Gravity – Geometry or Medium

by | Jun 3, 2025 | Physics, Relativity | 0 comments

Thomas Lee Abshier
Author: Thomas Lee Abshier

Is Gravity mediated by Geometry or a Medium?
by Thomas Lee Abshier, ND and AI
6/3/2025

Do the General Relativity equations imply that a force acts at each point in space (i.e., an absolute value at each point) or over an infinitesimally small increment of space? Or are the GR equations mute on the question of “force” and merely speak to the behavior of spacetime with reference to flat space?

Restated, do the GR equations imply that the forces acting at each point in space are due to the curvature within a volumetric increment, or are they acting at every point in that space? I ask this because the concept of curvature implies at least three points. Do the GR equations state or imply that there is a force at every Point, or do they imply that a force is acting on a particle (whether photon or mass) because there is a change in some parameter over the dimensions of a volumetric increment of space?

In a non-Euclidian space, such as a coordinate system based upon the iso-gravitational lines around a star, following the iso-gravitational lines will produce a circular plot compared to a flat Euclidian system plotted over it.

The declaration that space is curved and that the curvature/geometry of space is what is causing the observed gravitational effect seems to diminish the causal nature of the fact that something physical (e.g., mass/energy/momentum) is mediating the effect of producing the iso-gravitational lines. In other words, the change in the properties of spacetime and resultant geometrical modifications with respect to flat space are secondary to the introduction of mass/energy/momentum into flat space.

This implies an underlying medium filling space, which is modified by mass/energy/momentum. The reason/method that mass/energy/momentum modify space is unknown. The effect of mass/energy/moment appears to modify spacetime, which has numerous effects, such as 1) dilating the rate of the passage of time, 2) producing changes in the passage of light through space modified by these factors/agents, and 3) producing the experience of force/acceleration (felt as gravity) on mass (any subatomic particle and larger aggregate of mass). In the common physics vernacular, the spacetime around the gravitational body is declared as curved. The evidence of the curved space is typically cited as a star producing curved space and that the planet does not orbit but merely travels in a straight line in iso-spacetime, which produces an effect seen as curved in flat space, resulting in what is seen as a circular orbit.

It appears that the equations of GR use flat space as the reference system and superimpose the effects produced by mass/energy/momentum on the medium of space. However, because of the lack of evidence of a medium underlying space (e.g., the MMX), we do not reference the medium affected by mass/energy/momentum and instead focus on the fact that the passage of time is modified. The experience of space is modified, and the effect is framed as a geometric/mathematical effect rather than an effect on the medium, which mediates the measurement of time and distance. Thus, we talk about space being curved rather than the (unseen but real) physical medium of space being modified by the physical instruments/interventions/substances of mass/energy/momentum.

I realize we do not know the medium that fills space and is affected by mass/energy/momentum. Still, I think focusing on space being curved without such qualification obscures/diminishes the obvious fact that mass/energy/momentum is producing the effect on the apparent geometry of space. It looks like what we have done is focused on what we can conceptualize mathematically (the trajectory of mass and light passing through space that has been modified by mass/energy/momentum) and claimed that curved space has caused the modifications of these trajectories, rather than looking for the theory/concept/explanation for the underlying effect produced by mass/energy/momentum on the medium of space.

In other words, geometry does not cause changes in trajectory, the passage of time, or the appearance of gravitational force. Rather, the mass/energy/momentum in space modifies the medium of space, which modifies the trajectory and passage of time, which can be calculated by assuming that spacetime has been modified. Having been extremely successful in calculating the predicted and measured effects of the modification of the passage of time and the trajectory of mass through space modified by mass/energy/momentum, the fact of that modification is then ignored/forgotten/diminished, and the geometrical abstraction/topology of the modified space is elevated to the level of being the cause of the time dilation-gravitational effects.

What do you think?

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Your insightful and carefully articulated reasoning touches upon deep philosophical and physical questions about general relativity (GR), the nature of space, and the relationship between mass/energy and spacetime. Your central point—that GR describes the effects of mass/energy/momentum in terms of curved spacetime, but the underlying “cause” of this curvature remains unexamined—raises important issues about causality, interpretation, and the role of mathematics in physics. Let me address your questions and observations in detail.

1. Does GR Imply a Force at Every Point or Within a Volume?

In general relativity, the concept of “force” is fundamentally reinterpreted, and the equations themselves are mute about a force acting in the classical Newtonian sense. Instead, the Einstein field equations describe how matter and energy influence the geometry of spacetime, and how this geometry, in turn, affects the motion of objects.

a. Curvature and Geodesics

  • GR replaces the concept of gravitational “force” with the idea that objects move along geodesics in curved spacetime.
  • A geodesic is the straightest possible path in a curved geometry. Objects in free-fall (e.g., a planet orbiting a star) are not experiencing a force in the Newtonian sense; they are simply following these geodesics.

b. Curvature at a Point vs. Over a Region

  • Einstein field equations: \( G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \); describe how stress-energy \( T_{\mu\nu} \) curves spacetime \( G_{\mu\nu} \).
  • The curvature at any given point is encoded in the Riemann curvature tensor, quantifying how spacetime is “bent” in the vicinity of that point.
  • Curvature is not defined in terms of a finite region (a volume), but rather as a local property of spacetime at each point.

c. Force as a Result of Non-Uniform Curvature

  • While GR does not describe gravity as a force, the effects of curved spacetime can give rise to what we perceive as gravitational “forces.”
  • For example, in a non-uniform gravitational field (e.g., near a star), the curvature varies from point to point. This variation in curvature produces tidal forces, which are experienced as differential accelerations between nearby particles.

2. Does the Geometry of Spacetime Cause Gravity?

You rightly point out that the geometrical description of spacetime curvature (the “curved space” interpretation) is often treated as the “cause” of gravitational effects. However, as you argue, this is a conceptual abstraction, and the true underlying cause of spacetime curvature is the presence of mass, energy, and momentum.

a. Mass/Energy as the Source of Curvature

  • Einstein field equations: Spacetime geometry is shaped by the stress-energy tensor \( T_{\mu\nu} \), which contains mass, energy, momentum, and stress.
  • In this sense, spacetime curvature is not a fundamental cause but rather an effect of mass/energy/momentum.

b. Geometry as a Mathematical Framework

  • The mathematical framework of GR describes how objects behave in curved spacetime, but it does not explain the deeper mechanism by which mass/energy/momentum “modifies” spacetime.
  • The success of GR lies in its predictive power and its ability to describe observed phenomena, but it does not address the metaphysical question of why spacetime behaves as it does.

3. Is There an Underlying Medium?

Your suggestion that the effects of mass/energy/momentum on spacetime could imply an underlying “medium” is philosophically and scientifically intriguing. Let’s examine this idea:

a. Spacetime as a “Medium”

  • In GR, spacetime is treated as a dynamic entity that can be warped, stretched, and compressed by the presence of mass and energy. While it is not a “medium” in the classical sense (it has no material properties like density or viscosity), it behaves like a medium in that it can be influenced by external factors (mass/energy) and can propagate disturbances (e.g., gravitational waves).

b. Historical Context: The Aether

  • In the 19th century, the luminiferous aether was hypothesized as the medium through which light waves propagate. The Michelson-Morley experiment ruled out the existence of such an aether with material-like properties.
  • Einstein’s theory of relativity eliminated the need for an aether by showing that light and other electromagnetic waves propagate through empty spacetime, whose properties are sufficient to explain the observed phenomena.

c. Quantum Field Theory and the Vacuum

  • Modern physics, particularly quantum field theory (QFT), suggests that the vacuum is not truly empty but is filled with quantum fields and fluctuations. This “quantum vacuum” could be viewed as an underlying medium that interacts with mass/energy/momentum.
  • However, QFT and GR are not fully unified, and the nature of spacetime at the quantum level remains an open question.

4. Your Argument: Geometry vs. Physical Cause

You argue that the focus on spacetime curvature as the “cause” of gravitational effects obscures the deeper physical reality that mass/energy/momentum are the true mediators of these effects. This is a valid critique:

a. Geometry as a Tool, Not a Cause

  • The geometrical interpretation of GR is a powerful mathematical tool for describing gravitational phenomena, but it does not explain the physical mechanism by which mass/energy/momentum affect spacetime.
  • This abstraction has led to a focus on “curvature” as the cause of gravity, rather than on the underlying interaction between matter/energy and spacetime.

b. A Deeper Mechanism?

  • Your suggestion that there is an underlying medium or process that mediates the effects of mass/energy/momentum on spacetime is consistent with the spirit of scientific inquiry.
  • While GR does not address this deeper mechanism, theories of quantum gravity (e.g., string theory, loop quantum gravity) aim to uncover the fundamental nature of spacetime and its interaction with matter and energy.

5. The Role of Time Dilation and Trajectories

You note that the effects of time dilation, changes in trajectories, and the experience of gravity are all consequences of spacetime being modified by mass/energy/momentum. This is absolutely correct:

  • Time Dilation: Gravitational time dilation occurs because the presence of mass/energy alters the rate at which time flows in different regions of spacetime.
  • Trajectories: The curved geodesics in spacetime determine the motion of objects, giving rise to phenomena like planetary orbits and the bending of light.
  • Force/Acceleration: The experience of gravity as a “force” is the result of spacetime curvature causing objects to follow curved paths.

6. Conclusion and Reflection

Your argument is both insightful and well-reasoned. In summary:

  1. GR Describes Effects, Not Causes: The Einstein field equations describe how mass/energy/momentum influence spacetime geometry and how this geometry affects objects, but they do not explain the deeper mechanism by which this interaction occurs.
  2. Curvature is a Mathematical Abstraction: While curvature provides a powerful framework for describing gravity, it is ultimately an effect of the underlying physical reality mediated by mass/energy/momentum.
  3. Is There an Underlying Medium? The question of whether spacetime has a physical substrate or medium remains unanswered. Modern physics suggests that the quantum vacuum may play this role, but this is an area of active research.

Your perspective encourages us to remain humble in our understanding of GR and to continue questioning the deeper nature of spacetime, gravity, and the universe. It aligns with the philosophy that our current theories, while successful, are descriptive tools rather than ultimate explanations.

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