6.3 Wave–Particle Duality

Home ／ Chapter 6: Quantum Domain

Light and matter share the same origin of wave-like behavior: during propagation they tug on the surrounding energy sea, turning the local tensor landscape into a wavelike “sea map.” Particle-like clicks arise at the receiver when a threshold closes and records a single unit. In short: motion tugs the sea → the sea map is wave-shaped (wave) → a threshold closes (particle).

I. Observational Baseline (What We Actually See)

• Pointwise hits: When the source is dimmed to single quanta, detection events appear one by one on the screen.
• Two slits open, patterns emerge: With enough accumulated events, bright and dark fringes appear.
• One slit only: The pattern broadens but shows no fringes.
• Swap the probe, same story: Replace photons with electrons, atoms, neutrons, or even large molecules; in clean, stable setups the screen still builds “points that sum to fringes.”
• Obtain path information: If the apparatus marks “which slit,” fringes vanish; if path labels are erased in conditional statistics, fringes return.

Conclusion: A single event is a point determined by thresholded readout; fringes reflect the sea map present during propagation.

II. A Unified Three-Step Mechanism

1. Source-side grouping threshold
2. Only when a threshold is crossed does the source release a self-consistent disturbance/closed loop; failed attempts do not count.
3. Sea-map wavification during propagation
4. As the probe moves, it tugs the energy sea and wavifies the tensor landscape into a coherent “sea map” containing:
   • Tensor-potential relief: ridges and valleys that favor or hinder passage;
   • Orientation texture: locally “easier directions” or coupling channels;
   • Effective phase ridges/valleys: pathways whose superposition yields enhancement or suppression.
   • The sea map obeys linear superposition and boundary “engraving”: plates, slits, lenses, and beam splitters all write the map.
5. Receiver-side threshold closure
6. The detector records one unit when the local tensor conditions meet a closure threshold, leaving a single dot on the screen.

In summary: The wave is the wavified sea map (caused by motion tugging the sea); the particle is the thresholded one-shot readout. They connect in sequence rather than conflict.

III. Light and Matter: Same Wave Origin, Different Coupling Kernels

1. Common origin: For photons, electrons, atoms, or molecules, wave behavior arises from the same sea-map wavification—not from distinct “kinds of waves” for light versus matter.
2. Different coupling kernels: Charge, spin, mass, polarizability, and internal structure change how each probe samples and weights the same map (akin to different “coupling/convolution kernels”). Envelope, contrast, and fine detail vary; the common cause—landscape wavification—does not.
3. Unified reading:
   • Light: motion tugs the sea → the sea map is wavified → interference/diffraction appears.
   • Electrons/atoms/molecules: same chain; near-field internal texture modulates coupling but does not create wave behavior.

IV. Rereading the Double-Slit: The Apparatus Writes the Map

• Two slits engrave routes: The plate and slits inscribe ridges and channels in the sea map before the screen.
• Bright vs. dark: Bright fringes mark well-coupled relay zones; dark fringes mark suppressed ones.
• Marking “which slit”: Detection at the slit rewrites and coarsens the map, smearing fine coherence and erasing fringes.
• Erasure: Conditional selection can recover subsets that still retain fine structure, so fringes reappear.
• Delayed choice: It only finalizes the statistical criterion later; no superluminal rewrite of the sea map, so causality holds.
• Intensity composition (plain-language): With coherence, total intensity equals the sum of both paths plus a coherence term; without coherence, the extra term is zero and only the sum remains.

V. Near/Far Field and Multi-Element Setups (Different Projections of the Same Map)

• Near to far field: The near field reflects geometry and orientation texture more strongly; the far field emphasizes phase ridges/valleys. Both are distance-windowed projections of the same sea map.
• Mach–Zehnder interferometer: The two arms write two maps that recombine at the second beam splitter, reading out coherence and phase shifts.
• Multiple slits/gratings: The map gains denser ridges and valleys; the single-slit envelope sets the overall decay, while multi-slit superposition writes the fine fringes.
• Polarization/orientation elements: These write orientation texture onto the map, enabling suppression, rotation, or reconstruction of coherence.

VI. Matter-Side Addendum (Within the Common-Origin View)

• Internal cadence/near-field texture: For electrons and atoms, internal structure builds stable texture at near-field scales; this locks to slit-written features and shifts where closures are “easier” or “harder.”
• Self-bounded readout + thresholds: A closure can complete at only one place per event, so hits remain pointwise; long-time statistics then recover the map’s texture.

VII. Decoherence and “Erasure” as Material Processes (One Explanation)

• Decoherence = map coarsening: Weak measurements or scattering by the environment locally average the map, reducing visibility by smoothing fine structure.
• Quantum erasure = conditional slicing: It does not rewrite history; it re-partitions data to extract sub-ensembles that still carry fine structure.
• Measurable trends: Visibility drops with higher pressure, temperature, path mismatch, probe size, and longer time windows; echoes/decoupling can partially restore coherence.

VIII. Four-Dimensional Reading (Image Plane / Polarization / Time / Spectrum)

• Image plane: Beam deflection and fringe contrast reveal geometric and orientation details of the map.
• Polarization: Polarization-resolved fringes directly trace orientation and circulation textures.
• Time: After de-dispersion, shared steps or echo-like envelopes imply push-and-rebound episodes in the map.
• Spectrum: Soft-band lifts, narrow peaks, and micro-shifts expose boundary reprocessing that projects differently across energy windows.

IX. Cross-Check with Quantum Mechanics

• Where do waves come from? Quantum mechanics tallies “probability-amplitude superposition,” while this account materializes it as “motion tugs the sea → the sea map is wavified.”
• Why are particles discrete? Quantum mechanics counts “quantized emission/absorption,” while this account explains one-shot events through grouping and closure thresholds.
• Double-slit fringes: Predictions match for frequency distributions and apparatus changes; this account adds why—a concrete structure–medium–threshold origin.

X. Testable Predictions

• Chiral micro-structures on slit edges: Flippable chiral orientation near slit rims shifts fringe centers without changing geometric path length; electrons and positrons show mirrored shift signs.
• Tensor-gradient modulation: A controllable tensor gradient between slits (e.g., a micro-mass array or cavity field) linearly tunes fringe spacing and visibility in calculable ways.
• Conditional reconstruction via orbital angular momentum (OAM): Using probes that carry orbital angular momentum, conditional counting can reconstruct or rotate fringe orientation without geometric changes.
• Decoherence coarsening kernel: Visibility decays with adjustable scatterer density according to an integrable coarsening kernel; kernel shape depends on orientation texture and energy window.
• High-order tail polarity mirroring: Under identical orientation boundaries, electron versus positron high-order fringe tails show mirrored sign and amplitude, reflecting near-field coupling differences.

XI. Frequently Asked Questions

• “Why do light and particles show wave behavior?”
• Because propagation tugs the energy sea and wavifies the tensor landscape; the fringe pattern is the visible trace of that sea map.
• “Do particles have a different kind of wave?”
• No. The cause of wave behavior is common; internal structure only changes coupling weights to the same sea map.
• “Why does measurement destroy fringes?”
• Measurement at the slit/path rewrites and coarsens the map, clipping the coherence term.
• “How does erasure restore fringes?”
• By conditional regrouping that selects sub-ensembles still carrying fine structure—no history is rewritten.
• “Is there any action at a distance?”
• No. The sea map refreshes under local propagation limits. Apparent “long-distance synchrony” reflects simultaneous satisfaction of shared conditions in statistics.

XII. Summary

Wave-like behavior of light and matter has a single origin: motion tugs the energy sea and wavifies the tensor landscape into a sea map; particle-like clicks come from one-shot threshold closures. “Wave” and “particle” are not separate essences but two faces of one process: the sea map guides, the threshold books the event.