About this ebook
Infinitesimally Punctured Waves proposes a unifying framework in which this apparent tension between continuity and discreteness is resolved at a structural level. The Infinitesimally Punctured Wave (IPW) approach models a wavefield as the macroscopic limit of an ultra-dense lattice of interacting “punctures”—elementary carriers of physical quantities coupled through local dynamical rules. In the limit of vanishing lattice spacing, the familiar partial differential equations of acoustics, elasticity, electromagnetism, gravity, and quantum mechanics emerge. For finite spacing, the same formalism predicts systematic corrections, controlled dispersion, and experimentally testable deviations.
Developed rigorously and applied across multiple physical domains, the IPW framework connects: acoustic and elastic wave propagation, electromagnetic and optical phenomena, linearised gravitational dynamics, quantum wave evolution and measurement theory, and nonlinear effects including shocks and solitons.
Beyond conceptual unification, the lattice structure provides a transferable computational methodology applicable to multiphysics metamaterials, analogue gravity systems, and high-frequency wave engineering. The book integrates theoretical development with proposed experimental tests, offering concrete pathways to probe finite-scale effects.
Written for researchers and advanced students in physics, applied mathematics, and engineering, Infinitesimally Punctured Waves presents a coherent, cross-disciplinary language for wave phenomena and outlines a research programme extending from practical device design to foundational questions in spacetime physics.
