Quantum Consepts - that can be wrong-but Usually ain't

 Pythagorean Curvature-Correction Theorem This document walks from the fundamental axioms of Euclid through spherical and hyperbolic geometry, culminating with a Riemannian viewpoint and Gauss’s Theorema Egregium. Along the way, it shows precisely how and why the classic Pythagorean Theorem must gain a curvature-dependent correction when the underlying space is non-Euclidean. Table of Contents Overview and Statement of the Goal Foundational Elements: Axioms and Basic Definitions Recap of Euclidean Geometry and the Pythagorean Theorem 3.1. Euclid’s Fifth Postulate (Parallel Postulate) 3.2. Law of Cosines in Euclidean Geometry 3.3. Pythagorean Theorem as a Special Case Generalization to Curved Geometries 4.1. Why Curvature Requires a Correction 4.2. Geodesics vs. Straight Lines 4.3. Local vs. Global Curvature Spherical Geometry 5.1. Definition of a Sphere and Basic Properties 5.2. The Spherical Law of Cosines 5.3. Special Case: Right “Triangle” on a Sphere ...

Quantum Geometry: A Theoretical Foundation for Emergent Classical Measurements  Toward a Unified View of Curvature, Chirality, and Quantum Interference Abstract This thesis explores a novel framework in which classical geometric measurements —specifically distances—emerge from a deeper quantum description. By extending the Pythagorean theorem to include curvature corrections and a chirality factor, we encode all binary sign and chirality decisions into a five-qubit system. We prove that what ordinarily appears as a single, fixed distance   c \,c from classical geometry is, in fact, the result of destructive and constructive interference among 32 underlying quantum states. A combination of phase shifts and controlled interactions ensures that one classical outcome dominates the measurement. This reveals how classical metrics might be the macroscopic shadow of an inherently quantum foundation. Table of Contents Introduction Background and Literature Review Curvature-C...