Abstract On the orthodox (Diracvon Neumann) interpretation1 of quantum mechanics, an observable has a determinate (definite, sharp) value for a system in a given quantum state if and only if the state is an eigenstate of the observable. So, the orthodox interpretation selects a particular set of observables that have determinate values in a given quantum state; equivalently, a particular set of idempotent observables or propositions, represented by projection operators, Thanks to Guido Bacciagaluppi and Michael Dickson for helpful critical comments on a draft version of the paper. R. C. would like to thank the Social Sciences and Humanities Research Council of Canada for research support.
Abstract On the orthodox (Diracvon Neumann) interpretation1 of quantum mechanics, an observable has a determinate (definite, sharp) value for a system in a given quantum state if and only if the state is an eigenstate of the observable. So, the orthodox interpretation selects a particular set of observables that have determinate values in a given quantum state; equivalently, a particular set of idempotent observables or propositions, represented by projection operators, Thanks to Guido Bacciagaluppi and Michael Dickson for helpful critical comments on a draft version of the paper. R. C. would like to thank the Social Sciences and Humanities Research Council of Canada for research support.
Quantum mechanics describes certain systems as being in superpositions of their properties, yet every measurement on every system that we are able to perform yields a determinate result. The “orthodox” formulation of the theory builds this in by including a postulate that such superpositions “collapse” at the time of measurement. This strategy fails to really explain why such measurements are determinate, is unacceptably imprecise, and makes observation basic in fundamental physical theory, which looks like the wrong sort of process for the job. The problem of the interpretation of quantum mechanics is the problem of finding a more satisfactory understanding of the formalism in This project began in an independent study with Craig Callender, who provided much help in terms of direction, discussion, comments, and continuing support. Thanks also to Jerey Barrett for reading and commenting on an earlier draft of this paper, including helping me find some clearer and more economical way of putting some crucial points.
How is orthodoxy possible? How can an interpretation maintain both the eigenstate–eigenvalue link and indeterminism? Given the former, the properties possessed by a system are completely fixed by its quantum-mechanical state, but the quantum-mechanical state evolves deterministically, as I noted at the end of chapter 1. By themselves, then, the eigenstate–eigenvalue link and the quantum-mechanical equation of motion lead to determinism. Orthodoxy must change one of these things if it wants to maintain indeterminism. Of course, it cannot change the eigenstate–eigenvalue link, lest it no longer be orthdoxy. Hence it changes the equation of motion. In this chapter, I will discuss two ways to change the quantum-mechanical equation of motion: by ‘interupting’ it from time to time with some other (indeterminsitic) equation, or by making a wholesale replacement. The first strategy I discuss in the next section, and the second in the subsequent section. The projection postulate Collapse as an analogue of Lüder's rule Thus far, we have been working in the ‘Schrödinger picture’, according to which states evolve in time (according to the Scrödinger equation) and any given observable is at all times represented by the same operator. The Heisenberg picture reverses things: the states are constant in time and the operators representing observables change.
The distinguishing feature of ‘modal’ interpretations of quantum mechanics is their abandonment of the orthodox eigenstate–eigenvalue rule, which says that an observable possesses a definite value if and only if the system is in an eigenstate of that observable. Kochen's and Dieks' new biorthogonal decomposition rule for picking out which observables have definite values is designed specifically to overcome the chief problem generated by orthodoxy's rule, the measurement problem, while avoiding the no-hidden-variable theorems. Otherwise, their new rule seems completely ad hoc.The ad hoc charge can only be laid to rest if there is some way to give Kochen's and Dieks' rule for picking out which observables have definite values some independent motivation. And there is, or so I will argue here. Specifically, I shall show that theirs is the only rule able to save Schrödinger's cat from a fate worse than death, and sidestep the Bell–Kochen–Specker no-hidden-variables theorem, once we impose four independently natural conditions on such rules
Abstract This work sets out to answer a single question: what is the orthodox interpretation of quantum mechanics? However, we adopt a different approach to that normally used. Rather than surveying physicists, or poring over the precise details of the thoughts of Bohr and Heisenberg, we review a collection of 42 textbooks on quantum mechanics, encompassing the most popular and prominent works of this nature. We then gauge their response to 13 propositions to build up a picture of exactly what is believed by an orthodox quantum mechanic. We demonstrate that this orthodoxy has many aspects of Copenhagen-like viewpoints, but also shows some interesting emerging deviations. Moreover, it is more nuanced than some reductive characterisations that condense the orthodoxy down to the ontological primacy of the quantum state. The revealed orthodoxy has three consistent pillars: measurement inherently disturbs quantum states, these states refer to individual instances, not ensembles, and quantum systems do not have definite properties prior to measurement. More fully, it entails that individual particles exist in wave-like super-positions and present particle behaviours only when forced to by outside influences. The act of measuring such a system inherently induces random changes in its state, manifesting as a form of measurement error that corresponds to the uncertainty principle. This implies that measurement does not reveal underlying values of quantum properties.
The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal interpretation (of which a number of variants have been developed) answers this as follows. An observable may have a value even if the system is not in the corresponding eigenstate of that observable. The state of the system only constrains the possible values the observable can have, and (at least under certain conditions) the probabilities that it has those values. Hence, the eigenvalue–eigenstate link is violated. There is no collapse; the state of an isolated system always evolves in accordance with the Schroedinger equation. Hence the values of observables can change indeterministically, though this stochastic process is constrained by the deterministically evolving quantum state. Terminology varies but in this book the quantum state is then called the dynamical state, and a summary of the values of the observables pertaining to the system is called the value state. Since not all observables are mutually compatible, they will not all have simultaneous sharp values, but for each there is a minimum Borel set of values as its current range. The specific modal interpretation developed here is the Copenhagen Variant of the Modal Interpretation, which places holistic constraints on values of observables pertaining to parts of composite systems.
Abstract Bub and Clifton (1996) proved a uniqueness theorem for ‘no col lapse’ interpretations of quantum mechanics. The proof was repeated, with minor modifications, in Bub (1997). The original proof involved a ‘weak separability’ assumption (introduced to avoid a dimensionality constraint) that required several preliminary definitions and considerably complicated the formulation of the theorem. Sheldon Goldstein has pointed out that the proof goes through without this assumption. The question at issue is this: Consider an arbitrary ‘pure’ quantum state represented by a ray e on a Hilbert space 1t and the Boolean algebra or lattice, B(R), generated by the eigenspaces of a single observable R on Ji. The probabilities defined bye for the ranges of values of R can be represented by a probability measure over the 2valued homomorphisms on B(R). What is the maximal