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In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid , in cases where the velocities of moving objects are comparable to the speed of light c .
This condition implies that the speed of the particle is close to the speed of light. According to the Lorentz factor formula, this requires the particle to move at roughly 85% of the speed of light. Such relativistic particles are generated in particle accelerators, [a] as well as naturally occurring in cosmic radiation.
Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...
The relativistic mass is the sum total quantity of energy in a body or system (divided by c 2).Thus, the mass in the formula = is the relativistic mass. For a particle of non-zero rest mass m moving at a speed relative to the observer, one finds =.
The above formulation is inherently phrased in a non-relativistic language; and it is noted that elementary particles have relativistic decay products. This objection only serves to confuse the issue. The experiment can be reformulated so that the decay product is slow-moving. At any rate, special relativity is not in conflict with quantum ...
In 1929, the Breit equation was found to describe two or more electromagnetically interacting massive spin 1 / 2 fermions to first-order relativistic corrections; one of the first attempts to describe such a relativistic quantum many-particle system. This is, however, still only an approximation, and the Hamiltonian includes numerous ...
Radius–mass relations for a model white dwarf, relativistic relation vs non-relativistic. The Chandrasekhar limit is indicated as M Ch. The article has only treated the case in which particles have a parabolic relation between energy and momentum, as is the case in non-relativistic mechanics.
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).