The physical basis of natural units and truly fundamental constants

  • L. Hsu
  • J. P. Hsu
Open Access
Regular Article


The natural unit system, in which the value of fundamental constants such as c and ℏ are set equal to one and all quantities are expressed in terms of a single unit, is usually introduced as a calculational convenience. However, we demonstrate that this system of natural units has a physical justification as well. We discuss and review the natural units, including definitions for each of the seven base units in the International System of Units (SI) in terms of a single unit. We also review the fundamental constants, which can be classified as units-dependent or units-independent. Units-independent constants, whose values are not determined by human conventions of units, may be interpreted as inherent constants of nature.


Natural Unit Fundamental Constant Thermodynamic Temperature Luminous Intensity Planck Unit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    J.D. Jackson, Classical Electrodynamics, 3rd edition (John Wiley and Sons, New York, 1999) pp. 775-776Google Scholar
  2. 2.
    B.N. Taylor (Editor), NIST Special Publication 330: The International System of Units (SI) (National Institute of Standards and Technology, Gaithersburg, MD, 2001). See also the SI Brochure, (in particular, 2.1.1)
  3. 3.
    A. Ernst, J.P. Hsu, Chin. J. Phys. 39, 211 (2001) It is interesting to note that Voigt proposed the idea of the universal speed of light in 1887 long before Poincaré and Einstein wrote their milestone papers in 1905Google Scholar
  4. 4.
    L. Hsu, J.P. Hsu, D.A. Schneble, Nuovo Cimento B 111, 1229 (1996)Google Scholar
  5. 5.
    J.P. Hsu, L. Hsu, Nuovo Cimento B 112, 575 (1997)Google Scholar
  6. 6.
    J.P. Hsu, L. Hsu, Phys. Lett. A 196, 1 (1994)MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    I.M. Mills, P.J. Mohr, T.J. Quinn, B.N. Taylor, E.R. Williams, Metrologia 43, 227 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    J.P. Hsu, L. Hsu, Chin. J. Phys. 35, 407 (1977) and J.P. Hsu, Einstein’s Relativity and Beyond: New Symmetry ApproachesGoogle Scholar
  9. 9.
    E.F. Taylor, J.A. Wheeler, Spacetime Physics, 2nd edition (W. H. Freeman, New York, 1992) pp. 1-4 and pp. 58-59Google Scholar
  10. 10.
    T.A. Moore, A Traveler’s Guide to Spacetime: An Introduction to the Special Theory of Relativity (McGraw-Hill, New York, 1995), T.A. Moore, Six Ideas That Shaped Physics Unit R: The Laws of Physics and Frame-Independent, 2nd edition (McGraw-Hill, Boston, 2003)Google Scholar
  11. 11.
    V.S. Tuninsky, Metrologia 36, 9 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    J. Fischer, B. Fellmuth, Rep. Prog. Phys. 68, 1043 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    R.L. Wadlinger, G. Hunter, Phys. Teach. 26, 528 (1988)ADSCrossRefGoogle Scholar
  14. 14.
    A. Maksymowicz, Am. J. Phys. 44, 295 (1976)ADSCrossRefGoogle Scholar
  15. 15.
    M.J.T. Milton, J.M. Williams, S.J. Bennett, Metrologia 44, 356 (2007)ADSCrossRefGoogle Scholar
  16. 16.
    J.-M. Lévy-Leblond, Riv. Nuovo Cimento 7, 187 (1977)CrossRefGoogle Scholar
  17. 17.
    J.P. Hsu, Int. J. Mod. Phys. A 21, 5119 (2006) for a discussion of this gravitational constant in Yang-Mills gravity, see also 15b,15cADSCrossRefzbMATHGoogle Scholar
  18. 18.
    J.P. Hsu, Int. J. Mod. Phys. A 24, 5217 (2009)ADSCrossRefzbMATHGoogle Scholar
  19. 19.
    J.P. Hsu, Eur. Phys. J. Plus 126, 24 (2011)CrossRefGoogle Scholar
  20. 20.
    In a recent column in Physics Today (F. Wilczek, Physics Today 56 No. 5, 10 (2003)), Wilczek states that parameters such as $e$, $\hbar$, and the mass of the electron $m_{e}$ can be eliminated by a suitable choice of a system of units for length $(\hbar^{2}/m_{e}e^{2})$, time $(\hbar^{3}/m_{e}e^{4})$, and mass $(m_{e})$. This is much the same as choosing a system of natural units, in which parameters such as $c$, $\hbar$ and $k_{B}$ are eliminated. As Wilczek mentions later in the article, for a more complete theory, additional parameters such as the fine structure constant $\alpha$ inevitably come inGoogle Scholar
  21. 21.
    Peter J. Mohr, Barry N. Taylor, Rev. Mod. Phys. 72, 351 (2000)ADSCrossRefzbMATHGoogle Scholar
  22. 22.
    V. Kose, W. Wöger, Metrologia 22, 177 (1986)ADSCrossRefGoogle Scholar
  23. 23.
    J.P. Hsu, Mod. Phys. Lett. A. 26, 1707 (2011) This paper discusses a unified model of gravitational and electroweak forces based on the gauge symmetry $T(4)\times SU(2)\times U(1)$. The unified model suggests that the coupling constants of all these forces are equally fundamentalADSCrossRefzbMATHGoogle Scholar
  24. 24.
    P.A.M. Dirac, Sci. Am. 208, 48 (1963)CrossRefGoogle Scholar
  25. 25.
    Another method of deciding a truly fundamental and inherent constant of nature is that it must have the same value in both inertial and non-inertial frames. The result of this method is consistent with our discussion in this paper. The reason for this method is that all physically realizable frames of reference are, strictly speaking, non-inertial because of the long-ranged gravitational force and the accelerated cosmic expansion. Inertial frames are idealized frames when the accelerations of non-inertial frames approach zero. For a discussion of accelerated frames and the Wu transformations of space-time, see the appendix of L. Hsu, J.P. Hsu, Nuovo Cimento B, 112, 1147 (1997), J.P. Hsu, D. Fine, Int. J. Mod. Phys. A. 20, 7485 (2005), J.P. Hsu, Chin. J. Phys. 40, 265 (2002)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer 2012

Authors and Affiliations

  1. 1.Department of Postsecondary Teaching and LearningUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhysicsUniversity of Massachusetts-DartmouthNorth DartmouthUSA

Personalised recommendations