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. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... In science, a physical constant is a physical quantity whose numerical value does not change. ... In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. ... In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

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. The speed of light in a vacuum is denoted by the letter c. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ...

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: In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... Professor Michio Kaku Michio Kaku (Kanji: 加來 紀雄) (born January 24, 1947 in the United States) is a Japanese American theoretical physicist, tenured professor, and co-creator of string field theory, a branch of string theory. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... John Carlos Baez (b. ...

• 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: In particle physics, an elementary particle is a particle of which other, larger particles are composed. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... Maki-Nakagawa-Sakata Matrix is a matrix used in neutrino theory. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ... For other topics related to Einstein see Einstein (disambig) In physics, the Einstein field equation or the Einstein equation is a tensor equation in the theory of gravitation. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... The Right Honourable Martin John Rees, Baron Rees of Ludlow, FRS (born 23 June 1942) is a professor of astronomy. ...

• 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. In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. ... In physics, the gravitational coupling constant, a physical constant denoted αG, is the coupling constant characterizing the strength of gravitation. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) occurs in Einsteins theory of general relativity. ... // Degrees of freedom in mechanics In mechanics, for each particle belonging to a system, and for each independent direction in which movement is possible, two degrees of freedom, are defined, one describing the particles momentum in that direction, the other describing the particles position along an axis defined... A multiverse (or meta-universe) is the hypothetical set of multiple possible universes (including our universe) that together comprise all of physical reality. ... In cosmology, the anthropic principle in its most basic form states the truism that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ...

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. This article or section seems not to be written in the formal tone expected of an encyclopedia entry. ... One of Sir Arthur Stanley Eddingtons papers announced Einsteins theory of general relativity to the English-speaking world. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ...

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. Simon Plouffe is a Quebec mathematician born on June 11, 1956 in St-Jovite. ... ...

See also

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

In the standard model of particle physics the Cabibbo Kobayashi Maskawa matrix (CKM matrix, sometimes earlier called KM matrix) is a unitary matrix which contains information on the strength of flavour changing weak decays. ... Cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Maki-Nakagawa-Sakata Matrix is a matrix used in neutrino theory. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ...

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

John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... Frank J. Tipler is a professor of mathematical physics at Tulane University, New Orleans, physicist, theologian and cornucopian philosopher. ... In cosmology, the anthropic principle in its most basic form states the truism that any valid theory of the universe must be consistent with our existence as carbon-based human beings at this particular time and place in the universe. ... Professor Michio Kaku Michio Kaku (Kanji: 加來 紀雄) (born January 24, 1947 in the United States) is a Japanese American theoretical physicist, tenured professor, and co-creator of string field theory, a branch of string theory. ... Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1994) is a book by Michio Kaku, a theoretical physicist from the City College of New York. ... Oxford University Press (OUP) is a highly-respected publishing house and a department of the University of Oxford in England. ... The Right Honourable Martin John Rees, Baron Rees of Ludlow, FRS (born 23 June 1942) is a professor of astronomy. ...

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?