In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers.

Physicists have long tried to make their theories as simple and elegant as possible by reducing the number of arbitrary constants in these theories. For this reason, the system of natural units generally used for advanced physics chooses its base units in such a way as to set several of the most common physical constants such as the speed of light to unity by definition. This greatly simplifies the form of many equations.

However, other physical constants are dimensionless numbers which cannot be eliminated in this way, and still have to be discovered experimentally. For example, according to Michio Kaku, the Standard Model of physics contains "at least 19 arbitrary constants that describe the masses of the particles and the strengths of the various interactions". More recently, John Baez has estimated that 26 arbitrary constants are needed. These include:

• the ratios of the masses of fundamental particles
• the fine structure constant
• the electromagnetic coupling constant
• the strong coupling constant
• the gravitational fine structure constant
• and others

These constants represent constraints on any plausible theory of fundamental physics, which must either be able to produce these values from basic mathematics, or have these constants "plugged into" the theory as arbitrary constants. 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 relationship of these theories with the anthropic principle.

Some attempts at studying the fundamental constants have bordered on numerology. A famous example was that of the physicist Arthur Eddington, who because the fine structure constant was measured at a value very close to 1/137, argued that its value must be exactly 1/137. Further experiments have shown that this is not true.

The mathematician Simon Plouffe has made an extensive search for mathematical formulae for the mass ratios of fundamental particles, based on computer databases of mathematical formulae and their values.

See also

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

References

• Michio Kaku, Hyperspace, p124-7
• Martin Rees, Just Six Numbers: The Deep Forxes that Shape the Universe, London: Phoenix, 1999, ISBN 0753810220

External links

• John Baez, How Many Fundamental Constants Are There? (http://math.ucr.edu/home/baez/constants.html)
• Simon Plouffe. A search for a mathematical expression for mass ratios using a large database (http://www.lacim.uqam.ca/%7Eplouffe/Search.htm).
• a list of values (http://physics.nist.gov/cuu/Constants/Table/allascii.txt) CODATA 2002