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The quantity on the left is called the spacetime interval between events a 1 = (t 1, x 1, y 1, z 1) and a 2 = (t 2, x 2, y 2, z 2). The interval between any two events, not necessarily separated by light signals, is in fact invariant, i.e., independent of the state of relative motion of observers in different inertial frames, as is shown using ...
The usual treatment (e.g., Albert Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is described, for example, in the second volume of the Course of Theoretical Physics by Landau and Lifshitz), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say ...
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:
Then, for example, (0, 3 / 2 ) and (1, 1 / 2 ) are a spin representations of dimensions 2⋅ 3 / 2 + 1 = 4 and (2 + 1)(2⋅ 1 / 2 + 1) = 6 respectively. According to the above paragraph, there are subspaces with spin both 3 / 2 and 1 / 2 in the last two cases, so these representations cannot likely ...
The minimal subgroup in question can be described as follows: The stabilizer of a null vector is the special Euclidean group SE(2), which contains T(2) as the subgroup of parabolic transformations. This T(2), when extended to include either parity or time reversal (i.e. subgroups of the orthochronous and time-reversal respectively), is ...
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.
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 derivations of the Lorentz transformations.
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.