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The philosopher of physics Laura Reutsche argues in her book Interpreting Quantum Theories (review/summary here: http://philsci-archive.pitt.edu/9493/1/ruetsche-review.pdf ) that a "pristine" interpretation (1-1 correspondence between theory and reality) is impossible in quantum field theory, and all that exist are "adulterated" interpretations dependent on particular applications and contexts. Can anyone who thinks this is wrong explain why?

Thanks.

(I realize this is more a a philosophy of physics question, but I'm asking it here b/c Reutsche's book (with C*-Algebras, even a tiny bit of non-commutative geometry, and Hans Halvorson's comment that it is "perhaps the most sophisticated engagement that with mathematical physics that we have ever seen in a "philosophical" monograph") is way too mathematically advanced for most philosophers to understand.)

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    $\begingroup$ "is way too mathematically advanced for 99% of philosophers to understand" - A fair number of the philosophers I've learned from had graduate degrees in pure mathematics. And honestly, 99% of professional physicists don't know what a C*-algebra is, nor have they ever touched non-commutative geometry. Don't be so quick to assume a whole group of people is entirely stupid or incompetent. $\endgroup$
    – user10851
    Aug 24, 2014 at 7:20
  • $\begingroup$ Changed 99% to most, but I'm a philosophy and math student and I still think that more professional physicists than professional philosophers can understand C*-algebras and non-commutative geometry. $\endgroup$
    – Trent
    Aug 24, 2014 at 7:28
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    $\begingroup$ It would be better if you could expound the argument made in the book here. Try to nail it down to a specific point, so there is a objective question to be answered $\endgroup$ Aug 24, 2014 at 16:54

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It seems to me that the main argument given in the book is: while irreducible representations of CCR are all unitarily equivalent in finite dimensional QM, this is no more true in infinite dimensional QM. This leads, roughly speaking, to the necessity of choosing a specific Hilbert space (with a specific realization of the CCR) depending on the system considered. The concrete physical examples are related to spontaneous symmetry breaking effects, and choice of the Fock space vacuum.

If I should point out something that does not appear clear to me (however I have only read the linked review, not the original book) is that:

  • The non-unicity of CCR in infinite dimensional QM is true. I am not sure whether it is possible to infer the impossibility of a "pristine" interpretation of QFT from this, mainly because interacting quantum field theories (the only physically meaningful ones) are poorly understood from a mathematical point of view, and we are not able (hopefully not yet able) to define the Hilbert spaces of most physically relevant interacting QFTs. So it is not clear whether it is possible to write two inequivalent theories of QFT that produce different results, mainly because we cannot even construct one!

However, from a more general perspective, I think you may find interesting this (recent) discussion on the unicity of an eventual theory of everything (TOE).

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