The story of wave-particle duality in quantum mechanics has been told a thousand times. This modest contribution is to get back to a few points, including memories of a discussion we had on a possible experimental evidence of quantum effects at macroscopic scale, but in a way totally unrelated to the experiments he and his group made quite later to exhibit a model of wave-particle duality. The more general question of interpreting/understanding quantum mechanics will be also scrutinized once more.
The story of wave-particle duality in quantum mechanics has been told a thousand times. This modest contribution is to get back to a few points, including memories of a discussion we had on a possible experimental evidence of quantum effects at macroscopic scale, but in a way totally unrelated to the experiments he and his group made quite later to exhibit a model of wave-particle duality. The more general question of interpreting/understanding quantum mechanics will be also scrutinized once more.
1.1 Waves and particles in quantum mechanics In spite of the fact that the extraordinary progress of experimental techniques make us able to manipulate at will systems made of any small and well defined number of atoms, electrons and photons making therefore possible the actual performance of the gedankenexperimente that Einstein and Bohr had imagined to support their opposite views on the physical properties of the wavelike/particlelike objects (quantons) of the quantum world it does not seem that, after more than eighty years, a unanimous consensus has been reached in the physicist's community on how to understand their strange properties. Unfortunately, we cannot know whether Feynman would still insist in maintaining his famous sentence It is fair to say that nobody understands quantum mechanics. We can only discuss if, almost thirty years after his death, some progress towards this goal has been made. I believe that this is the case. I will show in fact that, by following the suggestions of Feynman himself, some clarification of the old puzzles can be achieved. This chapter therefore by no means is intended to provide an impartial review of the present status of the question but is focused on the exposure of the results of more than twenty years of research of my group in Rome, which in my opinion provide a possible way of connecting together at the same time the random nature of the events at the atomic level of reality and the completeness of their probabilistic representation by the principles of Quantum Mechanics.
After eighty years of Quantum Mechanics (QM) we have learned to live with wave functions without worrying about their physical nature. This attitude is certainly justifled by the extraordinary success of the theory in predicting and explaining not only all the phenomena encountered in the domain of microphysics, but also some spectacular nonclassical macroscopic behaviors of matter. Nevertheless one cannot ignore that the wave{particle duality of quantum objects not only still raises conceptual problems among the members of the small community of physicists who are still interested in the foundations of our basic theory of matter, but also induces thousands and thousands of physics students all around the world to ask each year, at their flrst impact with Quantum Mechanics, embarrassing questions to their teachers without receiving really convincing answers. Remember that Feynman once said \It is fair to say that nobody understands
In matter wave interferometry, detectors detect individual particles; the wave picture (interference pattern) emerges only as a statistical aggregation, after a large number of particles have been detected. Feynman, mystified by such facts, declared that 'nobody understands quantum mechanics'. A few decades later, Ketterle summed up the situation as 'one gets used to preparing waves and detecting particles'. But why are matter waves detected only as particles? Is there a law of nature forbidding their detection as waves? This question does not seem to have been addressed. The present communication suggests that it may be possible to detect matter waves as waves if there exists a nonlocal interaction - due to wave-particle duality - that causes a nonlocal transfer of energy and momentum from microscopic objects to mesoscopic or macroscopic ones. It describes the principle of a possible wave detector and the scheme of an experiment. The experiment may be feasible in the foreseeable future with a mesoscopic detector made of carbon nanostructures, or in an earth satellite in an elliptical orbit. The detection of a single atom or molecule as a wave will have enormous consequences, both practical and conceptual.
In a recent paper [J. Blackman and W. T. Hsiang, Phys. Essays 26, 34 (2013)], a mathematical model for quantum measurement was presented. The phenomenon of wave particle duality, which is introduced in every beginning course of quantum theory, can be explained using this model. Although the transformation of a wave into a particle as the result of a measurement of position is a special case of the general theory of measurement, it has historic interest and involves the use of a continuous spectrum, which was treated only casually in that paper.
In a recent article Jan Sperling, Syamsundar De, Thomas Nitsche, Johannes Tiedau, Sonja Barkhofen, Benjamin Brecht, and Christine Silberhorn discuss the wave-particle duality using an experiment to demonstrate that "neither the wave nor the particle description is sufficient to predict the utcomes of quantum-optical experiments." I would like to draw your attention to two previous papers that discuss feasible experiments in which a photon does not seem to behave either as particle or as wave and make some brief considerations on the topic.
*Hydrodynamic Pilot Waves on the Cairo Q-Lattice: How Couder’s Walking Droplets Prove the Procedural Mechanics of the KnoWellian Resonant Attractor Manifold (KRAM)* is a theoretical and experimental physics treatise that bridges macroscopic fluid mechanics, quantum foundations, and computational cosmology. The paper demonstrates that the hydrodynamic quantum analogs discovered by **Yves Couder and Emmanuel Fort (2005)**—specifically, millimetric silicone oil droplets bouncing on a vertically vibrating liquid bath near the **Faraday Instability Threshold (γ≈γF)**—provide the direct, visualizable, and macroscopic mechanical proof of the **KnoWellian Universe Theory (KUT)**. The treatise begins by reviewing how Couder’s self-propelled "walkers" deterministically replicate the canonical paradoxes of quantum mechanics: single-particle double-slit diffraction and interference, quantized orbital energy levels (analog Landau levels) in rotating frames, quantum tunneling through submerged barriers with exponential decay, and statistical probability density functions matching quantum corral eigenmodes (∣ψ∣2). The paper executes a rigorous **1:1 ontological and mathematical mapping** between Couder’s laboratory fluid system and KUT procedural field theory:1. The vibrating silicone oil bath is identified as the macroscopic mechanical analog of the **Cairo Q-Lattice (CQL)**—the five-fold pentagonal memory floor of the vacuum oscillating at the fundamental Planck clock frequency (νKW≈1.855×1043 Hz).2. The localized oil droplet corresponds to the **(3,2) Torus Knot Soliton core** (ΦM, Solid Ash).3. The surface Faraday waves correspond to the **KREM holographic field exhalation** (Aμ=E^[Λ]) and Chaos Field (ΦW).4. The hydrodynamic path memory (Me→∞) corresponds to the **KRAM memory manifold metric (gM(X))**.5. The droplet impact on the fluid surface corresponds to the **Instant Field (ΦI)** executing the 90∘i-Turn. The central theoretical breakthrough of the paper is **The Bohmian Reversal**. In classical de Broglie–Bohm pilot-wave theory (1952), an abstract, eternal wave guides a passive particle with zero back-reaction, violating Newton's Third Law. Couder's experiment proves that real pilot waves require a two-way feedback loop: the particle generates the wave, and the wave steers the particle. KUT formalizes this feedback by proving that the gradient of the Bohmian Quantum Potential (∇Q) acts as an active imprinting current (Jimprint∝∇Q) that physically deforms the KRAM substrate. The particle is not a passive slave to an eternal wave; **the particle's actualization events physically sculpt the memory landscape that guides future waves.** Using this mechanism, the paper provides a causal solution to the **Mott Problem (1929)**, demonstrating that an initially isotropic alpha decay wave naturally collapses into an arrow-straight track through a **self-reinforcing directional rendering cascade**, decaying angular dispersion as σθ∝1/N. Furthermore, the paper establishes the scale-invariance of this mechanism across the **Cosmic Octave (Ω=1024)**, showing that the Couder droplet (10−3 m) sits at the exact geometric square-root midpoint (Ω=1012 m) between the subatomic proton (10−15 m) and the astronomical star (109 m), and extends this fluid pilot-wave model to explain galactic flat rotation curves without particle dark matter (Relativistic Reflux). The treatise concludes with **three concrete, testable laboratory protocols**: simulating the Mott cascade in fluid tanks, testing orbital stability in Golden-Ratio Cairo pentagonal corrals, and measuring multi-droplet morphic resonance in hydrodynamic mazes. *** **Keywords:** Yves Couder, Emmanuel Fort, John Bush, walking droplets, hydrodynamic quantum analogs, Faraday instability threshold, path memory (Me), Bohmian mechanics, pilot-wave theory, Bohmian Reversal, KnoWellian Universe Theory (KUT), KRAM memory manifold, Cairo Q-Lattice, Mott Problem, rendering cascade, quantum potential gradient, Cosmic Octave (Ω=1024), scale invariance, wave-particle duality, quantized orbits, analog tunneling, morphic resonance, superfluid vacuum, Relativistic Reflux, Homo Textilis.