be enough for all practical purposes. This means that (1) is Galilean invariant up to a precision of $v^2$. More precisely both observers will consider the speed of light to be exactly 1, since they agree to use the same Maxwell's equations (1).

To use Maxwell's equations (1) requires specification of the coordinate system and the natural choice is to lock the coordinate system to the observation apparatus and so allow the possibility of different apparatus moving with respect to each other, with observations agreeing up to $v^2$ with $v<<1$ for human observers. Many-Minds Relativity expands the scope to $v<1$.

Sum up: Maxwell's equations requires specification of spatial coordinate system. Different observers may use different inertial coordinate systems moving with relative speed $v$ and will then agree up to  $v^2$, and exactly agree on the speed of light. The choice of a specific coordinate system effectively represents a choice of an aether, so there are as many aethers as coordinate systems. 

Let us now turn to Newtonian gravitation described by 

• $\Delta\phi =\rho$            (2)

where $\phi (x,t)$ is gravitational potential and $\rho (x,t)$ mass density, and $\Delta$ is the Laplacian in the coordinates $x$ of a Euclidean coordinate system $X$. We understand that (2) is exactly Galilean invariant since (2) reads the same independent of any motion of $X$ with constant velocity, because no time derivative is involved. All inertial coordinate systems thus give the same description of gravitation. 

In the sense of Einstein it means that (2) satisfies Einstein's definition of a (perfect fundamental) physical law, as a law of physics which takes exactly the same form in all inertial systems (as an expression of Galilean invariance). 

The speed of gravity in (2) is formally infinite if $\rho$ is viewed to be primary from which $\phi$ is created by formally instant action at distance, which is unthinkable. Viewing instead $\phi$ as primary with $\rho$ the result of differentiation replaces instant action at distance by instant local action, which is thinkable. It is also possible to view (2) as a side condition without specifying cause-effect. In the latter perspectives the notion of speed of gravity is not needed.  

Conclusion:  

1. Newton's law of gravitation (2) is Galilean invariant an so is a thinkable prefect physical law for which a notion of speed of gravity is not needed. No aether enters the discussion. 
2. Maxwell's equations is Galilean invariant up to $v^2$, where for human observers $v^2<10^{-9}$, with $c=1$ acting as an agreement. Each choice of coordinate system represents and aether. 
3. The speed of light serves a fundamental role, while a speed of gravity is not needed.
4. Massless electromagnetics and mass gravitation are fundamentally different, which contradicts Einstein. Search of gravitons as gravitational analog of photons is fruitless. 
5. There is no need to modify Newtonian mechanics, and so Einstein's relativity serves no purpose. 
6. A Grand Unified Theory as Maxwell + Newton is readily available.