A New Way to Think About the Constants of Nature

Modern physics rests on a small set of fundamental constants: the speed of light, the strength of gravity, the fine structure constant that governs electromagnetism, and the cosmological constant that sets the large-scale curvature of the universe. We measure these numbers with extraordinary precision, but we rarely ask a deeper question: do these constants have to fit together?

Traditionally, physics treats each constant as an independent input. They are measured, inserted into equations, and taken as given. But this modular picture leaves a troubling gap. Even if each constant is internally well defined, nothing in standard theory asks whether they are mutually compatible—whether they can coexist within a single, globally consistent spacetime.

The paper “A Geometric Closure Condition Linking Fundamental Constants” explores that missing question.

Geometry Before Dynamics

The starting point is a simple but radical shift in perspective. Instead of beginning with dynamics—fields evolving in time—the paper asks a geometric question: what does it take for spacetime itself to be globally consistent?

Imagine tiling the universe with the smallest meaningful units of area: Planck-scale cells, each about $10^{-70}\,\mathrm{m}^2$10−70m2. There are roughly $10^{122}$10122 of these tiles covering the cosmological horizon. If each tile contributes a tiny amount of geometric “twist” or phase, then global consistency requires that all those local contributions add up coherently. If they don’t, the geometry simply doesn’t close.

This requirement of closure is not about motion or expansion. It’s about admissibility: whether a given set of constants produces a geometry that fits together at all.

From Topology to a Constraint

Mathematically, this idea leads to a powerful result. If spacetime carries a U(1)-type phase structure at the most fundamental level—a minimal bookkeeping of parallel transport—then topology imposes a strict rule. By a standard result from differential geometry (the Chern–Weil integrality theorem), the total phase accumulated around a closed surface must be an integer multiple of $2\pi$2π.

When this condition is applied to the cosmological horizon and discretised into Planck-area cells, it yields a simple closure equation:$$N_\Sigma \cdot \alpha = \chi,$$NΣ​⋅α=χ,

where $N_\Sigma$NΣ​ is the number of Planck-area cells on the horizon, $\alpha$α is the fine structure constant, and $\chi$χ is an integer topological invariant.

This equation is not guessed. Its form follows directly from topology and symmetry. What remains physical—and testable—are the assumptions that spacetime admits such a phase structure and that the observed electromagnetic coupling reflects its normalisation.

Why the Fine Structure Constant Appears

One of the most important ideas in the paper is the bridge hypothesis. The U(1) structure that appears in the closure condition is not the electromagnetic field itself. Rather, it is an underlying phase bookkeeping structure associated with relational transport at the deepest geometric level.

Electromagnetism, in this view, inherits its phase normalisation from that deeper structure. That is why the fine structure constant appears in both contexts. This is not asserted dogmatically: the paper allows for the possibility that the geometric U(1) coupling could differ from the electromagnetic one, and shows how such a difference would be constrained.

The point is not that electromagnetism lives on Planck cells, but that phase itself—how relational information is compared across spacetime—has a universal normalisation, and that normalisation is what we observe as $\alpha$α.

What This Explains—and What It Doesn’t

The closure condition does not derive the numerical values of the constants. It does something subtler: it shows that the constants cannot be chosen independently. If you change one, the others must shift in a tightly constrained way, or the geometry ceases to close.

This reframes the cosmological constant problem. The notorious 120-order-of-magnitude mismatch between quantum vacuum energy estimates and the observed value of $\Lambda$Λ disappears once $\Lambda$Λ is understood as a geometric boundary condition rather than a substance filling space. In this picture, the huge number $\sim 10^{120}$∼10120 is not a fine-tuning accident—it is a topological count.

At the same time, the paper is careful about its limits. It does not claim uniqueness of the universe, nor does it replace standard cosmology. Instead, it proposes a global consistency test that any viable theory of fundamental constants must pass.

How the Idea Can Be Tested

Some aspects of the framework are structural rather than immediately measurable. The integer $\chi$χ is enormous, and current uncertainties allow many nearby integers. But the theory makes sharper predictions elsewhere.

In particular, if fundamental constants vary, they cannot do so independently. The closure condition predicts a specific pattern of correlated variation linking $\alpha$α, $G$G, $\hbar$ℏ, $c$c, and $\Lambda$Λ. It also predicts that smooth, scalar-field–driven evolution of dark energy would be incompatible with a purely geometric $\Lambda$Λ.

These are not philosophical claims. They are concrete, falsifiable statements about how the universe would have to behave if geometric closure is real.

A Different Kind of Question

At heart, this work asks a different kind of question than most of physics. Not “what evolves into what?” but “what is allowed to exist at all?”

If the universe must close geometrically, then the constants are not arbitrary inputs. They are parts of a single structure that either fits together—or doesn’t. Whether that structure is truly fundamental remains to be seen. But the paper shows that asking the question precisely leads to real mathematics, real constraints, and real ways to be wrong.

And that, in science, is exactly where progress begins.