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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 space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with dimension of mass ⋅ length ⋅ time −1. Mathematically, the duality between position and momentum is an example of Pontryagin duality.
The momentum transfer plays an important role in the evaluation of neutron, X-ray, and electron diffraction for the investigation of condensed matter. Laue-Bragg diffraction occurs on the atomic crystal lattice, conserves the wave energy and thus is called elastic scattering, where the wave numbers final and incident particles, and , respectively, are equal and just the direction changes by a ...
There are some notable similarities in equations for momentum, energy, and mass transfer [7] which can all be transported by diffusion, as illustrated by the following examples: Mass: the spreading and dissipation of odors in air is an example of mass diffusion. Energy: the conduction of heat in a solid material is an example of heat diffusion.
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.
For analysis of momentum and energy problems, the most convenient frame is usually the "center-of-momentum frame" (also called the zero-momentum frame, or COM frame). This is the frame in which the space component of the system's total momentum is zero. Fig. 3-11 illustrates the breakup of a high speed particle into two daughter particles.
The 3-space momentum = (,,) is conserved (not to be confused with the classic non-relativistic momentum ). Note that the invariant mass of a system of particles may be more than the sum of the particles' rest masses, since kinetic energy in the system center-of-mass frame and potential energy from forces between the particles contribute to the ...
Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether's theorem . [ 25 ]