Modern physics is remarkably good at the extremes. At one end, we have the Planck scale, where quantum gravity is expected to dominate. At the other, we have cosmological scales, set by the expansion of the universe. What’s far less understood is why the middle scales we actually live in — the scales of cells, objects, and coherent structures — are so stable at all.
In a new paper, Multiple Structural Derivations of the Mesoscopic Coherence Scale, I argue that this stability is not an accident. Instead, it points to a previously overlooked mesoscopic coherence scale, around 30–100 micrometers — roughly the width of a human hair. Below this scale, structure is destabilized by microscopic (quantum) effects. Above it, coherence is eroded by cosmological expansion. Only in between can physical facts persist robustly.
What’s striking is not just the existence of this scale, but how it arises. The paper presents five independent structural derivations — based on instability balance, boundary leakage, information bandwidth, entropy flux, and information-capacity crossover. Four of these turn out to be different expressions of the same deep principle: when ultraviolet and infrared failure modes compete, the only stable crossover is the geometric mean of the two extremes. A fifth derivation, using a completely different information-theoretic argument, lands on the same answer. This kind of overdetermination is rare — and it’s usually a sign that something real has been found.
How This Complements the Speed-of-Light Paper
This work is not standalone — it directly complements an earlier paper where I explored the idea that the speed of light is not an arbitrary constant, but the maximum rate at which the universe can propagate stable physical facts (see Testing the Mathematics: The Speed of Light as a Computational Throughput Limit). In that paper, a closure relation appears showing that once certain global constraints are imposed, the speed of light is no longer freely specifiable — provided a particular mesoscopic scale is known.
That raises an obvious question: was that mesoscopic scale simply assumed?
This new paper answers that question decisively. The mesoscopic coherence scale is not inserted by hand. It emerges inevitably from structural requirements on stability, coherence, and information flow. In other words, the speed-of-light closure rests on firmer ground because its key input — the mesoscopic scale — is itself derived, not chosen.
Why This Is Interesting (and Testable)
The most important point is that this isn’t abstract philosophy. A coherence scale in the tens of micrometers sits squarely in a regime now accessible to experiments in quantum optomechanics, interferometry, and mesoscopic physics. The framework predicts a scale-locked transition — a detectable change in coherence or noise behaviour — that should recur across different experimental platforms in roughly the same size range.
If such a feature is found, it would suggest that the constants of nature are not independent dials, but parts of a tightly constrained structure — one in which stability, information, and causality jointly determine how fast the universe can update, how gravity behaves, and why the world looks the way it does at human scales.