The Universe May Be Infinite Layers Deep — And Physics Has Ignored It

Physics has two rulebooks. Quantum mechanics governs the impossibly small — electrons, photons, the interior architecture of atoms. Relativity handles the large — planets, black holes, the curvature of space around massive objects. The trouble is, the two don't agree. They never have. French physicist Jean-François Geneste has now published a paper proposing a fix — not by adding new equations or positing new particles, but by deleting one geometric assumption that physicists have been silently hauling around since ancient Greece.

The Fracture at the Heart of Modern Physics

The incompatibility between quantum mechanics and general relativity is one of the most embarrassing open wounds in science. Both theories are extraordinarily precise within their own domains. Both have been confirmed by experiment, repeatedly. And yet when you try to apply them simultaneously — at the scale where gravity and quantum effects both matter, like the interior of a black hole — the math collapses into nonsense. Physicists have known this for over a hundred years. String theory, loop quantum gravity, and a parade of other frameworks have been floated as solutions. None has stuck. Geneste's starting point is blunter than most: the problem isn't missing physics. It's hidden assumptions.

Why 25 Axioms Make for a Fragile Theory

Geneste's critique zeroes in on something most physicists take for granted: the number of foundational assumptions quietly baked into modern physics. Quantum mechanics alone rests on five postulates, as laid out in Le Bellac's standard graduate text. Hilbert spaces — the mathematical scaffolding those postulates require — demand roughly twenty more axioms to construct properly. Toss in thermodynamics and relativity, and the combined axiomatic load climbs well past twenty-five. Every added axiom, Geneste points out, is another chance for a contradiction to sneak in. His solution is to go the other direction: strip one out. Specifically, he proposes discarding the axiom of Archimedes from the geometry underlying physics, replacing the familiar real-number line with a much larger mathematical object — John Conway's field of surreal numbers, constructed in 1974, which contains infinities and infinitesimals as fully legitimate values rather than limit cases.

Why Does Dropping One Axiom Change Everything?

The consequences cascade fast. In a non-Archimedean geometry, "empty space" becomes physically incoherent — if infinitely small scales exist and are real, something must occupy them. Geneste revives the concept of aether, but not the luminiferous ether that Michelson and Morley famously failed to detect in 1887. This is subtler: a medium made of infinitesimal particles, undetectable by any instrument confined to the real-number scale, yet capable of producing measurable effects at our level when enough of them interact collectively. The electron, in this picture, is not a dimensionless point — a fiction Geneste finds genuinely hard to accept, given that electrons carry mass, charge, spin, and a magnetic moment — but a structured object whose radius is smaller than any positive real number without being zero. That's not a contradiction in surreal-number geometry. It's just an infinitesimal. And crucially, spin stops being an intrinsic, unexplained property. It becomes a classical angular momentum, with equatorial velocities exceeding the speed of light at the infinitesimal scale where Lorentz constraints no longer apply.

From Dark Energy to Entanglement — What the Model Addresses

Dark energy — the unknown force apparently accelerating the universe's expansion — gets an unusual treatment here. Geneste invokes the Banach-Tarski theorem, a genuine result from set theory that says a sphere can be decomposed and reassembled into two identical spheres using isometric transformations — no energy input required, at least in theory. He argues that such "cuts" could occur spontaneously in the phase space of an isolated thermodynamic system, effectively doubling the energy of that system. The faster the universe expands, the more frequently these events occur, which accelerates expansion further. Whether this is physics or sophisticated mathematical wordplay is a question the paper does not settle. Quantum entanglement also finds a home in the model: two entangled particles are connected by a physical channel of infinitesimal thickness but real-scale length. Cut the channel, and both particles respond immediately — no faster-than-light signaling in the relativistic sense, because the interaction occurs at the infinitesimal scale where infinite speeds are normal values in the surreal-number field, not violations of causality.

The Questions This Paper Leaves Wide Open

Geneste is candid about what remains undone. The model produces no specific numerical predictions yet — no new particle masses, no precise dark energy density, no testable entanglement timescale. The paper is closer to a manifesto for a research program than a finished theory. He points to the Gibbs paradox in thermodynamics — a real inconsistency in the standard treatment of entropy for ideal gases — as one place where his framework already offers a cleaner resolution than the accepted one. That's a start, but it's a long way from falsifiable physics. What Geneste is really asking is whether the mathematical foundation of physics should be rebuilt on a structure that includes the infinitely small and infinitely large as concrete, calculable objects rather than limits and idealisations. That question has been sitting on the shelf since Georg Cantor introduced multiple infinities in 1874. The fact that it's still being asked in 2026 says something about how hard it is to answer — and how much may depend on getting it right.

• No vacuum, ever — Geneste's model leaves no room for true empty space; what looks like vacuum is filled with infinitesimal matter invisible to instruments bound to real-number measurement.
• Spin gets a physical cause — Instead of treating electron spin as an irreducible intrinsic property, the model explains it as classical rotation at sub-Planck scales, which is a testable conceptual shift if the infinitesimal scale ever becomes experimentally accessible.
• Physics becomes engineering — The paper's most audacious claim is that in a non-Archimedean geometry with infinite symmetry groups, humans could in principle design new local laws of nature — materials and phenomena that don't exist under our current geometric regime.

"Not only is man tiny in 'his' universe, but the latter is an infinitesimal part, in the non-Archimedean sense of the term, of an infinitely larger entity, which, in turn, is an infinitesimal, etc." — Jean-François Geneste, ResearchGate Preprint, 2026.