# Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics

## Abstract

**:**

## 1. Introduction

## 2. Classical Principles Apparently Cannot Account for Quantum Properties

## 3. Electrodynamical Electron Model Involves Numerous Fluctuating Subparticles

## 4. Realist Interpretation of Quantum Phenomena, Properties, and Principles

#### 4.1. Wave-Corpuscle Duality, Probability Densities, and Physical Reality

_{x}respectively represented the uncertainties in width and momentum, with Δx equated to ħ/mc and Δp

_{x}to mc/2 (corresponding to kinetic energy mc

^{2}/2), then Heisenberg’s uncertainty relation ΔxΔp

_{x}= ħ/2 would be directly deduced. Accordingly, Jabs [96] considered that subatomic particles had no sharp position or momentum, and that the ranges Δx and Δp

_{x}stemmed from properties of the associated wavepacket. Remarkably, in the granular electron model, the wavepacket may be conceived as an extended territory of radius ħ/mc containing all envelope subparticles, and envelope kinetic energy is precisely mc

^{2}/2 [57]. Note that both the nucleus and envelope are real and energetic [97] in the granular model, in agreement with Pusey et al.’s theorem [98], according to which unreal quantum states cannot reproduce the predictions of quantum theory. Noteworthy, Heisenberg’s original formulation of the uncertainty principle considered a particle with a definite but unknown trajectory, that would be subject to unpredictable and uncontrollable disturbance [94].

#### 4.2. Dynamical Systems, Stable States, and Quantization

_{ij}, specific to the connection (or synapse) between the two neurons. Synaptic weights can be positive or negative, corresponding to correlated or anticorrelated neurons respectively, and altogether constitute the memory of the system. Several convergent patterns of excited neurons, called attractors, can be memorized (Figure 4a). Attractors can be represented by vectors of N excitation states 0 or 1, hereby denoted |a

_{n}>, designating the n

^{th}attractor of the network. During the learning phase, synaptic weights are adjusted so as to make the whole system learn, memorize, count or dream [58].

_{i}(0 or 1) to every neuron i. The recurrent network will then enter a dynamical process, in which every neuron i receives the weighted signal (ω

_{ij}x

_{j}) from every incoming synapse and triggers a signal accordingly. In turn, this signal will be sent to all neurons connected through the weighted synapses. The network will reiterate this process until it reaches a stable state, i.e., an attractor |a

_{n}> of the system, which exhibits constant signal value for every neuron. The system can then be seen as having inferred answer |a

_{n}> from question |ψ>. Recurrent networks will often, but not necessarily, converge towards the attractor nearest to the question. Such systems are commonly used to recognize images from blurred inputs, such as hand-written post-codes on mail envelopes for instance.

#### 4.3. Collapse of the Wave-Packet, Measurement Problem, and Causality

#### 4.4. Simultaneous Multipath Exploration, Particle Detection, and Objectivity

#### 4.5. Unpredictability, Hidden Variables, and Determinism

#### 4.6. Entanglement, Memory Imprinting, and Locality

## 5. Conclusions and Perspectives

- Particles would be composed of subcorpuscles organized into an envelope and nucleus exhibiting wave-like and corpuscular behaviors respectively.
- All entities would ultimately be corpuscular, and wave properties would emerge from the undulation of the numerous corpuscles composing the envelope.
- The envelope would generally undergo unstable non-linear dynamics, but stable states would exist, much like modes for a vibrating rope; the eigenstates of quantum mechanics would correspond to those stable states.
- The envelope would guide the nucleus as in the de Broglie-Bohm pilot-wave interpretation.
- The act of measurement would force the envelope to converge and stabilize into an eigenstate (collapse of wavepacket), possibly because of interactions between system and apparatus subparticles.
- Measurements would alter the envelope wave-state, perturbing the values of other dependent (noncommuting) observables.
- Particle detection would involve direct interaction between nucleus subparticles of system and apparatus particles.
- Partial particle history (i.e., its creation and encounters with other particles and fields) would be imprinted within the envelope dynamical wave-state;
- Entangled particles would have characteristics imprinted from the start, thus exhibiting correlations and preserving locality.
- Positions and momenta of subparticles would be determined, while higher-level observables would not generally.
- High-level indeterminism and contextuality (i.e., unknown positions and momenta of system and apparatus subparticles) would cause the unpredictability of measurement outcomes.
- Quantum mechanics would constitute a high-level wave-like description of underlying causal, objective, local and realist processes, and would not be probabilistic in essence.
- Probability densitieswould describe average territories occupied by the subcorpuscles composing the extended particles.
- Matter, which seems almost empty in the quantum mechanical picture, would appear full of numerous fluctuating subparticles, constituting exclusive territories in the atom (Pauli’s principle).

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Mach–Zehnder interferometer experiment. (

**a**) Interference occurring at beam-splitter BS2 causes particles to be detected only at detector D1. (

**b**) Particles undetected by detector D3 do not undergo interference at BS2 and are detected by both detectors D1 and D2.

**Figure 2.**(

**a**) Colorless triolets made of three colored (±e/6) sparks exhibit four different electric charges, represented by filled or hollow upward or downward triangles. (

**b**) The granular model of the electron at rest presents triolets revolving at light velocity and constituting an envelope and nucleus.

**Figure 4.**(

**a**) Pattern (attractor) memorized in a recurrent neural network. (

**b**) Each neuron receives the weighted signal from all other neurons and emits a signal accordingly.

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Avner, S.
Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics. *Entropy* **2021**, *23*, 1338.
https://doi.org/10.3390/e23101338

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Avner S.
Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics. *Entropy*. 2021; 23(10):1338.
https://doi.org/10.3390/e23101338

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2021. "Conceiving Particles as Undulating Granular Systems Allows Fundamentally Realist Interpretation of Quantum Mechanics" *Entropy* 23, no. 10: 1338.
https://doi.org/10.3390/e23101338