Topic
Stochastic interpretation
About: Stochastic interpretation is a research topic. Over the lifetime, 1173 publications have been published within this topic receiving 37682 citations.
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Papers
TL;DR: In this paper, 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.
Abstract: 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 modined 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 1umann's assumptions. In two appendixes, we treat the problem oi 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.
6,118 citations
3,436 citations
TL;DR: In this article, the authors present a reformulation of quantum theory in a form believed suitable for application to general relativity, from which the conventional interpretation of quantum mechanics can be deduced.
Abstract: The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.
3,415 citations
TL;DR: The Mathematical Foundations of Quantum Mechanics as mentioned in this paper were the first to provide a rigorous mathematical formulation of quantum theory and a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed.
Abstract: Classical mechanics was first envisaged by Newton, formed into a powerful tool by Euler, and brought to perfection by Lagrange and Laplace. It has served as the paradigm of science ever since. Even the great revolutions of 19th century phys icsnamely, the FaradayMaxwell electro-magnetic theory and the kinetic t h e o r y w e r e viewed as further support for the complete adequacy of the mechanistic world view. The physicist at the end of the 19th century had a coherent conceptual scheme which, in principle at least, answered all his questions about the world. The only work left to be done was the computing of the next decimal. This consensus began to unravel at the beginning of the 20th century. The work of Planck, Einstein, and Bohr simply could not be made to fit. The series of ad hoc moves by Bohr, Eherenfest, et al., now called the old quantum theory, was viewed by all as, at best, a stopgap. In the period 1925-27 a new synthesis was formed by Heisenberg, Schr6dinger, Dirac and others. This new synthesis was so successful that even today, fifty years later, physicists still teach quantum mechanics as it was formulated by these men. Nevertheless, two foundational tasks remained: that of providing a rigorous mathematical formulation of the theory, and that of providing a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed. These tasks are, of course, related, and a possible fringe benefit of the second task might be the pointing of the way 'beyond quantum theory'. These tasks were taken up by von Neumann as a consequence of a seminar on the foundations of quantum mechanics conducted by Hilbert in the fall of 1926. In papers published in 1927 and in his book, The Mathemat ical Foundations of Quantum Mechanics, von Neumann provided the first completely rigorous
1,859 citations
TL;DR: In this paper, the authors examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient of 2m and no friction and conclude that Newton's law is equivalent to the Schrodinger equation.
Abstract: We examine the hypothesis that every particle of mass $m$ is subject to a Brownian motion with diffusion coefficient $\frac{\ensuremath{\hbar}}{2m}$ and no friction. The influence of an external field is expressed by means of Newton's law $\mathbf{F}=m\mathbf{a}$, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schr\"odinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.
1,806 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 7 |
| 2023 | 12 |
| 2022 | 24 |
| 2021 | 7 |
| 2020 | 9 |