PrimerField Gravity — Paper IV
Experimental Discriminator: Geometry-Dependent Gravitational Sourcing
Plain English Version
David Allen LaPoint
PrimerField Foundation
January 18, 2026
Certified v12
What This Paper Is About
This paper shows how we can test whether PrimerField (PF) gravity theory is correct. We compare two ways of thinking about gravity: the traditional view (Newtonian gravity) says only the total amount of mass matters. PF gravity says that where the mass is located—its shape and arrangement—also matters because the gravitational field itself carries energy.
We examine two objects with the same total mass: a solid ball and a hollow shell. Traditional physics says they should pull on things exactly the same way. PF gravity predicts a small difference. This paper calculates how big that difference should be and where we might be able to detect it.
1. Why This Test Matters
For over 300 years, Newton's theory of gravity has worked extremely well. It says that to calculate how strongly something pulls on you gravitationally, you only need to know its total mass and how far away you are. Two objects with the same mass at the same distance should pull equally hard, no matter what shape they are.
PF gravity proposes something different. It says the gravitational field itself has energy, and this field energy also contributes to gravity. Since different arrangements of the same mass create different field patterns inside them, they should produce slightly different gravitational pulls.
This gives us a clean test: take two objects with identical total mass, arrange them differently, and measure their gravity. If the gravity is identical, Newton was right. If there's a small difference matching our prediction, PF gravity is supported.
2. The Science Behind the Prediction
In Newtonian gravity, a famous result called the "shell theorem" says that a solid sphere and a thin hollow shell of equal mass produce exactly the same gravitational pull at any point outside them. This is why we can treat planets as if all their mass were concentrated at the center—as long as we stay outside the surface.
PF gravity agrees with Newton in most situations but adds a detail: gravitational fields carry energy, and energy itself has gravitational effects. Think of it this way—the gravitational field isn't just empty space with lines we draw to show the direction of pull. The field is real, it takes energy to create it, and that energy should have its own gravitational effects.
This leads to the key insight: a solid sphere and a hollow shell have different amounts of gravitational field energy stored inside them, even if they have the same total mass. The solid sphere has a gravitational field throughout its interior (pulling toward the center), while the hollow shell has no gravitational field in its empty interior at all. That difference in internal field energy should create a measurable difference in their gravitational pull.
3. The Two Test Objects
Object A: Solid Ball. Imagine a uniform ball of material—same density throughout, like a ball bearing. Inside this ball, gravity pulls everything toward the center. The gravitational field strength increases as you move from the center outward, reaching maximum at the surface.
Object B: Hollow Shell. Now imagine all that same mass compressed into a thin shell—like a basketball, but made of incredibly dense material and with the same total mass as the solid ball. Inside this hollow shell, something remarkable happens: the gravitational field is zero everywhere. Every direction pulls equally, canceling out perfectly.
Both objects have identical mass, the same outer size, and the same center of mass. Newton says they pull identically from outside. PF gravity says Object A (solid ball) has more internal field energy and should pull slightly harder.
4. The PF Prediction: How Big Is the Difference?
Using the mathematical framework from Paper I in this series, we can calculate exactly how big the difference should be. The result is remarkably simple and elegant:
The fractional difference in gravitational pull equals one-twentieth of the "compactness" of the object.
In equation form: Δa/a = (1/20) × (Rₛ/R)
Here, Rₛ is called the "Schwarzschild radius"—a measure of how much space the object's mass would occupy if compressed into a black hole. R is the object's actual radius. The ratio Rₛ/R tells us how "compact" the object is—how close it is to being a black hole.
This is a tiny correction to standard gravity, not a dominant effect. For normal objects like rocks or metal balls in a laboratory, this ratio is incredibly tiny—about one part in a trillion trillion. The effect is far too small to measure with any equipment we have. But for extremely dense objects in space—white dwarfs and especially neutron stars—the effect becomes much larger and potentially measurable.
5. Where Could We Detect This?
Laboratory experiments: Not possible. For a 10 kg (22 pound) ball with a 10 cm (4 inch) radius, the predicted difference is about 7 parts in 10²⁷ (that's a 1 followed by 27 zeros). This is roughly 18 orders of magnitude—a billion billion times—smaller than our best measuring equipment can detect. Laboratory tests are ruled out.
White dwarf stars: Potentially detectable. A white dwarf (the dense remnant left when a star like our Sun dies) packs about 60% of the Sun's mass into an object the size of Earth. The predicted effect reaches about 15 parts per million—still tiny, but getting closer to measurable.
Neutron stars: Best candidates. Neutron stars are the collapsed cores of massive stars, cramming more mass than our Sun into a ball just 20 kilometers (12 miles) across. For these extreme objects, the predicted effect is about 2%—a difference large enough to potentially affect their behavior in measurable ways. Detectability depends on disentangling this effect from equation-of-state uncertainties—the fact that we don't yet fully understand the internal structure of neutron stars.
6. How Could We Test This?
Since laboratory experiments are impossible, we need to look to space for our laboratory. Several approaches could work:
Neutron star pairs. When two neutron stars orbit each other, their extreme gravity affects their orbital motion in precise ways. A 2% difference in how gravity works could influence these orbits measurably over time.
Gravitational waves. When neutron stars or black holes merge, they release ripples in space itself called gravitational waves. The detailed pattern of these waves depends on exactly how gravity works. If internal field energy matters, it could, in principle, leave a distinguishable signature in these wave patterns.
Pulsar timing. Pulsars are rapidly spinning neutron stars that emit regular pulses of radio waves like cosmic lighthouses. By tracking these pulses with extreme precision over years, we can detect tiny changes in their motion that might reveal geometry-dependent gravitational effects.
7. Can This Be Proven Wrong?
Yes—and that's what makes it good science. PF gravity makes a specific, numerical prediction: the difference should be exactly (1/20) × (Rₛ/R). This can be checked against observations in two ways:
If observations match: This would support PF gravity's claim that field energy contributes to gravitational effects. It would contradict the pure Newtonian view that only mass matters.
If observations don't match: If we can measure neutron star behavior precisely enough and find no geometry-dependent effects at the 2% level, PF gravity would be falsified or at least strongly constrained in this regime.
Either outcome advances our understanding. A theory that cannot be tested cannot be trusted. By providing a clear numerical prediction and identifying where to look for it, this paper makes PF gravity scientifically testable.
8. The Bottom Line
This paper identifies a fundamental question about gravity: does only mass create gravity (Newton's view), or does the energy in gravitational fields also contribute (PF gravity's view)?
For everyday objects and situations, both theories give the same answer—the effect is too tiny to matter. But for extremely dense objects like neutron stars, the theories diverge enough to potentially test.
The predicted effect scales with how compact an object is. More compact objects (closer to becoming black holes) should show larger effects. This makes the extreme objects in our universe—neutron stars and their collisions—natural laboratories for testing this prediction.
Key prediction: The fractional difference in gravitational acceleration between differently-shaped objects of equal mass is (1/20) × (Rₛ/R), where Rₛ is the Schwarzschild radius and R is the actual radius.
Document Status: Plain English Version of Certified v12. This version rewrites the technical paper for general audiences. Mathematics is described rather than derived. All scientific content is preserved. v12 incorporates clarity refinements from adversarial review.