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The energy and momentum of an object measured in two inertial frames in energy–momentum space – the yellow frame measures E and p while the blue frame measures E ′ and p ′. The green arrow is the four-momentum P of an object with length proportional to its rest mass m 0.
Momentum: the drag experienced by a rain drop as it falls in the atmosphere is an example of momentum diffusion (the rain drop loses momentum to the surrounding air through viscous stresses and decelerates). The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are
Calculating the Minkowski norm squared of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the speed of light c) to the square of the particle's proper mass: = = = + | | = where = is the metric tensor of special relativity with metric signature for definiteness chosen to be (–1, 1, 1, 1).
If the energy–momentum tensor T μν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting T μν = 0 in the trace-reversed field equations , the vacuum field equations, also known as 'Einstein vacuum equations' (EVE), can be written as R μ ν = 0 . {\displaystyle R ...
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.
From this valuable relation (a very generic continuity equation), three important concepts may be concisely written: conservation of mass, conservation of momentum, and conservation of energy. Validity is retained if φ is a vector, in which case the vector-vector product in the second term will be a dyad .
Energy–momentum may refer to: Four-momentum; Stress–energy tensor; Energy–momentum relation This page was last edited on 28 December 2019, at 10:37 (UTC). Text ...
In 1953, in order to express Mach's Principle in quantitative terms, the Cambridge University physicist Dennis W. Sciama proposed the addition of an acceleration dependent term to the Newtonian gravitation equation. [9] Sciama's acceleration dependent term was = where r is the distance between the particles, G is the gravitational constant, a ...