Information Content of the Model for Calculating the Finite Precision of Measurements

Main Article Content

Boris Menin

Abstract

Aims: We argue that the choice of a specific qualitative–quantitative set of variables in a model by a conscious observer fundamentally limits the achievable accuracy of the measurement process.

Place and Duration of Study: Mechanical & Refrigeration Consultation Expert, between January 2020 and July 2020.

Methodology: Using the concept of “finite information quantities” introduced by Gisin, we try to present it as a practical tool in science and engineering in calculating the proximity indicator of a model to the phenomenon being studied.

Results: The formulated metric (comparative uncertainty) allows us to set the optimal achievable uncertainty of the model and to confirm the impossibility of implementing the principle of infinite precision.

Conclusion: Any attempt to search for a universal physical theory must consider the uncertainty caused by the observer’s vision and the working of the human brain.

Keywords:
Information entropy, measurement uncertainty, measurement units, mathematical model, observability, precision engineering, modeling, random variables

Article Details

How to Cite
Menin, B. (2020). Information Content of the Model for Calculating the Finite Precision of Measurements. Physical Science International Journal, 24(7), 33-46. https://doi.org/10.9734/psij/2020/v24i730201
Section
Original Research Article

References

Popper KR. Objective knowledge: An evolutionary approach. Oxford University Press, New York; 1979.

Lloyd S. Ultimate physical limits to computation. Nature. 2000;406:1047–1054.

Blum M, Vempala S. The complexity of human computation via a concrete model with an application to passwords. Proceedings of the National Academy of Sciences of the United States of America. 2020;1–8.
Available:https://scihub.tw/10.1073/pnas.1801839117
Accessed 5 August 2020.

Huang H. Comparison of three approaches for computing measurement uncertainties. Measurement. 2020;1-35.
Available:https://scihub.tw/10.1016/j.measurement.2020.107923
Accessed 5 August 2020.

Pavese F. Mathematical and statistical tools in metrological measurements. 2013: 1-69. Available:https://www.researchgate.net/publication/259366249
Accessed 5 August 2020.

Porod W, Grondin RO, Ferry DK, Porod G. Dissipation in computation – Reply. Phys. Rev. Lett. 1984;52:1206–1206.

Norton JD. All shook up: Fluctuations, Maxwell’s demon and the thermodynamics of Computation. Entropy. 2013;15:4432–4483.

Kish LB, Ferry DK. Information entropy and thermal entropy: Apples and oranges. Journal of Computational Electronics. 2017;17(1):43–50.
Available:https://scihub.tw/10.1007/s10825-017-1044-1
Accessed 5 August 2020.

Brillouin L. Science and information theory. Dover, New York; 2004.

Hobson A. Concepts in Statistical Mechanics. New York: Gordon and Breach; 1971.

Bekenstein JD. Universal upper bound on the entropy-to-energy ratio for bounded systems. Phys. Rev. D. 1981;23: 287–298.

Landauer R. The physical nature of information. Phys. Lett. A. 1996;217:188–193.

Srivastava YN, Vitiello G, Windom A. Quantum measurements, information and entropy production. International Journal of Modern Physics B. 1999;13(28):3369–3382.
Available:https://scihub.tw/10.1142/S0217979299003076
Accessed 5 August 2020.

t Hooft G. Obstacles on the way towards the quantisation of space, time and matter and possible resolutions. Stud. Hist. Phil. Mod. Phys. 2001;32(2):157–180.

Ben-Naim A. A farewell to entropy: Statistical thermodynamics based on information.Singapore: World Scientific; 2008.

Zeng B, Chen X, Zhou DL, Wen XG. Quantum Information Meets Quantum Matter.Springer; 2018.
Available:https://arxiv.org/pdf/1508.02595.pdf
Accessed 5 August 2020.

Vopson MM. The mass-energy-information equivalence principle. AIP Advances. 2019;9:1–4.
Available:https://aip.scitation.org/doi/pdf/10.1063/1.5123794.
Accessed 5 August 2020.

Burgin M. Information theory: A multifaceted model of information. Entropy. 2003;5(2):146–160.
Available:https://scihub.tw/10.3390/e5020146
Accessed 5 August 2020.

The BIG Bell Test Collaboration. Challenging local realism with human choices. Nature. 2018;557:212–216.

Abramowitz M, Stegun IA., Handbook of mathematical functions. National Bureau of Standards Applied Mathematics Series – 55, Washington; 1964.

Available:http://people.math.sfu.ca/~cbm/aands/frameindex.htm
Accessed 5 August 2020.

Burgin M. Theory of information: Fundamentality, diversity and unification. University of California, Los Angeles, USA; 2003.

Del Santo Gisin FN. Physics without determinism: Alternative interpretations of classical Physics. Phys. Rev. A. 2019;100:1–9.
Available:https://scihub.tw/10.1103/PhysRevA.100.062107
Accessed 5 August 2020.

Shannon C. Communication in the presence of noise. Proc. IRE. 1949;37:10–21.

Baranger M. Chaos, complexity and entropy. 2001;1–17.
Available:http://necsi.edu/projects/baranger/cce.pdf
Accessed 5 August 2020.

Kotelnikov VA. On the transmission capacity of ‘ether’ and wire in electro-communications, First All-Union Conf. Questions of Communications. 1933;1–23. Available:https://goo.gl/wKvBBs
Accessed 5 August 2020.

Bell S. A Beginner’s guide to uncertainty of measurement. National Physical Laboratory, Teddington, Middlesex, United Kingdom. 1999;1–41.

Available:https://www.dit.ie/media/physics/documents/GPG11.pdf
Accessed 5 August 2020.

Bose D, Wright MJ, Palmer GE. Uncertainty analysis of laminar aeroheating predictions for Mars entries. Journal of Thermophysics and Heat Transfer. 2006;20(4):652–662.
Available:https://scihub.tw/10.2514/1.20993
Accessed 5 August 2020.

Golay MW, Seong PN, Manno VP. A measure of the difficulty of system diagnosis and its relationship to complexity. International Journal of General Systems. 1989;16(1):1–23.
Available:https://scihub.tw/10.1080/03081078908935060
Accessed 5 August 2020.

Piccinini G. Epistemic divergence and the publicity of scientific methods.Stud. Hist. Phil. Sci. 2003;34:597–612.

Available:http://www.umsl.edu/~piccininig/Epistemic_Divergence_and_Publicity_of_Scientific_Methods.pdf
Accessed 5 August 2020.

Uzan JP. The role of the (Planck) constants in physics; 2018.

Available:https://www.bipm.org/utils/common/pdf/CGPM-2018/Presentation-CGPM26-Uzan.pdf
Accessed 5 August 2020.

British-American System of Units; 2020.
Available:https://physics.info/system-english/.

Cgs system; 2020.
Available:https://www.maplesoft.com/support/help/AddOns/view.aspx?path=Units%2FCGS
Accessed 5 August 2020.

Mohr PJ. et al. Data and analysis for the CODATA 2017 special fundamental constants Adjustment. Metrologia. 2018; 55:125–146.
Available:https://iopscience.iop.org/article/10.1088/1681-7575/aa99bc/pdf
Accessed 5 August 2020.

Sonin AA. The physical basis of dimensional analysis, 2nd ed. Department of Mechanical Engineering, MIT, Cambridge; 2001.
Available:http://web.mit.edu/2.25/www/pdf/DA_unified.pdf
Accessed 5 August 2020.

NIST Special Publication 330 (SP330), The International System of Units (SI); 2008.
Available: https://www.nist.gov/pml/special-publication-330
Accessed 5 August 2020.

The International System of Units (SI) BIPM. 2019;1–218.
Available:https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
Accessed 5 August 2020.

Jakulin A. symmetry and information theory. 2004;1–20.
Available: https://goo.gl/QGBVoU
Accessed 5 August 2020.

Yarin L. The Pi-Theorem. Springer-Verlag, Berlin; 2012.
Available:https://goo.gl/dtNq3D
Accessed 5 August 2020.

Adamatzky A, et al. East-west paths to unconventional computing. Progress in Biophysics and Molecular Biology. 2017;8:1–84.

Available:https://scihub.tw/10.1016/j.pbiomolbio.2017.08.004
Accessed 5 August 2020.

Laszlo, A. Systematization of dimensionless quantities by group theory. International Journal of Heat and Mass Transfer. 1964;7(4):423–430.

Sedov LI. Similarity and Dimensional Methods in Mechanics, 10th ed., CRC Press; 1993.

Landsberg PT. Entropy and order. In: Kilmister CW. (Ed.) Imbalance and self-organization. mathematics and its applications. Springer, Dordrecht. 1986;30: 19–21.

Schroeder MJ. An alternative to entropy in the measurement of information. Entropy. 2004;6:388–412.
Available: https://goo.gl/vg8fk5
Accessed 5 August 2020.

Menin B. Hubble constant tension in terms of information approach. Physical Science International Journal. 2019;23(4): 1–15.
Available:https://doi.org/10.9734/psij/2019/v23i430165
Accessed 5 August 2020.

Taylor J. An Introduction to Error Analysis. University Science Books, Mill Valley, California. 1982.

Milton MJT, Possolo A. Trustworthy data underpin reproducible research. Nature Physics. 2020:16(2):117–119,
Available:https://scihub.tw/10.1038/s41567-019-0780-5
Accessed 5 August 2020.

Chapman CA, et al. Games academics play and their consequences: How authorship. h-index and journal impact factors are shaping the future of academia. Proceedings of the Royal Society B: Biological Sciences. 2019;286:1–9.
Available:https://scihub.tw/10.1098/rspb.2019.2047
Accessed 5 August 2020.

Buchanan M. The certainty of uncertainty. Nature Physics. 2020;16(2):120–120.
Available:https://scihub.tw/10.1038/s41567-020-0786-z
Accessed 5 August 2020.

Baker M. Is there a reproducibility crisis? Nature. 2017;533:452–454.
Available:https://www.nature.com/news/polopoly_fs/1.19970!/menu/main/topColumns/topLeftColumn/pdf/533452a.pdf
Accessed 5 August 2020.

Freedman LP, Cockburn IM, Simcoe TS. The economics of reproducibility in preclinical Research. PLoS Biol. 2015; 13(6):1002165.
Available:https://doi.org/10.1371/journal.pbio.1002165
Accessed 5 August 2020.

Ellis G, Silk J. Scientific method: Defend the integrity of physics. Nature. 2014; 516(7531).
Available:https://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535
Accessed 5 August 2020.

Menin B. Uncertainty assessment of refrigeration equipment using an information Approach. Journal of Applied Mathematics and Physics. 2020;8(1):23–37.
Available:https://www.scirp.org/journal/Paperabs.aspx?PaperID=97483
Accessed 5 August 2020.

Gavioso RM. A determination of the molar gas constant R by acoustic thermometryin helium. Metrologia. 2015;52:274–304.
Available:http://sci-hub.tw/10.1088/0026-1394/52/5/S274
ccessed 5 August 2020.

Haddad D, et al. Measurement of the Planck constant at the national institute of standards and technology from 2015 to 2017. Metrologia. 2017;54:633–641.
Available:http://iopscience.iop.org/article/10.1088/1681-7575/aa7bf2/pdf
Accessed 5 August 2020.

Haensch T, ‎Leschiutta S, ‎Wallard A. Metrology and fundamental constants. IOS Press, Bologna Italy; 2007.

Willink R. Principles of probability and statistics for metrology. Metrologia. 2006: 43:211–219.

Gödel K. Formally undecidable propositions of principia mathematica and related systems; 1931.

Pavese F. Analysis of current scientific data on climate and on their extrapolationbeyond 2100. 2020;1–31.
Available:https://www.researchgate.net/publication/339843361_On-Climate_F-Pavese_feb2020
Accessed 5 August 2020.

Falkovich G. Physical nature of information. 2020;1–122.
Available:https://www.weizmann.ac.il/complex/falkovich/sites/complex.falkovich/files/uploads/statphysII13.pdf
Accessed 5 August 2020.

Menin B. High accuracy when measuring physical constants: from the perspective of the information-theoretic approach. Journal of Applied Mathematics and Physics. 2020; 8(5):861–887.
Available:https://www.scirp.org/journal/paperabs.aspx?paperid=100314
Accessed 5 August 2020.

Pavese F. Replicated observations in metrology and testing: Modeling repeated and non-repeated measurements. Accred. Qual. Assur. 2007;12:525–534.
Available:https://scihub.tw/10.1007/s00769-007-0303-4
ccessed 5 August 2020.

BIPM Guide to the Expression of the Uncertainty in Measurement (the GUM). 2008;1–134.
Available:https://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf
Accessed 5 August 2020.

Pavese F. On the interpretation of systematic effects in metrology. Traceability to support CIPM MRA and other international agreements. 2008; 1–8.

Wheeler JA. Information, physics, quantum: The search for links, in: Complexity, entropy and the physics of information, ed. Zurek WH, Westview Press USA. 1990;3-28.

Grégis F. On the meaning of measurement uncertainty. Measurement. 2018;133:41-46.
Available:https://scihub.tw/10.1016/j.measurement.2018.09.073
Accessed 5 August 2020.

Brumley LN, Kopp C, Korb KB. Cutting Through the tangled web: An information-theoretic perspective on information warfare. Air Power Australia Analysis. 2012;2.
Available:http://www.ausairpower.net/APA-2012-02.html
Accessed 5 August 2020.

Sternlieb A. The principle of finiteness- A guideline for physical laws. Journal of Physics: Conference Series. 2013;437:012010:1-12.
Available:https://www.scihub.tw/10.1088/1742-6596/437/1/012010
Accessed 5 August 2020.

Linde A. Inflation, Quantum Cosmology and the Anthropic Principle. 2002;1-35.
Available:https://arxiv.org/pdf/hepth/0211048.pdf
Accessed 5 August 2020.