Gravitational Force

Is Gravity an Attractive Force?

Gravitation (or gravity) is the mutual attraction between masses.

In the 17th century, two competing theories emerged: one by Newton, the other by Le Sage. Newton formulated the mathematical law of gravitation, while Le Sage proposed a physical mechanism based on external pressure from "ultramundane particles".

Ultimately, physicists favored Newton’s model over Le Sage’s, but this choice may have been mistaken.

Newton or Le Sage?

Le Sage does not explain the origin of his 'ultramundane particles'. However, despite its imperfections, his theory appears more credible than Newton's, as the latter offers no explanation for the origin of the phenomenon of gravitation.

Current Theories of Gravitation

Until now, no one has been able to provide a rational explanation for the phenomenon of gravitation. The diagrams commonly used to illustrate spacetime curvature are misleading. They offer no real explanation and contain at least two major inconsistencies:

1. The small sphere does not move toward the center of the large sphere but merely passes by it. This contradicts the nature of gravitation, which originates from the center of masses, not their periphery.
2. The figure below shows a deformation of spacetime so pronounced that two identical masses cannot be drawn toward each other. You can verify this yourself.

Real Theories of Gravitation

Gravitation as the convergence of three Theories:

1. Le Sage: Le Sage was the first to propose that gravitation might result from a pressure that brings objects together, rather than from an attractive force as traditionally conceived since Newton.
2. Einstein: Einstein demonstrated that spacetime possesses elastic properties, which can generate pressure on the surface of closed volumes.
3. The Spacetime Model: Introduced in 2005, the Spacetime Model challenged conventional notions of volume. It also revived Le Sage’s ideas by replacing his 'ultramundane particles' with Einstein’s concept of spacetime. This substitution offers a clearer and more coherent framework.

Thus, when two or more closed volumes are present, they curve spacetime. This curvature induces a pressure force on the outer surfaces of these volumes. As a result, the volumes are effectively "pushed" toward each other by the pressure generated through spacetime deformation. From an external perspective, this pressure manifests as an attractive force.

Mass–Gravitation Relationship

Ultimately, mass and gravitation are closely related phenomena:

• Closed volumes curve spacetime...
• ...This curvature generates pressure on the surface of these closed volumes...
• ...This pressure leads to the emergence of mass (see Fig. A) and/or gravitation (see Fig. B).

Note: Unlike the Higgs theory, the Spacetime Model considers mass and gravitation to be closely related phenomena.

Earth–Moon Gravitation

The Earth–Moon system curves spacetime, which results in external pressure exerted by the universe on both bodies.

The Moon absorbs part of this universal pressure, as illustrated by the blue arrows labeled P3 in the figure below. Consequently, a shadow zone forms on Earth. This shadow zone causes slight differences between the pressures P1 and P2, which are generated by spacetime curvature on each hemisphere of the Earth. Pressure P2 is lower than P1, since part of it is absorbed by P3.

Due to this pressure imbalance, the Earth moves to the right, as if it were being pulled by the Moon. Conversely, the Moon moves to the left under the influence of universal pressure. From an external perspective, this interaction appears as mutual gravitational attraction between the Earth and the Moon.

For educational purposes, this figure has been significantly simplified. Although the shadow has been idealized for illustrative clarity, it does not fully correspond to physical reality.

Split Principle

A tensor is a mathematical object—essentially a generalized matrix—where each component can represent variables such as partial derivatives.

Gravitation can also be interpreted through the split principle, a concept used since the 1850s in the formulation of the Cauchy tensor (see next paragraph). This tensor expresses Hooke’s law of elasticity in fluid mechanics. Later, Einstein and Grossmann employed it to construct the energy-momentum tensor in the Einstein Field Equations (EFE) of general relativity.

Imagine a sphere subjected to uniform pressure (Fig. A). In this context, the pressure arises from the elastic properties of spacetime. Now, consider a thought experiment in which the sphere is split into two halves (Fig. B). These halves will tend to move toward each other—not due to an undefined attractive force labeled “gravitation,” but because of the external pressure exerted by spacetime on both sides of the sphere.

Cauchy Tensor

In 1822, Augustin-Louis Cauchy introduced a tensor in fluid mechanics — now known as the Cauchy stress tensor (see Fig. A). This tensor describes internal pressure and stress distributions within a continuous medium.

Around 1915, Einstein and Grossmann incorporated this structure into the Einstein Field Equations (EFEs) of general relativity (see Fig. B). This new tensor, known as the energy-momentum tensor, plays a central role in describing how matter and energy influence the curvature of spacetime.

Cauchy’s tensor fundamentally deals with pressure and stress, not attraction. Therefore, if Einstein’s tensor is conceptually derived from Cauchy’s, it should also be interpreted in terms of pressure forces, rather than as an abstract attractive force.

This supports the idea that gravitation may be better understood as a pressure phenomenon—specifically, as a manifestation of isostatic pressure—rather than as the mysterious attractive force proposed by Newton.

Mass–Gravitation Interaction Map