Instant Action at Distance vs Pre-Established Harmony

Pre-Established Order of Fighter Airplanes.

The 2022 Nobel Prize in Physics puts the light on the the apparent instant action at distance in Newtonian gravitation, which Leibniz brought up but Newton did not want to discuss: The gravitational force between two bodies at a given common time $t$ is supposed to depend on the position of the bodies at time $t$ without any time delay. 

But instant action at distance appears to violate principles of locality and finite speed of propagation of physical effects as principles held holy by Einstein, but being under fire by the 2022 Prize. Can something enlightening be said? 

We see the same phenomenon in the basic model of the harmonic oscillator in the form of a body attached to one end of a linear elastic spring fixed at its other end, which in 1d takes the form:

• $\frac{dv}{dt} = - x(t)$,
• $\frac{dx}{dt} = v(t)$,  

with $x(t)$ is position, $v(t)$ velocity and $-x(t)$ spring force at time $t$ and the solution is $x(t)=sin(t)$ and $v(t)=cos(t)$ if started at $t=0$ with the body at $x=0$ with $v=1$ (with the spring fixed at $x=0$). 

Here the restoring body force $-x(t)$ and acceleration $\frac{dv}{dt}$ appears to instantly react to the present length of the spring $x(t)$ as a global quantity. It appears that the body and spring act in perfect harmony without time delay as an expression of pre-established order in the words of Leibniz. 

The harmonic oscillator can be seen as a model of a Sun-Earth system with the gravitational pull from the Sun as a spring force with instant action and the resulting elliptical orbit as pre-established order from instant action at distance. With time delay the planet system would spin out of order (as well as the harmonic oscillator).

To give perspective, let us imagine the the fixed end of the spring in the harmonic oscillator is subject to a perturbation at a certain time. We expect the perturbation to trigger a wave in the elastic spring, which will reach the body with some time delay and alter its motion, and so we move away from instant action at distance under perturbations. We may expect the same effect if the Sun suddenly would take a leap. 

So we have a harmonic oscillator which appears to move under instant action at distance from an elastic spring as long as the fixed end of the spring is not moved, but with delayed action if the fixed end is suddenly perturbed. So we see a form of pre-established order of motion under instant action at distance if the system is not subjected to sudden perturbations. We do not expect the Sun to take a sudden leap.

This is like two fighter jets acting in perfect coordination seeming under instant action at distance as long as no pilot makes a sudden move. Does this resolve the apparent mystery of instant action at distance of the gravitational pull from the Sun? Is this an illusion which does not hold under perturbations? Can pre-established harmony rule the World as long as there are no sudden perturbations? Maybe. 

PS We can make a connection to group think, with all Swedes in unison politically moving in the same direction (e g NATO and FossilFree Society) as under a pre-established order, where there is no place for perturbations of view.  See also: