one of the greatest remaining tasks of physical research

From: Kacem Rochd <rochdkacem@gmail.com>

Subject: Emergence of gravity as a thermodynamic property of the gravitational system

I have a strong believe that gravity is a thermodynamic property as the temperature or the pressure, but it is not a force, because the superposition of two forces is additive (F = F1 + F2), while the mixture of two bodies temperatures is not additive, but instead an average of the two temperatures (T = (T1 + T2) / 2).

From a simple dimensional analyses of the Newtonian potential, it is found that the Newtonian potential and its dual (isomorphic) give rise to gravity by superposition, so that the orbital velocities or the gravitational accelerations are equal to the sommation to the half-velocities and the half-accelerations obtained with the first and the second derivatives of distance relative to time using equation of Newtonian potential and its dual respectively.

That the orbital velocity and the acceleration are respectively : V = (V(Newton) + V(Dual)) / 2 and A = (A(Newton) + A(Dual)) / 2

This is consistent with solar system dynamics.

Please, find my work (in progress) attached herewith.

Waiting for your critical response, I would like to thank you very much for your considerations and your time.

Kind regards,

kacem.

Preliminaries to a new theory of gravity

Introduction: Understanding Newtonian potential is one of the greatest remaining tasks of

physical research.

Dual to the Newtonian potential: From a simple dimensional analysis of the Newtonian
potential, we derive a dual to the Newtonian potential in the form of the ratio of the mass density in
4-dimensional temporal space to the mass density in 3-dimensional Euclidean space times the time squared times the inverse distance, that is :
∅ Newton = ∅ dual = τ ^{−2}
With
∅ Newton = − G ∗ M ∗ r ^{−3}
And
∅ dual = −ρ^t/ρ^d∗ τ^2 ∗ r^{−3}
In where ρ^t is the mass density in 4-dimensional temporal space, ρ^d is the mass density in 3-
dimensional Euclidean space, τ^{−2} is the temporal curvature, r is the radius of curvature, M is the
gravitational mass, and G is the Newtonian gravitational constant.
Gravitation: It follows from dimensional analysis of the Newtonian potential two ingredients for
a theory of gravity : 1) Duality of the Newtonian potential 2) D = (4 + 6) gravity which can be reduced to D = (1 + 3) gravity by assuming a coaxial superposition of two 3-dimensional Euclidean spaces and a spherical symmetry of one 4-dimensional temporal space.
Duality of the Newtonian potential implies that the radial velocities and the gravitational
accelerations are equal to the summation of the half-radial velocities and the half-gravitational
accelerations obtained by taking the first and the second derivatives of the distance relative to the
time using equations of the Newtonian potential and its dual respectively
...
Application: Computations based on the summation of the half-radial velocities and the half-
gravitational accelerations reveal that the 1D orbital velocities of the solar system planets and the
3D free-full accelerations at the surface of the Earth are consistent with the theoretical predictions
of the Newtonian gravity, ...
...
Cosmological implications : The theory implies that the 1D radial velocities and the 3D gravitational accelerations are consistent with the theoretical predictions of the Newtonian gravity
in the solar system region. There is a reasonable expectation that the dimensionality of the radial
velocities and the gravitational accelerations is a direct cause of discrepancy between the
gravitational mass and the visible matter mass in galaxies, galaxy clusters, and universe.
In fact, the departure of the 3D radial velocities and the 1D gravitational accelerations from the 1D
radial velocities and the 3D gravitational accelerations respectively is responsible for 1) an
underestimation of the gravitational mass by a factor of 9 relative to the 1D radial velocities, leading
to the problem of the dark matter (a negative mass shift), and 2) an overestimation of the
gravitational mass by a factor of 3 relative to the 3D gravitational accelerations, leading to the
problem of the dark energy (a positive mass shift).
Besides, the departure of the 3D radial velocities and the 3D gravitational accelerations from the 1D
radial velocities and the 3D gravitational accelerations respectively is responsible for 1) an
underestimation of the gravitational mass by a factor of 9 relative to the 1D radial velocities, leading
to the problem of the dark matter (a negative mass shift), and 2) no overestimation of the
gravitational mass relative to the 3D gravitational accelerations without causing the problem of the
dark energy (a null mass shift).
Negative mass shift : It follows from the coincidence of the 3D radial velocities with the 1D
gravitational accelerations or the 3D radial velocities with the 3D gravitational accelerations in a
gravitational system that the gravitational mass is equal to the luminous mass multiplied by a factor
of 9 relative to the 1D radial velocities...

Implication for extra dimensions: It follows from duality of the Newtonian potential the
emergence of (4+6)-dimensional spacio-temporal space which can be reduced to (1+3)-dimensional
spacio-temporal space by assuming a coaxial superposition of two 3-dimensional Euclidean spaces
and a spherical symmetry of one 4-dimensional temporal space centered on their origin.