The measurement problem is the key set of questions that every interpretation of quantum mechanics must answer. The problem is that the wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states but the actual measurements always find the physical system in a definite state, typically a position eigenstate.
The best known example is the "paradox" of the Schrödinger's cat: 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 particular observation of the cat does not measure the probabilities: it always finds either an alive cat, or a dead cat. The measurement problem is the question how are the probabilities converted to an actual, sharply well-defined outcome.
Different interpretations of quantum mechanics propose different solutions of the measurement problem.
- The old Copenhagen interpretation was rooted in the philosophical positivism. It claimed that the probabilities are the only quantities that should be discussed, and all other questions were considered as unscientific ones. One could either imagine that the wavefunction collapses, or one could think of the wavefunction as an auxilliary mathematical tool with no direct physical interpretation whose only role is to calculate the probabilities.
While this viewpoint was sufficient to understand the outcome of all known experiments, it did not explain why it was legitimate to imagine that the cat's wavefunction collapses once the cat is observed, but it is not possible to collapse the wavefunction of the cat or the electron before it is measured. The collapse of the wavefunction used to be linked to one of two different properties of the measurement:
- The measurement is done by a conscious being. In this specific interpretation, it was the presence of a conscious being that caused the wavefunction to collapse. However, this interpretation depends on a definition of "consciousness". Because of its spiritual flavor, this interpretation was never fully accepted as a scientific explanation.
- The measurement apparatus is a macroscopic object. Perhaps, it is the macroscopic character of the apparata that allows us to replace the logic of quantum mechanics with the classical intuition where the positions are well-defined quantities.
The latter approach was put on firm ground in the 1980s when the phenomenon of quantum decoherence was understood. The calculations of quantum decoherence allow the physicists to identify the fuzzy boundary between the quantum microworld and the world where the classical intuition is applicable. Quantum decoherence was proposed in the context of the many-worlds interpretation, but it has also become an important part of modern update of the Copenhagen interpretation that is based on Consistent Histories ("Copenhagen done right"). 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 classical probabilities.
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 particle(s). 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. One of the many problems of the Bohm interpretation is that it does not explain what happens with the wavefunction once the particle is observed.
References
- Schlosshauer, Maximilian (2005): 'Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics', to appear in Rev. Mod. Phys., on arxiv.org: quant-ph/0312059