The complex amplitude X₁+iX₂≡(x+ipmω)e^iωt of a harmonic oscillator is constant in the absence of driving forces. Although the uncertainty principle forbids precise measurements of X₁ and X₂ simultaneously (ΔX₁ΔX₂>~2mω), X₁ alone can be measured precisely and continuously ("quantum nondemolition measurement"). Examples are given of measuring systems that do this job. Such systems might play a crucial role in gravitational-wave detection and elsewhere.
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Thorne et al. (1978) studied this question.
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