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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

The heisenberg uncertainty relation and the resolving power in optics

Mario Di Jorio

Published Jun 1, 1982• 0 citations
Publisher
DOI
10.1007/bf02817071

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A reviewing of many published experimental and theoretical papers demonstrate that the resolving powers of microscopes, spectroscopes and telescopes can be enhanced by orders of magnitude better than old classical limits by various advanced techniques including de-convolution of the CW-response function of these instruments. Heisenberg's original analogy of limited resolution of a microscope, to support his mathematical uncertainty relation, is no longer justifiable today. Modern techniques of detecting single isolated atoms through fluorescence also over-ride this generalized uncertainty principle. Various nano-technology techniques are also making atoms observable and location precisely measurable. Even the traditional time-frequency uncertainty relation or bandwidth limit δvδt ≥ 1 can be circumvented while doing spectrometry with short pulses by deriving and de-convolving the pulse-response function of the spectrometer just as we do for CW input.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 8, 2011•0 citations
Abstract 1. In the general synthesis of classical dynamics with the quantum theory, the Uncertainty Principle plays a most useful part. It is of course only one aspect of the new mechanics, but it is a very helpful one since by its means it becomes easy to see where the old classical ideas broke down. The state of affairs in the quantum theory is not unlike that of the early days of relativity, when most of those who studied the subject felt the need of supporting the formal theory by seeing how the old ideas failed in specific cases. Here the formal theory is very abstract and is not easy to follow intuitively, and the Uncertainty Principle plays much the same rôle as did the examples of clocks and rods in relativity theory. For this reason it is more appropriate for illustrative examples, than for any extreme generality, and though a number of examples have been already given by Heisenberg and Bohr, it may not be amiss to have some more. There are probably some who will have shared my experience that it is often by no means easy to detect how the uncertainty enters into a given experiment, though once detected the arguments are usually very simple. In a recent conversation Professor Bohr criticised some rather careless remarks that I had made, and the present work was undertaken to clear matters up. It may be shortly described as a study of the Uncertainty Principle in connection with electrometers and magnetometers. It may be of interest to point out that the Uncertainty Principle can be regarded from a rather different aspect. The "resolving power" of optical instruments was discussed very fully by Rayleigh on wave principles, but as long as matter was regarded in the classical manner, a mechanical instrument could be considered as capable of measuring quantities with absolute accuracy. Now that we know that matter also has wave properties, there is need of a theory of the resolving power of mechanical instruments, and this is exactly what the Uncertainty Principle supplies.
In quantum mechanics, the Heisenberg uncertainty relations and the Cramér-Rao inequalities typically limit the precision in the estimation of a parameter through the standard deviation of a conjugate observable. Here we extend these relations by giving a bound to the precision of a parameter in terms of the expectation value of the conjugate observable. This has both foundational and practical consequences: in quantum optics it resolves a controversy over which is the ultimate precision in interferometry.
A reviewing of many published experimental and theoretical papers demonstrate that the resolving powers of microscopes, spectroscopes and telescopes can be enhanced by orders of magnitude better than old classical limits by various advanced techniques including de-convolution of the CW-response function of these instruments. Heisenberg's original analogy of limited resolution of a microscope, to support his mathematical uncertainty relation, is no longer justifiable today. Modern techniques of detecting single isolated atoms through fluorescence also over-ride this generalized uncertainty principle. Various nano-technology techniques are also making atoms observable and location precisely measurable. Even the traditional time-frequency uncertainty relation or bandwidth limit δvδt ≥ 1 can be circumvented while doing spectrometry with short pulses by deriving and de-convolving the pulse-response function of the spectrometer just as we do for CW input.