Galilean transformation
The Galilean transformation is used to transform between the coordinates of two coordinate systems in constant relative motion in Newtonian physics. The equations below, although apparently obvious, break down at speeds that approach the speed of light.
Unlike the Galilean transformation, the relativistic Lorentz transformations can be shown to apply at all velocities so far measured, and the Galilean transformation can be regarded as low-velocity approximations to the Lorenz transformation.
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Under the Erlanger program, the space-time (no longer spacetime) of nonrelativistic physics is described by the symmetry group generated by Galilean transformations, spacial and time translations and rotations.
Central extension of the Galilean group
- The Galilean group: Here, we will only look at its Lie algebra. It's easy to extend the results to the Lie group. The Lie algebra of L is spanned by E, Pi, Ci and Lij (antisymmetric tensor) subject to
We can now give it a central extension into the Lie algebra spanned by E', P'i, C'i, L'ij (antisymmetric tensor), M such that M commutes with everything (i.e. lies in the center, that's why it's called a central extension) and
Referenced By
Aether hypothesis | Aether theory | Ether hypothesis | Ether theory | Galilean-Newtonian relativity | Galilean relativity | Galileo Galilei | Glide reflection | Inertia | Inertial force | Inertial frame | Inertial frame of reference | Inertial reference frame | Inertial reference frames | Invariance | Invariant | Isometry | List of astronomical topics | List of astronomical topics (N-Z) | List of linear algebra topics | List of mathematical topics (G-I) | List of mathematical topics (G-Z) | List of physics topics F-L | Lorentz invariance | Lorentz transformation | Lorentz transformation equations | Lorentz transformations | Lorentz transforms | Luminiferous aether | Luminiferous ether | Newtonian physics | Newtonian relativity | Principle of Relativity | SPECIFICATION OF A FUNDAMENTAL TEMPORAL QUANTUM MASS | Space-time | Space-time interval | Spacetime | Spacetime interval | The Principle of Relativity | Time-space continuum
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