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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).
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
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 ...
is called the Lorentz factor and c is the speed of light in free space. Lorentz factor (γ) is the same in both systems. The inverse transformations are the same except for the substitution v → −v. An equivalent, alternative expression is: [3]
The momentum compaction or momentum compaction factor is a measure for the momentum dependence of the recirculation path length for an object that is bound in cyclic motion (closed orbit). It is used in the calculation of particle paths in circular particle accelerators (like synchrotrons ), and for astronomical objects that are bound by ...