Is there any difference in the nature of emergence in quantum and classical systems?
What is the difference between strong and weak emergence?
An emergent property of a system is one that is:
a. not present in the individual components of the system
b. difficult to predict a priori from a knowledge of the components and their interactions
c. independent of the finer details of the components
Equivalently emergent properties are
a. qualitatively different
b. usually discovered empirically and sometimes are given a reductionist explanation a posteriori
c. universal and stable to perturbations
This can be illustrated with the rigidity of a solid
a. the individual atoms that make up a solid are not rigid.
b. elasticity theory preceded crystallography
c. all solids are rigid, regardless of their chemical composition.
Emergence occurs in both quantum and classical systems. The properties that emerge can be distinctly different. Superconductivity and superfluidity are intrinsically quantum.
However, the associated issues and challenges: scientific, methodological, and philosophical are essentially the same. Emergence in classical systems is just as fascinating and challenging as for quantum systems.
Hence, last year I was surprised and disappointed to read the details of The Physics of Emergence program at the Templeton Foundation.
It appears to be based on two significant misunderstandings:
Emergence in quantum and classical systems is profoundly different.
In particular, quantum and classical emergence should be identified with strong and weak emergence, respectively.
I disagree with both the preceding two statements.
What is the difference between strong and weak emergence?
Some philosophers equate these with ontological and epistemological emergence.
For practical scientists the issue boils down to the following possible
answers to the question, "Is it possible to predict emergent properties?":
i. No. It is impossible.
ii. No. But, one can make postdictions, i.e., once the phenomena has been observed very smart people can construct reductionist models that explain the phenomena. [BCS theory is an example].
iii. Yes. But, it is difficult. BECs and topological insulators give us hope.
iv. Yes. We just need a little more computer power and creativity.
The believer in strong emergence says i. All the other answers amount to weak emergence.
Different scientists will answer ii, iii, or iv.
I would probably go with ii.
The only scientist who I think might answer i. is Bob Laughlin on his more cantankerous days.
Yet i. appears to be serious option for many philosophers. This seems to be largely because of the thorny issue of consciousness.
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I presume physicists would also assume consciousness to be weak emergence? I'm a neurobiologist, and that's my assumption.
ReplyDeleteI cannot speak for most physicists, but I suspect that most would say this. However, physicists tend to be philosophically naive and so may not appreciate the subtlety of the philosophical issues associated with consciousness.
DeleteFor what it's worth, I'm a naive physicist and make that assumption.
DeleteFor instance, I don't understand why a 3D computer, of sufficient complexity, could not make a cat, and therefore, make me too (this came up last night funnily enough)
I've been told by people who know more than me that this is nonsense, and I believe it. But I still don't get why.
woops, 3D printer
DeleteI think it depends on your definitions... Seeing as one can't - given a jumble of atoms - predict what crystal structure they will ultimately assume when cooled, even non-interacting "band structure"-esque physics is emergent.
ReplyDeleteBut even that aside... I'm not sure that the categorization above is helpful (I'm happy to be wrong), as one can easily fall into "no true Scotsman" fallacies about what one can or cannot predict about emergent behavior. "e.g. true emergent behavior is not predictable".
In this regard, I'm not sure "predictability" is the best measure of emergence. Its clear that new physics arises in the thermodynamic limit irrespective of whether we can predict it or not. So I think emergence retains its usefulness as a idea independent of preditability. The best example I can think of is BCS superconductivity. The BCS wavefunction with its finite # uncertainty is only an approximation for any real finite system. So reality falls short of the perfection as written down in BCS. There is no real system describable by BCS because all real systems have an actual real # of electrons. But this doesn't stop the BCS wavefunction from being some kind of archetype or platonic ideal acheivable only in some non-physically reachable limit.
Hi Peter,
DeleteThanks for the thoughtful and helpful comment.
Perhaps the post is not as clear as it should be. I am not suggesting non-predictability is the best measure of emergence. Rather, that believing in strong emergence means one abandons predictability AND microscopic explanations.
Don't the examples in iii mean that iii is at least sometimes correct? Or are you saying they're not emergence for some reason? What about solitons (did SSH predate the relevant experiments on polyacetylene), and anyons, and nonabelian anyons in FQHE. Aren't these all predicted from various theories that predated experiments? And what about spin liquids, or at least topological spin liquids?
ReplyDeleteAlso, this may seem like a silly one, but what about all the high Tc theories that aren't right? Aren't they predicting an emergence that, although it stemmed from experiment, incorrectly did so. So then, really they're predicting an emergence that hasn't been observed yet?
Finally, why would you suggest something like BCS wouldn't have been predicted without the experiments? Given a computer and a lot of time, those much smarter than me might have gotten there. I mean, there's nothing terribly exotic in BCS is there? FQH I'd believe, because there's no order parameter, and so it's really very exotic I think. But given the concept of OPs, I'd be surprised if we'd never gotten there if liquid Helium hadn't been invented (or whatever the crucial experimental step was 100 years ago).
With all these people doing exact diagonalisation of fractionally filled Chern insulators, I wouldn't be surprised if genuinely new emergent properties were predicted long before experiment. Unless you're right, and ii is basically correct.
Hi Tony,
DeleteA few points of clarification.
There are plenty of cases where people have made successful predictions from an effective Hamiltonian [e.g., a Heisenberg model]. The issue is can one start with Coulomb's law and Schrodinger's equation and predict a new phase of matter. The Laughlin-Pines 2000 PNAS paper claims no. They specifically consider the case of superconductivity and flux quantisation.
I see. Thank you for the clarification.
DeleteI don't quite appreciate the significance of the distinction (presumably words akin to "fundamental" would arise), but I agree that this particular approach may well be impossible - though I hope it's not.
So FQHE (5/2 at least) doesn't count because Coulomb is approximated with a pseudopotential? Or because CFT preceded ED?
Maybe Laughlin-Pines will clarify this for me - thanks.
I've always thought that emergence just represents a particular class of properties of a physical system, namely those that are independent of details of the microscopic model. This leads to two interrelated approaches
ReplyDelete1. Descriptions in which the microvariables do not appear. This is exemplified by thermodynamics, hydrodynamics, and perhaps reaches its apotheosis in the study of critical phenomena. To quote Michael Fisher (RMP 1998)
...the order parameter, as a dynamic, fluctuating object in many cases intervenes on an intermediate or mesoscopic level characterized by scales of tens or hundreds of ang- stroms up to microns (say, 10^6.5 to 10^3.5 cm)
(love those half integer orders of magnitude!)
2. The study of grossly simplified microscopic models (Anderson, Hubbard, Kondo, etc.) that are presumed to nevertheless capture the essence of the phenomena (which usually means: describe the same phases, have identical coarse grained or hydrodynamic descriptions, etc.).
The emergent extremist's point of view I'd caricature as: I can't predict the Tc of a superconductor, therefore nobody can, and anyway it's not interesting.
However, the boundary between the two types of properties (emergent and non-emergent) is perhaps fuzzier than people admit. To continue on the theme: doesn't any repulsive Fermi system have a superconduting transition (after Kohn--Luttinger)? Then the central problem of high Tc is to explain why a certain (non-emergent) property (namely Tc) has the value it has.