Editing Scientific law (section)

== Laws as consequences of mathematical symmetries ==
{{main|Symmetry (physics)}}
Some laws reflect mathematical symmetries found in nature (e.g. the [[Pauli exclusion principle]] reflects identity of electrons, conservation laws reflect [[Homogeneity (physics)|homogeneity]] of [[space]], time, and [[Lorentz transformations]] reflect rotational symmetry of [[spacetime]]). Many fundamental physical laws are mathematical consequences of various [[symmetries]] of space, time, or other aspects of nature. Specifically, [[Noether's theorem]] connects some conservation laws to certain symmetries. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different from any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the [[Fermi–Dirac statistics|Dirac]] and [[Bose–Einstein statistics|Bose]] quantum statistics which in turn result in the [[Pauli exclusion principle]] for [[fermion]]s and in [[Bose–Einstein condensation]] for [[boson]]s. [[Special relativity]] uses [[rapidity]] to express motion according to the symmetries of [[hyperbolic rotation]], a transformation mixing [[space]] and time. Symmetry between [[inertial]] and gravitational [[mass]] results in [[general relativity]].

The [[inverse square law]] of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of [[space]].

One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.