Decoherence

Schrodinger’s cat is the best known example of the paradox regarding the measurement problem in the interpretation of quantum mechanics. A cat is apparently evolving into a linear superposition of basis vectors that can be characterized as an alive cat and states that can be described as a dead cat. Each of these possibilities is associated with a specific nonzero probability amplitude. The cat seems to be in a mixed state. However, a single observation of the cat does not measure the probabilities. It always finds either a living cat, or a dead cat. After the measurement the cat is definitively alive or dead. The question is, how are the probabilities converted into an actual, sharply well-defined outcome?

The measurement problem is the key set of questions that every interpretation of quantum mechanics must address. The wavefunction in quantum mechanics evolves according to the Schrodinger equation into a linear superposition of different states, but the actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement did something to the process under examination. Whatever that something may be does not appear to be explained by the basic theory.

Different interpretations of quantum mechanics propose different solutions of the measurement problem. Quantum decoherence was proposed in the context of the many worlds interpretation, but it has also become an important part of some modern updates of the Copenhagen interpretation based on consistent histories. Quantum decoherence does not describe the actual process of the wavefunction collapse, but it explains the conversion of the quantum probabilities that are able to interfere to the ordinary physical probabilities.

Hugh Everett’s relative state interpretation, also referred to as a many worlds interpretation, attempts to avoid the problem by suggesting it is an illusion. Under this system there is only one wavefunction, the superposition of the entire universe, and it never collapses, so there is no measurement problem. Instead the act of measurement is actually an interaction between two quantum entities, which entangle to form a single larger entity, for instance living cat and happy scientist. Everett also attempted to demonstrate the way that in measurements the probabilistic nature of quantum mechanics would appear. Everett’s interpretation posits a single universal wavefunction, but with the added condition that reality from the point of view of any single observer is defined as a single path in time through the superpositions. Under this system our reality is one of many similar ones.

The Bohm interpretation tries to solve the measurement problem very differently. This interpretation contains not only the wavefunction, but also the information about the position of the particles. The role of the wavefunction is to create a quantum potential that influences the motion of the real particle in such a way that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics. According to the Bohm interpretation, once the particle is observed, other wave function channels remain empty and thus ineffective, but there is no true wavefunction collapse.

The present situation is slowly clarifying. Several proposals have been put forward to elucidate the meaning of probabilities and arrive at the Born rule. No decisive conclusion appears to have been reached as to the success of these derivations. Only the physical interactions between systems then determine a particular decomposition into classical states from the view of each particular system. 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.

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