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A Classical Explanation of Quantum Tunneling: An Energy Transfer Model Based on Electron Collisions

Fan Xie

Published Aug 13, 2026• 0 citations
Publisher

Abstract

This paper proposes a classical alternative explanation for the tunneling effect in quantum mechanics. Standard quantum theory describes tunneling as a particle "penetrating" a potential barrier whose energy exceeds the particle's own kinetic energy with a certain probability. However, this explanation focuses only on the mathematical initial and final states, completely ignoring any dynamical process the electron may undergo before the barrier, and lacks a physical picture. This paper argues that tunneling is not an intrinsic quantum property of a single electron, but rather a collective statistical fluctuation event involving multiple electrons: electrons near the barrier, through a series of random collisions in the correct direction, gradually transfer and concentrate kinetic energy onto the electron closest to the barrier, enabling it to instantaneously acquire kinetic energy exceeding the barrier threshold and thus classically fly over the barrier. During the crossing, the electron must do work against the barrier, converting kinetic energy into potential energy; therefore, after crossing, its kinetic energy is reduced and it cannot cross the same barrier again. Tunneling probability is reinterpreted as the success probability of such a "directed energy relay" event. This model is fully self-consistent within the framework of classical electromagnetism and statistical mechanics, requiring no wave functions or probability waves, with a clear physical picture and explicit causal chain. This paper further points out that under strictly single-electron conditions, this model predicts that tunneling will completely disappear, a prediction that stands in fundamental opposition to the standard quantum model and can serve as a decisive experiment to test the two theories.

DOI
10.5281/zenodo.21918750

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arXiv:0706.3510•Jun 24, 2007•0 citations
This paper proposes a classical alternative explanation for the tunneling effect in quantum mechanics. Standard quantum theory describes tunneling as a particle "penetrating" a potential barrier whose energy exceeds the particle's own kinetic energy with a certain probability. However, this explanation focuses only on the mathematical initial and final states, completely ignoring any dynamical process the electron may undergo before the barrier, and lacks a physical picture. This paper argues that tunneling is not an intrinsic quantum property of a single electron, but rather a collective statistical fluctuation event involving multiple electrons: electrons near the barrier, through a series of random collisions in the correct direction, gradually transfer and concentrate kinetic energy onto the electron closest to the barrier, enabling it to instantaneously acquire kinetic energy exceeding the barrier threshold and thus classically fly over the barrier. During the crossing, the electron must do work against the barrier, converting kinetic energy into potential energy; therefore, after crossing, its kinetic energy is reduced and it cannot cross the same barrier again. Tunneling probability is reinterpreted as the success probability of such a "directed energy relay" event. This model is fully self-consistent within the framework of classical electromagnetism and statistical mechanics, requiring no wave functions or probability waves, with a clear physical picture and explicit causal chain. This paper further points out that under strictly single-electron conditions, this model predicts that tunneling will completely disappear, a prediction that stands in fundamental opposition to the standard quantum model and can serve as a decisive experiment to test the two theories.
The mainstream theory describes quantum tunneling as a special quantum behavior in which particles can cross energy barriers, relying on abstract concepts such as wave functions and probability clouds. It can only describe phenomena but cannot achieve precise control, lacking practical engineering guidance value. Abandoning fictional assumptions divorced from objective laws, this paper returns to the basic laws of classical physics and the real structure of matter, demonstrating that the essence of quantum tunneling is an equivalent phenomenon formed by the transmission of electromagnetic forces and relay replacement of electrons in a multi-layer atomic structure. It clarifies that particle collision angle and barrier thickness are the two core factors determining the tunneling success rate. This theory can not only restore the physical essence, but also directly guide practical engineering design and process optimization, realize the controllable utilization of tunneling effect, and has strong practicability and application value.
In traditional quantum mechanics, electron tunneling is described as a quantum penetration effect through a potential barrier. This paper proposes a new physical framework based on the Energy Gradient Model 2.0 (EGM 2.0), which reinterprets the tunneling phenomenon from the perspective of electron cloud deformation and energy gradient driving. Experiments show that when an external potential is applied to a stable electronic system, the electron cloud distribution is reconstructed without destroying the basic electronic structure. A clear energy threshold exists: below the threshold, only electron cloud deformation and spatial rearrangement occur, which corresponds to the tunneling effect; above the threshold, the original quantum state is destroyed, leading to quantum transition. The EGM 2.0 model unifies the mechanism of electron tunneling and quantum transition, providing a consistent classical-quantum physical explanation.
The tunnel effect, commonly defined as the phenomenon in which a microparticle overcomes a potential barrier that exceeds its total energy, is often cited in quantum mechanics. However, this effect does not actually occur in its described form in nature, and the quantum mechanical interpretation of tunneling does not accurately represent the real physical processes involved, but rather provides a mathematical model. The true physical mechanism of the tunnel effect remains unidentified. An analysis of the tunnel effect reveals that its manifestation creates a “paradox” in classical physics. Explanations based on the Heisenberg uncertainty principle and the wave nature of particles fail to offer a comprehensive understanding of the actual physical process.This study proposes a new explanation of the tunneling phenomenon based on the principles of classical physics and electrodynamics. It is shown that the overcoming of the Coulomb barrier by low-energy microparticles occurs exclusively due to brief localized decreases in potential within the Coulomb barrier, allowing certain charged microparticles to penetrate. The formation mechanism of these short-lived localized regions, which manifest as volume channels with lower potential within the Coulomb barrier, is examined.It is established that the creation of these channels is linked to the properties of atomic nuclear and their associated electric fields. This facilitates the supra barrier penetration of the Coulomb barrier by individual low-energy microparticles that pass through these channels while experiencing a reduction in their total energy. This explanation resolves the “paradox” of the tunneling effect, eliminating the contradiction with classical physics laws.Moreover, the derived estimates of the tunneling process parameters are in qualitative agreement with the results obtained from quantum-mechanical models. The proposed framework aligns with nuclear physics findings, is supported by experimental evidence, and provides a new mechanism for controlling the tunneling effect in various energy-related applications.
At the turn of the twentieth century, the establishment of quantum theory propelled rapid advancements, particularly in the understanding of quantum tunnelling—a fundamental phenomenon in quantum mechanics crucial for various physical processes. The quantum phenomenon of particle passes through potential barriers is of great importance. In classical physics, when the energy of a particle is less than the height of a double barrier structure, it is impossible for it to pass through. However, quantum mechanics allows a particle to penetrate the barrier and emerge on the other side. This paper explores the quantum tunnelling effect, focusing on the single potential barrier model in one dimension and subsequently extending to the double potential barrier model. The Schrödinger equation provides the foundational framework for elucidating the motion of microscopic particles, emphasizing wave-particle duality inherent in quantum mechanics. The analysis of the single potential barrier model involves solving the Schrödinger equation in different regions, determining wave functions and coefficients through boundary conditions. The transmission coefficient is derived, representing the probability of a particle passing through a barrier. In the case of a “thick” barrier, an approximate form for transmission coefficient is provided, demonstrating the exponential decrease in transmission probability with increasing barrier thickness.
The quantum tunneling phenomenon has long been explained by quantum mechanics using abstract concepts such as probability waves and wave function collapse. However, the essence of its microscopic physical mechanism—how and why a particle can traverse a classically forbidden region—has never been clearly elucidated, leading to a schism between the physical laws governing the micro- and macro-worlds. Based on the Great Tao Model and the Unified Theory of Atomic and Molecular Structure, this paper, for the first time, constructs a complete, self-consistent, and quantifiable framework for a classical physical explanation. The core of this framework clarifies the microscopic physical mechanisms of "local weakening of the Existence Field" and "formation of a directional field channel", reducing the tunneling process to a deterministic sequence of events: "information coupling → field weakening → channel formation → classical penetration". The study rigorously derives the quantitative relationships between the field strength weakening coefficient, the field channel width, and the penetration probability. Its mathematical form is compatible with the empirical formula of quantum mechanics, but its physical connotation is fundamentally different. Case studies demonstrate that this theory can uniformly explain the atomic-scale resolution of scanning tunneling microscopy (STM), the deterministic energy release in α-decay, and the physical necessity for the impossibility of macroscopic object tunneling. Starting from the first principles of classical physics, this paper provides a new paradigm for understanding tunneling that aligns with physical intuition, has a clear mechanism, and is subject to experimental verification, achieving a logical unification of micro- and macro-physical laws.
There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of an electron tunneling through a rectangular barrier are numerically calculated. No superluminal effect (Hartman effect) is found for the tunneling electron. Heisenberg's energy-time uncertainty relation for the tunneling effect is verified by calculating an introduced coefficient representing uncertainty. The present author argues that phase time, dwell time and Bütticker-Landauer time are not appropriate expressions for the actual transit time in a tunneling process. A quantum high-jumping model is presented to resolve the paradox that kinetic energy of the tunneling particle is negative and its momentum is imaginary.