The Nonergodic Interpretation of Quantum Mechanics
Recently, the work of the Brazilian physicist Vicent Buonomano has come to my attention through two different ways.
On the one hand, I have found a citation of a 1986 Buonomano's paper (appeared in the Nuovo Cimento journal) in the book "The Einstein, Podolski, and Rosen Paradox, in Atomic, Nuclear, and Particle Physics" by A. Afriat and F. Selleri (Plenum, New York, 1999). In their Chapter 5, devoted to the "Proposed solutions of the paradox", they mention the nonergodic interpretation (NEI) of quantum mechanics, according to which:
The second way by which I became aware of Buonomano's NEI has been a personal communication from Prof. A. Khrennikov. He saw a relationship between my proposal, where he had the impression that memory effects play a crucial role, and violation of ergodicity. In a recent paper devoted to this topic, he has deeply discussed the ergodicity of the quantum processes.
A stationary stochastic process is ergodic if the ensemble average coincides with the time average. In quantum mechanics, ergodicity is often trivially assumed. However, there have been (almost, see later) no experiments to test this assumption. In all quantum experiments what is calculated are the time averages. Experiments to truly calculate ensemble averages are in reality impossible. So experimenters have to generate successive copies of the system under study multiple times and try to destroy possible effects of the previous instances. Of course, to perform such experiments is a complicated problem.
The only experiment known that has been aimed at testing ergodicity was the 1989 Summhammer experiment. It was performed with a neutron interferometer, by generating neutrons one by one and randomly blocking one of the two interfering paths with a shutter, thus permitting a sudden switching from interfering to noninterfering conditions and viceversa. Statistics were built over the whole enseble of interfering neutrons, and over those which were recorded soon after the opening of the shutter. It was found that the latter ensemble shows the same amplitude of interference as in the former. This fact seemed to confirm Copenhagen interpretation and rule against NEI.
Even the proponent of the NEI, V. Buonomano, in a 1989 paper, acknowledged these findings and seemed to renounce to his own interpretation. Some years later, in 1999, he made a new but related proposal, named Co-operative phenomena type local-realistic theory, which however attracted even less attention than his 1989 paper.
According to Khrennikov, the NEI was abandoned too soon:
Coming to Summhammer's experiment, the proposed model is not incompatible with its results. According to our model, particles along the single non-interfering path (shutter closed) arrive at interfering sites (a beam splitter in the original experiment, as well as in most Mach-Zender interferometers) at expected times that are generally different from those at which they arrive when both paths are available (shutter open). This is because the two configurations 'shutter open' and 'shutter closed' are in reality two generally different settings with their own characteristics influencing the particls' dynamics. As a consequence, particles coming from the single path (shutter closed) do not 'find' bosons built by particles coming from the other path and so they do not feel interference effects. Conversely, when the shutter is opened, particles from the two paths find immediately the bosons already built during previous periods with the shutter open, and immediately experience interference effects.
Time coincidences play also a very important role in spin entanglement, as it will be shown in a future post.
On the one hand, I have found a citation of a 1986 Buonomano's paper (appeared in the Nuovo Cimento journal) in the book "The Einstein, Podolski, and Rosen Paradox, in Atomic, Nuclear, and Particle Physics" by A. Afriat and F. Selleri (Plenum, New York, 1999). In their Chapter 5, devoted to the "Proposed solutions of the paradox", they mention the nonergodic interpretation (NEI) of quantum mechanics, according to which:
a sequence of quantum objects, even if separated by large time intervals, do not behave independently in their interactions with the measuring apparatus. These objects may interact with one another by means of memory effects in a hypothetical medium, filling the space they cross on their way toward the measuring instruments. [...] Obviously, interference can happen only after a sufficiently large number of particles have crossed the apparatus and conditioned the medium. In this way particles interfere with other particles, but only indirectly through the medium.The reader of this blog will recognize that such mechanism is at the heart of the proposed local-realistic model for quantum mechanics, as expressed, e.g., in this post. However, some differences arise with respect to NEI, as it will be discussed later.
The second way by which I became aware of Buonomano's NEI has been a personal communication from Prof. A. Khrennikov. He saw a relationship between my proposal, where he had the impression that memory effects play a crucial role, and violation of ergodicity. In a recent paper devoted to this topic, he has deeply discussed the ergodicity of the quantum processes.
A stationary stochastic process is ergodic if the ensemble average coincides with the time average. In quantum mechanics, ergodicity is often trivially assumed. However, there have been (almost, see later) no experiments to test this assumption. In all quantum experiments what is calculated are the time averages. Experiments to truly calculate ensemble averages are in reality impossible. So experimenters have to generate successive copies of the system under study multiple times and try to destroy possible effects of the previous instances. Of course, to perform such experiments is a complicated problem.
The only experiment known that has been aimed at testing ergodicity was the 1989 Summhammer experiment. It was performed with a neutron interferometer, by generating neutrons one by one and randomly blocking one of the two interfering paths with a shutter, thus permitting a sudden switching from interfering to noninterfering conditions and viceversa. Statistics were built over the whole enseble of interfering neutrons, and over those which were recorded soon after the opening of the shutter. It was found that the latter ensemble shows the same amplitude of interference as in the former. This fact seemed to confirm Copenhagen interpretation and rule against NEI.
Even the proponent of the NEI, V. Buonomano, in a 1989 paper, acknowledged these findings and seemed to renounce to his own interpretation. Some years later, in 1999, he made a new but related proposal, named Co-operative phenomena type local-realistic theory, which however attracted even less attention than his 1989 paper.
According to Khrennikov, the NEI was abandoned too soon:
This [Summhammer's] experiment can be considered as rejecting this hypothesis and confirming ergodicity of quantum statistical data. However, it definitely cannot be considered as a decisive experiment rejecting completely the hypothesis on nonergodicity of quantum mechanics. New experiments are badly needed.In fact,
Summhammer destroyed possible memory effects only in one component of the neutron interference experiment. However, sequential dependence leading to difference between the time and ensemble averages can be generated by other components of the experimental arrangement, even by the source of neutrons.In addition, we must emphasize that the local-realistic model supported by this blog uses a similar idea than the NEI's one, that is, interactions between successive particles of the same ensemble are mediated by the lattice, which stores in its nodes "bosons" keeping memory of particles that had visited these nodes. There main of course differences with respect to NEI, the main one being that the lattice is intended to be a spatio-temporal entity, not just a spatial medium. In order to capture bosons and feel the effects of interference, a particle must visit a spatial node at the same time than particles having a different span (e.g., emitted from a different source or having a different phase) did.
Coming to Summhammer's experiment, the proposed model is not incompatible with its results. According to our model, particles along the single non-interfering path (shutter closed) arrive at interfering sites (a beam splitter in the original experiment, as well as in most Mach-Zender interferometers) at expected times that are generally different from those at which they arrive when both paths are available (shutter open). This is because the two configurations 'shutter open' and 'shutter closed' are in reality two generally different settings with their own characteristics influencing the particls' dynamics. As a consequence, particles coming from the single path (shutter closed) do not 'find' bosons built by particles coming from the other path and so they do not feel interference effects. Conversely, when the shutter is opened, particles from the two paths find immediately the bosons already built during previous periods with the shutter open, and immediately experience interference effects.
Time coincidences play also a very important role in spin entanglement, as it will be shown in a future post.
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