An alternative calculational procedure for quantum theory is presented, employing three features which differ from the corresponding features of orthodox quantum theory. These are: (1) the state vector is never to be “reduced”; (2) quantum theory only makes predictions about ensembles of identical experiments (not about individual experiments); and (3) the measuring apparatus must always be included in the state vector. What is new about this alternative theory is the demonstration that Features 2 and 3 (which have hitherto been discussed separately) can be consistently combined to yield an interpretation of quantum theory which has the additional advantage of Feature 1. It is shown that alternative and orthodox theories yield identical predictions for any practical experiment. However, two classes of experiments (which are impractical) for which the orthodox and alternative theories yield different predictions are described. Therefore, it is, in principle, possible to decide which theory Nature has chosen to obey. It is concluded that there is no reason, based upon experimental evidence, for preferring one theory over the other.
An alternative calculational procedure for quantum theory is presented, employing three features which differ from the corresponding features of orthodox quantum theory. These are: (1) the state vector is never to be “reduced”; (2) quantum theory only makes predictions about ensembles of identical experiments (not about individual experiments); and (3) the measuring apparatus must always be included in the state vector. What is new about this alternative theory is the demonstration that Features 2 and 3 (which have hitherto been discussed separately) can be consistently combined to yield an interpretation of quantum theory which has the additional advantage of Feature 1. It is shown that alternative and orthodox theories yield identical predictions for any practical experiment. However, two classes of experiments (which are impractical) for which the orthodox and alternative theories yield different predictions are described. Therefore, it is, in principle, possible to decide which theory Nature has chosen to obey. It is concluded that there is no reason, based upon experimental evidence, for preferring one theory over the other.
The incompatibility of Orthodox Quantum Mechanics with philosophical realism poses a serious challenge to scientists upholding such a philosophical doctrine. The desire to find a solution to this and other conceptual problems that quantum mechanics confronts has motivated many authors to propose alternative versions to Orthodox Quantum Mechanics. One of them is the Spontaneous Projection Approach, a theory grounded on philosophical realism. It has been introduced in previous papers and, with a few exceptions, it yields experimental predictions coincident with those of Orthodox Quantum Mechanics. One of these exceptions is analyzed in detail. The difference in predictions becomes apparent in a suggested experiment which could put both theories to the test.
Abstract This work sets out to answer a single question: what is the orthodox interpretation of quantum mechanics? However, we adopt a different approach to that normally used. Rather than surveying physicists, or poring over the precise details of the thoughts of Bohr and Heisenberg, we review a collection of 42 textbooks on quantum mechanics, encompassing the most popular and prominent works of this nature. We then gauge their response to 13 propositions to build up a picture of exactly what is believed by an orthodox quantum mechanic. We demonstrate that this orthodoxy has many aspects of Copenhagen-like viewpoints, but also shows some interesting emerging deviations. Moreover, it is more nuanced than some reductive characterisations that condense the orthodoxy down to the ontological primacy of the quantum state. The revealed orthodoxy has three consistent pillars: measurement inherently disturbs quantum states, these states refer to individual instances, not ensembles, and quantum systems do not have definite properties prior to measurement. More fully, it entails that individual particles exist in wave-like super-positions and present particle behaviours only when forced to by outside influences. The act of measuring such a system inherently induces random changes in its state, manifesting as a form of measurement error that corresponds to the uncertainty principle. This implies that measurement does not reveal underlying values of quantum properties.
An understanding of quantum theory is manifested by the ability successfully and unproblematically to use it to further the scientific goals of prediction, explanation, and control of natural phenomena. An Interpretation seeks further to formulate or reformulate it as a fundamental theory that provides a self-contained description of the world. I critically review three prominent but radically different Interpretations of quantum theory (Bohmian mechanics, non-linear theories, Everettian quantum mechanics) and give my reasons for rejecting each as a way of understanding quantum theory. These include problems associated with non-locality, failure of relativistic invariance, empirical inaccessibility, and decision-making. We can achieve a satisfactory understanding of quantum theory and how it successfully advances the goals of science without providing an Interpretation of the theory.
In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of "hidden" variables, developed in a previous paper. We find that in principle, these "hidden" variables determine the precise results of each individual measurement process. In practice, however, in measurements that we now know how to carry out, the observing apparatus disturbs the observed system in an unpredictable and uncontrollable way, so that the uncertainty principle is obtained as a practical limitation on the possible precision of measurements. This limitation is not, however, inherent in the conceptual structure of our interpretation. We shall see, for example, that simultaneous measurements of position and momentum having unlimited precision would in principle be possible if, as suggested in the previous paper, the mathematical formulation of the quantum theory needs to be modified at very short distances in certain ways that are consistent with our interpretation but not with the usual interpretation.We give a simple explanation of the origin of quantum-mechanical correlations of distant objects in the hypothetical experiment of Einstein, Podolsky, and Rosen, which was suggested by these authors as a criticism of the usual interpretation.Finally, we show that von Neumann's proof that quantum theory is not consistent with hidden variables does not apply to our interpretation, because the hidden variables contemplated here depend both on the state of the measuring apparatus and the observed system and therefore go beyond certain of von Neumann's assumptions.In two appendixes, we treat the problem of the electromagnetic field in our interpretation and answer certain additional objections which have arisen in the attempt to give a precise description for an individual system at the quantum level.
The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism.Here we utilize the concepts of identical and similar preparation procedures to show the conceptual differences between the statistical and the conventional interpretation of quantum formalism.Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficulties, both recent experimental results and theoretical developments seem to support an epistemic alternative closer to the conventional one.Nevertheless, we must not rule out the possibility that new theorems or new explanatory principles may modify the reigning supremacy of this interpretation. 1.-Introduction.Although the conventional interpretation of the quantum mechanical formalism (CIQM), very close to the Copenhagen interpretation, is still dominant (is used in almost all textbooks), there are physical situations that ask for an interpretation of the quantum mechanical formalism (QMF) in terms of the Statistical Interpretation of Quantum Mechanics (SIQM) or even for hidden variables theories (HVT).The SIQM and HVT are different research programs, but they are closely related, as we will see further below.To introduce properly the distinctions between the three previous acronyms we will ask an old and apparently simple question.Is the wave function associated to an individual system or to a statistical ensemble?A first tentative answer could be formulated as follows.QMF introduces probabilities, and probabilities are related to statistical ensembles.Otherwise, the same concept of probability would lose its meaning.In QM, if it is said that you would get some concrete result with 0,63 probability it means that if the experiment is carried out 100 times, that concrete result would appear approximately 63 times.Hence, the obvious answer will be that the wave function should be related with statistical ensembles.However, despite its intuitiveness this idea does not capture completely what we want to express.The real problem to analyze could be best introduced with the following example.Imagine that we prepare identically two radioactive atoms with half-life of 30 minutes.By preparation we understand all those theoretical methods and physical procedures necessary to fully characterize the state of the system.It is, thus, a macroscopic reproducible act that lefts the system, without destroying it, in a concrete state after the procedure.In quantum theory, this preparation is represented by a vector state (or a density matrix).Identically in this context will mean identity of procedures, that is that the experimenter has repeated all previous operations, so that there is no difference whatsoever between them.Note, however, that identical preparations are not necessarily followed by identical results, so there is
The usual interpretation of the quantum theory is self-consistent, but it involves an assumption that cannot be tested experimentally, viz., that the most complete possible specification of an individual system is in terms of a wave function that determines only probable results of actual measurement processes. The only way of investigating the truth of this assumption is by trying to find some other interpretation of the quantum theory in terms of at present "hidden" variables, which in principle determine the precise behavior of an individual system, but which are in practice averaged over in measurements of the types that can now be carried out. In this paper and in a subsequent paper, an interpretation of the quantum theory in terms of just such "hidden" variables is suggested. It is shown that as long as the mathematical theory retains its present general form, this suggested interpretation leads to precisely the same results for all physical processes as does the usual interpretation. Nevertheless, the suggested interpretation provides a broader conceptual framework than the usual interpretation, because it makes possible a precise and continuous description of all processes, even at the quantum level. This broader conceptual framework allows more general mathematical formulations of the theory than those allowed by the usual interpretation. Now, the usual mathematical formulation seems to lead to insoluble difficulties when it is extrapolated into the domain of distances of the order of ${10}^{\ensuremath{-}13}$ cm or less. It is therefore entirely possible that the interpretation suggested here may be needed for the resolution of these difficulties. In any case, the mere possibility of such an interpretation proves that it is not necessary for us to give up a precise, rational, and objective description of individual systems at a quantum level of accuracy.