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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
[2] The immutability of these fundamental constants is an important cornerstone of the laws of physics as currently known; the postulate of the time-independence of physical laws is tied to that of the conservation of energy (Noether's theorem), so that the discovery of any variation would imply the discovery of a previously unknown law of ...
For example, if x is a quantity, then x c is the characteristic unit used to scale it. As an illustrative example, consider a first order differential equation with constant coefficients : a d x d t + b x = A f ( t ) . {\displaystyle a{\frac {dx}{dt}}+bx=Af(t).}
For example, the speed of light is defined as having the numerical value of 299 792 458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a ...
In spectroscopy, oscillator strength is a dimensionless quantity that expresses the probability of absorption or emission of electromagnetic radiation in transitions between energy levels of an atom or molecule. [1] [2] For example, if an emissive state has a small oscillator strength, nonradiative decay will outpace radiative decay.
A quantity of dimension one is historically known as a dimensionless quantity (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is . Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension.
Although named for Edgar Buckingham, the π theorem was first proved by the French mathematician Joseph Bertrand in 1878. [1] Bertrand considered only special cases of problems from electrodynamics and heat conduction, but his article contains, in distinct terms, all the basic ideas of the modern proof of the theorem and clearly indicates the theorem's utility for modelling physical phenomena.