Theory of the dynamic medium of reference: Exterior case and interior case
Authors: Pignard Olivier 
Published: September 2021

The theory of the dynamic medium of reference (DMR) has already been presented in several articles by this author [O. Pignard, Phys. Essays 32, 422 (2019); 33, 395 (2020); 34, 61 (2021)], and in particular, in the first one titled “Dynamic medium of reference:
A new theory of gravitation.” This theory proposes the existence of a medium made up of entities called gravitons. A gravitational field is a flux of the medium, whose speed is defined by the formula <mml:math display="inline"> <mml:mrow> <mml:mover accent="true"> <mml:mrow>
<mml:msub> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>/</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo stretchy="true">→</mml:mo> </mml:mover> <mml:mo
stretchy="false">(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mrow> <mml:msubsup> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo>
<mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>G</mml:mi> </mml:msub> </mml:mrow> </mml:msubsup> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:msub> <mml:mi
mathvariant="normal">V</mml:mi> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>/</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo stretchy="true">→</mml:mo> </mml:mover> </mml:mrow>
</mml:mrow> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>G</mml:mi> </mml:msub> </mml:mrow> </mml:mfrac> </mml:mrow> </mml:math> = <mml:math display="inline"> <mml:mover accent="true"> <mml:mrow>
<mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext mathvariant="normal">flux</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo> </mml:mover> <mml:mo stretchy="false">(</mml:mo>
<mml:mi>M</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , where <mml:math display="inline"> <mml:mover accent="true"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>G</mml:mi>
<mml:mo>/</mml:mo> <mml:mi>R</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo> </mml:mover> </mml:math> is the speed of the gravitons with regard to the reference frame R and NG is the number of
gravitons contained in an elementary volume centered in M. A massive body of mass M creates a flux of the medium of acceleration <mml:math display="inline"> <mml:mover accent="true"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow>
<mml:mrow> <mml:mtext mathvariant="normal">flux</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mo> </mml:mo> <mml:mo>−</mml:mo>
<mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">GM</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup>
<mml:mo stretchy="false">)</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo>
</mml:mover> </mml:math> and speed <mml:math display="inline"> <mml:mover accent="true"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mtext mathvariant="normal">flux</mml:mtext>
</mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo> </mml:mover> <mml:mo>=</mml:mo> <mml:mo> </mml:mo> <mml:mo>−</mml:mo> <mml:msqrt> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn>
<mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">M</mml:mi> <mml:mo>/</mml:mo> <mml:mi>r</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:msqrt> <mml:mover accent="true"> <mml:mrow> <mml:msub>
<mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>→</mml:mo> </mml:mover> </mml:math> , both centripetal. While the relationship between
the acceleration and the speed of the flux of the medium has already been demonstrated, the formula of the acceleration has not yet been demonstrated. This article proposes to provide the demonstration of the formula of acceleration in the exterior case (point M outside the massive body creating
the gravitational field) and in the interior case (point M inside the massive body creating the gravitational field). It is then given the link between the theory of the DMR and general relativity in the exterior case and the interior case. Finally, the article presents reflections between
the two theories and then gives arguments in favor of a propagation speed of the gravitational field much greater than that of light, noting that the theory of the DMR establishes a difference between the gravitational fields, which propagate at the speed of the gravitons and gravitational
waves, which propagate at the speed of light.