ZapperZ said:
But at some point, there is a "transition" from quantum behavior to the classical behavior that we all know and love. You must make such a distinction or else you will get into the mystical world of mumbo-jumbo.
Treat a classical entity as it should, and treat a quantum entity as it should. But don't mix them up or you'll get absurdities. When you apply a set of rules that were never meant to be applied to that particular situation, you get quackeries.
Zz.
As ZapperZ noted in his journal entry "A theory of everything?", there is indeed at the basis a difference in philosophy (between him and me) and the "quantum quackeries" are indeed only a reason to worry for people like me. The fundamental distinction is essentially the "belief in reductionism" which he cites in his journal entry and to which I adhere and to which some others don't - this is probably because both attitudes reflect different (successful) working attitudes in different domains.
However, I don't agree 100% with ZapperZ's definition of "reductionism". Reductionism (at least, how I understand it) does NOT have to mean that many-particle effects are simply the addition of few-particle interactions. Reductionism (as I understand it) simply holds that there is supposed to be a single, coherent, mathematical description of ALL what happens in nature. In other words, that there is a 1-1 mapping between a certain mathematical structure, and all physical aspects of the universe. That doesn't mean that we think that we KNOW of such a structure, but we assume that such a structure exists and we try to discover aspects of it. Another way of stating that is that there exist universal physical laws that apply to everything. It has always been my idea that this was the very working hypothesis of physics, and as such am surprised that there are physicists (good ones even, like those ZapperZ cites, and ZapperZ himself
) claiming the opposite.
Of course, the simplest ways (in the mind of a reductionist) to find hints of that structure is to explore the most "elementary" interactions, in the few-particle case. (and that's probably why most adherents of this view are particle physicists)
Their idea is that, from these basic laws, once we know them, we can in principle mathematically deduce what will happen in more complicated settings, with gazillions of particles - under the hypothesis that we found the correct behaviour for ANY set of particles, starting from the study of a few, and good mathematical and esthetic intuition for building a theory.
Now, condensed matter physicists (like ZapperZ) have of course a different approach. They observe certain phenomena in the lab, and try to build models of those phenomena, finding out sometimes general laws of behaviour that way. And some take on the attitude that each phenomenon can have its own different laws, INDEPENDENT of what lies underneath. This is then a holistic approach: the whole follows laws that are independent of the laws followed by the underlying constituents.
I would first like to point out that "emergent phenomena" are, in themselves, NOT a proof that the holistic view is correct. Indeed, there are a lot of toy examples of simple laws governing constituents that give rise to "special" behaviour of a whole set of those constituents. Phase transitions included. The school example of the Ising model comes to mind of course. The problem is more with real-world situations, where 1) deriving the special behaviour of the constituents and 2) solving for the behaviour of the entire system is mathematically so hopelessly complicated that it is much more PRODUCTIVE to use the condensed matter people approach, and build directly a model around the observed properties, without bothering with the underlying constituents and their laws.
But the whole discussion is:
is this "model building approach" (practical holism) just a matter of getting results in a feasible way, or is this fundamental ? It is the discussion between reductionism and holism.
I have, however, an argument, that, to me, goes strongly against holism. It goes as follows. Any possible measurement we could make on a many-constituent system, and from which holistic models could be build, will have some (statistical or definite) regularity. In the reductionist vision, it will hence correspond to a property of the mathematical structure that maps onto the many-constituent system, as built up by the rules given by the theory that ALSO governs the few-constituent systems and for which the theory is supposed to be known. The mathematical property that corresponds to the measurement on the macroscopic theory will hence have a (at least Platonic) existence. It may be practically intractable, but it is supposed to exist (as in "existence proofs" in mathematics).
Now, there are two possibilities: or this mathematical property corresponds to the effectively measured property, in which case holism is not necessary (we DEDUCED the property from the fundamental laws of the constituents, exactly as reductionism claims), OR this mathematical property does NOT correspond to the measured property, in which case the theory of the fundamental interactions has been falsified, and there is a CLASH between the fundamental laws from which a certain prediction is derived, and the observations.
But in no case, we can have living happily together, a holistic vision, and a theory of interactions of fundamental constituents.
To make the above statement more concrete: imagine we are looking at the evaporation of water (a phase transition). We can measure, for instance, the bending of a light beam through a bottle of water, when we heat it by sending a current through a resistance in the water, and observe that when the water is evaporated, then the index of refraction has changed and the spot of the beam changes position. The position of the light beam corresponds to the "possible measurement" I was talking about in the abstract, above, and, *in principle* it corresponds to a clear property of the EM field (beam left or beam right), which is a property of the mathematical structure of the entire field structure of the whole experimental setup (including the matter fields of the electrons, protons,... in the water, the wire, the resistor, the battery, the light source...). No matter how mindbogglingly complicated this setup is, there is no reason why this mathematical structure doesn't exist: there are rules for setting up, say, the Hilbert space of 10^30 particles. Even though it cannot be done in practice, by a human, or a humanly designed computer, mathematically, this structure exists. As such, there will, in this mathematical structure describing the entire setup starting from fundamental principles, be an observable that corresponds to the measurement of the position of the beam after the resistor has been heating the water. It might be a probabilistic answer, but no matter, there will be *A* response to the question: is the beam here or there ?
This answer can be, or cannot be, in agreement with what is observed. But it is not INEXISTANT. The reductionist answer to a potentially holistic phenomenon EXISTS (in a mathematical sense). In most cases it is hopeless to FIND it, but nevertheless it exists.
In the case that there is agreement, we've then simply shown that (for the case at hand) no holism is involved: this aspect of the boiling of water is entirely contained in the elementary interactions of its constituents.
In the case that there is disagreement, well, we've falsified the theory of behaviour of the constituents of water in this case (because IF they were all following the proposed laws, then there wouldn't be any disagreement). But you cannot have that the constituents follow individually certain laws, and the whole follows OTHER laws, without there being a clash at some point.
What has all this to do with the OP ?
The point is of course that QM "pretends" to be a universal theory. So in the reductionist view, well, that means that it should make just as well sense to talk about the Hilbert space of states of a human being as it makes sense to talk about the hilbert space of states of the electron and proton in a hydrogen atom. Everybody agrees that it is for sure NOT PRACTICAL to talk about the hilbert space of states of a human being, but reductionists say: well, if that's to be the case for a set of atoms, it is also the case for a BIG set of atoms (unless my theory says that it only works for less than exactly N atoms). And then you run in a few difficulties. Bohr resolved the issue in the "holistic" way, by simply saying that there is some kind of "phase transition" between a classical world of humans and so, and the "weird microscopic world" of atoms. If you take on that view, there is no difficulty. The Born rule and the projection postulate simply TELL you how to link both theories. The totally unanswerable question in this view is then: WHEN do we apply the Born rule ? Because if there were a precise answer, that would be in reductionist terms!
There is of course a kind of "intermediate" view between the holistic and reductionist view. The mathematical structure of reality (the theory of everything) MIGHT not reveil all its aspects by only studying elementary interactions ; or, in other words, the laws we deduce from studying elementary interactions MAY of course be approximations to the "true" laws, which are so very good in the case of elementary interactions that we do not have data with enough accuracy to notice the approximation. As such, reductionists, with their misplaced arrogance, will only deduce "tangent laws" to the true mathematical structure of nature, and then claim that they know everything, if only they could solve the mathematical problem of many particle interactions. But that is not a blow to reductionism as such. It is only a blow to the hope that we can deduce the mathematical structure of reality from JUST elementary interactions. It might be then, indeed, that condensed matter experiments are more sensitive to the approximations made. We are now in the case of "disagreement" in the above explanation. But it has not undone the belief that there EXISTS a single mathematical description of all of nature. It only showed that there were limits to the structure we derived from our elementary interactions. If this is the case, however, our hopes of EVER deriving the true mathematical structure of nature may be totally hopeless, and as such, a practical form of holism is itself an emergent property of reductionism
As far as I know, the above situation has never been found (that there is a clear prediction of a macroscopic behaviour from elementary laws, and that observation is in contradiction with it). That's of course cheap, because of the mathematical difficulty in DERIVING the predictions for big systems, the test has not been conducted very often (predict interesting condensed-matter properties ab initio).
cheers,
Patrick.
