- Physical quantity
A

**physical**is a physical property that can be quantified. This means it can be measured and/or calculated and expressed in numbers. The value of a physical quantity "Q" is expressed as the product of a numerical value {"Q"} and aquantity physical unit [Q] . ::Q = {Q} x [Q]SI units are usually preferred today. The notion of "physical dimension" of a physical quantity was introduced by Fourier (1822).**Example**If a certain value of power is written as:"P" = 42.3 x 10

^{3}W = 42.3 kW,then:"P" represents the physical quantity of power:42.3 x 10

^{3}is the numerical value {P}:k is theSI prefix kilo , representing 10^{3}:W is the symbol for the unit of power [P] , thewatt **Symbols for physical quantities**Usually, the

symbol s for physical quantities are chosen to be a single lower case or capital letter of the Latin orGreek alphabet written in italic type. Often, the symbols are modified bysubscript s andsuperscript s, in order to specify what they pertain to — for instance "E"_{p}is usually used to denotepotential energy and "c_{p}"heat capacity at constantpressure .Symbols for quantities should be chosen according to the international recommendations from

ISO 31 , theIUPAP red book and theIUPAC green book . For example, the recommended symbol for a physical quantity of mass is "m", and the recommended symbol for a quantity of charge is "Q".**Units of physical quantities**Most physical quantities "Q" include a unit ["Q"] (where ["Q"] means "unit of "Q"). Neither the name of a physical quantity, nor the symbol used to denote it, implies a particular choice of unit. For example, a quantity of mass might be represented by the symbol "m", and could be expressed in the units kilograms (kg), pounds (lb), or daltons (Da).

**Base quantities, derived quantities and dimensions**By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension. In the

SI system of units, there are seven base units, but other conventions may have a different number offundamental units . The base quantities according to theInternational System of Quantities (ISQ) and their dimensions are listed in the following table:All other quantities are derived quantities since their dimensions are derived from those of base quantities by multiplication and division. For example, the physical quantity velocity is derived from base quantities length and time and has dimension L/T. Some derived physical quantities have dimension 1 and are said to be dimensionless quantities.

**Extensive and intensive quantities**A quantity is called:

***"extensive**" when its magnitude is additive for subsystems (volume, mass, etc.)

***"intensive**" when the magnitude is independent of the extent of the system (temperature, pressure, etc.)Some extensive physical quantities may be prefixed in order to further qualify their meaning:

***"specific**" is added to refer to the quantity divided by its mass (such asspecific volume )

***"molar**" is added to refer to the quantity divided by the amount of substance (such asmolar volume )There are also physical quantities that can be classified as neither extensive nor intensive, for example

angular momentum ,area ,force ,length , andtime .**Physical quantities as "coordinates" over spaces of physical "qualities"**The meaning of the term physical "quantity" is generally well understood (everyone understands what is meant by "the frequency of a periodic phenomenon", or "the resistance of an electric wire"). It is clear that behind a set of quantities like temperature − inverse temperature − logarithmic temperature, there is a qualitative notion: the "cold−hot" quality. Over this one-dimensional quality space, we may choose different "coordinates": the temperature, the inverse temperature, etc. Other quality spaces are multidimensional. For instance, to represent the properties of an ideal elastic medium we need 21 coefficients, that can be the 21 components of the elastic stiffness tensor $c\_\{ijkl\}$ , or the 21 components of the

elastic compliance tensor (inverse of the stiffness tensor), or the proper elements (six eigenvalues and 15 angles) of any of the two tensors, etc. Again, we are selecting coordinates over a 21-dimensional quality space. On this space, each point represents a particular elastic medium.It is always possible to define the distance between two points of any quality space, and this distance is —inside a given theoretical context— uniquely defined. For instance, two periodic phenomena can be characterized by their periods, $T\_1$ and $T\_2$, or by their frequencies, $u\_1$ and $u\_2$ . The only definition of distance that respects some clearly defined invariances is $D\; =\; |$log$(T\_2/T\_1\; )\; |\; =\; |$log$(\; u\_2/\; u\_1\; )\; |$.

These notions have implications in physics. As soon as we accept that behind the usual physical quantities there are quality spaces, that usual quantities are only special "coordinates" over these quality spaces, and that there is a metric in each space, the following question arises: Can we do physics intrinsically, i.e., can we develop physics using directly the notion of physical quality, and of metric, and without using particular coordinates (i.e., without any particular choice of physical quantities)? In fact, physics can (and must?) be developed independently of any particular choice of coordinates over the quality spaces, i.e., independently of any particular choice of physical quantities to represent the measurable physical qualities. This point of view has recently been developed (Tarantola, 2006 [

*http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/ElementsForPhysics-ScreenViewing.pdf*] ).**Books***Cook, Alan H. "The observational foundations of physics", Cambridge, 1994. ISBN 0-521-45597-9.

*Fourier, Joseph. "Théorie analytique de la chaleur", Firmin Didot, Paris, 1822. (In this book, Fourier introduces the concept of "physical dimensions" for the physical quantities.)

*Tarantola, Albert. "Elements for physics - Quantities, qualities and intrinsic theories", Springer, 2006. ISBN 3-540-25302-5. [*http://www.ipgp.jussieu.fr/~tarantola/Files/Professional/Books/ElementsForPhysics-ScreenViewing.pdf*]**See also***

Physical property

*Fundamental unit

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