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Infinitesimally Punctured Wave (IPW)
The Infinitesimally Punctured Wave, Infinitesimally Punctured Surface, Infinitesimally Punctured Space, and in general Infinitesimally Punctured Manifold in any field — where a manifold is visualized as an aggregation of infinitely many infinitesimally spaced particles, were all proposed by Florentin Smarandache [ https://fs.unm.edu/FS.htm ] in 2019 and developped in 2025-2026. When these particles are densely packed, the ensemble appears as a continuous wave, surface, or space respectively; but when a measurement isolates a single constituent, particle-like behavior emerges. The model is situated alongside established alternative interpretations (e.g., de Broglie–Bohm pilot wave theory, wave packet descriptions) and linked to Neutrosophic Quantum Theory, which supplies a logical framework for handling indeterminacy. By offering a concrete visual metaphor, the punctured wave/surface/space/manifold picture aims to bridge the discrete continuous divide and stimulate further discussion on the foundations of quantum physics/mechanics. The "infinitesimal distance" (which is virtual, theoretical) was further on extended to "very tiny real distance" (which is practical) - to be able to "break" a wave in a real sense at any point [ From Infinitesimally Punctured Wave (IPW) to Finitesimally Punctured Wave (FPW): https://fs.unm.edu/IPW/IPW-to-FPW.pdf ].
Articles: The Infinitesimally Punctured Wave: A
Corpuscular Visualization of Wave-Particle Duality https://fs.unm.edu/NSS/39Infinitesimally.pdf Comparisons
of Infinitesimally Punctured Wave with Copenhagen and De Broglie-Bohm
Interpretations, Neutrosophic Quantum Mechanics, and Non-Linear
Electromagnetics https://fs.unm.edu/NSS/6InfinitesimallyPunctured.pdf Infinitesimally Punctured Wave and the
Spectrum of Physical Waves https://fs.unm.edu/IPW/IPW-PP-72-04.pdf Infinitesimally Punctured Physics and Extended Nonstandard Analysis: A Unified Neutrosophic Geometric Framework https://fs.unm.edu/IPW/IPW-PP-72-07.pdf The Quantum System represented as an
Infinitesimally Punctured Wave https://fs.unm.edu/IPW/InfinitesimallyPuncturedQuantumSystem.pdf Books: Book1: Infinitesimally Punctured
Geometry https://fs.unm.edu/IPW/InfinitesimallyPuncturedGeometry.pdf Book2:
Infinitesimally Punctured Physics https://fs.unm.edu/IPW/InfinitesimallyPuncturedPhysics.pdf Book3:
Infinitesimally Punctured Structures https://fs.unm.edu/IPW/InfinitesimallyPuncturedStructures.pdf Book4: Infinitesimally
Punctured Physics and Extended Nonstandard Analysis https://fs.unm.edu/IPW/MoBiNad.pdf https://fs.unm.edu/IPW/InfinitesimallyPuncturedManyWaves.pdf Book6: Finitesimally Punctured Structures: Waves · Surfaces · Manifolds · Geometry · Contradictions https://fs.unm.edu/IPW/FinitesimallyPuncturedStructures.pdf
[ free downloads of all articles and books also from: https://fs.unm.edu/IPW/ ]
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