# Galilean relativity principle

A fundamental principle of classical mechanics, stating that the laws of mechanical motion are invariant if one inertial system is replaced by another. The existence of inertial coordinate systems is postulated. The principle was formulated as a result of the development of classical mechanics from Antiquity to the Renaissance; G. Galilei (1636) must be credited with its ultimate formulation. Mathematically, the principle is described by the Galilean transformation, which involves the assumption of the existence of an absolute time and an absolute space, not related to matter or to each other, which may be experimentally confirmed. If the velocities considered are small relative to the velocity of light, such experimental verification gives positive results. However, the results become negative for velocities approaching the velocity of light. This fact, as well as generalizations of the Galilean relativity principle to electromagnetic phenomena, were the main stimuli in the creation of the special theory of relativity, which also postulates the existence of inertial coordinate systems, but interconnects them by the group of Lorentz transformations (cf. Lorentz transformation), with respect to which the relativistic equations of mechanics (generalizations of the equations of classical mechanics) and the equations of electrodynamics are invariant. Subsequent development of the Galilean relativity principle forms part of the general theory of relativity.

#### References

[1] | V.A. [V.A. Fok] Fock, "The theory of space, time and gravitation" , Macmillan (1964) (Translated from Russian) |

#### Comments

#### References

[a1] | V.I. Arnol'd, "Mathematical methods of classical mechanics" , Springer (1978) (Translated from Russian) |

**How to Cite This Entry:**

Galilean relativity principle. A.Z. Petrov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Galilean_relativity_principle&oldid=17376