[Paper Review] Classical sources of non-classical physics: the case of linear superposition

Ghenadie N. Mardari, J. A. Greenwood|arXiv (Cornell University)|Sep 28, 2004

Quantum Mechanics and Applications3 citations

TL;DR

This paper argues that linear superposition in classical wave physics can be interpreted as a local energy redistribution process rather than non-interacting wave passage, offering a classical framework that explains quantum-like phenomena without invoking non-classicality. The key contribution is showing that quantum superposition can be understood as a classical process under this reinterpretation, dissolving the perceived gap between classical and quantum mechanics.

ABSTRACT

Classical linear wave superposition produces the appearance of interference. This observation can be interpreted in two equivalent ways: one can assume that interference is an illusion because input components remain unperturbed, or that interference is real and input components undergo energy redistribution. Both interpretations entail the same observable consequences at the macroscopic level, but the first approach is considerably more popular. This preference was established before the emergence of quantum mechanics. Unfortunately, it requires a non-classical underlying mechanism and fails to explain well-known microscopic observations. Classical physics appears to collapse at the quantum level. On the other hand, quantum superposition can be described as a classical process if the second alternative is adopted. The gap between classical mechanics and quantum mechanics is an interpretive problem.

Motivation & Objective

• To challenge the widespread assumption that waves pass through each other unperturbed during superposition.
• To demonstrate that energy redistribution in wave interference is a local, physical process rather than a non-local or illusory phenomenon.
• To show that quantum superposition can be understood as a classical process if energy redistribution is taken seriously.
• To resolve the interpretive inconsistency in classical physics that arises from rejecting local energy flow in superposition.
• To argue that the distinction between classical and non-classical physics lies not in scale but in interpretation of fundamental physical processes.

Proposed method

• Analyzes wave interference using the principle of superposition, where net amplitude is the vector sum of components.
• Applies energy conservation by relating wave energy to the square of net amplitude, revealing surplus energy at constructive interference points.
• Compares three interpretations: non-interaction (waves pass through unperturbed), specular reflection (waves bounce), and net state merging (waves form a single state).
• Uses mathematical modeling to show identical macroscopic predictions across all three interpretations, even with distinguishable waves (different amplitude, frequency, polarization).
• Applies relativistic and momentum conservation principles to argue against non-local energy redistribution.
• Evaluates the ontological consistency of each interpretation, favoring the local redistribution model to preserve classical mechanics.

Experimental results

Research questions

• RQ1 Is wave interference in classical physics truly non-interacting, or is energy redistribution a real local process?
• RQ2 Can quantum superposition be explained using a classical framework based on local energy redistribution?
• RQ3 Why does the non-interaction assumption lead to foundational inconsistencies in classical physics?
• RQ4 Are the predictions of classical wave superposition dependent on the interpretation of interference, or are they invariant across interpretations?
• RQ5 What are the implications of reinterpreting superposition as a local process for the classical-quantum divide?

Key findings

• The non-interaction assumption — that waves pass through each other unperturbed — leads to non-local energy redistribution, which violates classical principles of relativity and momentum conservation.
• The alternative interpretation, where waves undergo local energy redistribution, produces identical macroscopic predictions and is ontologically consistent with classical mechanics.
• Even with distinguishable waves (different amplitude, frequency, polarization), the three interpretations yield quantitatively identical output beams, proving their physical indistinguishability.
• The assumption of non-interaction requires non-Newtonian mechanisms, such as particles moving in two directions simultaneously without transmitting momentum.
• The paper shows that quantum superposition can be interpreted as a classical process if local energy redistribution is accepted, suggesting that quantum mechanics need not be inherently non-classical.
• The fundamental distinction between classical and non-classical physics is not scale-based but lies in the interpretation of wave superposition and the nature of physical reality.