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Noise vs Noise: Tracking Quantum Particles Without Wave Function Collapse

AWATIF ALLHYANI

Published Jan 1, 2026• 0 citations

Abstract

One of the most fundamental principles of quantum mechanics is the collapse of the wave function upon measurement. Here, we present a novel approach called Noise vs Noise that enables continuous tracking of a quantum particle (specifically, an electron in a double-slit experiment) without causing wave function collapse. Instead of directly interacting with the particle, we introduce a well-defined reference noise field into the medium. The electron perturbs this noise through its electric field, and by analyzing the noise distortion, we extract information about the electron’s position and velocity. Numerical simulations demonstrate that the wave function remains intact (correlation = 1.0000) while achieving positional accuracy on the order of 10−8 m and velocity estimates within the correct order of magnitude (106 m/s). The uncertainty product ∆x · ∆p remains above the Heisenberg limit (ħ/2), confirming that the method re- spects quantum mechanical principles while offering a gentle measurement paradigm. This work opens new possibilities for quantum sensing, continuous monitoring, and fundamental tests of quantum mechanics.

DOI: 10.5281/zenodo.19091699

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One of the most fundamental principles of quantum mechanics is the collapse of the wave function upon measurement. Here, we present a novel approach called Noise vs Noise that enables continuous tracking of a quantum particle (specifically, an electron in a double-slit experiment) without causing wave function collapse. Instead of directly interacting with the particle, we introduce a well-defined reference noise field into the medium. The electron perturbs this noise through its electric field, and by analyzing the noise distortion, we extract information about the electron’s position and velocity. Numerical simulations demonstrate that the wave function remains intact (correlation = 1.0000) while achieving positional accuracy on the order of 10−8 m and velocity estimates within the correct order of magnitude (106 m/s). The uncertainty product ∆x · ∆p remains above the Heisenberg limit (ħ/2), confirming that the method re- spects quantum mechanical principles while offering a gentle measurement paradigm. This work opens new possibilities for quantum sensing, continuous monitoring, and fundamental tests of quantum mechanics.

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We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.