A harmonic function satisfies Laplace's equation ∇2Φ=0. In a harmonic coordinate system, coordinate axes can only be those functions which satisfy this condition. However in the theory of general relativity they are solutions of the wave equation,   ∂2Φ/∂t2 - c2∇2Φ=0  not just Laplace's equation.

https://en.wikipedia.org/wiki/Harmonic_coordinates

https://en.wikipedia.org/wiki/Harmonic_coordinate_condition

"Coordinates do not convey any intrinsic meaning: they allow you to express physical objects (tensors) in terms of functions."

Coordinates should not convey any additional meaning. But it seems that they have especially for 3D modeling. They make a difference which is not marginal in describing the systems. Regarding the GR, in harmonic coordinates the energy conservation for Isolated system is complied, for different kind of coordinates this is not complied while it should be.

"A harmonic function satisfies Laplace's equation ∇2Φ=0. In a harmonic coordinate system, coordinate axes can only be those functions which satisfy this condition. However in the theory of general relativity they are solutions of the wave equation,   ∂2Φ/∂t2 - c2∇2Φ=0"

which is the D'ALembert operator.

https://en.wikipedia.org/wiki/D%27Alembert_operator.

The harmonic coordinate condition is one of several coordinate conditions in general relativity, which make it possible to solve the Einstein field equations. A coordinate system is said to satisfy the harmonic coordinate condition if each of the coordinate functions xα (regarded as scalar fields) satisfies d'Alembert's equation. The parallel notion of a harmonic coordinate system in Riemannian geometry is a coordinate system whose coordinate functions satisfy Laplace's equation. Since d'Alembert's equation is the generalization of Laplace's equation to space-time, its solutions are also called "harmonic".

The laws of physics can be expressed in a generally invariant form. In other words, the real world does not care about our coordinate systems. However, for us to be able to solve the equations, we must fix upon a particular coordinate system. A coordinate condition selects one (or a smaller set of) such coordinate system(s). The Cartesian coordinates used in special relativity satisfy d'Alembert's equation, so a harmonic coordinate system is the closest approximation available in general relativity to an inertial frame of reference in special relativity.

http://physics.stackexchange.com/questions/33123/what-is-the-physical-intepretation-of-harmonic-coordinates

"so a harmonic coordinate system is the closest approximation available in general relativity to an inertial frame of reference in special relativity."

this is already something...

The laws of physics can be expressed in a generally invariant form. In other words, the real world does not care about our coordinate systems.

if this brings to the same phenomena ok, but if I don't use Harmonic coordinates the issue of energy conservation for isolated system in GR is not solved. And I think it is the best way to try to "harmonize" GR with EM theory which will not eventually be unified.

https://graphics.pixar.com/library/HarmonicCoordinatesB/paper.pdf

If one interprets harmonic coordinates as the preferred coordinates of some absolute Newtonian background, then one can interpret the harmonic condition itself as the continuity and Euler equations for the Lorentz ether. See http://ilja-schmelzer.de/ether

Dear Ilja,

thanks a lot, I'm reading your link.

so basically with the Harmonic coordinates widely used by Fock and strongly supported by him.

I advise you to have a talk with Frank Tangherlini.

Basically you bulid a "framework" based on the EM waves propagation since the the Harmonic coordinates are based on

the D'alembert operators for waves.

"All the conceptual problems of GR quantization simply disappear if we have a fixed Newtonian background and absolute time. And even non-renormalizability is no longer problematic "

I totally agree..in addition the renormalization is born out of the respect of the Lorentz invariance you may avoid also that since also the space-time disappears if you make the time absolute. The pseudo galilean transformations of Tangherlini...