In 1927, Earle Hesse Kennard derived an inequality describing Heisenberg’s uncertainty principle. Since then, we have traditionally been using the standard deviation as the measure of uncertainty in quantum mechanics. But Jan Hilgevoord asserts that the standard deviation is neither a natural nor a generally adequate measure of quantum uncertainty. Specifically, he asserts that the standard deviations are inadequate to use as the quantum uncertainties in the single- and double-slit diffraction experiments. He even tells that from these examples it will become clear that the standard deviation is the wrong concept to express the uncertainty principle generally and that the Kennard relation has little to do with the uncertainty principle. We will investigate what are adequate as the measures of quantum uncertainty. And, beyond that, we will investigate the effects of multiplying the two uncertainties; namely, characteristics which is hiding in deep interior of the Kennard inequality. Through investigations we’ll come to naturally realize that his assertions were wrong. All of our discussions will help raise understanding of the Heisenberg uncertainty principle. Our discussions will afford us an opportunity to think about the essence of the Fourier transform. The aim of this paper is to draw conclusions about whether the Kennard inequality is justified or not.
| Published in | American Journal of Modern Physics (Volume 9, Issue 5) |
| DOI | 10.11648/j.ajmp.20200905.12 |
| Page(s) | 73-76 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2020. Published by Science Publishing Group |
Kennard Inequality, Quantum Uncertainty, Uncertainty Relation, Uncertainty Principle, Absolute Deviation, Standard Deviation
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| [2] | E. H. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Z. Physik, vol. 44, pp. 326–352, April 1927. |
| [3] | D. J. Griffiths and D. F. Schroeter, Introduction to Quantum Mechanics, 3rd ed., Cambridge University Press, 2020. |
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| [6] | M. A. de Gosson, The Principles of Newtonian and Quantum Mechanics, 2nd ed., World Scientific, 2017. |
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| [8] | J. Baggott, The Quantum Cookbook, Oxford University Press, 1st ed., 2020. |
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| [10] | S. J. Gustafson and I. M. Sigal, Mathematical Concepts of Quantum Mechanics, 3 ed., Springer, 2020. |
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| [12] | J. B. M. Uffink, J. Hilgevoord, “Uncertainty principle and uncertainty relations,” J. Found. Phys, vol. 15, pp. 925–944, September 1985. |
| [13] | J. Hilgevoord, “The standard deviation is not an adequate measure of quantum uncertainty,” Am. J. Phys, vol. 70, pp. 983, October 2002. |
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APA Style
Haengjin Choe. (2020). On the Justification and Validity of the Kennard Inequality. American Journal of Modern Physics, 9(5), 73-76. https://doi.org/10.11648/j.ajmp.20200905.12
ACS Style
Haengjin Choe. On the Justification and Validity of the Kennard Inequality. Am. J. Mod. Phys. 2020, 9(5), 73-76. doi: 10.11648/j.ajmp.20200905.12
AMA Style
Haengjin Choe. On the Justification and Validity of the Kennard Inequality. Am J Mod Phys. 2020;9(5):73-76. doi: 10.11648/j.ajmp.20200905.12
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Download@article{10.11648/j.ajmp.20200905.12,
author = {Haengjin Choe},
title = {On the Justification and Validity of the Kennard Inequality},
journal = {American Journal of Modern Physics},
volume = {9},
number = {5},
pages = {73-76},
doi = {10.11648/j.ajmp.20200905.12},
url = {https://doi.org/10.11648/j.ajmp.20200905.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20200905.12},
abstract = {In 1927, Earle Hesse Kennard derived an inequality describing Heisenberg’s uncertainty principle. Since then, we have traditionally been using the standard deviation as the measure of uncertainty in quantum mechanics. But Jan Hilgevoord asserts that the standard deviation is neither a natural nor a generally adequate measure of quantum uncertainty. Specifically, he asserts that the standard deviations are inadequate to use as the quantum uncertainties in the single- and double-slit diffraction experiments. He even tells that from these examples it will become clear that the standard deviation is the wrong concept to express the uncertainty principle generally and that the Kennard relation has little to do with the uncertainty principle. We will investigate what are adequate as the measures of quantum uncertainty. And, beyond that, we will investigate the effects of multiplying the two uncertainties; namely, characteristics which is hiding in deep interior of the Kennard inequality. Through investigations we’ll come to naturally realize that his assertions were wrong. All of our discussions will help raise understanding of the Heisenberg uncertainty principle. Our discussions will afford us an opportunity to think about the essence of the Fourier transform. The aim of this paper is to draw conclusions about whether the Kennard inequality is justified or not.},
year = {2020}
}
TY - JOUR T1 - On the Justification and Validity of the Kennard Inequality AU - Haengjin Choe Y1 - 2020/12/04 PY - 2020 N1 - https://doi.org/10.11648/j.ajmp.20200905.12 DO - 10.11648/j.ajmp.20200905.12 T2 - American Journal of Modern Physics JF - American Journal of Modern Physics JO - American Journal of Modern Physics SP - 73 EP - 76 PB - Science Publishing Group SN - 2326-8891 UR - https://doi.org/10.11648/j.ajmp.20200905.12 AB - In 1927, Earle Hesse Kennard derived an inequality describing Heisenberg’s uncertainty principle. Since then, we have traditionally been using the standard deviation as the measure of uncertainty in quantum mechanics. But Jan Hilgevoord asserts that the standard deviation is neither a natural nor a generally adequate measure of quantum uncertainty. Specifically, he asserts that the standard deviations are inadequate to use as the quantum uncertainties in the single- and double-slit diffraction experiments. He even tells that from these examples it will become clear that the standard deviation is the wrong concept to express the uncertainty principle generally and that the Kennard relation has little to do with the uncertainty principle. We will investigate what are adequate as the measures of quantum uncertainty. And, beyond that, we will investigate the effects of multiplying the two uncertainties; namely, characteristics which is hiding in deep interior of the Kennard inequality. Through investigations we’ll come to naturally realize that his assertions were wrong. All of our discussions will help raise understanding of the Heisenberg uncertainty principle. Our discussions will afford us an opportunity to think about the essence of the Fourier transform. The aim of this paper is to draw conclusions about whether the Kennard inequality is justified or not. VL - 9 IS - 5 ER -
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