Dimensionless physical constant

In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. However, the term may also be used (for example, by NIST) to refer to any dimensioned universal physical constant, such as the gravitational constant.

Physicists try to make their theories simpler and more elegant by reducing the number of physical constants appearing in the mathematical statement of their theories. This is accomplished by defining the units of measurement in such a way that several of the most common physical constants, such as the speed of light, are normalized to unity. The resulting system of units, known as natural units, has a fair following in the literature on advanced physics because it considerably simplifies many equations.

Some physical constants, however, are dimensionless numbers which cannot be eliminated in this way. Their values have to be ascertained experimentally. For example, according to Michio Kaku (1994: 124-27), the Standard Model of physics contains "at least 19 arbitrary [dimensionless] constants that describe the masses of the particles and the strengths of the various interactions". More recently, John Baez (2002) has estimated that 26 arbitrary constants are needed including:

• Masses of fundamental particles
• Fine structure constant
• Strong coupling constant
• The parameters of the CKM matrix and the Maki-Nakagawa-Sakata matrix
• Cosmological constant of Einstein field equation of general relativity.

In his book Just Six Numbers, Martin Rees considers the following numbers:

• Nu: ratio of the electroweak to the gravitational force (also see gravitational coupling constant);
• Epsilon: related to the strong force;
• Omega: the number of electrons and protons in universe;
• Lambda: cosmological constant;
• Q: ratio of fundamental energies;
• Delta: number of spatial dimensions.

These constants constrain any plausible fundamental physical theory, which must either be able to produce these values from basic mathematics, or accept these constants as arbitrary. The question then arises: how many of these constants emerge from pure mathematics, and how many represent degrees of freedom for multiple possible valid physical theories, only some of which can be valid in our Universe? This leads to a number of interesting possibilities, including the possibility of multiple universes with different values of these constants, and the relation of these theories to the anthropic principle.

Some study of the fundamental constants has bordered on numerology. For instance, the physicist Arthur Eddington argued that for several mathematical reasons, the fine structure constant had to be exactly 1/137. Experiments since his day have shown that this cannot be true; that constant is about 1/137.036.

The mathematician Simon Plouffe has made an extensive search of computer databases of mathematical formulae, seeking formulae giving the mass ratios of the fundamental particles.

See also

• CKM matrix
• Physical cosmology
• Maki-Nakagawa-Sakata Matrix
• Standard Model

References

• John D. Barrow, 2002. The Constants of Nature. Pantheon Books.
• John D. Barrow and Frank J. Tipler, 1986. The Anthropic Cosmological Principle. Oxford Univ. Press.
• Michio Kaku, 1994. Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension. Oxford University Press.
• Martin Rees, 1999. Just Six Numbers: The Deep Forces that Shape the Universe. London: Phoenix. ISBN 0753810220

External articles

General

• Fundamental Physical Constants from NIST
• John Baez, 2002, "How Many Fundamental Constants Are There?".
• Simon Plouffe. "A search for a mathematical expression for mass ratios using a large database."
• Values of fundamental constants. CODATA, 2002.

Variable fundamental constants

• "Michael Murphy's Research". Institute of astronomy, University of Cambridge.
• Webb, John K., "Do the laws of Nature change with time?". The University of New South Wales, Australia.

Articles

• Bahcall, J.N., C L Steinhardt, and D Schlegel, 2004 "Does the fine-structure constant vary with cosmological epoch?" Astrophys. J. 600: 520.
• Martins, J.A.P. et al., 2004, "WMAP constraints on varying α and the promise of reionization," Phys.Lett. B585: 29-34.
• Marion, H., et al. 2003, "A search for variations of fundamental constants using atomic fountain clocks," Phys.Rev.Lett. 90: 150801.
• Olive, K.A., et al., 2002, "Constraints on the variations of the fundamental couplings," Phys.Rev. D66: 045022.
• Uzan, J-P, 2003, "The fundamental constants and their variation: observational status and theoretical motivations," Rev.Mod.Phys. 75: 403.
• Webb, J.K. et al., 2001, "Further evidence for cosmological evolution of the fine-structure constant," Phys. Rev. Lett. 87: 091301.
• Scientific American Magazine (June 2005 Issue) Inconstant Constants - Do the inner workings of nature change with time?