** Relativistic dynamics, a combination of relativistic and quantum concepts

Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics.

The spin-statistics theorem holds that, in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions.

Similar effects impart a golden hue to metallic caesium ( see relativistic quantum chemistry ).

Both in relativistic and non-relativistic quantum physics, we can identify the group velocity of a particle's wave function with the particle velocity.

For instance, the motion of a spacecraft, regarding its orbit and attitude ( rotation ), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.

A relativistic formulation in terms of covariant field tensors is used in special relativity, while in quantum mechanics, a version based on the electric and magnetic potentials is preferred.

In nonrelativistic quantum mechanics all particles are either bosons or fermions ; in relativistic quantum theories also " supersymmetric " theories exist, where a particle is a linear combination of a bosonic and a fermionic part.

Although spin and the Pauli principle can only be derived from relativistic generalizations of quantum mechanics the properties mentioned in the last two paragraphs belong to the basic postulates already in the non-relativistic limit.

In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin.

A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field ( rather than a fixed set of particles ).

The first step in solving a quantum chemical problem is usually solving the Schrödinger equation ( or Dirac equation in relativistic quantum chemistry ) with the electronic molecular Hamiltonian.

Most theories in modern particle physics, including the Standard Model of elementary particles and their interactions, are formulated as relativistic quantum field theories.

The second shortcoming, related to the first, is that in quantum mechanics there is no mechanism to describe particle creation and annihilation ; this is crucial for describing phenomena such as pair production which result from the conversion between mass and energy according to the relativistic relation E = mc < sup > 2 </ sup >.

Quantum electrodynamics ( QED ) is the relativistic quantum field theory of electrodynamics.

In relativistic quantum field theory, just as in classical field theory, Minkowski spacetime is the fixed background of the theory.

* Quantum field theory, a generic type of relativistic quantum theory, which includes:

Via the Dirac equation, Dirac spinors are required in the mathematical description of the quantum state of the relativistic electron.

In the language of four-vectors and tensors the angular momentum of a particle in relativistic mechanics is expressed as an antisymmetric tensor of second order

Eddington's proposed solution to the perceived problem was to modify relativistic mechanics so as to make the law P = K < sub > 1 </ sub > ρ < sup > 5 / 3 </ sup > universally applicable, even for large ρ.

As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of ( special ) relativistic mechanics.

Within the domain of classical mechanics, relativistic momentum closely approximates Newtonian momentum: at low velocity, is approximately equal to, the Newtonian expression for momentum.

In dimension 3, defining the gamma matrices to be the Pauli sigma matrices gives rise to the familiar two component spinors used in non relativistic quantum mechanics.

Also like Newton's Second law, the Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem that is not as severe in matrix mechanics and completely absent in the path integral formulation.

The specific nonrelativistic version is a simplified approximation to reality, which is quite accurate in many situations, but very inaccurate in others ( see relativistic quantum mechanics ).

The Many-Worlds Interpretation deals with it by discarding the collapse-process, thus reformulating the relation between measurement apparatus and system in such a way that the linear laws of quantum mechanics are universally valid ; that is, the only process according to which a quantum system evolves is governed by the Schrödinger equation or some relativistic equivalent.

In the general theory of relativity, too, acceleration is not an effect ( since it is not a generally relativistic vector ); the general relativistic effects comparable to those of Newtonian mechanics are the deviations from geodesic motion in curved spacetime.

New subtleties must be taken into account when we investigate causality in quantum mechanics and relativistic quantum field theory in particular.

( Other familiar deformations in physics involve the deformation of classical Newtonian into relativistic mechanics, with deformation parameter v / c ; or the deformation of Newtonian gravity into General Relativity, with deformation parameter Schwarzschild-radius / characteristic-dimension.

This allows the potential energy from the charged particle in an electrostatic potential and the Lorentz force on the charged particle moving in a magnetic field to be incorporated in a compact way, in relativistic quantum mechanics

** In the realm of relativistic many-bodied mechanics, namely the time-symmetric Wheeler – Feynman absorber theory: the equivalence between an advanced Liénard – Wiechert potential of particle j acting on particle i and the corresponding potential for particle i acting on particle j was demonstrated exhaustively to order before being proved mathematically.

The theory used by physicists was thereafter changed from Newtonian to relativistic mechanics.

This inconsistency was resolved by the development of relativistic mechanics.

* The Gaussian coherent states of nonrelativistic quantum mechanics can be generalized to relativistic coherent states of Klein-Gordon and Dirac particles.

The curves of radius against mass for the non-relativistic and relativistic models are shown in the graph.

Wilhelm Anderson applied a relativistic correction to this model, giving rise to a maximum possible mass of approximately 1. 37 kg.

In 1930, Stoner derived the internal energy-density equation of state for a Fermi gas, and was then able to treat the mass-radius relationship in a fully relativistic manner, giving a limiting mass of approximately ( for μ < sub > e </ sub >= 2. 5 ) 2. 19 · 10 < sup > 30 </ sup > kg.

Dark matter's existence is inferred from gravitational effects on visible matter and gravitational lensing of background radiation, and was originally hypothesized to account for discrepancies between calculations of the mass of galaxies, clusters of galaxies and the entire universe made through dynamical and general relativistic means, and calculations based on the mass of the visible " luminous " matter these objects contain: stars and the gas and dust of the interstellar and intergalactic medium.

The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the relativistic one-they can reach the speed of light limit at finite energy ; also the faster-than-light propagation is possible without requiring moving objects to have imaginary mass.

This same equation also connects relativistic mass and " relativistic energy " ( total system energy ).

The latter two " relativistic " mass and energy are concepts that are related to their " rest " counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum.

All unaccelerated observers agree on the amount of invariant mass in closed systems at all times, and although different observers may not agree with each other on how much relativistic mass is present in any such system, all agree that the amount does not change over time.

In special relativity, relativistic mass is a formalism which accounts for relativistic effects by having the mass increase with velocity.

* Curvature of spacetime is a relativistic manifestation of the existence of mass.

Neutron star relativistic equations of state provided by Jim Lattimer include a graph of radius vs. mass for various models.

Note that that while bound orbits around a point mass or around a spherical body with an Newtonian gravitational field are closed ellipses, which repeat the same path exactly and indefinitely, any non-spherical or non-Newtonian effects ( as caused, for example, by the slight oblateness of the Earth, or by relativistic effects, changing the gravitational field's behavior with distance ) will cause the orbit's shape to depart from the closed ellipses characteristic of Newtonian two-body motion.

* Relativity: In relativistic physics which deals with velocities close to the speed of light, it is found that different observers may observe different values for the length, time rates, mass, and many other properties of an object, depending on the observer's velocity relative to the object.

This is used in conjunction with the ship's warp drive's alteration of the ship's relativistic mass, to achieve mid-to-high sub-light speeds.

* de Sitter precession a general relativistic correction accounting for the Schwarzschild metric of curved space near a large non-rotating mass.

* Lense-Thirring precession a general relativistic correction accounting for the frame dragging by the Kerr metric of curved space near a large rotating mass.

( where p is the relativistic momentum of the bradyon and m is its rest mass ) should still apply, along with the formula for the total energy of a particle: