Informally, a physical quantity is a physical property that can be quantified. This means it can be measured and/or calculated and expressed in numbers. For example, "length" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as metres or inches, while "beauty" is a property that is difficult to describe with a number.
Formally, the International Vocabulary of Metrology', 3rd edition (VIM) defines quantity as:
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference[1]
The International Vocabulary of Metrology', 2nd ed. definied quantity as:
an attribute of a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively.[2]
The value of a physical quantity Q is expressed as the product of a numerical value {Q} and a physical unit [Q].
-
- Q = {Q} x [Q]
The relationship between different physical quantities are described by quantity calculus. SI units are usually preferred today. The notion of physical dimension of a physical quantity was introduced by Fourier in 1822.[3]
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Examples
If a person weighs 120 pounds, then "120" is the numerical value and "pound" is the unit. This physical quantity would be written as "120 lbs."
If the temperature outside is 30 degrees Celsius, then "30" is the numerical value and "degree Celsius" is the unit. This quantity would be written as "30 °C".
In equation form, a measurement of power, employing SI units and scientific notation for the number, might be written as
- P = 42.3 x 103 W,
Here, P represents the physical quantity 'power', 42.3 x 103 is the numerical value {P}, and W is the symbol for the unit of power [P], the watt
Symbols for physical quantities
Usually, the symbols for physical quantities are chosen to be a single letter of the Latin or Greek alphabet written in italic type. Often, the symbols are modified by subscripts and superscripts, in order to specify what they pertain to — for instance Ek is usually used to denote kinetic energy and cp heat capacity at constant pressure.
Symbols for quantities should be chosen according to the international recommendations from ISO 31, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity 'mass' is m, and the recommended symbol for the quantity '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 of fundamental units. The base quantities according to the International System of Quantities (ISQ) and their dimensions are listed in the following table:
| Name | Symbol for quantity | Symbol for dimension | SI base unit | Symbol for unit |
|---|---|---|---|---|
| Length | l, x, r, etc. | L | meter | m |
| Time | t | T | second | s |
| Mass | m | M | kilogram | kg |
| Electric current | I, i | I | ampere | A |
| Thermodynamic temperature | T | θ | kelvin | K |
| Amount of substance | n | N | mole | mol |
| Luminous intensity | Iv | J | candela | cd |
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 physical quantities are prefixed in order to further qualify their meaning:
- specific is added to refer to a quantity which is expressed per unit mass (such as specific heat capacity)
- molar is added to refer to a quantity which is expressed per unit amount of substance (such as molar volume)
There are also physical quantities that can be classified as neither extensive nor intensive, for example angular momentum, area, force, length, and time.
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 cijkl , 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, T1 and T2, or by their frequencies, ν1 and ν2 . The only definition of distance that respects some clearly defined invariances is D = | log(T2 / T1) | = | log(ν2 / ν1) | .
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.[4]
See also
References
- Cook, Alan H. The observational foundations of physics, Cambridge, 1994. ISBN 0-521-45597-
- ^ Joint Committee for Guides in Metrology (JCGM), International Vocabulary of Metrology, Basic and General Concepts and Associated Terms (VIM), III ed., Pavillon de Breteuil : JCGM 200:2008, 1.1 (on-line)
- ^ ISO Technical Advisory Group 4 (TAG 4), International vocabulary of basic and general terms in metrology, second edition, 1993, Geneva : International Organization for Standardization, 1993, 1.1
- ^ 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. [1]
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