Lorentz Transformation - Transformation of Other Physical Quantities

Transformation of Other Physical Quantities

For the notation used, see Ricci calculus.

The transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If Z is any four-vector, then:

or in tensor index notation:

in which the primed indices denote indices of Z in the primed frame.

More generally, the transformation of any tensor quantity T is given by:

T^{\alpha' \beta' \cdots \zeta'}_{\theta' \iota' \cdots \kappa'} = \Lambda^{\alpha'}{}_{\mu} \Lambda^{\beta'}{}_{\nu} \cdots \Lambda^{\zeta'}{}_{\rho} \Lambda_{\theta'}{}^{\sigma} \Lambda_{\iota'}{}^{\upsilon} \cdots \Lambda_{\kappa'}{}^{\phi} T^{\mu \nu \cdots \rho}_{\sigma \upsilon \cdots \phi}

where is the inverse matrix of

Read more about this topic:  Lorentz Transformation

Famous quotes containing the words transformation of other, transformation of, physical and/or quantities:

    “Whoever undertakes to create soon finds himself engaged in creating himself. Self-transformation and the transformation of others have constituted the radical interest of our century, whether in painting, psychiatry, or political action.”
    —Harold Rosenberg (1906–1978)

    “The transformation of the impossible into reality is always the mark of a demonic will. The only way to recognize a military genius is by the fact that, during the war, he will mock the rules of warfare and will employ creative improvisation instead of tested methods and he will do so at the right moment.”
    —Stefan Zweig (18811942)

    “Parents’ accepting attitudes can help children learn to be open and tolerant. Parents can explain unfamiliar behavior or physical handicaps and show children that the appropriate response to differences should be interest rather than revulsion.”
    —Dian G. Smith (20th century)

    “Compilers resemble gluttonous eaters who devour excessive quantities of healthy food just to excrete them as refuse.”
    —Franz Grillparzer (1791–1872)