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)

    “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)

    “Hemingway is great in that alone of living writers he has saturated his work with the memory of physical pleasure, with sunshine and salt water, with food, wine and making love and the remorse which is the shadow of that sun.”
    —Cyril Connolly (1903–1974)

    “The Walrus and the Carpenter
    Were walking close at hand:
    They wept like anything to see
    Such quantities of sand:
    “If this were only cleared away,”
    They said, “it would be grand!”
    “If seven maids with seven mops
    Swept it for half a year,
    Do you suppose,” the Walrus said,
    “That they could get it clear?”
    “I doubt it,” said the Carpenter,
    And shed a bitter tear.”
    —Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)