PrimerField Gravity I
Gravity as a Field-Energy Gradient
Plain English Companion
David Allen LaPoint
PrimerField Foundation
January 17, 2026
PrimerField Gravity Paper Series — Paper I of IV
What This Paper Is About
This paper presents a new way to understand gravity. Instead of thinking about gravity as a mysterious force that pulls things together, or as a bending of space itself, we describe gravity as something simpler: objects naturally move from areas of high energy to areas of low energy.
Think of it like a ball rolling downhill. The ball doesn't need a force to "pull" it down—it simply moves toward the lower position because that's where there's less stored energy. In our view, gravity works the same way. Objects move toward regions where the field energy is lower.
The mathematical framework we develop here recovers all the predictions of Newton's gravity—the same equations scientists have used successfully for over 300 years—but explains them through energy gradients rather than through a pulling force or curved spacetime.
1. The Basic Idea
There are two common ways people explain gravity. The first, from Newton, says gravity is a force that acts between masses—the Earth pulls you down, the Sun pulls the planets. The second, from Einstein, says massive objects bend the fabric of spacetime, and things move along these bends.
The PrimerField approach is different. We don't start with forces or with bending spacetime. Instead, we start with a simple principle: energy stored in fields varies from place to place, and objects naturally move toward regions where this energy is lower.
This paper focuses only on establishing this basic framework. We don't address extreme situations like near black holes, quantum effects, or the large-scale structure of the universe. Those would require extensions beyond what we present here.
2. Energy Differences Create Motion
Imagine you have a room where the temperature is exactly the same everywhere—perfectly uniform. In that room, there's no natural flow of heat because there are no differences from one place to another.
Now imagine one corner of the room is warmer than the rest. Heat will naturally flow from that warm corner toward the cooler areas. The flow happens because there's a difference—a gradient—in temperature.
Gravity works similarly. If the energy stored in fields were exactly the same everywhere throughout infinite space, nothing would accelerate—there would be no "downhill" to roll toward. But when field energy varies from place to place, objects naturally accelerate toward regions of lower energy. We describe the geometry of spacetime as a way to map these energy differences, not as the fundamental cause of gravity.
3. The Gravitational Potential
Scientists use a concept called "potential" to describe how much stored energy a position has. Think of it like altitude on a hill—higher positions have more gravitational potential energy than lower positions.
We define a PrimerField gravitational potential (we call it Φp) that tells us about the local field-energy configuration. Φp is defined precisely so that its rate of change from place to place reproduces the observed gravitational acceleration. The gravitational acceleration—how fast things speed up as they fall—comes from how this potential changes with position:
acceleration = −(change in potential with position)
The negative sign means objects accelerate toward lower potential—just like a ball rolls downhill, not uphill.
4. Field Energy as the Source
What creates these energy differences? We use a quantity called field energy density (ρe), which tells us how much energy is stored in the fields at each location. Where there's more field energy, there's more gravitational effect.
Here's a key insight: we treat mass as a bookkeeping label for concentrated field energy, consistent with Einstein's famous equation E = mc². This equation already tells us energy and mass are equivalent. We use this directly:
Mass = (Total field energy) ÷ c²
This bridges the gap between thinking about distributed field energy spread throughout space and the concentrated "point mass" that Newton's equations use.
5. The Field Equation
The gravitational potential follows a mathematical relationship called the Poisson equation—the same type of equation that describes how electric fields relate to electric charges. In our framework:
(curvature of potential) = κ × (field energy density)
The symbol κ (kappa) is a coupling constant that determines how strongly field energy creates gravitational effects. To match Newton's gravity, this constant must equal:
κ = 4πG ÷ c²
Here, G is Newton's gravitational constant (the number that determines how strong gravity is) and c is the speed of light. We don't choose κ arbitrarily—its value is uniquely fixed by requiring that our framework reproduce the same predictions Newton's law makes for falling apples and orbiting planets. Any other value of κ would give wrong answers. This specific value ensures our framework produces exactly the same predictions as Newton's laws.
6. Recovering Newton's Law
The real test of any gravity theory is whether it matches what we observe. Newton discovered that gravitational acceleration follows an inverse-square law—double the distance and the acceleration drops to one-quarter.
Our framework recovers this exactly. For a spherical source (like a planet or star), the solution to our field equation gives:
acceleration = GM ÷ r²
This is Newton's famous formula. G is the gravitational constant, M is the mass (which we calculate from field energy), and r is the distance from the center. Newton's constant G isn't something we put in by hand—it emerges naturally from our coupling constant κ and the mass-energy relationship.
7. Why Things Fall Down
Why does the inverse-square law work? It's not a mysterious property of gravity—it comes from the geometry of three-dimensional space. Imagine light spreading out from a lamp. At twice the distance, the same light is spread over four times the area (since surface area grows with the square of distance). Energy gradients dilute the same way.
Why is gravity always attractive? Because systems naturally move toward lower potential energy configurations. The potential near a massive object is lower (more negative) than far away. The mathematical rule that acceleration equals the negative gradient of potential automatically converts "moving toward lower potential" into "accelerating toward the source."
8. What This Framework Assumes
Every scientific framework has limits. Our framework assumes:
• Weak gravitational fields (not near black holes)
• Smooth, continuous fields (no quantum jumps)
• Static or slowly changing configurations
• Classical (non-relativistic) conditions
These are the same conditions where Newton's gravity works well. Extending to extreme conditions would require modifications beyond this introductory paper.
9. Summary
We've presented a way to understand gravity as movement down energy gradients rather than as a fundamental force or as an effect of curved spacetime. The key elements are:
• A gravitational potential that describes local field-energy configurations
• Field energy density as the source of gravitational effects
• Mass understood as concentrated field energy (M = total energy ÷ c²)
• A coupling constant κ = 4πG/c² that connects field energy to gravitational potential
• Complete recovery of Newton's inverse-square law
This first paper establishes only the foundational framework. Future papers in this series will build upon these concepts to address additional aspects of gravitational physics.