What if the fine-structure constant — the number that governs how electrons and photons interact — were slightly different from what it is? What if gravity were 20% stronger, or the ratio between the proton and electron masses shifted by a few percent?
The standard intuition is that everything would unravel. The chemistry would change. Nuclear binding would shift. Stars would form differently, or not at all. Physical structure seems fragile — precariously balanced at the specific values the constants happen to take.
This investigation tests that intuition directly. And the answer is more nuanced than either fragility or robustness — it is selectivity.
Read more: Beyond Scale: How α Aligns Some Structures and Not Others
Crystallography can tell us what structure a crystal has — its symmetry, its lattice, its unit cell, its polymorphs. But there is another question hiding underneath all of that: when matter reorganizes itself into different ordered forms, how close does it come to the boundary where ordered structure stops being comfortably realizable?
We evaluated eight crystallographic material families — ferroic phase chains, polymorph oxide systems, a metallic pair, and a single-phase control — under the admissibility inequality. Every tested phase chain and polymorph family remained admissible. But they did not sit equally deep inside the safe interior. The law held throughout. And in doing so, it revealed a geometry.
Admissibility Constraints Across Physical and Biological Systems — An Empirical Extension of the Universal Structural Law into the biological domain, establishing that the same instability bound governing atomic spectra, gravity, and large-scale structure also holds inside the fitness landscape of a self-replicating ribozyme.
Read more: The Universal Structural Law: Admissibility Bounds on Ordering Instability
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