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Derivation of the relativistic Doppler shift If an object emits a beam of light or radiation, the frequency, wavelength, and energy of that light or radiation will look different to a moving observer than to one at rest with respect to the emitter.
The relativistic energy–momentum equation holds for ... The torque acting on a point-like particle is defined as the derivative of the angular momentum tensor ...
Before the advent of general relativity, changes in physical processes were generally described by partial derivatives, for example, in describing changes in electromagnetic fields (see Maxwell's equations). Even in special relativity, the partial derivative is still sufficient to describe such changes. However, in general relativity, it is ...
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.
Substituting the relativistic aberration equation Equation 8 into Equation 6 yields Equation 7, demonstrating the consistency of these alternate equations for the Doppler shift. [ 12 ] Setting θ r = 0 {\displaystyle \theta _{r}=0} in Equation 6 or θ s = 0 {\displaystyle \theta _{s}=0} in Equation 7 yields Equation 1 , the expression for ...
These equations, together with the geodesic equation, [8] which dictates how freely falling matter moves through spacetime, form the core of the mathematical formulation of general relativity. The EFE is a tensor equation relating a set of symmetric 4 × 4 tensors. Each tensor has 10 independent components.
The term Friedmann equation sometimes is used only for the first equation. [3] a is the scale factor, G, Λ, and c are universal constants (G is the Newtonian constant of gravitation, Λ is the cosmological constant with dimension length −2, and c is the speed of light in vacuum).
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.