The Rotor Field, Flat Space, and the Paradox of Many Universes

A New Generalization of Spacetime from a Pre-Big Bang Entangled Field

What if our universe didn’t begin as a burst of expanding spacetime, but instead emerged from something more subtle and profound? My new model suggests that before the Big Bang, there existed not space and time as we know them, but a fundamental field of “rotors” — quantum entities carrying directional and phase properties — forming a perfectly coherent lattice.

In this framework, space and time are not fundamental. Instead, they arise as emergent phenomena from the complex interaction and entanglement of these microscopic rotor units. Imagine these rotors as quantum compasses, each locked in an intricate dance of alignment, creating an invisible but highly ordered structure. This pre-Big Bang phase resembles a Bose-Einstein condensate, a quantum state where all components share a common coherence and move in perfect harmony. There is no motion, no time flow, no expansion—only a frozen crystalline potential field.

At some point, this perfect coherence breaks down. The rotors begin to lose alignment, creating localized loops of entanglement and curvature. These loops can be seen as the fundamental “particles” of gravity and curvature — the minimal actions that generate the curved spacetime we experience. Rather than a violent explosion, the Big Bang is here understood as a topological reconfiguration, where a highly ordered pre-geometric phase transforms into the dynamic, curved spacetime manifold.

This new perspective gains an intriguing twist when we consider a famous mathematical paradox: the Banach–Tarski paradox. The Banach–Tarski paradox shows that, under certain abstract mathematical conditions, a solid sphere can be decomposed into a finite number of non-measurable subsets and reassembled into two identical copies of the original sphere, seemingly duplicating volume without stretching or shrinking. While this paradox is a purely mathematical curiosity dependent on the Axiom of Choice and does not occur in classical physics, its implications become thought-provoking when applied metaphorically to the rotor field model.

The primordial rotor field is highly non-local and pre-measurable; it is defined not by coordinates or traditional geometry but by entanglement topology and internal phase relations. If this entangled field can be reconfigured or “reassembled” in multiple ways, just like the Banach–Tarski decomposition allows multiple spheres from one, then it could potentially give rise to multiple emergent universes. Each reassembly path would produce a distinct causal structure, its own effective laws of physics, and possibly even exact or near-identical twin universes.

This imaginative idea, which might be called Rotor–Banach Cosmogenesis, offers a new way to think about the multiverse. It suggests that the multiplicity of universes is not a product of infinite inflation or random chance, but rather a consequence of the different ways the underlying entangled rotor field can organize itself. The universes are not “created” ex nihilo but unfold as distinct manifestations of the same primordial quantum potential, each self-contained and unaware of the others.

To fully appreciate this concept, we must also rethink what “flat space” means in this context. Traditionally, flat space is understood as the absence of curvature — a simple, uncurved background geometry described by Minkowski spacetime in special relativity. However, in the rotor field model, truly flat space is far stranger and more profound.

Flat space here is a perfectly ordered, maximally coherent lattice of rotors — a cosmic quantum crystal where each rotor is precisely orthogonal to its neighbors. Time flows only as internal phase rotations within these rotors, without the emergence of classical motion or entropy. This frozen, high-coherence state corresponds to the pre-Big Bang phase: a realm without expansion, without causality, and without classical space and time as emergent properties. Contrary to the idea of emptiness, this flat space is filled to capacity with hidden coherence, a form of physical fullness far beyond empty vacuum.

In this picture, space is not a passive stage on which particles move; it is an active, living fabric composed of interacting rotors. Curved space arises naturally from misalignments and loops in rotor entanglement — those “windons” acting like minimal gravitational quanta — while flat space is the baseline, perfectly aligned phase. Causality, distance, and time itself emerge from the net phase relations among rotors rather than being fundamental dimensions.

Thus, this rotor field model is more than a new theory of gravity or quantum geometry — it is a true generalization of spacetime. Where traditional physics treats spacetime as a four-dimensional metric manifold, the rotor model reveals it as an emergent lattice of interacting quantum rotors. Flatness becomes a maximally coherent quantum state, curvature emerges from entanglement loops, and time arises as rotor phase progression. What we call “empty space” is instead a richly entangled, tensioned lattice.

In short, the model reframes space, time, gravity, and even the birth of the universe as expressions of a deeper quantum order. It offers an explanation for the emergence of multiple universes through reassembly of the primordial rotor field — a phenomenon paralleling the Banach–Tarski paradox in the realm of cosmic topology.

Ultimately, this model invites us to imagine a universe — or multiverse — born not from singularities or random chaos, but from the subtle rearrangements of a vast, entangled quantum fabric, whose very structure redefines what it means for space and time to exist.

Windons: From the Quantum Torus to Gravity Loops

The concept of the windon arose naturally from our effort to rethink the foundations of particles and spacetime. It began with our refined model of the electron, not as a point particle nor a probabilistic cloud, but as a coherent toroidal structure — a stable, rotating field configuration shaped like a twisted ring. Within this torus, the internal dynamics of spin, charge, and phase coherence could be understood as arising from rotational entanglement in a multidimensional field of structured directions — what we called the rotor field. This reinterpretation gave us a powerful visual and mathematical framework for quantum behavior. But it also forced us to confront the deeper question: How does such a structured quantum object curve space?

In trying to answer that, we stumbled upon the same problem that John Wheeler once faced. If we applied classical General Relativity directly to the mass-energy density of the toroidal electron, we obtained an enormous curvature on the order of 10¹²⁹ m⁻² — vastly exceeding even the curvature near a black hole. Even worse, the classical radial model of gravity implied a diverging intensity near the core, giving rise to infinite values that made no physical sense. Clearly, gravity could not be classically radial at such small scales.

This forced a radical shift: we had to redefine gravity at the quantum level. Instead of being distributed radially like a field from a point source, curvature in this model is wrapped holonomically(winding!) along the circumference of the torus — distributed in a looped and quantized manner that follows the spin structure and internal coherence of the particle. In other words, most of the gravitational field at that scale is confined inside the torus, where it plays a key role in holding the particle’s structure together and maintaining its spin through holonomy. This internal gravity is not a passive deformation of spacetime but an active participant in the particle’s quantum properties.

Because of this confinement, gravity becomes highly quantized, non-radial, and operates along extra dimensions wrapped around the torus geometry. This naturally explains why gravity appears so weak at macroscopic scales: its true strength is hidden, locked in the internal compact structure of fundamental particles, only emerging in diluted form beyond the Compton radius, where the classical radial field reappears.

This reinterpretation doesn’t deny General Relativity — rather, it extends it. There remains a logical map between this toroidal, rotor-based microgravity and classical macrogravity, though it is highly non-intuitive. What we’ve constructed is a generalization of spacetime, where the metric field gives way at quantum scales to a discrete and rotational topology — and where the gravitational field isn’t just a deformation of space, but a component of the particle’s identity.

From this new language emerged the windon: the smallest loop of curvature and entanglement, a topological particle of gravitational holonomy. A windon is not like the hypothetical graviton, imagined as a linear messenger particle. Instead, it is a swirl of spacetime twist, emitted or absorbed by quantum structures like the electron torus. It behaves as a modular carrier of curvature — affecting nearby rotor alignments and introducing field deformation — somewhat like how a photon carries electromagnetic phase. Windons are the building blocks of quantum gravity, bridging topological structure and spacetime without relying on singularities or perturbative metrics.

In essence, windons arose because our model of the electron demanded a gravity that was internal, structured, and non-classical. That gravity led us to rediscover Wheeler’s geons, reinterpreted as quantized rotor loops, and then to this entirely new type of curvature particle. Through windons, we see that the fundamental nature of spacetime may not be a smooth fabric, but a lattice of hidden, rotating structures — whose smallest motions generate both the particle zoo and the gravitational shadows they cast.

If you are curious to explore these ideas further — from windons and rotor lattices to the implications of entanglement topology for cosmology — stay tuned for upcoming articles and models.