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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 .
The relativistic Lagrangian can be derived in relativistic mechanics to be of the form: = (˙) (, ˙,). Although, unlike non-relativistic mechanics, the relativistic Lagrangian is not expressed as difference of kinetic energy with potential energy, the relativistic Hamiltonian corresponds to total energy in a similar manner but without including rest energy.
Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.
Special relativity corrects the hitherto laws of mechanics to handle situations involving all motions and especially those at a speed close to that of light (known as relativistic velocities). Today, special relativity is proven to be the most accurate model of motion at any speed when gravitational and quantum effects are negligible.
In relativistic quantum mechanics, elementary particles have spin and this is an additional contribution to the orbital angular momentum operator, yielding the total angular momentum tensor operator. In any case, the intrinsic "spin" addition to the orbital angular momentum of an object can be expressed in terms of the Pauli–Lubanski ...
The differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a body approaches the speed of light. For instance, in Newtonian mechanics , the kinetic energy of a free particle is E = 1 / 2 mv 2 , whereas in relativistic mechanics, it is E = ( γ − 1) mc 2 (where γ is the Lorentz ...
The Dirac equation relativistic spectrum is, however, easily recovered if the orbital-momentum quantum number l is replaced by total angular-momentum quantum number j. [12] In January 1926, Schrödinger submitted for publication instead his equation, a non-relativistic approximation that predicts the Bohr energy levels of hydrogen without fine ...
Diagram for locality in quantum mechanics. Simple spacetime diagrams can help clarify the issues related to locality. [2] A way to describe the issues of locality suitable for discussion of quantum mechanics is illustrated in the diagram. A particle is created in one location, then split and measured in two other, spatially separated, locations.