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Physics Today

Coherence and precision in classical systems

R. J. Sewell, Morgan W. Mitchell

Published Jun 1, 2012• 0 citations
Publisher

Abstract

Sewell and Mitchell reply: Spencer Klein’s insightful comments wonderfully illustrate the connections between seemingly disparate areas of research. His May 2008 article with Francis Halzen is indeed well worth going back for if you missed it the first time around.© 2012 American Institute of Physics.
DOI
10.1063/pt.3.1585

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The Quick Study “Collaboration and precision in quantum measurement” (PHYSICS TODAY, December 2011, page 72) by Rob Sewell and Morgan Mitchell points out that some quantum mechanical coherence, “quantum collaboration” in their language, allows for the magnetization of a gas to be measured with a precision of 1/N, where N is the number of photons. For large N, 1/N is smaller than 1/√N, so improves upon the usual 1/√N measurement limit; the authors comment that for noninteracting particles, the central limit theorem precludes better classical measurements.However, coherence is not merely a quantum mechanical effect; many classical systems exhibit similar behavior. For example, one can search for ultrahigh-energy neutrino interactions in Antarctic ice by observing the coherent radio pulses emitted by the resulting particle showers. The observed electric field strength of the pulse scales as the square of the number of particles in the shower (reference 11. P. W. Gorham et al., Phys. Rev. D 72, 023002 (2005). https://doi.org/10.1103/PhysRevD.72.023002; see also the article I wrote with Francis Halzen, PHYSICS TODAY, May 2008, page 29), so for a given uncertainty in field-strength measurement, the uncertainty in the number of shower particles scales as 1/N. That is purely classical electromagnetism.There are also examples of 1/N scaling without coherence. Consider a system consisting of a noninteracting gas in a reservoir at pressure P, and a small valve that controls access to a gas sensor. The best measurement of the valve’s opening time comes from the first gas molecule observed by the sensor. As one increases the pressure (number of probe molecules N), the time delay between the gate opening and the sensor decreases in a 1/N fashion. For large N, that is more accurate than finding the mean arrival time of the molecules, with an accuracy of 1/√N, and trying to correct for the average delay time.These comments are not to take anything away from the nice study by Sewell and Mitchell. However, measurements that exhibit 1/N scaling are not limited to quantum systems, and are more common than one might imagine.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. W. Gorham et al., Phys. Rev. D 72, 023002 (2005). https://doi.org/10.1103/PhysRevD.72.023002, Google ScholarCrossref© 2012 American Institute of Physics.

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The Quick Study “Collaboration and precision in quantum measurement” (PHYSICS TODAY, December 2011, page 72) by Rob Sewell and Morgan Mitchell points out that some quantum mechanical coherence, “quantum collaboration” in their language, allows for the magnetization of a gas to be measured with a precision of 1/N, where N is the number of photons. For large N, 1/N is smaller than 1/√N, so improves upon the usual 1/√N measurement limit; the authors comment that for noninteracting particles, the central limit theorem precludes better classical measurements.However, coherence is not merely a quantum mechanical effect; many classical systems exhibit similar behavior. For example, one can search for ultrahigh-energy neutrino interactions in Antarctic ice by observing the coherent radio pulses emitted by the resulting particle showers. The observed electric field strength of the pulse scales as the square of the number of particles in the shower (reference 11. P. W. Gorham et al., Phys. Rev. D 72, 023002 (2005). https://doi.org/10.1103/PhysRevD.72.023002; see also the article I wrote with Francis Halzen, PHYSICS TODAY, May 2008, page 29), so for a given uncertainty in field-strength measurement, the uncertainty in the number of shower particles scales as 1/N. That is purely classical electromagnetism.There are also examples of 1/N scaling without coherence. Consider a system consisting of a noninteracting gas in a reservoir at pressure P, and a small valve that controls access to a gas sensor. The best measurement of the valve’s opening time comes from the first gas molecule observed by the sensor. As one increases the pressure (number of probe molecules N), the time delay between the gate opening and the sensor decreases in a 1/N fashion. For large N, that is more accurate than finding the mean arrival time of the molecules, with an accuracy of 1/√N, and trying to correct for the average delay time.These comments are not to take anything away from the nice study by Sewell and Mitchell. However, measurements that exhibit 1/N scaling are not limited to quantum systems, and are more common than one might imagine.REFERENCESSection:ChooseTop of pageREFERENCES <<1. P. W. Gorham et al., Phys. Rev. D 72, 023002 (2005). https://doi.org/10.1103/PhysRevD.72.023002, Google ScholarCrossref© 2012 American Institute of Physics.
This work is the result of the research which I started independently late in the 60s in Russia and since August 1992 have proceeded with abroad. The subject of the research was initially chosen to be Systems Theory, because it seemed rather close to the theory of communications, the then field of my occupation, on the one hand, and because it sounded intriguing enough and worth attempting at, on the other. But there was no idea of how and where to start the research, and it was decided to begin with the simplest type of system – a linear system. The first step proved rather successful: there was found quite an elegant solution of the problem, imagined by myself, of determining the functional complexity of linear systems by their characteristics. That work was published in the 1969, No.2, issue of the Transactions of the Research Institute of Radio (Moscow) where I worked then. Although it was unclear how to proceed with that result, there was a vague indication in it to some connection between the abstract theory of linear systems and statistical physics, which seemed promising. To make that puzzle out, I set off to supplement my knowledge of theoretical physics, and soon the above indication became more articulate: there is indeed some deep connection between the problem of the synthesis of linear systems and quantum mechanics. Intrigued by that clue, I attempted for several years to apply the solutions of Schroedinger’s-like equations, with the potential determined by characteristics of the system, to its synthesis. However, the results were unsatisfactory: something essential was missing in comprehending both the objects of theoretical physic and linear systems. The solution came suddenly from where nobody could have expected it - from philosophy. Looking once through Hegel’s works, I was struck by a strangely close analogy between the conceptions of duality in dialectical logic and particle physics. That revelation triggered another stage of self-education, this time in dialectical philosophy. As a result, there arose conviction that Hegel's dialectical logic is actually the general theory of systems sought for, but the philosopher’s peculiar way of thinking and the extremely abstract language of that his work made its interpretation in scientific terms almost impossible, with the exception of some most simple cases. So I had no choice but to endeavor my own interpretation of the dialectical logic, on the one hand, and, simultaneously, a revision of some theories and principles of theoretical physics in accordance with that logic, on the other hand, which eventually resulted in the theory expounded in this book. The first rough results, such as the existence of ether, its composition and the phenomenon of spontaneous generation of neutrons in it, were achieved early in the 80s, but it took me about fifteen years more to complete this research in a sufficiently adequate and convincing form.
Douglas Scalapino was professor of physics at University of California, Santa Barbara and co-founder of the Institute for Theoretical Physics (now the Kavli Institute for Theoretical Physics). He seems to have written to Wheeler for comments on the Institute's direction. Wheeler approves of whatever he sent, but also recommends that the Institute promote research on the measurement problem. It is notable that he also suggests that Everett might be a good person for the Institute to hire, and even indicates that Everett might be willing to go, at least temporarily.