From "Many Worlds? An Introduction" by Simon Saunders.
“As Popper once said, physics has always been in crisis, but there was a special kind of crisis that set in with quantum mechanics. For despite all its obvious empirical success and fecundity, the theory was based on rules or prescriptions that seemed inherently contradictory. There never was any real agreement on these matters among the founding fathers of the theory.Saunders' introductory chapter from the book, "Many Worlds?" underlines the central puzzle of quantum mechanics. What would reality have to be like to make the theory of quantum mechanics so incredibly accurate?
“In what sense are the rules of quantum mechanics contradictory? They break down into two parts. One is the unitary formalism, notably the Schrödinger equation, governing the evolution of the quantum state. It is deterministic and encodes spacetime and dynamical symmetries.
“Whether for a particle system or a system of fields, the Schrödinger equation is linear: the sum of two solutions to the equation is also a solution (the superposition principle). This gives the solution space of the Schrödinger equation the structure of a vector space (Hilbert space).
“However, there are also rules for another kind of dynamical evolution for the state, which is - well, none of the above. These rules govern the collapse of the wavefunction. They are indeterministic and non-linear, respecting none of the spacetime or dynamical symmetries. And unlike the unitary evolution, there is no obvious route to investigating the collapse process empirically.
“Understanding state collapse, and its relationship to the unitary formalism, is the measurement problem of quantum mechanics. There are other conceptual questions in physics, but few if any of them are genuinely paradoxical. None, for their depth, breadth, and longevity, can hold a candle to the measurement problem.
“Why not say that the collapse is simply irreducible, ‘the quantum jump’, something primitive, inevitable in a theory which is fundamentally a theory of chance? Because it isn’t only the collapse process itself that is under-specified: the time of the collapse, within relatively wide limits, is undefined, and the criteria for the kind of collapse, linking the set of possible outcomes of the experiment to the wavefunction, are strange.
“They either refer to another theory entirely - classical mechanics - or worse, they refer to our ‘intentions’, to the ‘purpose’ of the experiment.
“They are the measurement postulates - (‘probability postulates’ would be better, as this is the only place where probabilities enter into quantum mechanics). One is the Born rule, assigning probabilities (as determined by the quantum state) to macroscopic outcomes; the other is the projection postulate, assigning a new microscopic state to the system measured, depending on the macroscopic outcome.
“True, the latter is only needed when the measurement apparatus is functioning as a state-preparation device, but there is no doubt that something happens to the microscopic system on triggering a macroscopic outcome.
“Whether or not the projection postulate is needed in a particular experiment, the Born rule is essential. It provides the link between the possible macroscopic outcomes and the antecedent state of the microscopic system. As such it is usually specified by giving a choice of vector basis - a set of orthogonal unit vectors in the state space - whereupon the state is written as a superposition of these. The modulus square of the amplitude of each term in the superposition, thus defined, is the probability of the associated macroscopic outcome.
“But what dictates the choice of basis? What determines the time at which this outcome happens? How does the measurement apparatus interact with the microscopic system to produce these effects? From the point of view of the realist the answer seems obvious. The apparatus itself should be modelled in quantum mechanics, then its interaction with the microscopic system can be studied dynamically. But if this description is entirely quantum mechanical, if the dynamics is unitary, it is deterministic. Probabilities only enter the conventional theory explicitly with the measurement postulates. The straightforwardly physicalistic strategy seems bound to fail. How are realists to make sense of this?
“The various solutions that have been proposed down the years run into scores, but they fall into two broadly recognizable classes. One concludes that the wavefunction describes not the microscopic system itself, but our knowledge of it, or the information we have available of it (perhaps ‘ideal’ or ‘maximal’ knowledge or information). No wonder modelling the apparatus in the wavefunction is no solution: that only shifts the problem further back, ultimately to ‘the observer’ and to questions about the mind, or consciousness, or information - all ultimately philosophical questions.
“Anti-realists welcome this conclusion; according to them, we neglect our special status as the knowing subject at our peril. But from a realist point of view this just leaves open the question of what the goings-on at the microscopic level, thus revealed, actually are. By all means constrain the spatiotemporal description (by the uncertainty relations or information-theoretic analogues), but still some spatiotemporal description must be found, down to the length-scales of cells and complex molecules at least, even if not all the way to atomic processes.
“That leads to the demand for equations for variables that do not involve the wavefunction, or, if none is to be had in quantum mechanics, to something entirely new, glimpsed hitherto only with regard to its statistical behaviour. This was essentially Einstein’s settled view on the matter.
“The only other serious alternative (to realists) is quantum state realism, the view that the quantum state is physically real, changing in time according to the unitary equations and, somehow, also in accordance with the measurement postulates.
“How so? Here differences in views set in. Some advocate that the Schrödinger equation itself must be changed (so as to give, in the right circumstances, collapse as a fundamental process). They are for a collapse theory.
“Others argue that the Schrödinger equation can be left alone if only it is supplemented by additional equations, governing ‘hidden’ variables. These, despite their name, constitute the real ontology, the stuff of tables and chairs and so forth, but their behaviour is governed by the wavefunction. This is the pilot-wave theory.
“Collapse in a theory like this is only ‘effective’, as reflecting the sudden irrelevance (in the right circumstances) of some part of the wavefunction in its influence on these variables. And once irrelevant in this way, always irrelevant: such parts of the wavefunction can simply be discarded. This explains the appearance of collapse.
“But for others again, no such additional variables are needed. The collapse is indeed only ‘effective’, but that reflects, not a change in the influence of one part of the quantum state on some hidden or ‘real’ ontology, but rather the change in dynamical influence of one part of the wavefunction over another - the decoherence of one part from the other.
“The result is a branching structure to the wavefunction, and again, collapse only in a phenomenological, effective sense. But then, if our world is just one of these branches, all these branches must be worlds. Thus the many worlds theory - worlds not spatially, but dynamically separated.”
Realists driven to the 'Many Worlds Interpretation' can still make no sense of it (Sean Carroll is a consistent defender, though). As Saunders observes on page 20,
“How does talk of macroscopic objects so much as get off the ground? What is the deep-down ontology in the Everett interpretation? It can’t just be wavefunction [...]; it is simply unintelligible to hold that a function on a high-dimensional space represents something physically real, unless and until we are told what it is a function of - of what inhabits that space, what the elements of the function’s domain are.
“If they are particle configurations, then there had better be particle configurations, in which case not only the wavefunction is real.”
And so I have bought "The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction, and the Meltdown of a Nuclear Family" by Peter Byrne.