Non-Relativistic Quantum Mechanics

Dickson, Michael

doi:10.1016/b978-044451560-5/50007-5

Cited by 36 publications

(29 citation statements)

References 131 publications

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“…This terminology, which sounds like a tautology in mathematics, is often used in the philosophy of physics; see, e.g. [4,8]. The link in question is the postulate that if A is an observable and |ψ is an eigenstate of A with eigenvalue λ, then a measurement of A in the state |ψ yields the result λ with certainty.…”

Section: Introductionmentioning

confidence: 99%

“…Instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation will just assume that pure states in classical physics have the usual interpretation as 'truthmakers' that assign sharp values to observables. 8 Philosophical realists adhering to the eigenstate-eigenvalue link would simply say that A has the value λ in the eigenstate |ψ , but precisely among realists it has become fashionable to deny the eigenstate-eigenvalue link for the reasons mentioned in the main text [4,8]. For example, in Bohmian mechanics position always has a sharp value, whereas in the modal interpretation of quantum mechanics the link is dropped in a more flexible way.…”

Section: Introductionmentioning

confidence: 99%

“…The link in question is the postulate that if A is an observable and |ψ is an eigenstate of A with eigenvalue λ, then a measurement of A in the state |ψ yields the result λ with certainty. 8 The eigenstate-eigenvalue link is, of course, a special case of the Born rule, but the whole point of the exercise is to derive the Born rule from the eigenstate-eigenvalue link, rather than the other way round.…”

Section: Introductionmentioning

confidence: 99%

“…The eigenstate-eigenvalue link is the source of the measurement problem in quantum mechanics and hence is held to be unsound by most contemporary specialists in the foundations of quantum mechanics (see [4,8] and references therein). Indeed, the eigenstate-eigenvalue link cannot be found in the writings of Bohr and Heisenberg; it was first postulated by Dirac [9].…”

Section: Introductionmentioning

confidence: 99%

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Macroscopic Observables and the Born Rule, I: Long Run Frequencies

Landsman

2008

Rev. Math. Phys.

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We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C * -algebra of observables is empirically accessible only through associated commutative C * -algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program -notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) -in replacing infinite tensor products of Hilbert spaces by continuous fields of C * -algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Macroscopic Observables and the Born Rule, I: Long Run Frequencies

Landsman

2008

Rev. Math. Phys.

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“…13 For recent examples, see Albert and Loewer (1996), Barrett (1999), Lewis (2003), and Dickson (2007).…”

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confidence: 99%

A Prolegomenon to the Ontology of the Everett Interpretation*

Wallace¹

2013

The Wave Function

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This article began as an attempt to explain, without assuming any technical physics or advanced mathematics, what the metaphysical (and in particular, the ontological) implications are of the Everett interpretation of quantum theory, often known as the many-worlds interpretation.The difficulty is that physics is not, by and large, gratuitiously technical. It is possible to give a non-technical impression of what Everettian quantum theory is like, but metaphysicians don't just need impressions: they need clear statements of just what a given physical theory is saying.In my view -and this is an underlying theme of the article -this has led to trouble. Physical theories don't, straightforwardly, say anything: the theory, shorn of any interpretation, is a piece of mathematics. In the case of classical point-particle mechanics -that is, in the case of Newton's physics -that piece of mathematics is relatively easy to understand intuitively, at least at a surface level. But in the case of quantum theory, the mathematics is very abstract and its connection to observable facts is both indirect and controversial. There is a great temptation, in trying to communicate quantum physics to philosophers, to tacitly smuggle in controversial interpretative posits as if they were part of the formalism; there is a comparable temptation to present certain, relatively-simply-describable special cases as if they were general; there is, in short, a serious danger of miscommunication, and this is exacerbated by the very different styles of philosophy and modern physics, a difference not entirely recognised by philosophers whose model of physics remains something like Newton's Laws.In this article, I do not pretend to present the mathematics of quantum theory more carefully, in a way that avoids any such communications failure; such a task lies far beyond its scope. My goal, instead, is to give some insight into the features of quantum mechanics, mathematically and interpretationally, that must be understood before any metaphysical discussion of the Everett interpretation can get off the ground. Much of what has been said so far on the subject, I believe, has failed to fully understand those features; as such, it has begun the discussion on the wrong foot. By the end of the article, I will have begun a positive discussion of the Everett interpretation's metaphysical consequences, but I can do no more than begin it without presuming a good 1

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Just a Matter of Knowledge?

Boge

2018

European Studies in Philosophy of Science

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Non-Relativistic Quantum Mechanics

Cited by 36 publications

References 131 publications

Macroscopic Observables and the Born Rule, I: Long Run Frequencies

Macroscopic Observables and the Born Rule, I: Long Run Frequencies

A Prolegomenon to the Ontology of the Everett Interpretation*

Just a Matter of Knowledge?

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