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Physics Reports

Decoherence in generalized measurement and the quantum Zeno paradox

G. Mack, Sascha Wallentowitz, P. E. Toschek

Published Feb 18, 2014• 3 citations
Publisher
DOI
10.1016/j.physrep.2014.02.004

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We propose Holographic Zeno Gravity (HZG), a stochastic modification of General Relativity that resolves the conflict between the superposition principle and the thermodynamic structure of spacetime. Addressing the “Heating Paradox” that invalidates standard Diósi-Penrose models, we postulate that the metric background is subject to non-Markovian “Red Noise” fluctuations (Sh(ω) ∝ 1/ω²) driven by the entropic drift of the holographic horizon. We derive a single-parameter Relational Master Equation where the decoherence rate is governed by a geometric coupling K = mcL/ħ and a single phenomenological amplitude A_eff ≈ 10⁻⁵⁴ s⁻¹, constrained by LISA Pathfinder bounds. The “Zeno” nomenclature reflects the continuous monitoring of spatial superpositions by the metric background, analogous to the quantum Zeno effect where frequent measurements inhibit state evolution. We demonstrate that while atomic interferometers remain transparent to these fluctuations, mesoscopic test masses in the proposed MAQRO mission will exhibit a measurable collapse time of τ ≈ 10³ seconds (L = 1 m). Distinctively, HZG predicts a geometric decoherence scaling (L⁻²) and a unique phase-space squeezing signature, providing a falsifiable alternative to environmental noise models.
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.
Quantum non-integrable systems have pseudochaos in the phase of the eigenfunctions. In particular, correlation function of wave functions at two different points disappears, when observation process, which requires space and/or time average over a small range, is taken into account. This gives rise to the realization of decoherence in measuring processes. By virtue of this property of quantum chaos, various problems and paradoxes are explained in the framework of conventional quantum mechanics. The subjects treated here are the duality of wave and particle, the wave function collapse in measurement, Stern–Gerlach experiments, Schrödinger's cat paradox, the Einstein–Podolsky–Rosen paradox and quantum Zeno effect.