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Definition of the Lorentz factor γ. The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in ...
Time t = 2: Time t = 3: These figures — made using ρ = 28, σ = 10 and β = 8 / 3 — show three time segments of the 3-D evolution of two trajectories (one in blue, the other in yellow) in the Lorenz attractor starting at two initial points that differ only by 10 −5 in the x-coordinate. Initially, the two trajectories seem ...
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost. In Minkowski space—the mathematical model of spacetime in special relativity—the Lorentz transformations preserve the spacetime interval between any two events. They describe only the transformations in which the spacetime event at the ...
21:45, 2 March 2010: 1,102 × 1,118 (17 KB) Trassiorf {{Information |Description=Lorentz factor as a function of velocity. Graph created with KmPlot, edited with Inkscape. This is well enough, but it takes more than 1000 segments to draw the curve. I simplify it to 4 bézier arcs. |So: 12:53, 6 October 2007: 1,102 × 1,118 (195 KB) Egg: 12:23 ...
The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems.
Assume two inertial reference frames (t, x, y, z) and (t′, x′, y′, z′), and two points P 1, P 2, the Lorentz group is the set of all the transformations between the two reference frames that preserve the speed of light propagating between the two points:
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.