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Criminal procedure and quantum Zeno effect

Bartosz W. Wojciechowski

Published Aug 1, 2023• 0 citations
Publisher

Abstract

The quantum Zeno effect is the suppression of unitary time evolution in quantum systems and can be caused by measurement or interactions with the environment. It is a feature of a systems under which time evolution of a particle can be slowed down by measuring it frequently enough. In other words, when a system is being constantly watched, it cannot change. Evolution of the system can be slowed down or even frozen by the act of frequent measurement or interaction with the environment. The name of the phenomena comes from Zeno’s arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In this chapter, we will present results of a study conducted on a group of 45 judges adjudicating in criminal cases. We will analyse if preliminary rulings, interim orders and other numerous intermediate decisions related to the course of the criminal trial and affect the final judgement of the case. The findings show whether a quantum effect can be observed in the criminal trials.

DOI
10.4324/9781003402480-5

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The quantum Zeno effect is the suppression of unitary time evolution in quantum systems and can be caused by measurement or interactions with the environment. It is a feature of a systems under which time evolution of a particle can be slowed down by measuring it frequently enough. In other words, when a system is being constantly watched, it cannot change. Evolution of the system can be slowed down or even frozen by the act of frequent measurement or interaction with the environment. The name of the phenomena comes from Zeno’s arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In this chapter, we will present results of a study conducted on a group of 45 judges adjudicating in criminal cases. We will analyse if preliminary rulings, interim orders and other numerous intermediate decisions related to the course of the criminal trial and affect the final judgement of the case. The findings show whether a quantum effect can be observed in the criminal trials.
Introduction Quantum theory predicts the striking and paradoxical result that when a system is continuously watched, it does not evolve! Although this effect was noticed much earlier by a number of people [146], [147], [148], [149], [150], it was first formally stated by Misra and Sudarshan [151] and given the appellation ‘Zeno's paradox’ because it evokes the famous paradox of Zeno denying the possibility of motion to a flying arrow. It is as startling as a pot of water on a heater that refuses to boil when continuously watched. This is why it is also called the ‘watched pot effect’. The effect is the result of repeated, frequent measurements on the system, each measurement projecting the system back to its initial state. In other words, the wave function of the system must repeatedly collapse. It is also necessary that the time interval between successive measurements must be much shorter than the critical time of coherent evolution of the system, called the Zeno time [152]. For decays this Zeno time is the time of coherent evolution before the irreversible exponential decay sets in, and is governed by the reciprocal of the range of energies accessible to the decay products. For most decays this is extremely short and hard to detect [153]. In the case of non-exponential time evolution, the relevant Zeno time can be much longer.
Although the quantum Zeno effect takes its name from Zeno's arrow paradox, the effect of frequently observing the position of a freely moving particle on its motion has not been analyzed in detail in the frame of standard quantum mechanics. We study the evolution of a moving free particle while monitoring whether it lingers in a given region of space, and explain the dependence of the lingering probability on the frequency of the measurements and the initial momentum of the particle. Stopping the particle entails the emergence of Schr\"odinger cat states during the observed evolution, closely connected to the high-order diffraction modes in Fabry-P\'erot optical resonators.
Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated measurements on the quantum dynamics of multilevel systems that exhibit the quantum localization of classical chaos. The analysis is based on the wave function and Schr\"odinger equation, without introduction of the density matrix. We show how the quantum Zeno effect in simple few-level systems can be recovered and understood by formal modeling the effect of measurement on the dynamics by randomizing the phases of the measured states. This analysis is extended to investigate the dynamics of multilevel systems driven by an intense external force and affected by frequent measurements. We show that frequent measurements of such quantum systems results in delocalization of the quantum suppression of classical chaos. This result is the opposite of the quantum Zeno effect. The phenomenon of delocalization of the quantum suppression and restoration of quasi-classical time evolution of these systems, owing to repetitive frequent measurements, can therefore be called the quantum anti-Zeno effect. From this analysis we furthermore conclude that frequently or continuously observable quasiclassical systems evolve basically in a classical manner.
Classical probability theory has been influential in modelling decision processes, despite empirical findings that have been persistently paradoxical from classical perspectives. For such findings, some researchers have been successfully pursuing decision models based on quantum theory (QT). One unique feature of QT is the collapse postulate, which entails that measurements (or in decision-making, judgements) reset the state to be consistent with the measured outcome. If there is quantum structure in cognition, then there has to be evidence for the collapse postulate. A striking, a prioriprediction, is that opinion change will be slowed down (under idealized conditions frozen) by continuous judgements. In physics, this is the quantum Zeno effect. We demonstrate a quantum Zeno effect in decision-making in humans and so provide evidence that advocates the use of quantum principles in decision theory, at least in some cases.
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.
The evolution of a quantum system undergoing very frequent measurements takes place in a subspace of the total Hilbert space (quantum Zeno effect). The dynamical properties A quantum system, prepared in a state that does not belong to an eigenvalue of its total Hamiltonian, starts to evolve quadratically in time [1, 2]. This behavior leads to the so-called quantum Zeno phenomenon: by performing frequent measurements on the system, in order to check whether it is still in its initial state, one can “slow