Dimensionless physical constant

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"Fundamental physical constant" redirects here. For other uses, see Fundamental physical constant (disambiguation).

In physics, dimensionless or fundamental physical constants are, in the strictest sense, universal physical constants that are independent of systems of units and hence are dimensionless quantities. However, the term may also be used (for example, by NIST) to refer to any dimensioned universal physical constant, such as the speed of light (free space)or the gravitational constant. While both mathematical constants and fundamental physical constants are dimensionless, the latter are determined only by physical measurement and not defined by any combination of pure mathematical constants. The list of fundamental physical constants decreases when physical theory advances and shows how some previously fundamental constant can be computed in terms of others. The list increases when experiments measure new effects.

Physicists try to make their theories simpler and more elegant by reducing the number of physical constants appearing in the mathematical expression 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, among others, 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. A classic example is the fine structure constant,

where is the elementary charge, is the reduced Planck's constant, is the speed of light in a vacuum, and is the permittivity of free space. In simple terms, the fine structure constant determines how strong the electromagnetic force is. Nobody knows why it has the value it does.

A long-sought goal of theoretical physics is to reduce the number of fundamental constants that need to be put in by hand, by calculating some from first principles. The reduction of chemistry to physics was an enormous step in this direction, since properties of atoms and molecules can now be calculated from the Standard Model, at least in principle. A successful Grand Unified Theory or Theory of Everything might reduce the number of fundamental constants further, ideally to zero. However, this goal remains elusive.

According to Michio Kaku (1994: 124-27), the Standard Model of particle physics contains 19 arbitrary dimensionless constants that describe the masses of the particles and the strengths of the various interactions. This was before it was discovered that neutrinos can have nonzero mass, and his list includes a quantity called the theta angle which seems to be zero. After the discovery of neutrino mass, and leaving out the theta angle, John Baez (2002) noted that the new Standard Model requires 25 arbitrary fundamental constants, namely:

• the fine structure constant,
• the strong coupling constant,
• the masses of the fundamental particles (normalized to the mass of some natural unit of mass), namely the 6 quarks, the 6 leptons, the Higgs boson, the W boson and the Z boson,
• the 4 parameters of the CKM matrix, which describe how quarks can oscillate between different forms,
• the 4 parameters of the Maki-Nakagawa-Sakata matrix, which does the same thing for neutrinos.

If we take gravity into account we need at least one more fundamental constant, namely

• the cosmological constant of Einstein's equations, which describe general relativity.

This gives a total of 26 fundamental physical constants. There are presumably more constants waiting to be discovered which describe the properties of dark matter. If dark energy turns out to be more complicated than a mere cosmological constant, even more constants will be needed.

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 the observable 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.

Note that Delta = 3; being simply an integer, most physicists would not consider this a dimensionless physical constant of the usual sort.

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 1/136. When its value was discovered to be closer to 1/137, he changed his argument to match that value. Experiments since his day have shown that his arguments are still wrong; the 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.

[edit] See also

• CKM matrix
• fine structure constant
• Physical cosmology
• Maki-Nakagawa-Sakata Matrix
• Standard Model
• Weinberg angle
• Cabibbo angle

[edit] References

• John D. Barrow, 2002. The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe. Pantheon Books. ISBN 0-375-42221-8.
• 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 0-7538-1022-0

[edit] 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?