An experimentalist trying to work his way through the impressive body of literature in quantum measurement theory rapidly notices that the theory, at least hitherto, does not make any predictions for experiments aimed at its own test. Rather one has the impression that most experiments discussed in the context of that theory serve more the purpose of trying to demonstrate its internal consistency. An early example is the beautiful paper by Mott (1929) where he presents the wave mechanical analysis of a seemingly particle-like phenomenon, the α-ray tracks in a cloud chamber.
An experimentalist trying to work his way through the impressive body of literature in quantum measurement theory rapidly notices that the theory, at least hitherto, does not make any predictions for experiments aimed at its own test. Rather one has the impression that most experiments discussed in the context of that theory serve more the purpose of trying to demonstrate its internal consistency. An early example is the beautiful paper by Mott (1929) where he presents the wave mechanical analysis of a seemingly particle-like phenomenon, the α-ray tracks in a cloud chamber.
This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real.
Quantum mechanics is one of our most successful physical theories; its predictions agree with experimental observations to an extremely high accuracy. However, the bare formalism of quantum theory does not provide straightforward answers to seemingly simple questions: for example, how should one model systems that include agents who are themselves using quantum theory? These foundational questions may be investigated with a theorist's tool – the thought experiment. Its purpose is to turn debates about the interpretation of quantum theory into actual physics questions. In this article, we give a state-of-the-art overview on quantum thought experiments involving observers, from the basic Wigner's friend to the recent Frauchiger-Renner setup, clarifying their interpretational significance and responding to objections and criticism on the way.
The aim of this paper is to discuss in a pedagogical way the problem of the emergence of classical behaviour in certain physical systems which, in principle, are correctly described by quantum mechanics. It is stressed that the limit ℏ → 0 is not sufficient and the crucial role played by the environment must be taken into account. In particular, recalled is the old problem raised by Mott in 1929 ( Proc. R. Soc. Lond. A 126 79) concerning the straight tracks observed in a cloud chamber, produced by an α-particle emitted by a source in the form of a spherical wave. The conceptual relevance of the problem for a clearer understanding of the classical limit is discussed in a historical perspective. Moreover, a simple mathematical model is proposed, where the result of Mott is obtained in a rigorous mathematical way.
Abstract The present note is suggested by a recent paper by Prof. Darwin,* and is intended to show how one of the most typically particle-like properties of matter can be derived from the wave mechanics. In the theory of radioactive disintegration, as presented by Gamow, the ∝-particle is represented by a spherical wave which slowly leaks out of the nucleus. On the other hand, the ∝-particle, once emerged, has particle-like properties, the most striking being the ray tracks that it forms in a Wilson cloud chamber. It is a little difficult to picture how it is that an outgoing spherical wave can produce a straight track ; we think intuitively that it should ionise atoms at random throughout space. We could consider that Gamow’s outgoing spherical wave should give the probability of disintegration, but that, when the particle is outside the nucleus, it should be represented by a wave packet moving in a definite direction, so as to produce a straight track. But it ought not to be necessary to do this. The wave mechanics unaided ought to be able to predict the possible results of any observation that we could make on a system, without invoking, until the moment at which the observation is made, the classical particle-like properties of the electrons or α-particles forming that system. If we consider the ∝-ray alone as the system under consideration, then the gas of the Wilson chamber must be considered as the means by which we observe the particle ; so in this case we must consider the ∝-ray as α-particle as soon as it is outside the nucleus, because that is the moment at which the observation is made. If, however, we consider the α-particle and the gas together as one system, then it is ionised atoms that we observe ; interpreting the wave function should give us simply the probability that such and such an atom is ionised. Until this final interpretation is made, no mention should be made of the ∝-ray being a particle at all. The difficulty that we have in picturing how it is that a spherical wave can produce a straight track arises from our tendency to picture the wave as existing in ordinary three dimensional space, whereas we are really dealing with wave functions in the multispace formed by the co-ordinates both of the α-particle and of every atom in the Wilson chamber.
In recent notes by Einstein, Podolsky and Rosen and by Bohr, attention has been called to the fact that certain results of quantum mechanics are not to be reconciled with the assumption that a system has independently real properties as soon as it is free from mechanical interference. We here investigate in general, and in abstract terms, the extent of this disagreement. When suitably formulated, such an assumption gives to certain types of questions the same answers as does quantum mechanics; this is true of the formulas usually given in discussions of the theory of measurement. There exists, however, a general class of cases in which contradictions occur. That such contradictions are not restricted to the abstract mathematical theory, but can be realized in the commonest physical terms, is shown by the working out of an example..
Abstract Measurement lies at the core of the quantum formalism. This may seem a statement of the intuitively obvious for any theoretical structure with a pretension to predict the outcomes of observations made or experiments performed on objects in the real world. But classical mechanics is a theorys of the physical properties of objects and their behaviour when exposed to different kinds of forces, and there is no particularly significant role for measurement other than a passive role involving the recording of those properties or behaviour. In contrast, measurement in quantum theory takes on a far deeper, almost ominous, significance