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arXiv · 2607.07970

Associating Trajectories with Quantum Processes by Equivalent Spectra

Elliott Tammaro·Sriram Gundla·Arunabh Pratik·Shyla Rathore
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Abstract

Quantum mechanics abandoned the classical notion of a particle trajectory, yet trajectories remain conceptually appealing for resolving foundational issues in quantum mechanics. Bohmian mechanics offers one route to associating trajectories with quantum processes, but it requires explicit non-locality to remain consistent with EPR-type experiments, placing it in tension with special relativity. We propose an alternative approach: rather than deriving trajectories from a quantum guidance equation, we search for classical trajectories whose radiated frequency spectra match those of quantum processes such as atomic transitions. Using the Li\'enard-Wiechert potentials, we compute the electric and magnetic fields generated by a point charge along a given trajectory, numerically solving the retarded-time and from these fields obtain the power spectrum of emitted radiation. By fitting the parameters of a chosen family of trajectories, we identify "equivalent spectrum" trajectories that reproduce a target frequency distribution, including ones of quantum mechanical origin. We discuss the implications of this method and propose future work to determine whether equivalent spectrum trajectories belong to a family governed by a differential equation, which would constitute a quantum-equivalent equation of motion.

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Elliott Tammaro, Sriram Gundla, Arunabh Pratik, Shyla Rathore. 2026-07-08. Associating Trajectories with Quantum Processes by Equivalent Spectra. https://arxiv.org/abs/2607.07970

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