Proper Velocity Addition Formula
The proper velocity addition formula:
where is the beta factor given by .
This formula provides a proper-velocity gyrovector space model of hyperbolic geometry that uses a whole space compared to other models of hyperbolic geometry which use discs or half-planes.
In the unidirectional case this becomes commutative and simplifies to a Lorentz-factor product times a coordinate-velocity sum, e.g. to wAC = γABγBC(vAB+vBC), as discussed in the application section below.
Read more about this topic: Proper Velocity
Famous quotes containing the words proper, addition and/or formula:
“Children ... seldom have a proper sense of their own tragedy, discounting and keeping hidden the true horrors of their short lives, humbly imagining real calamity to be some prestigious drama of the grown-up world.”
—Shirley Hazzard (b. 1931)
“Depend upon it there comes a time when for every addition of knowledge you forget something that you knew before. It is of the highest importance, therefore, not to have useless facts elbowing out the useful ones.”
—Sir Arthur Conan Doyle (1859–1930)
“I feel like a white granular mass of amorphous crystals—my formula appears to be isomeric with Spasmotoxin. My aurochloride precipitates into beautiful prismatic needles. My Platinochloride develops octohedron crystals,—with a fine blue florescence. My physiological action is not indifferent. One millionth of a grain injected under the skin of a frog produced instantaneous death accompanied by an orange blossom odor.”
—Lafcadio Hearn (1850–1904)