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.

Thursday, August 09, 2007

Sheri S. Tepper: The Fresco

Sheri Tepper's The Fresco wasn't very satisfying. The plot is simple: the aliens arrive, promise to solve many of our problems, and cause a few minor disasters before resolving most social issues and welcoming us to apply for membership in the galactic brotherhood. The science is inconsistent, and other than the protagonist, the characters are fairly one-dimensional. Tepper makes a few attempts to show that some of the abilities of the ETs could be explained by nanotech or other sufficiently advanced technology, but she feels free to introduce new tools and powers whenever it suits her fancy. The solutions to social problems (which include unexplained psychological adjustments) are mostly in the too-complex-to-explain-to-the-reader category.

The conflict and action are split between the disasters on Earth caused by the conflicts among ETs about their rules of engagement with us and an exploration of the psychology of the aliens. The local disasters are side-show; the real action concerns the eponymous fresco. The society of the race of ETs that makes first contact is based on wisdom drawn from a set of ancient murals produced by a distant progenitor. The murals are holy enough that they haven't been touched—or cleaned—in many generations. The standard interpretation of their meaning comes from a revered scribe several generations removed from the drawings' creation, and there are clear indications that the murals were already illegible at that point.

The analogy to religions based on frozen interpretations of an ancient text are obvious, though Tepper doesn't dwell on them. In this case, we're merely shown that the ETs have lost any sense of the original meaning, that their society is unstable if they suddenly have to figure things out for themselves, and that an external agent (benevolent humans) can fix everything by ensuring that the accepted interpretation is a benign update of the interpretation everyone is used to.

Unsatisfying morality, unsatisfying epistemology, unsatisfying story-telling.

Sunday, August 05, 2007

Tracy Kidder, House

A friend (thanks Hal) loaned me his copy of Tracy Kidder's House when I mentioned that we were planning a remodel. I think he intended me to take it as a cautionary tale of the hazards of underspecifying the design before beginning work, but I read it more for the interesting story of interpersonal (management) struggles and the details of design and construction.

Many years ago, I thoroughly enjoyed Kidder's The Soul of a New Machine. Kidder is exceptionally good at showing what is going on when a group works together to build something that is bigger than any of them can manage on their own. There are always political struggles, but it is heartening to see everyone striving to overcome strained interpersonal relations to ensure that the house turns out the best it can.

House is about a new company formed by a small group of experienced carpenters (but inexperienced businessmen) building a house in Massachusetts for a young lawyer under the direction of an architect who is just starting his practice. The house won design awards for the architect, and the lawyer (according to Kidder's story) was happy with the house, but the builders didn't make much money for their effort. The story describes the process of building the house in a fair amount of detail, but the focus is always on negotiations about who will pay for changes, who should have foreseen their necessity, and what was agreed to up front. The builders would have been much happier with the outcome if they had understood better how to write an estimate that left them room for profit. As it was, they were constantly squeezed when the lawyer pushed back on the price of materials and asked for trade-offs to his advantage.

Most of the blame for the particular problems goes to the agreement to proceed with construction before the design was complete. This meant the builders couldn't proof the totality of the design, to ensure, for instance, that there was room for the landing of the grand staircase where the architect was envisioning it. Another acrimonious conflict involved the architect's grand vision for how the greek revival decorations would be built, but this mostly impacted the financial accounting and people's attitudes toward one another without affecting the finished house significantly.

Of course, my reading of all this is heavily influenced by the fact that my father is an architect, that I helped (a little; after the first I was mostly off at college during the construction) him build three different houses, and that I'm a software developer and development manager. I often say that one of the most important lessons for software developers to learn is how to get requirements from a customer. As Extreme Programming points out, the customer isn't in a position to actually say what she wants at the beginning of a project; the designer has to evoke the needs, and show how they might be filled in order to allow the customer to fill in the details that the designer isn't familiar with. XP teaches the developer to make the design visible as early as possible so the customer can react to the parts that work and those that aren't right. When building or remodeling, many parts are harder to change once in place, but there are still opportunities to improve and solidify the design as a project proceeds.

In our own remodel, we've been trying to explain to the contractor that we understand that he expects us to change our minds; we've left room in our budget to make changes as we see how things turn out. He doesn't seem to understand that from a different industry we could understand the kind of flexibility he has to leave himself. Maybe he deals with changes as part of an attitude of adaptiveness, rather than as an articulated understanding of how it affects planning and budgeting. He shows so much flexibility that it's hard at times to pin him down on anything. We did finally get a rough schedule of construction so we can coordinate on the things we have to specify and buy ourselves. (countertops, flooring, new stove, tub, sinks, finish details, etc.) We also have to plan for how and when we will vacate each part of the house, and when we'll have to be out of the house entirely.

House is very engaging. If you have any interest in how houses are put together, or how teams work, there is a lot of meat here. While all the parties try to be tough negotiators at key times, they all want to end up with a beautiful house. Kidder builds a beautiful story out of the process.