Physics in spacetime
Here, we see how to write the equations of special relativity in a manifestly Lorentz covariant In standard physics, Lorentz covariance is a key property of spacetime that follows from the special theory of relativity, where it applies globally. Local Lorentz covariance refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point, which follows from general relativity. Lorentz covariance has two form. The position of an event in spacetime is given by a contravariant four vector In the theory of relativity, a four-vector is a vector in a four-dimensional real vector space, called Minkowski space. It differs from a vector in that it can be transformed by Lorentz transformations. The usage of the four-vector name tacitly assumes that its components refer to a standard basis. The components transform between these bases as whose components are:
where x1 = x and x2 = y and x3 = z as usual. We define x0 = ct so that the time coordinate has the same dimension of distance as the other spatial dimensions; in accordance with the general principle that space and time are treated equally, so far as possible.[44][45][46] Superscripts are contravariant indices in this section rather than exponents except when they indicate a square. Subscripts are covariant indices which also range from zero to three as with the spacetime gradient of a field φ:
<<Table of Contents Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies" | Next>> | Show All>>
