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The dimension of a physical quantity is more fundamental than some scale or unit used to express the amount of that physical quantity. For example, mass is a dimension, while the kilogram is a particular reference quantity chosen to express a quantity of mass. The choice of unit is arbitrary, and its choice is often based on historical precedent.
Dimension Comments Amount of substance: n: The quantity proportional to the number of particles in a sample, with the Avogadro constant as the proportionality constant: mole (mol) N: extensive, scalar Length: l: The one-dimensional extent of an object metre (m) L: extensive: Time: t: The duration of an event: second (s) T: scalar, intensive ...
Examples are a cloud, a human body, a banana, a billiard ball, a table, or a proton. This is contrasted with abstract objects such as mental objects, which exist in the mental world, and mathematical objects. Other examples that are not physical bodies are emotions, the concept of "justice", a feeling of hatred, or the number "3".
For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc. The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded.
A physical property is any property of a physical system that is measurable. [1] The changes in the physical properties of a system can be used to describe its changes between momentary states. A quantifiable physical property is called physical quantity. Measurable physical quantities are often referred to as observables.
Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. The fine-structure constant α is the best known dimensionless fundamental physical constant. It is the value of the elementary charge squared expressed in Planck units. This value has become ...
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
For example, consider the formulas for the area enclosed by a circle in two dimensions (=) and the volume enclosed by a sphere in three dimensions (=). One might guess that the volume enclosed by the sphere in four-dimensional space is a rational multiple of π r 4 {\displaystyle \pi r^{4}} , but the correct volume is π 2 2 r 4 {\displaystyle ...