Wednesday, August 22, 2007

Sunny Auyang, How is Quantum Field Theory Possible?

Sunny Auyang's How is Quantum Field Theory Possible? is the densest and most difficult book I have actually read all the way through. There are sections that seem brilliantly written, and sections that seem absolutely opaque. All together, I didn't learn as much as I had hoped, but I did come to understand a few points about the way QFT suggests we view the world.

"Until now almost all philosophical investigation of quantum theories have either taken the concept of objectivity for granted or prescribed it as some external criterion, according to which the theories are judged. The judgments often deny the objectivity or even the possibility of microscopic knowledge. I adopt the opposite approach. I start with the premise that quantum field theory conveys knowledge of the microscopic world and regard the general meaning of objects as a question whose answer lies within the theory. This work asks quantum field theory to demonstrate its own objectivity by extracting and articulating the general concept of objects it embodies. We try to learn from it, not only the specifics of elementary particles, but also the general nature of the world and our status in it. What general conditions hold for us and the world we are in so that objects, classical and quantum, which are knowable through observations and experiments, constitute reality?"

A large proportion of the book is dedicated to explaining Kant's Categorical Framework, which I'm willing to summarize by saying that everything in the universe consists of objects and their properties, and relations between the objects and between the properties. Many philosophers of QFT have presented a vision of quantum reality in which the quantum objects don't have definite properties except at the moment of measurement. Auyang shows that this isn't the only possible interpretation. Auyang's major goal in writing this book may have been to rescue Kant's Categorical Framework.

"The world described by quantum theories is remote to sensory experiences and is different from the familiar classical world. There are scientific puzzles, such as what happens during the process of measurement. Quantum theories disallow certain questions that we habitually ask about physical things, for example, the moment when a radioactive atom decays. [...] The working interpretation of quantum theories, which physicists use in practice, invokes the concept of observed results as distinct from physical states. [...] These factors prompt many interpreters to adopt the phenomenalist position asserting that quantum objects have no definite property [...] the observer creates what he observes."

Auyang wants readers to see how the world-view she refers to as "Kant's Categorical Framework" applies not just to the classical world, but also to quantum reality. This contrasts with the view presented by many prominent interpreters of QFT, and understood in the popular lingo as "it tells us that there isn't any truth of the matter with respect to quantum objects." Auyang shows how the quantum world can be described in the same objective way as the real world. QFT doesn't undermine our belief that everything is built up out of objects, properties and relations.

"This work presents a parallel analysis of the conceptual structures of quantum field theory and our everyday thinking. I do not try to describe quantum phenomena in substantive classical terms or vice versa. I try to articulate the categorical framework of objective knowledge, of which quantum field theory is one instance and common sense another. The categorical framework enables us to match logically the formal structures of quantum theories and everyday thinking element by element. The structural fit illuminates their philosophical significance."

The main thing I learned about the shape of the universe is that it's improper to think of space-time as fundamental and of objects (and their properties and relations) as inhabiting a pre-existing space-time continuum. Instead, according to QFT, particles and space-time itself are emergent phenomena that arise from the interplay between fermions (matter fields) and bosons (interaction fields). I've seen Feynman diagrams many times before, but I don't remember seeing a statement as clear as Auyang's "In Feynman diagrams, a matter field is [...] represented by a straight line and an interaction field by a wavy line." Section 8 contains this gem along with a table of the fermions and bosons and how they combine to form the four basic interactions (gravity, electromagnetism, strong and weak forces). Auyang makes it clear that at the quantum level, the fundamental elements are the fermions and bosons, that bosons mediate all interactions between fermions, and that bosons and fermions are emergent phenomena of something more fundamental.

At the classical level, we're used to objects interacting directly: billiard balls collide and reflect in predictable directions. At the quantum level, bosons meditate the interactions between fermions. Photons, which are colloquially described as half-particles and half-wave aren't particles at all in this sense, they're the entities that mediate the electromagnetic force. Classical photons are just as much an emergent phenomena as electrons are, but they're part of the constellation of interaction fields while electrons are a kind of matter field. Auyang says "space-like separated transformations do not affect each other, for causality demands that physical effects propagate from point to point with finite velocity." That includes everything from billiard balls caroming to planets tugging on every body in the universe. (Though Auyang admits that "the gravitational interaction is not well understood.")

She goes on to explain how to think of the fields as exhausting space time:

Absolute positions are identities of events. There is no identity without an event. [...] Fields, which are spatio-temporally structured matter, exhaust the universe. It is not that the matter fills space-time; rather, the spatio-temporal structure spans the physical universe.

Auyang also attempts to explain (in § 16) how to think about QFT without invoking the consciousness of the observer. Her explanation seems plausible to me, but I'm not sure I ever understood why the standard model required a special status for the observer. Her explanation seems to boil down to arguing that the proponents of the Copenhagen interpretation are confused by the claim that quantum mechanics is a complete and final theory. (Apparently the term originates in the 1935 EPR paper.) According to Auyang, later proponents pushed the definition too far, insisting that observation required an observer. Auyang says that the observer is implicit, and to the extent that QM provides a complete theory, it's only a complete theory about quantum objects, so the observation has to be at the quantum, not classical level, in order to be part of the theory. I don't know whether theoretical physicists will accept her argument, but I think that's the interesting test of her argument.

While she is talking about the general concept of objects (§ 15), Auyang makes an observation that seems relevant beyond her intention. She says "When we look around, we see objects, books and pens. The presence of objects is immediate, we do not infer them from sense data." Her point is that we learn that our senses can be in error, and that objects we perceive may not actually be present (due to optical illusions, hallucinations, etc.). But the point is more fundamental: the process of coming to awareness is a process in which our sensory apparatus learns how to lump perceptions together based on in-built notions of permanence, cohesiveness, and various kinds of conservation rules. By the time we're doing anything that can be called thinking, we no longer have (if we ever did) access to raw perceptions; we think and perceive in terms of lumpy objects. Artists have to work hard to learn to see the colors, textures, and contours that make up an image. Greg Egan illustrated this brilliantly in a passage in his novel Diaspora. Jeff Hawkins' On Intelligence relies on the same effect at a different level.


william h. stoddard said...

Huh. Does she talk about "anyons"? They're a speculative idea some physicists have apparently played with: where bosons have integral spin (which can, for example, equal zero) and fermions have half-integral spin—and these imply different properties of statistical ensembles—anyons have spin that is in between: for example, spin 1/4, or 3/4, or e, presumably implying different and weird ensemble properties. At this point the whole concept is purely speculative, which would justify her not going into it, but she might have mentioned it in passing.

Chris Hibbert said...

Nary a word. She doesn't get into anything speculative. She barely mentions string theory, and dark energy and dark matter only come up in an appendix on Cosmology.

Parsifal said...

I have a copy of her book and have been reading some chapters...I can appreciate her critical views on realizing how ''our mind'' constellates meaning to sense perceptions...but there is one fundamental problem with her view which is she in the domain of perception and description, there are levels of realization. I wonder if she had the exact epxerience of Burning Bush (refer p. 195 of her book) would she speak of her experience as something constructed by her mind as he does in current writing...?


Parsifal said...
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