A first stab at the problem of measurement in quantum mechanics is this: there is a difficulty in accounting for measurements having any outcomes at all. In Heisenberg's words: "it is the 'factual' character of an event describable in terms of the concepts of daily life which is not without further comment contained in the mathematical formalism of quantum theory, and which appears in the Copenhagen interpretation by the introduction of the observer." He might have added, or it appears with the introduction of the experimental apparatus (described differently from in quantum mechanics), or with the introduction of 'the classical world'.
The problem is about conflicting rules. At the level of the formalism of quantum mechanics, and in particular the quantum state, it is a conflict between the unitary dynamics for the state (which is deterministic, continuous in time, and constrained by elegant and subtle symmetries, as intensively studied by physicists), and the measurement postulates, by means of which information is extracted from the state (which alone involves indeterminism, and which breaks these various symmetries, but which is not the object of study of physicists). Which of the two rules is to be used depends on whether or not a measurement is performed, or whether or not an observation is made, or any records are available. Which invites the question, as posed by Einstein, 'so is the Moon there if nobody looks?'. What is to count as a measurement, or an observation, or a record, anyway?
The puzzle has all the hall-marks of a philosophical problem, but if that is what it is it has preoccupied physicists like no other. It was clearly visible by the mid 1920s; many of the founding father of quantum mechanics rejected the theory (as based on these two rules) in consequence: de Broglie, Schrodinger, and Einstein. Moreover, it can clearly be solved in at least three ways: the de Broglie-Bohm pilot-wave theory (a so-called 'hidden-variable' theory); the Ghirardi-Rimini-Weber-Pearle theory (a 'wave-packet collapse' theory); and - but more controversially - the Everett many-worlds theory. It is unusual for a philosophical problem to be solved by physical theories -- doubly so, if it can be solved in various ways.
But of these ways only one goes with the grain of quantum theory and special relativity. Or so it seemed to me in the early 1990s. Neither pilot-wave theories or collapse theories do very well in modelling relativistic phenomena, which are best understood in terms of the unitary formalism. But the Everett interpretation, specifically as based on decoherence-theory, is truly built in. Most of my papers on the measurement problem have been on decoherence-based Everttian quantum theory. However, I have also written on alternatives to quantum mechanics (pilot-wave theory and collapse theories), and on Bohr's philosophy of quantum mechanics; Bohr's writings established an orthodoxy of sorts in the first half-century of quantum mechanics.
Copyright Simon Saunders 2001. Last updated: 9 Mar 2012.