American Journal of Physics and Applications

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The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference

Received: Dec. 15, 2018    Accepted: Jan. 11, 2019    Published: Feb. 22, 2019
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Abstract

We report an observer effect in an Einstein solid, a quantum-mechanical system, induced by fluctuations of an observer’s frame of reference; which has been studied so far under the assumption that the observer’s frame of reference remains constant throughout the performance of a measurement, thus, what is actually measured throughout the performance of a measurement is an unresolved problem during which the observer’s frame of reference is assumed to fluctuate. We investigate the average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference. The Einstein solid consists of N identical non-interacting simple harmonic oscillators per mole, where N is the Avogadro’s number at temperature T. The average energy and molar specific heat at constant volume of the Einstein solid are formulated for two types of fluctuations of the observer’s frame of reference in order to consider pedagogical and experimental demonstrations. The average energy of the Einstein solid is formulated from the definition of canonical ensemble average and the molar specific heat at constant volume of it is calculated by differentiating the average energy with T. The molar specific heat at constant volume of the Einstein solid exhibits novel features at low temperatures according to the distribution of fluctuations of the observer’s frame of reference: 0 and 3R at T = 0 K for square-wave and sawtooth-wave fluctuations, respectively, where R is the gas constant.

DOI 10.11648/j.ajpa.20190701.14
Published in American Journal of Physics and Applications ( Volume 7, Issue 1, January 2019 )
Page(s) 21-26
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), 2024. Published by Science Publishing Group

Keywords

Einstein Solids, Specific Heat, Harmonic Oscillators, Fluctuations, Observer Effect, Thermodynamic Law

References
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[4] W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Z. Physik, vol. 43, pp. 172-198, 1927.
[5] E. H. Kennard, “Zur Quantenmechanik einfacher Bewegungstypen,” Z. Physik, vol. 44, pp. 326-352, 1927.
[6] H. P. Robertson, “The uncertainty principle,” Phys. Rev., vol. 34, pp. 163-164, 1929.
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[8] K. Okamura, M. Ozawa, “Universally valid uncertainty relations in general quantum systems,” arXiv: 1808. 10615v2, pp. 1-16, 2018.
[9] R. Penrose, The road to reality: a complete guide to the laws of the universe, Jonathan Cape, 2004, pp. 516-517.
[10] S. Weinberg, The Oxford History of the Twentieth Century, Oxford University Press, 1998, pp. 22-34.
[11] S. Weinberg, “Einstein’s Mistakes,” Physics Today, pp. 31-35, 2005.
[12] W. H. Zurek, “Decoherence, einselection, and the quantum origins of the classical,” Rev. Mod. Phys., vol. 75, pp. 715-775, 2003.
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[14] H. D. Zeh, E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd ed., Springer-Verlag, 2003, pp. 16-26.
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[18] M. Schlosshauer, “Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics,” Ann. Phys., vol. 321, pp. 112-149, 2006.
[19] M. Schlosshauer, “Measuring the quantum state of a single system with minimum state disturbance,” Phys. Rev. A, vol. 93, pp. 012115, 2016.
[20] E. Schrödinger, “Der stetige Übergang von der Mikro- zur Makromechanik,” Die Naturwissenschaften, vol. 14, pp. 664-666, 1926.
[21] A. T. Petit and P. L. Dulong, “Recherches sur quelques points importants de la Théorie de la Chaleur,” Annales de Chimie et de Physique, vol. 10, pp. 395-413, 1819.
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    Yun-Sok Shin. (2019). The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference. American Journal of Physics and Applications, 7(1), 21-26. https://doi.org/10.11648/j.ajpa.20190701.14

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    ACS Style

    Yun-Sok Shin. The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference. Am. J. Phys. Appl. 2019, 7(1), 21-26. doi: 10.11648/j.ajpa.20190701.14

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    AMA Style

    Yun-Sok Shin. The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference. Am J Phys Appl. 2019;7(1):21-26. doi: 10.11648/j.ajpa.20190701.14

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  • @article{10.11648/j.ajpa.20190701.14,
      author = {Yun-Sok Shin},
      title = {The Average Energy and Molar Specific Heat at Constant Volume of an Einstein Solid Measured by an Observer with Fluctuating Frame of Reference},
      journal = {American Journal of Physics and Applications},
      volume = {7},
      number = {1},
      pages = {21-26},
      doi = {10.11648/j.ajpa.20190701.14},
      url = {https://doi.org/10.11648/j.ajpa.20190701.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajpa.20190701.14},
      abstract = {We report an observer effect in an Einstein solid, a quantum-mechanical system, induced by fluctuations of an observer’s frame of reference; which has been studied so far under the assumption that the observer’s frame of reference remains constant throughout the performance of a measurement, thus, what is actually measured throughout the performance of a measurement is an unresolved problem during which the observer’s frame of reference is assumed to fluctuate. We investigate the average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference. The Einstein solid consists of N identical non-interacting simple harmonic oscillators per mole, where N is the Avogadro’s number at temperature T. The average energy and molar specific heat at constant volume of the Einstein solid are formulated for two types of fluctuations of the observer’s frame of reference in order to consider pedagogical and experimental demonstrations. The average energy of the Einstein solid is formulated from the definition of canonical ensemble average and the molar specific heat at constant volume of it is calculated by differentiating the average energy with T. The molar specific heat at constant volume of the Einstein solid exhibits novel features at low temperatures according to the distribution of fluctuations of the observer’s frame of reference: 0 and 3R at T = 0 K for square-wave and sawtooth-wave fluctuations, respectively, where R is the gas constant.},
     year = {2019}
    }
    

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    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
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    AB  - We report an observer effect in an Einstein solid, a quantum-mechanical system, induced by fluctuations of an observer’s frame of reference; which has been studied so far under the assumption that the observer’s frame of reference remains constant throughout the performance of a measurement, thus, what is actually measured throughout the performance of a measurement is an unresolved problem during which the observer’s frame of reference is assumed to fluctuate. We investigate the average energy and molar specific heat at constant volume of an Einstein solid measured by an observer with fluctuating frame of reference. The Einstein solid consists of N identical non-interacting simple harmonic oscillators per mole, where N is the Avogadro’s number at temperature T. The average energy and molar specific heat at constant volume of the Einstein solid are formulated for two types of fluctuations of the observer’s frame of reference in order to consider pedagogical and experimental demonstrations. The average energy of the Einstein solid is formulated from the definition of canonical ensemble average and the molar specific heat at constant volume of it is calculated by differentiating the average energy with T. The molar specific heat at constant volume of the Einstein solid exhibits novel features at low temperatures according to the distribution of fluctuations of the observer’s frame of reference: 0 and 3R at T = 0 K for square-wave and sawtooth-wave fluctuations, respectively, where R is the gas constant.
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Author Information
  • Sejong Academy of Science and Arts, Sejong, Republic of Korea

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