Fundamental physical constants
In physics, physical constants that are independent of systems of units are in general dimensionless numbers, and are known as fundamental physical constants.
Physicists have long tried to make their theories as simple and elegant as possible by reducing the number of arbitary 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.
These include:
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 arbitary constants. The question then arises: how many of these constants emerge from 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 possiblities, including the possibility of multiple universes, 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 it's value must be exactly 1/137, which it is not.
See also:
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