I'm home with SteelyKid today, because Shavuot is important enough to close the JCC for two days. This will mean essentially no Internet for me, as it's difficult to type when you're lying on the floor being jumped on by a toddler.
As a filler post, let me take a cue from Making Light and offer you some analogies:
Choose only one, and be prepared to defend your choice in an essay of no more than 500 words, using examples drawn from the reading.
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Well, I want to vote for a lot of them, but also none of them at the same time. I find it helpful to think about the theory hypercube, which I first heard about from Joy Christian. Actually he only had a cube, but I have added many extra dimensions over time. Starting from Newtonian mechanics, we can move in a number of orthogonal directions to obtain other vertices of the hypercube. For example, there is a "probabilization" direction that takes us from Newtonian mechanics to Liouville mechanics. There is also a "(special) relativistation" direction that takes us from Newtonian mechanics to special relativity. There is a quantization direction that takes us to nonrelativistic quantum mechanics, and many other directions.
By combining moves in various directions we obtain a whole host of conceivable theories. For example, we can go from Newtonian mechanics to special relativity via the relativization direction and then from relativity to quantum field theory via the quantization direction to get QFT (or maybe it should be relativistic quantum particle theory followed by a move in the "fieldization" direction to get QFT).
Some of the vertices of this cube turn out to me mathematically inconsistent, or are ruled out for physical reasons such as having negative energy states (c.f. the aforementioned relativistic quantum particle theory). Some of them are consistent, but uninteresting because the various limits they assume don't occur naturally in our universe, e.g. a quantum theory of Newtonian gravity. Other vertices represent theories that are good approximations to reality in various regimes, and way over in the opposite corner from Newtonian mechanics is the unified theory of absolutely everything (assuming such a thing actually exists).
The point of explaining all this is just so I can reinterpret the poll question as saying, "Which other direction on the hypercube is most like the quantization direction?". If I have to choose, I would say it is most similar to the probabilization direction, but it also has elements of genuine paradigm change that probabilization lacks. Therefore, it is like a large dose of probabilization with a little hint of something like relitivization.
However, the true answer is: fish, because, after all, the different directions on the cube are all orthogonal to one another.
None of the answers given are really all that good. Arguments can be made for three of them (GR:Newtonian Mechanics, Stat Mech:Thermo, and TOE:Standard Model), but even those are a real stretch. Most of the others range from silly to "What are you smoking and where do I get some?" The last choice you offer, however, has a Zen-like attraction.
So by a much different line of reasoning I come to the same conclusion as Matt: the best answer is "Fish".
Hi, Matt,
Not bad. The comparability of conventional Probabilization with quantization stops short, as you know, at the difference between the sometimes negative Wigner function presentation of a quantum state and a positive semi-definite probability distribution over phase space as a presentation of a Liouville-type state, despite the otherwise rather good equivalence.
If one instead introduces algebraic presentations of quantum fields and of random fields, one can show them to be empirically equivalent, at least for the free (complex) Klein-Gordon field case, as I do in EPL 87 (2009) 31002, http://dx.doi.org/10.1209/0295-5075/87/31002 , http://arxiv.org/abs/0905.1263 . The algebras concerned are isomorphic, but the bridge principles between the empirical data and the abstract mathematics are somewhat different. FWIW, this introduces a somewhat subtle spanner in the works.
So, in terms of a theory not-quite-a-cube, "introducing a Lorentz invariant vacuum state over an algebraic presentation" of a quantum field or of a random field results in the same mathematical structure. Of course I've been working for some time on whether anything approximately similar can be said for interacting fields.
I suggest another direction for your theory cube relevant to quantization: contextualization, the ability to describe multiple experiments using a single state (and incompatible measurements).
The idea that QM:NM::SM:TD is to me almost perfectly wrong-headed, in that I could more happily vote for QM:NM::TD:SM, although the attraction of QM:NM::SM:TD for some voters is only to be expected. QM:NM::Fish.