In one of Jorge Luis Borges’ historical fictions, an elderly Averroes, remarking on a misguided opinion of his youth, says that to be free of an error it is well to have professed it oneself. Something like this seems to have happened on a shorter time scale in the ArXiv, with last November’s The quantum state cannot be interpreted statistically sharing two authors with this January’s The quantum state can be interpreted statistically. The more recent paper explains that the two results are actually consistent because the later paper abandons the earlier paper’s assumption that independent preparations result in an ontic state of product form. To us this seems an exceedingly natural assumption, since it is hard to see how inductive inference would work in a world where independent preparations did not result in independent states. To their credit, and unlike flipflopping politicians, the authors do not advocate or defend their more recent position; they only assert that it is logically consistent.
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Charles, yours is the second essay known to me that draws parallels between Borges’ wonderful story Averroes’s Search and the issues in fundamental physics that are associated to quantum localization and separability—a search for the phrase “quantum narratives of the future” will find my own remarks on this theme.
One wonders why this particular Borges’ story appeals to quantum physicists?
As a concrete meditation upon this theme, I have posted a (presentlyactive) question on MathOverflow (MOFL) titled “Quantum dynamics on varieties: asymptotic quantum trace distance on SHL varieties” — a question that was initially inspired by Borges’ meditations upon Averroes.
This MOFL question centers upon a class of varietal statespaces that — in striking parallel with the themes of this particular Quantum Pontiff post — accurately approximates “ontic states of product form” for loworder quantum correlations, and yet for highorder quantum correlations these same statespaces describe “a world where independent preparations do not result in independent states” (in the felicitous phrasing of your post).
The point being, that nonproduct ontic statespaces need not be vaguely imagined, but rather are wellknown to algebraic geometers as generic determinantal varieties, and moreover these statespaces are algebraically and geometrically natural objects onto which quantum physicists can pullback (1) the structures that we know and cherish (metric, symplectic, and complex), and (2) the functional forms that we know and cherish (Hamiltonian and Lindbladian), and finally (3) the conservation laws that we know and cherish (arising from local Noetherian symmetries).
As a further enticement to physicists, these same generic determinantal varieties are equipped with a natural ruled structure (that algebraic geometers have long appreciated) which advantageously makes integral curves similarly efficient to compute as upon Hilbert statespaces (which is wonderful news from a quantum systems engineering pointofview)
So perhaps the algebraic geometers have been playing the role of Greek dramatists for a 21st century QC community that now is realizing that a considerable portion of the history of 20th century quantum physics has been an Averroes’s Search?
Almost without regard to content, it seems (to me) plausible that someday an essay will appear titled “The Averroes’s Search of 20th century quantum physics,” and this will be an essay that is wellworth read and/or writing and/or imagining.
Dear chb,
A new (philosophical) paper analysing the PBR result has appeared in philsci archive, titled “Statistical VS Wave Realism in the Foundations of Quantum Mechanics” by Calosi et al : http://philsciarchive.pitt.edu/9021/
Take a look. 🙂
These mathematical ideas are new to me, but perhaps it makes sense to ask how one would recognize if one were living in a world with such complicated correlations, and how one would do science in it.
Ben Toner and I once spent some time thinking about how to get our universe from a universe with unlimited non locality (and hence capable of producing arbitraryish correlations). Eventually this led me to a different kind of universe: one in which correlations can only exist along “particle” space time curves and through interactions in only certain ways. An odd universe, but definitely closer to our current understanding of our own. Ignorance of future interactions leads one to statistical interpretations, but I could never quite find quantum theory among this muck.
To chb’s question about science in universes with strange (perhaps scale free) correlations: the more I think about this the more it reminds me of much that makes me distrust statements about complex systems. But maybe there is a way to make progress there using the tools we have learned work for such systems.
Science at the critical point sounds like good fodder for a Borgesesque story.