M.A.B. Whitaker

Reflections on the quantum Zeno paradox

The authors clarify some of the controversial aspects involved in the treatment of the quantum Zeno paradox. An argument for the paradox is given on the basis of the uncertainty principle, and the conditions for the paradox are analysed. Flemings rule is proved in a simple way. Connection with the standard time-dependent perturbation theory is discussed. They compare the Zeno paradox with the other well known paradoxes of quantum mechanics and point out that the quantum Zeno paradox is immune to the use of the ensemble interpretation which has some success in tackling the other paradoxes. Remarks are made concerning the broader significance of the quantum Zeno paradox.

Role of the observer in quantum mechanics and the Zeno paradox

We discuss the role of the observer in quantum mechanics. We briefly discuss various interpretations of quantum‐mechanical measurement currently used in the literature. Then we point out the difficulty in deciding what occurrences should be classified as ’’observations.’’ Using the Copenhagen Interpretation, we discuss the effect of successive measurements on the decay rate of an unstable quantum system. For two types of systems, those with a small finite number of decay levels and those with a continuum or semicontinuum, we review the decay behavior, and in the latter case distinguish between: small time behavior, with survival probability falling off as t2; the intermediate region, where it varies exponentially with time; and the long‐time region, where the decay is less than exponential. If we cannot define an observation, we show that only an exact exponential decay is allowed. Attempts at solutions of this difficulty are mentioned. Lastly, we take an example of a polarized beam of light passing throu...

Interpretations of quantum measurement without the collapse postulate

Abstract Interpretations of quantum measurement without the collapse postulate are discussed. That in which the final state-function is a linear superposition of macroscopic states is analysed, and contrasted with an interpretation in which macroscopic states are represented by a mixture in the final state. Application is made to a thought-experiment previously analysed by the present authors, and by Hnizdo.

The relative states and many-world interpretations of quantum mechanics and the EPR problem

The basic contributions to the concept of the many-worlds interpretation of quantum mechanics are analysed. It is found necessary to divide them into two classes corresponding to (a) the relative-states interpretation (RSI), which avoids problems of measurement, but is found generally unconvincing, and (b) the many-worlds interpretation (MWI), which is more comprehensible, but has all the problems of the von Neumann scheme. The EPR problem is tackled using each interpretation. The RSI finds no problem, while the MWI meets the same difficulties as conventional interpretations.

The ensemble interpretation and context-dependence in quantum systems

Abstract We probe the validity of the assumptions underlying a particular form of ensemble interpretation of quantum mechanics which presumes pre-assigned individual values for dynamical observables. It is pointed out that Bells theorem can be discussed in a form which indicates inconsistency of such an assumption with quantum mechanical statistical results. Its significance in revealing context-dependence of physical attributes of quantum systems is analysed.

The many-worlds and relative states interpretations of quantum mechanics, and the quantum Zeno paradox

The quantum Zeno paradox is examined within the many-worlds and relative states interpretations of quantum mechanics. In the many-worlds interpretation the effect is predicted to persist. The possibility of recombining worlds is not expected to be relevant. In the simplest form of relative states interpretation the effect may be avoided but this form of interpretation experiences difficulties in coping with conventional problems of quantum theory. The more complex version of the relative states interpretation, which takes account of the correlations of system with apparatus, predicts the occurrence of the paradox.

Improved treatment of Fresnel equations

Present treatments of the Fresnel equations are criticised. A full treatment without the defects is presented, the amplitudes and phases of the electric fields being calculated, and curves displayed for a variety of cases.

Quantum theory, EPR experiments and locality

Abstract Kraus has claimed that there is no evidence that the quantum predictions for experiments of EPR-type exhibit non-locality. We suggest he has not considered fully correlations between the observations on the two arms of the apparatus.

Is the wavefunction collapse a physical reality

Abstract We probe the question of wavefunction collapse using a general analysis of the measurement process. A thought experiment is suggested to clarify the question of empirical verifiability of the collapse postulate.

Use of reduced density matrix for the EPR paradox

Abstract Cantrell and Scully have recently claimed that the EPR paradox may be resolved by use of the reduced density matrix. We show that the wave-function and reduced density-matrix treatments give identical results.