Mass as Temporal Interface: A Geometric Framework for Unifying Interactions

 J. Rogers, SE Ohio

Abstract: We propose a highly speculative model in which mass arises from the inertial coupling between the internal time scale of a nucleon’s resonance and the external vacuum time of spacetime. In this framework, the four fundamental interactions are not distinct forces but different geometric manifestations of a single invariant interaction law, $F=I_1\times I_2$, where field intensities are scaled by geometric factors derived from phase‑time mismatches. Gravity emerges as the long‑range leakage of this time‑scale disparity, while the strong force reflects short‑range synchronization of internal clocks. The model offers a Machian interpretation of inertia, eliminates arbitrary coupling constants, and reduces all interactions to geometry. We stress that this is an exploratory exercise and almost certainly incorrect—but it may stimulate thinking about unification from a different angle.

1. Introduction

Modern physics describes four fundamental interactions, each with its own coupling constants, mediation mechanisms, and distance dependencies. Despite tremendous success, this fragmented picture leaves deep questions unanswered: Why are the force strengths so hierarchical? What is the origin of mass and inertia? How can gravity be so weak yet universally attractive?

We suggest that these questions might be addressed by radically re‑imagining what a “force” is. Instead of four distinct interactions, we posit a single, invariant interaction law that operates on geometric projections of source “counts.” The apparent differences arise from distinct geometries—concrete physical configurations of a universal substrate—that scale the counts before they enter the interaction engine. In this picture, mass is not a primary property but a measure of the time‑scale mismatch between a localized resonance (the nucleon) and the surrounding vacuum. Inertia becomes the resistance to changing this phase relationship, implementing a Machian connection to the whole universe.

We emphasize that this model is speculative and likely wrong in its details. It is presented not as a finished theory but as a provocative exploration of how geometry and time might underpin physical reality.

2. The Invariant Interaction Law

At the heart of the model is a single, local interaction law:

$$\mathrm{<span\; style="background-color:\; white;">F</span>}<span\; style="background-color:\; white;">=</span>{\mathrm{<span\; style="background-color:\; white;">I</span>}}_{\mathrm{<span\; style="background-color:\; white;">1</span>}}<span\; style="background-color:\; white;">\times </span>{\mathrm{<span\; style="background-color:\; white;">I</span>}}_{\mathrm{<span\; style="background-color:\; white;">2</span>}}<span\; style="background-color:\; white;">,</span>$$

where $I$ represents a field intensity defined by

$$\mathrm{<span\; style="background-color:\; white;">I</span>}<span\; style="background-color:\; white;">=</span>\frac{\text{<span style="background-color: white;">Count</span>}<span\; style="background-color:\; white;">\times </span>\text{<span style="background-color: white;">Geometry</span>}}{\text{<span style="background-color: white;">Length</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Here, Count is an integer quantum number (e.g., baryon number, charge), Geometry is a fixed scaling factor specific to an interaction channel, and Length is the separation. The law has no arbitrary constants; it is pure arithmetic. The familiar inverse‑square laws emerge as the product of two $1\mathrm{/}r$ intensities.

3. The Four Geometries

The substrate supports four distinct geometric configurations, each acting as a “gear” that scales the count before interaction.

3.1 Strong Geometry ($sg=1$)

The strong interaction corresponds to direct contact between substrate excitations—like meshed gears with no lever arm. The geometry factor is unity, giving maximum intensity. This interaction is short‑range because the substrate’ topological confinement localizes the resonance to a region of about 1 fm.

3.2 Electromagnetic Geometry ($cg\approx 0.034$)

Charge interactions are scaled by a fixed lever arm of the vacuum. The factor $0.034$ (approximately $1\mathrm{/}29.5$) is a geometric property of the substrate around a charge. It reduces the effective intensity, making electromagnetism about ${10}^{-3}$ times as strong as the strong force at comparable distances.

3.3 Weak Geometry ($wg\approx {10}^{-6}$)

The weak interaction involves a torsional stress within particle transducers. Its geometry factor of about ${10}^{-6}$ reflects the high energy cost of twisting the substrate. This yields a very weak, short‑range interaction.

3.4 Gravitational Geometry ($mg\approx {10}^{-20}$)

Gravity uses the same 1:1 gear as the strong force, but the count itself is a tiny fraction: the ratio of the nucleon mass to the Planck mass. This factor, $mg=m_n\mathrm{/}{m}_P$, is interpreted as the ratio of external vacuum time to internal nuclear time (see Section 4). The gravitational intensity is thus scaled down by ${10}^{-20}$, making gravity appear ${10}^{-40}$ times weaker than the strong force.

4. Mass as a Temporal Interface

We propose that the nucleon (proton or neutron) is a stable resonance of the substrate—a localized excitation with its own internal time scale, ${\tau }_{\text{nuc}}$, corresponding to its Compton frequency. The surrounding vacuum has a much slower time scale, ${\tau }_{\text{vac}}$. The interface between these two phases defines mass.

The gravitational geometry factor is exactly this time‑scale ratio:

$$\mathrm{<span\; style="background-color:\; white;">m</span>}\mathrm{<span\; style="background-color:\; white;">g</span>}<span\; style="background-color:\; white;">=</span>\frac{{\mathrm{<span\; style="background-color:\; white;">\tau </span>}}_{\text{<span style="background-color: white;">vac</span>}}}{{\mathrm{<span\; style="background-color:\; white;">\tau </span>}}_{\text{<span style="background-color: white;">nuc</span>}}}<span\; style="background-color:\; white;">\approx </span>\frac{{\mathrm{<span\; style="background-color:\; white;">m</span>}}_{\mathrm{<span\; style="background-color:\; white;">n</span>}}}{{\mathrm{<span\; style="background-color:\; white;">m</span>}}_{\mathrm{<span\; style="background-color:\; white;">P</span>}}}<span\; style="background-color:\; white;">\approx </span>{\mathrm{<span\; style="background-color:\; white;">10</span>}}^{<span\; style="background-color:\; white;">-</span>\mathrm{<span\; style="background-color:\; white;">20</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Mass, in this view, is the coupling strength between internal and external time. When an external force tries to accelerate a nucleon, it must alter the phase relationship between these two times. The substrate resists this change, and that resistance is inertia. This is a geometric implementation of Mach’s principle: inertia arises from the nucleon’s interaction with the entire substrate network.

5. Gravity and the Strong Force as Two Faces of One Interaction

Gravity is the long‑range leakage of the internal time‑scale mismatch. Each nucleon’s rapid internal clock “leaks” a faint temporal distortion into the vacuum, falling off as $1\mathrm{/}r$. When two such distortions meet, their intensities multiply according to $F=I_1\times I_2$, yielding the familiar inverse‑square law with an overall strength set by $(mg{)}^2$.

The strong force, by contrast, is the short‑range synchronization of internal clocks inside a phase changed region of space time inside the nucleus. When two nucleons approach within ~1 fm, their internal phases can couple directly through the substrate, with geometry factor $sg=1$. The immense attraction is the tendency of the substrate to minimize phase differences. At even shorter distances (<0.7 fm), the two resonances cannot occupy the same topological slot, leading to a repulsive core—a geometric exclusion principle.

Thus, gravity and the strong force are not separate; they are the same substrate interaction manifesting at different ranges and with different effective counts.

6. Predictions and Speculative Extensions

If this picture were correct, several unconventional consequences would follow:

• Time‑varying constants: In extreme environments (near black holes, early universe), the vacuum time scale ${\tau }_{\text{vac}}$ might change, altering effective masses and forces.

• Nuclear spacetime: Inside nuclei, the high density of resonances could create a local spacetime with different geometric properties, potentially affecting decay rates and binding energies.

• Dark matter: Might correspond to regions where the substrate is in a different phase with its own time scale, weakly coupling to ours.

• Quantum gravity: At the Planck scale, internal and external times become comparable ($mg\to 1$), and the geometric description would need to incorporate quantum effects.

We stress that these are speculative extrapolations; no empirical evidence currently supports them.

7. Conclusion

We have outlined a geometric framework that reduces all interactions to one invariant law, replaces force constants with geometric ratios, and interprets mass as a temporal interface. The model is deliberately simplistic and almost certainly incorrect in its current form. It ignores quantum field theory, general relativity’s detailed structure, and a host of experimental constraints.

Yet, it serves as a thought experiment: What if physics is simpler than we think? What if forces are just geometry, and mass is just time? By entertaining such radical simplifications, we may eventually stumble upon a deeper truth—or at least learn why the universe cannot be this simple.

Acknowledgments: The author thanks the physics community for tolerating wild speculation.

Disclaimer: This paper is intended as a creative exploration, not a serious theoretical proposal. It is likely wrong, but perhaps interestingly wrong.

Section: The Epistemological Boundary

All empirical physics is conducted from within the vacuum phase. Our detectors—whether Geiger counters, LIGO interferometers, or particle colliders—register only signals that have crossed the phase boundary from the internal resonance of the nuclear region to the external spacetime. Thus, what we call “mass,” “charge,” “spin,” etc., are not intrinsic properties of the internal reality, but relational quantities defined at the interface. This is why our theories—relativity and quantum mechanics—are so successful yet conceptually disjoint: they model the leakage, not the source.

Section: Empirical Hints of Geometric Modification

The dramatic difference between free neutron decay (half-life ~880 s) and the stability of bound neutrons in nuclei provides a compelling hint that the nuclear environment fundamentally modifies interaction geometries. While standard explanations invoke Pauli blocking and energy conservation, these too may be viewed as emergent consequences of a local geometric phase. In our framework, the dense packing of nucleons creates a collective resonance that alters the effective weak geometry factor ($wg$), suppressing flavor-changing transitions. This suggests that geometric factors are not absolute constants but can be environmentally modulated—a possibility that extends to other interactions and could explain phenomena like the EMC effect and nuclear binding saturation.

Implications for Superheavy Nuclei

The geometric framework naturally suggests an upper limit to nuclear stability. In very large, man‑made nuclei (superheavy elements with Z ≥ 104), the collective resonance becomes so stressed that the substrate can no longer maintain geometric coherence.

Two effects likely compete:

1. Breakdown of weak‑geometry suppression: The modified weak interaction that stabilizes neutrons in ordinary nuclei begins to fail, restoring the full weak‑coupling strength and accelerating β‑decay channels.

2. Fragmentation of strong‑geometry binding: The phase‑locked network of resonances reaches a point where the substrate’s topological capacity is exceeded, leading to spontaneous fission as the system seeks a lower‑energy geometric configuration.

Thus, the extreme instability of superheavy elements—with lifetimes often measured in milliseconds—may be interpreted as a geometric phase transition. The nucleus exceeds the substrate’s ability to sustain a coherent, stable resonance across all nucleons. This aligns with the observed rapid drop in half‑lives for elements beyond copernicium and hints that the periodic table ends not just due to Coulomb repulsion, but because the underlying geometric architecture of nuclear matter has a fundamental capacity limit.

In this view, every superheavy synthesis experiment is probing the boundary conditions of the substrate’s geometric phase diagram.