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Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case

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Abstract

Heisenberg's position-measurement-momentum-disturbance relation is derivable from the uncertainty relation σ(q)σ(p) ≥ h/2 only for the case when the particle is initially in a momentum eigenstate. Here I derive a new measurement-disturbance relation which applies when the particle is prepared in a twin-slit superposition and the measurement can determine at which slit the particle is present. The relation is d × Δp ≥ 2h/π, where d is the slit separation and Δp = DM(Pf, Pi) is the Monge distance between the initial Pi(p) and final Pf(p) momentum distributions.

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  1. H. M. Wiseman
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Wiseman, H.M. Extending Heisenberg's Measurement-Disturbance Relation to the Twin-Slit Case. Foundations of Physics 28, 1619–1631 (1998). https://doi.org/10.1023/A:1018889508782

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