Ghirardi–Rimini–Weber theory
The Ghirardi–Rimini–Weber theory (GRW) is a spontaneous collapse theory in quantum mechanics, proposed in 1986 by Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber.[1] Quantum mechanics has two fundamentally different dynamical principles: the linear and deterministic Schrödinger equation, and the nonlinear and stochastic wave packet reduction postulate.The orthodox interpretation, or Copenhagen interpretation of quantum mechanics, posits a wave function collapse every time an observer performs a measurement.Another issue of quantum mechanics is that it forecasts superpositions of macroscopic objects, which are not observed in nature (see Schrödinger's cat paradox).The aforementioned issues constitute the measurement problem in quantum mechanics.Collapse theories avoid the measurement problem by merging the two dynamical principles of quantum mechanics in a unique dynamical description.The physical idea that underlies collapse theories is that particles undergo spontaneous wave-function collapses, which occur randomly both in time (at a given average rate), and in space (according to the Born rule).The imprecise “observer” and “measurement” that plague the orthodox interpretation are thus avoided because the wave function collapses spontaneously.Among these are The first assumption of the GRW theory is that the wave function (or state vector) represents the most accurate possible specification of the state of a physical system.This is a feature that the GRW theory shares with the standard Interpretations of quantum mechanics, and distinguishes it from hidden variable theories, like the de Broglie–Bohm theory, according to which the wave function does not give a complete description of a physical system.The GRW theory differs from standard quantum mechanics for the dynamical principles according to which the wave function evolves.These principles can be expressed in a more compact way with the statistical operator formalism.Since the localization process is Poissonian, in a time intervalis the Hamiltonian of the system, and the square brackets denote a commutator.Two new parameters are introduced by the GRW theory, namely the collapse rateThese are phenomenological parameters, whose values are not fixed by any principle and should be understood as new constants of Nature.The collapse rate should be such that microscopic object are almost never localized, thus effectively recovering standard quantum mechanics.,[1] while more recently Stephen L. Adler proposed that the valueThis is a mesoscopic distance, such that microscopic superpositions are left unaltered, while macroscopic ones are collapsed.When the wave function is hit by a sudden jump, the action of the localization operator essentially results in the multiplication of the wave function by the collapse Gaussian., and let us assume that this undergoes a localization process at the positionOne thus finds that after the sudden jump has occurred, the initially delocalised wave function has become localized.We thus see that the Gaussian that is hit by the localization is left unchanged, while the other is exponentially suppressed.This is one of the most important features of the GRW theory, because it allows us to recover classical mechanics for macroscopic objects.particles whose statistical operator evolves according to the master equation described above.One thus sees that the center of mass collapses with a rateIf for simplicity one assumes that all particles collapse with the same rateAn object that consists of in the order of the Avogadro number of nucleons () collapses almost instantly: GRW's and Adler's values ofFast reduction of macroscopic object superpositions is thus guaranteed, and the GRW theory effectively recovers classical mechanics for macroscopic objects.