Physical Constant - Dimensional and Dimensionless Physical Constants

Dimensional and Dimensionless Physical Constants

Whereas the physical quantity indicated by any physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on the unit used. Therefore, these numerical values (such as 299,792,458 for the constant speed of light c expressed in units of meters per second) are not values that a theory of physics can be expected to predict.

Because their units cancel, ratios of like-dimensioned physical constants do not depend on unit systems in this way, so they are pure dimensionless numbers whose values a future theory of physics could conceivably hope to predict. Additionally, all equations describing laws of physics can be expressed without dimensional physical constants via a process known as nondimensionalisation, but the dimensionless constants will remain. Thus, theoretical physicists tend to regard these dimensionless quantities as fundamental physical constants.

However, the term fundamental physical constant is also used in other ways. For example, the National Institute of Standards and Technology uses the term to refer to any universal physical quantity believed to be constant, such as the speed of light, c, and the gravitational constant G.

The fine-structure constant α is probably the best known dimensionless fundamental physical constant. Many attempts have been made to derive its value (currently measured at about 1/137.035999) from theory, but so far none have succeeded. The same holds for the dimensionless ratios of masses of fundamental particles (the most apparent is m_p/m_e, approximately 1836.152672). With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory. As such, some theoretical physicists still hope for continued progress in explaining the values of other dimensionless physical constants.

It is known that the Universe would be very different, if these constants took values significantly different from those we observe. For example, a few percent change in the value of the fine structure constant would be enough to eliminate stars like our Sun. This has prompted attempts at anthropic explanations of the values of some of the dimensionless fundamental physical constants.