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arXiv:cond-mat/9705108

On Experimental Evidence of Uncertainty of Quantized Electromagnetic Potential from QHE

F. Ghaboussi

Published May 12, 1997• 0 citations
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Abstract

It is shown that the observed potential drops on QHE samples can be considered as a realization of uncertainty relation for the quantized two dimensional electromagnetic potential.
DOI
10.48550/arxiv.cond-mat/9705108

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We discuss a model where the relation between Hall potential AHA_HAH​ = and gate potential AGA_GAG​, which is manifested by the stepped QHE = curve, is described by an uncertainty relation ΔAH.=ΔAG=3DB(ℏ/e)ΔA_H . = ΔA_G =3D B(\hbar/e)ΔAH​.=ΔAG​=3DB(ℏ/e).
Investigating the quantum nature of gravity is an important issue in modern physics. Recently, studies pertaining to the quantum superposition of gravitational potential have garnered significant interest. Inspired by Mari et al. [Sci. Rep. 6, 22777 (2016)] and Baym and Ozawa [Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)], Belenchia et al. [Phys. Rev. D 98, 126009 (2018)] considered a gedanken experiment involving such a quantum superposition and mentioned that the superposition renders causality and complementarity inconsistent. They resolved this inconsistency by considering the quantized dynamical degrees of freedom of gravity. This suggests a strong relationship between the quantum superposition of the gravitational potential and the quantization of the gravitational field. In our previous study [Phys. Rev. D 106, 125002 (2022)], we have shown that the quantum uncertainty of a field guarantees the consistency between causality and complementarity. In this study, we focus on the entanglement between two particles' states due to the electromagnetic/gravitational potential and investigate its relationship with quantum uncertainty, causality, and complementarity. Our numerical analyses show that the quantum uncertainty of the electromagnetic/gravitational field results in vacuum fluctuations and prohibits the entanglement between two particles' states when causality is satisfied. We further demonstrate that complementarity holds when the particles do not get entangled. The uncertainty relation does not cause the entanglement between two particles' states, which guarantees complementarity.
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