International Journal of Applied Mathematics and Theoretical Physics

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Timing in Simultaneity, Einstein’s Test Scenario, and Precise Clock Synchronization

Received: 21 August 2016    Accepted: 25 August 2016    Published: 26 September 2016
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Abstract

Although seemingly different, these topics are all related to timing events. Einstein gave examples of simultaneous events as witnessed by one inertial observer may not be simultaneous for other inertial observers. This paper eliminates a common misconception. Simultaneous events are confused with separated events occurring at the same coordinate time. Simultaneous events are witnessed by all observers, whether inertial or accelerated, because simultaneous events occur when phenomena collide, merge, overlap, or superimpose into one point at the same instant of time. Chronometric events occur at the same coordinate time of a reference frame, but at separate locations. Simultaneous events are perceived as simultaneous by all observers, because a point defines an observer’s location at some instantaneous time. Chronometric events occur at identical coordinate times, but are usually not simultaneous, because the distances to convey the information to an observer are usually unequal arrival times. Einstein’s train scenario involving dual lightning strikes is explained by Newtonian physics without relativity. The mathematics concerning an embellished version of Einstein’s train scenario is derived in this paper. Synchronizing coordinate clocks to less than 1 ns is difficult. Unless the observer precisely compensates for the whole velocity between the transmitted time from some point and the observer’s local frame, synchronizing coordinate clocks far apart is surprisingly impossible by electronic transmission through free space. An experiment is suggested to obtain the effective velocity using one-way measurements for the speed of light to improve clock synchronization by several orders.

DOI 10.11648/j.ijamtp.20160204.12
Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 2, Issue 4, October 2016)
Page(s) 31-40
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

Simultaneity, Synchronization, Timing, Speed of Light

References
[1] Lorrain, P. & Corson, D. A., Electromagnetic Fields and Waves, W. H. Freeman and Company, 2nd ed., (1970) p. 461.
[2] Einstein, A., “On the Electrodynamics of Moving Bodies” Ann. Phys., 17 (1905) p. 549-560, (translated from 1923 edition of W. Perrett and G. B. Jeffery in The Principle of Relativity, Metheuen, London.).
[3] Einstein, A., “Relativity: the Special and the General Theory” (1916) Three Rivers Press, Random House Inc., 15th ed., pub. 1961.
[4] Rindler, W., Special Relativity, University Mathematical Texts, Interscience Publishers Inc., John Wiley & Sons, (1966) reprinted 1969.
[5] Pound, R. V.; Rebka Jr. G. A., "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters, (November 1, 1959) 3 (9): 439–441.
[6] Chandler, S. C., “On the Variation of Latitude”, Astron. J., (1891) 248, 59-61.
[7] Seidelmann, P. K. [ed.], Explanatory Supplement to the Astronomical Almanac, U. S. Naval Observatory, University Science Books, (1992).
[8] Vanier, J., and Audoin, C., “The classical caesium beam frequency standard: fifty years later”, Metrologia, 42 (3), June 2005, S31-S42.
[9] Vessot, R. F. C., “The atomic hydrogen maser oscillator”, Metrologia, 42 (3), June 2005, S80-S89.
[10] Wynands, R. and Weyers, S., “Atomic fountain clocks”, Metrologia, 42 (3), June 2005, S64-S79.
[11] Piester, D., Bauch, A., Breakiron, L., Matsakis, D., Blanzano, B., Koudelka, O., “Time transfer with nanosecond accuracy for the realization of International Atomic Time” Metrologia (2008) 45 (2), 185-198.
[12] Bauch, A., Piester, D., Fujieda, M., Lewandowski, W., “Directive for operational use and data handling in two-way satellite time and frequency transfer (TWSTFT)”, Rapport BIPM-2011/01, Pavillon de Breteuil, F-92312 SEVRES Cedex, (2011) 1-25.
[13] ITU Radiocommunication Sector 2003 “The operational use of two-way satellite time and frequency transfer employing PN codes”, Recommendation ITU-R TF.1153-2 (Geneva, Switzerland).
[14] TF.1153-2 “The operational use of two-way satellite time and frequency transfer employing PN codes”, Recommendation ITU-R, ITU Radiocommunication Assembly (1995, 1997, 2003).
[15] Britting, K. R., Inertial Navigation Systems Analysis, Wiley-Interscience (1971).
[16] Deines, S. “Noninertial Freely Falling Frames Affected by Gravity”, IJAMTP, 2, (2016).
[17] Branets , V. N., Landau, B. E., Korkishko, Y. N., Lynch, D., Raspopov, V. Y., “Gyroscopic Devices and Sensors”, Chapter 6, in Aerospace Sensors, Nebylov A. V. (ed.), Momentum Press, LLC, New York (2013).
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  • APA Style

    Steven D. Deines. (2016). Timing in Simultaneity, Einstein’s Test Scenario, and Precise Clock Synchronization. International Journal of Applied Mathematics and Theoretical Physics, 2(4), 31-40. https://doi.org/10.11648/j.ijamtp.20160204.12

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    ACS Style

    Steven D. Deines. Timing in Simultaneity, Einstein’s Test Scenario, and Precise Clock Synchronization. Int. J. Appl. Math. Theor. Phys. 2016, 2(4), 31-40. doi: 10.11648/j.ijamtp.20160204.12

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    AMA Style

    Steven D. Deines. Timing in Simultaneity, Einstein’s Test Scenario, and Precise Clock Synchronization. Int J Appl Math Theor Phys. 2016;2(4):31-40. doi: 10.11648/j.ijamtp.20160204.12

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  • @article{10.11648/j.ijamtp.20160204.12,
      author = {Steven D. Deines},
      title = {Timing in Simultaneity, Einstein’s Test Scenario, and Precise Clock Synchronization},
      journal = {International Journal of Applied Mathematics and Theoretical Physics},
      volume = {2},
      number = {4},
      pages = {31-40},
      doi = {10.11648/j.ijamtp.20160204.12},
      url = {https://doi.org/10.11648/j.ijamtp.20160204.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijamtp.20160204.12},
      abstract = {Although seemingly different, these topics are all related to timing events. Einstein gave examples of simultaneous events as witnessed by one inertial observer may not be simultaneous for other inertial observers. This paper eliminates a common misconception. Simultaneous events are confused with separated events occurring at the same coordinate time. Simultaneous events are witnessed by all observers, whether inertial or accelerated, because simultaneous events occur when phenomena collide, merge, overlap, or superimpose into one point at the same instant of time. Chronometric events occur at the same coordinate time of a reference frame, but at separate locations. Simultaneous events are perceived as simultaneous by all observers, because a point defines an observer’s location at some instantaneous time. Chronometric events occur at identical coordinate times, but are usually not simultaneous, because the distances to convey the information to an observer are usually unequal arrival times. Einstein’s train scenario involving dual lightning strikes is explained by Newtonian physics without relativity. The mathematics concerning an embellished version of Einstein’s train scenario is derived in this paper. Synchronizing coordinate clocks to less than 1 ns is difficult. Unless the observer precisely compensates for the whole velocity between the transmitted time from some point and the observer’s local frame, synchronizing coordinate clocks far apart is surprisingly impossible by electronic transmission through free space. An experiment is suggested to obtain the effective velocity using one-way measurements for the speed of light to improve clock synchronization by several orders.},
     year = {2016}
    }
    

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