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The most general proper Lorentz transformation Λ(v, θ) includes a boost and rotation together, and is a nonsymmetric matrix. As special cases, Λ(0, θ) = R(θ) and Λ(v, 0) = B(v). An explicit form of the general Lorentz transformation is cumbersome to write down and will not be given here.
In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.
Hendrik Antoon Lorentz (1853–1928), after whom the Lorentz group is named.. In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena.
In the special relativity, Lorentz transformations exhibit the symmetry of Minkowski spacetime by using a constant c as the speed of light, and a parameter v as the relative velocity between two inertial reference frames. Using the above conditions, the Lorentz transformation in 3+1 dimensions assume the form:
The experimental and theoretical work was honored with the Nobel prize in physics in 1902. Lorentz' name is now associated with the Lorentz–Lorenz equation, the Lorentz force, the Lorentzian distribution, the Lorentz oscillator model and the Lorentz transformation.
The theory of special relativity plays an important role in the modern theory of classical electromagnetism.It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another.
Working with Lorentz's aether theory, Henri Poincaré, having earlier proposed the "relativity principle" as a general law of nature (including electrodynamics and gravitation), used this principle in 1905 to correct Lorentz's preliminary transformation formulas, resulting in an exact set of equations that are now called the Lorentz ...
These transformations imply a form of time dilation and were an approximation of the full Lorentz transformations. 1898 – Henri Poincaré states that simultaneity is relative. 1899 – Hendrik Antoon Lorentz publishes an early version of his coordinate transformations, including the local time.