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The Effective de Broglie Wavelength of Macroscopic Objects via Thermal Superposition

Patel, Vyom

Published Nov 17, 2025• 0 citations
Publisher

Abstract

Macroscopic objects do not exhibit quantum interference, even though the de Broglie relation applies universally. A common argument is that their momentum is too large for observable wavelengths. However, this does not explain why an object at rest does not display an infinite wavelength. This work develops a thermal-ensemble-based explanation: the internal degrees of freedom of any object at finite temperature possess a Maxwell--Boltzmann distribution of momenta, each associated with its own de Broglie wavelength. By integrating over this thermal momentum distribution, we show that the internal wave contributions cancel due to isotropy and rapid phase oscillations. This yields an effectively vanishing internal de Broglie wavelength and provides an intuitive mechanism for intrinsic decoherence in macroscopic matter.

DOI
10.5281/zenodo.17632684

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Macroscopic objects do not exhibit quantum interference, even though the de Broglie relation applies universally. A common argument is that their momentum is too large for observable wavelengths. However, this does not explain why an object at rest does not display an infinite wavelength. This work develops a thermal-ensemble-based explanation: the internal degrees of freedom of any object at finite temperature possess a Maxwell--Boltzmann distribution of momenta, each associated with its own de Broglie wavelength. By integrating over this thermal momentum distribution, we show that the internal wave contributions cancel due to isotropy and rapid phase oscillations. This yields an effectively vanishing internal de Broglie wavelength and provides an intuitive mechanism for intrinsic decoherence in macroscopic matter.
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There exists a paradigm in which Quantum Mechanics is an exclusively developed theory to explain phenomena on a microscopic scale. As the Planck's constant is extremely small, h∼10−34J.sh\sim10^{-34}{J.s}h∼10−34J.s, and as in the relation of de Broglie the wavelength is inversely proportional to the momentum; for a mesoscopic or macroscopic object the Broglie wavelength is very small, and consequently the undulatory behavior of this object is undetectable. In this paper we show that with a particle oscillating around its classical trajectory, the action is an integer multiple of a quantum of action, S=nhoS = nh_{o}S=nho​. The quantum of action, hoh_{o}ho​, which plays a role equivalent to Planck's constant, is a free parameter that must be determined and depends on the physical system considered. For a mesoscopic and macroscopic system: ho≫hh_{o}\gg hho​≫h, this allows us to describe these systems with the formalism of quantum mechanics.
Louis de Broglie's proposal that every material particle possesses an associatedwavelength transformed modern physics by extending wave behavior beyond light tomatter itself. The relation𝜆 = ℎ/𝑝has since been confirmed experimentally through electron diffraction, neutron diffraction,atom interferometry, and Bose-Einstein condensates. Yet despite its remarkable predictivesuccess, the physical mechanism responsible for the emergence of matter wavelengthremains one of the conceptual mysteries of quantum mechanics.This paper proposes a qualitative Space-Phase (SP3) interpretation in which de Brogliewavelength represents the effective coherence span available within a momentumconditioned Space-Phase envelope surrounding matter. A simple mechanical analogy—aflexible rickshaw carrying either an elephant or a mouse—is presented to illustrate howincreasing momentum produces deeper deformation of the surrounding medium, naturallyreducing the effective coherence distance. The analogy does not replace quantummechanics; rather, it offers an intuitive mechanism consistent with the observed inverserelationship between wavelength and momentum.
For quantum particles in a Boltzmann state, we derive an inequality between momentum uncertainty ΔpΔpΔp and thermal de Broglie wavelength λthλ_{\rm th}λth​, expressed as Δp≥2πℏ/λthΔp \geq \sqrt{2π}\hbar/λ_{\rm th}Δp≥2π​ℏ/λth​, as a corollary of the Boltzmann lower bound for the Heisenberg uncertainty product proposed in the previous work [EPL, 143, 20001 (2023)]
We propose a geometric interpretation of the wavelengths associated with the dynamics of a confined structure. This approach is based on a distinction between impulse, associated with the intrinsic dynamics of the phase, and momentum, associated with the translation of the structure in the coherence landscape from the point of view of the reference observer. The construction gives rise to two wavelengths with distinct statuses : impulse leads to the Compton wavelength, while momentum leads to the de Broglie wavelength. These two wavelengths thus result from the same decomposition of the dynamics of the confined structure, applied to two contributions of different nature.