This object can be understood as a four-by-four matrix with diagonal entries hyperbolic cosine rapidity, hyperbolic cosine rapidity, 1, and 1 and upper-left off-diagonal entries negative hyperbolic sine rapidity. In that representation, the rapidity angle is given by minus half the principle logarithm of the ratio of the speed of light minus x-speed and speed of light plus x-speed, so this operation can be understood as a hyperbolic rotation of (*) Minkowski space. Applying this operation to a spatial coordinate yields the quantity coordinate minus parallel velocity times time all times square root quantity one minus square of parallel speed over speed of light. It r
This object can be understood as a four-by-four matrix with diagonal entries hyperbolic cosine rapidity, hyperbolic cosine rapidity, 1, and 1 and upper-left off-diagonal entries negative hyperbolic sine rapidity. In that representation, the rapidity angle is given by minus half the principle logarithm of the ratio of the speed of light minus x-speed and speed of light plus x-speed, so this operation can be understood as a hyperbolic rotation of (*) Minkowski space. Applying this operation to a spatial coordinate yields the quantity coordinate minus parallel velocity times time all times square root quantity one minus square of parallel speed over speed of light. It reduces to the Galilean at low speeds. For 10 points, name this transform that converts between different inertial reference frames' spacetime and that is fundamental to special relativity.
This object can be understood as a four-by-four matrix with diagonal entries hyperbolic cosine rapidity, hyperbolic cosine rapidity, 1, and 1 and upper-left off-diagonal entries negative hyperbolic sine rapidity.
the {Lorentz} transformation [or {Lorentz} group or {Lorentz}ian]