Search results
Results from the WOW.Com Content Network
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 ...
Heaviside–Lorentz units, like the Gaussian CGS units by which they generally differ by a factor of about 3.5, are frequently of rather inconvenient sizes. The ampere (coulomb/second) is reasonable unit for measuring currents commonly encountered, but the ESU/s, as demonstrated above, is far too small.
Replacing the Lorentz factor in the original formula leads to the relation = / In this equation both and are measured parallel to the object's line of movement. For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object.
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.
Lorentz factor as a function of speed (in natural units where c = 1). Notice that for small speeds (as v tends to zero), γ is approximately 1. In addition to the light clock used above, the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation. [28]
Lorentz force acting on fast-moving charged particles in a bubble chamber.Positive and negative charge trajectories curve in opposite directions. In physics, specifically in electromagnetism, the Lorentz force law is the combination of electric and magnetic force on a point charge due to electromagnetic fields.
For a map distance of Δx AB, the first equation above predicts a midpoint Lorentz factor (up from its unit rest value) of γ mid = 1 + α(Δx AB /2)/c 2. Hence the round-trip time on traveler clocks will be Δτ = 4(c/α)cosh −1 [γ mid], during which the time elapsed on map clocks will be Δt = 4(c/α)sinh[cosh −1 [γ mid]].
If a Lorentz covariant 4-vector is measured in one inertial frame with result , and the same measurement made in another inertial frame (with the same orientation and origin) gives result ′, the two results will be related by ′ = where the boost matrix () represents the rotation-free Lorentz transformation between the unprimed and primed ...