Abstract
The uncertainty relation formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable so that their product should be no less than a limit set by Planck's constant. In 1980, Braginsky, Vorontsov, and Thorne claimed that this relation leads to a sensitivity limit for gravitational wave detectors. However, in 1988 a model of position measurement was constructed that breaks both this limit and Heisenberg's relation. Here, we discuss the problems as to how we reformulate Heisenberg's relation to be universally valid and how we experimentally quantify the error and the disturbance to refute the old relation and to confirm the new relation.
Highlights
For the standard deviations σ(Q) and σ(P ) of the position Q and the momentum P in the state described by a Gaussian wave function [1, p. 69], which Kennard [3] subsequently generalized as the relation σ(Q)σ(P )
The standard deviation is defined for any observable A by σ(A)2 = A2 − A 2, where · · · stands for the mean value in a given state
In the light of modern theory of quantum measurement, (RH) has been abandoned as proposed by Davies and Lewis [6]: One of the crucial notions is that of repeatability which we show is implicitly assumed in most of the axiomatic treatments of quantum mechanics, but whose abandonment leads to a much more flexible approach to measurement theory [6, p.239]
Summary
We discuss the von Neumann model and show that this long-standing standard model satisfies the Heisenberg error-disturbance relation (EDR) (2). This belief was enforced by Arthurs and Kelly [15] suggesting that all the joint unbiased measurement of position and momentum satisfy the Heisenberg error tradeoff relation.
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