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This research establishes that specific uncertainty relations governing position and momentum variances hold universally across classical light beams, coherent states, and individual photons. The finding bridges fundamental gaps between classical electromagnetism and quantum optics by demonstrating identical mathematical constraints ($\Delta r \Delta k \ge 5/2$) in all three regimes. For the community, this suggests that certain "quantum" limits may be intrinsic to wave phenomena regardless of whether a particle description is applied.

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Uncertainty relations in classical and quantum theories of electromagnetism

arXiv4 august 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2605.28906v2 Announce Type: replace Abstract: Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the quantum theory of coherent light beams, and in the quantum theory of individual photons.

Abstract:Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the quantum theory of coherent light beams, and in the quantum theory of individual photons.

arXiv:2605.28906 [quant-ph]

(or arXiv:2605.28906v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.28906 Focus to learn more arXiv-issued DOI via DataCite

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