Seeing quantum fractals

Kolesnikov Igor

EHK-SCCI Photonic Quantum of Information Theory: Chirality as the Unit of Information Beyond Bits — How Photonics Breaks Gödel IncompletenessDescription / Abstract:We present a new definition of information, where the fundamental unit is not the classical bit but the photonic quantum of information.The classical bit is defined as a memoryless, one-dimensional, decoherent entity: 0 or 1. It is a projection of a wave onto a plane, losing its depth, phase, and chirality. It requires external memory to preserve history.We define the Quantum of Information as a 3D chiral wave with intrinsic memory, natively carried by photonics.Properties of the Quantum of Information:It is not a single value but a multidimensional fractal entity holding simultaneously:Spectrum: Coherent interference, not decoherent summation. The wave holds the full interference field.Frequency: The angular velocity of the helical rotation.Color / Phase: The directional orientation of the field.Spin / Chirality: The instantaneous left-handed (R-) or right-handed (R+) state.Depth Lu: The width of the chiral gap (luft) — the tolerance and memory depth of the flip.Volume Pi: The spatial capacity of the helical field to sustain the flip.Fractal Dimensionality: 3 + Lu/Pi. A helical memory loop containing another helical memory loop. History is preserved recursively via vectorial correction eg -> eg'.The central operation is vectorial correction eg -> eg' that preserves history. The quantum remembers its own reversal. This helical memory loop is the physical carrier of information.Why Photonics Breaks Gödel:Gödel's incompleteness theorem states that a system cannot prove its own consistency from within the system. It must remain on the leaf.Chirality breaks this. To distinguish left from right, an observer must be above the leaf. The act of flipping from R+ to R- is a topological exit from the planar system. The existence of chirality itself is proof of an outside reference frame.We define:R+ = right-handed system, sees only right.R- = left-handed anti-system, sees only left.W = f = the wind above the field, sees the flip.The flip is the first act of consciousness and information. Information is not in left or right, but in the act of reversal.Experimental Proof:Gate A: p99 latency bounded under 3-regular 100-node graph. Average latency is a metric of bits. p99 bounded is a metric of quantum interference stability. It proves that depth Lu does not collapse under load and that volume Pi holds the field. This is stability of the wind, not just the ripple.Conclusion:Information Theory is redefined: Information is not a bit. Information is a chiral, fractal, photonic quantum with intrinsic memory that breaks Gödel by topological chirality.The photon does not emulate information. The photon IS information.Keywords: photonic quantum of information, chirality, Gödel incompleteness, EHK-SCCI, helical memory loop, fractal dimension, intrinsic memory, photonic AI, interference stabilityRelated Identifiers:DOI 10.5281/zenodo.23445576 (V3.5)DOI 10.5281/zenodo.23467555 Kolesnikov Igor ( Mark)

Anonymous

Lei Wang, Matthias Troyer

We propose a way to detect the fractal energy spectrum of the Hofstadter model from the density distributions of ultracold fermions in an external trap. At low temperature, the local compressibility is proportional to the density of states of the system, which reveals the fractal energy spectrum. However, thermal broadening and noises in the real experimental situation inevitably smear out fine features in the density distribution. To overcome this difficulty, we use the maximum entropy method to extract the density of states directly from the noisy thermal density distributions. Simulations show that one is able to restore the core feature of the Hofstadter's butterfly spectrum with current experimental techniques. By further reducing the noise or the temperature, one can refine the resolution and observe fine structures of the butterfly spectrum.

Michael Berry

Olalla A. Castro-Alvaredo, Benjamin Doyon

We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as d/2 logm, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.