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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Presence of a particle in a given space-time region and the continuous action of a particle detector

Ingram Bloch, D. A. Burba

Published Nov 15, 1974• 14 citations
Publisher

Abstract

We attempt to answer several questions relating to the presence of a particle, with known initial state, in a given region of space during a given period of time. In the process, we try to extend the quantum theory of observation to the case in which the observation goes on continuously. Although this mode of observation is common in practice, the theory does not seem to describe it adequately. In general, questions like those that we are asking do not have simple, unambiguous answers in quantum theory. In order to approach such a question, we usually have to assume that the particle interacts with something in the space-time region of interest, and then to infer the probability of the particle's presence from the probability of its interacting with the other object. This fact suggests either that we are asking the wrong questions or that perhaps quantum mechanics should be regarded as a theory of interaction events rather than a theory of systems.

DOI
10.1103/physrevd.10.3206

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We attempt to answer several questions relating to the presence of a particle, with known initial state, in a given region of space during a given period of time. In the process, we try to extend the quantum theory of observation to the case in which the observation goes on continuously. Although this mode of observation is common in practice, the theory does not seem to describe it adequately. In general, questions like those that we are asking do not have simple, unambiguous answers in quantum theory. In order to approach such a question, we usually have to assume that the particle interacts with something in the space-time region of interest, and then to infer the probability of the particle's presence from the probability of its interacting with the other object. This fact suggests either that we are asking the wrong questions or that perhaps quantum mechanics should be regarded as a theory of interaction events rather than a theory of systems.
More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.
In classical physics, the ‘state’ of a particle, at any particular time, is taken to involve a definite position in space and a definite motion; and the state of a system of particles is taken to involve a definite position in space and a definite motion for each of the particles. The situation in relation to quantum mechanics is completely different. As in classical physics, calculations can be made concerning the position and motion of a particle. However, this representation is not by means of symbols for scalar or vector quantities: it is by a more complex mathematical object. This quantum state does not indicate or represent position or motion in any direct way: what it does in substance is to enable calculation of the probability of the particle in question being found to have a position or momentum if an appropriate measurement is made.
The words: determinism, hidden variables, subjectivism, information, objectivism, informational-theoretic axioms,observers have some connection with physical reality? What we mean with "description" of physical reality? When we say that we understand this reality? Certain parameters:position, velocity are sufficient? We will focus only to conceptual considerations regarding the relation between the "questions" and the relative "answers" in general and specifically in quantum mechanics. It is usually believed that the answers are more important of the questions, for this reason we can read many answers everywhere and in different field of knowledge. We need to add and clarify some things: (i) usually an answers require a question, (ii) but, as we know, their relation is not so simple and immediate, (iii) For instance: a)an epistemic questions give us ontic answers? b)the answer has a connection with the question and vice versa? c)we could to infer a question starting from an answer? d)there are answers without questions? These answers could be in some framework considered as ontic answers? The relative scientific works are the same time ontic? Speaking of quantum mechanics we see around many answers in the meantime we do not see the correspondent questions, these answers seem completely independent, and this seem a right road, the road of the independent nature unlinked from human thoughts. We retain instead that questions can affect the possible answers. Exist "something" before the question?