[1][2] The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states.
To express matters differently (paraphrasing Steven Weinberg),[3][4] the Schrödinger equation determines the wave function at any later time.
The views often grouped together as the Copenhagen interpretation are the oldest and, collectively, probably still the most widely held attitude about quantum mechanics.
Everett also attempted to demonstrate how the probabilistic nature of quantum mechanics would appear in measurements, a work later extended by Bryce DeWitt.
However, proponents of the Everettian program have not yet reached a consensus regarding the correct way to justify the use of the Born rule to calculate probabilities.
[19][20] The de Broglie–Bohm theory tries to solve the measurement problem very differently: the information describing the system contains not only the wave function, but also supplementary data (a trajectory) giving the position of the particle(s).
These nonlinear modifications are of stochastic nature and lead to behaviour that for microscopic quantum objects, e.g. electrons or atoms, is unmeasurably close to that given by the usual Schrödinger equation.
Particles have a non-zero probability of undergoing a "hit", or spontaneous collapse of the wave function, on the order of once every hundred million years.
Erich Joos and Heinz-Dieter Zeh claim that the phenomenon of quantum decoherence, which was put on firm ground in the 1980s, resolves the problem.
Zeh further claims that decoherence makes it possible to identify the fuzzy boundary between the quantum microworld and the world where the classical intuition is applicable.
[25][26] Quantum decoherence becomes an important part of some modern updates of the Copenhagen interpretation based on consistent histories.
[29] The present situation is slowly clarifying, described in a 2006 article by Schlosshauer as follows:[30] Several decoherence-unrelated proposals have been put forward in the past to elucidate the meaning of probabilities and arrive at the Born rule ...
The experimental evidence for superpositions of macroscopically distinct states on increasingly large length scales counters such a dictum.
Thus classical concepts are to be understood as locally emergent in a relative-state sense and should no longer claim a fundamental role in the physical theory.