Dimensionless physical constant

In physics, a dimensionless physical constant, sometimes called a fundamental physical constant, is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of ​1⁄137.036.There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the 'hand of God' wrote that number, and 'we don't know how He pushed his pencil.' We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly! In physics, a dimensionless physical constant, sometimes called a fundamental physical constant, is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of ​1⁄137.036. The term fundamental physical constant is normally used to refer to the dimensionless constants, but has also been used (primarily by NIST and CODATA) to refer to certain universal dimensioned physical constants, such as the speed of light c, vacuum permittivity ε0, Planck constant h, and the gravitational constant G, that appear in the most basic theories of physics. Other physicists do not recognize this usage, and reserve the use of the term fundamental physical constant solely for dimensionless universal physical constants that currently cannot be derived from any other source. This narrower usage will be followed here. There is no exhaustive list of such constants but it does make sense to ask about the minimal number of fundamental constants necessary to determine a given physical theory. Thus, the Standard Model requires 25 physical constants, about half of them the masses of fundamental particles (which become 'dimensionless' when expressed relative to the Planck mass or, alternatively, as coupling strength with the Higgs field along with the gravitational coupling constant). Fundamental physical constants cannot be derived and have to be measured. Developments in physics may lead to either a reduction or an extension of their number: discovery of new particles, or new relationships between physical phenomena, would introduce new constants, while the development of a more fundamental theory might allow the derivation of several constants from a more fundamental constant. A long-sought goal of theoretical physics is to find first principles ('Theory of Everything') from which all of the fundamental dimensionless constants can be calculated and compared to the measured values. The large number of fundamental constants required in the Standard Model has been regarded as unsatisfactory since the theory's formulation in the 1970s. The desire for a theory that would allow the calculation of particle masses is a core motivation for the search for 'Physics beyond the Standard Model'. In the 1920s and 1930s, Arthur Eddington embarked upon extensive mathematical investigation into the relations between the fundamental quantities in basic physical theories, later used as part of his effort to construct an overarching theory unifying quantum mechanics and cosmological physics. For example, he speculated on the potential consequences of the ratio of the electron radius to its mass. Most notably, in a 1929 paper he set out an argument based on the Pauli exclusion principle and the Dirac equation that fixed the value of the reciprocal of the fine-structure constant as ?−1 = 16 + ½ × 16 × (16 − 1) = 136. When its value was discovered to be closer to 137, he changed his argument to match that value. His ideas were not widely accepted, and subsequent experiments have shown that they were wrong (for example, none of the measurements of the fine-structure constant suggest an integer value; in 2018 it was measured at α = 1/137.035999046(27)). Though his derivations and equations were unfounded, Eddington was the first physicist to recognize the significance of universal dimensionless constants, now considered among the most critical components of major physical theories such as the Standard Model and ΛCDM cosmology. He was also the first to argue for the importance of the cosmological constant Λ itself, considering it vital for explaining the expansion of the universe, at a time when most physicists (including its discoverer, Albert Einstein) considered it an outright mistake or mathematical artifact and assumed a value of zero: this at least proved prescient, and a significant positive Λ features prominently in ΛCDM. Eddington may have been the first to attempt in vain to derive the basic dimensionless constants from fundamental theories and equations, but he was certainly not the last. Many others would subsequently undertake similar endeavors, and efforts occasionally continue even today. None have yet produced convincing results or gained wide acceptance among theoretical physicists.