Questions About Quantum Theory: What's Wrong?

[Locrian]

From everything I read they derive reductionist models from emergent properties, not the otherway around. And that's the trick, isn't it?

 

[ZapperZ]

There is something potentially misunderstandable here.
To make it clear, this knowledge is NOT practical knowledge on how to handle the formidable mathematical problem. The knowledge is just the axioms of "reductionist" physics at an appropriate level (say, non-relativistic quantum mechanics). So, in the case of condensed matter, it is the masses, charges and spins of the nucleae, the charge and spin of the electron, the EM interaction (maybe treated semi-classically, maybe some elements of QED have to be included).

In that case, I don't understand what you mean by "point 3)" because my points 1) and 2) are logically complete:
point 1) says that the fundamental laws as we know them, are responsible for the collective phenomena
and point 2) says that they aren't.
I don't see room for a point 3), except if it would mean some necessary change in our understanding of our fundamental "reductionist" laws, but that brings us back to point 1) ! We then simply didn't have the correct laws to start with, then, and once we're using the correct ones, we ARE back in the reductionist scheme.

OK, let's try this with a possibly-bad analogy (meaning if this doesn't work, I have wiggle room to sneak out of it.) :)

Look at the behavior of a crowd at a sporting game. I don't know about you, but being near the Chicago Cubs baseball field (Wrigley Field), I've seen some "interesting" fan behavior when they're in a large group of people. Yet, if you simply take that person out, analyze his behavior, you could get a mild-mannered, law-abiding citizen. Yet, put him in a group of people at a baseball game, and he's a foul-mouthed maniac. The individual behavior cannot explain the "collective" behavior.

In condensed matter, there are "higher order" collective behavior that simply do not emerge out of looking at all the interactions at the individual particle level. Does that mean the interactions at the individual particle level are completely irrelevant (your Point 2)? No. Without those, you don't have the material or the fabric. But the fabric does not explain the shape of the clothing, or the pattern of the collar, or the shape of the sleeves, etc. (Your Point 1). There is an additional "hand" at work here.

For CM physicists, what additionally indicates that this is the case is the so-called "quantum protectorate"[1], in which the "uneveness" and disorder at the individual particle scale do NOT play any role in various collective behavior such as superconductivity. These emergent phenomena are immune to such details.

Zz.

[1] P.W. Anderson, Science v.288, p.480 (2000); http://arxiv.org/abs/cond-mat/0007287

 

[seratend]

In condensed matter, there are "higher order" collective behavior that simply do not emerge out of looking at all the interactions at the individual particle level. Does that mean the interactions at the individual particle level are completely irrelevant (your Point 2)? No. Without those, you don't have the material or the fabric. But the fabric does not explain the shape of the clothing, or the pattern of the collar, or the shape of the sleeves, etc. (Your Point 1). There is an additional "hand" at work here.

For CM physicists, what additionally indicates that this is the case is the so-called "quantum protectorate"[1], in which the "uneveness" and disorder at the individual particle scale do NOT play any role in various collective behavior such as superconductivity. These emergent phenomena are immune to such details.

Zz.

It seems that the problem always stays with the interpretation of the words (causality, etc...).
Probability theory has given the main result; the weak law of large numbers. From a collective set of independant objects (choosing the good representation), we have a deterministic global result that does not depend on the individual values (we can even mix different sets of independant objects). In other words there is no functionnal relation (a cause, one possible interpretation of causality) between the global average value (for example the form of the collection of objects) and the values of the individual objects.
Therefore, we may say that this collective set of objects has porperties that do not depend on the individual object values.

This is a very formal statement (more strict versions can be found in probability texts).
Therefore, what Zzaper says about condensed matter seem to be very raisonnable.


Seratend.

 

[reilly]

If the Law of Large Numbers, in any form, describes some sort of emergent property, then this property is virtually universal, almost as much as is the use of algebra in the sciences. That is, the LLN can apply to clinical trials of new pharmaceutical drugs, survey research, compilation of the "best" particle data from individual laboratories, calibration of lab equipment, advertising evaluations,...

Remarkably free of assumptions as it is the LLN is, it does require a few restrictions on the sample. The classic formulation requires a sample space of independent events
all governed by the same probability distribution. And, most importantly, this distribution must have a finite variance. So that, ultimately, the big errors are less probable, and they average out -- and this happens for smaller and smaller big errors, until the distribution of the mean becomes a very sharp Gaussian, as the sample size goes to infinity.

My sense is that the LLN is a powerful property of our language, and, perhaps the idea is more reflective of "emergence" in human thought rather than in nature.

Regards,
Reilly Atkinson

 

[Stingray]

Zz, your sports analogy seems to imply that "reductionists" don't look at interactions. I know that's not what you really meant, but the analogy breaks down without it.

For CM physicists, what additionally indicates that this is the case is the so-called "quantum protectorate"[1], in which the "uneveness" and disorder at the individual particle scale do NOT play any role in various collective behavior such as superconductivity. These emergent phenomena are immune to such details.

What is the difference between this and what happens in the regimes where classical physics is (nearly) correct? Isn't that also a "quantum protectorate?"

 

[seratend]

If the Law of Large Numbers, in any form, describes some sort of emergent property, then this property is virtually universal, almost as much as is the use of algebra in the sciences.

In addition, it is the way to reconciliate the determinist with the probabilist view. In other words, each deterministic value may be viewed, formally, as the value of a collection of random variables (while we are used to view probability results as unknown deterministic variables).

Remarkably free of assumptions as it is the LLN is, it does require a few restrictions on the sample. The classic formulation requires a sample space of independent events all governed by the same probability distribution. And, most importantly, this distribution must have a finite variance.

Note (for the users of PF) this is the weak LLN. The strong LLN does not require a finite variance, just a finite mean value. There are other formulations (mainly with the finite variance restriction) that allow different mean values for each random variable and we still get a "deterministic" result.

Seratend.

 

[ZapperZ]

Zz, your sports analogy seems to imply that "reductionists" don't look at interactions. I know that's not what you really meant, but the analogy breaks down without it.

Humm... does the fact that you didn't comment on my "fabric" analogy means that it is ok? :)

I'll be the first people to point out that analogies are very, very weak technique to illustrate physics ideas (and I have!). I would have chopped up that analogy even more vigorously than what you did. :)

What is the difference between this and what happens in the regimes where classical physics is (nearly) correct? Isn't that also a "quantum protectorate?"

I dunno. I've never thought about that other than to point out that phenomena falling under the quantum protectorate regime are not classical phenomena. Whether they share similarities in "principle", that's something I do not know.

Zz.

 

[Stingray]

Humm... does the fact that you didn't comment on my "fabric" analogy means that it is ok? :)

The fabric analogy did help, but I'm still a little confused. Once you know the fabric, you could in principle find all possible types of clothing that could be constructed out of it. Of course you're right that knowing the fabric won't uniquely fix the end result, but the class of all possible results can be known beforehand (again, in principle).

Going back to physics, it seems like different types of laboratory materials could in principle be "predicted" as different subsets of the class of all possible "stable" states with a sufficiently large number of degrees of freedom, large mass, etc. Of course defining all of those things appropriately, and carrying out the solution from microscopic physics would be extremely difficult, but it is logically possible.

Most anything in physics can be put into the form of an initial value problem (at least formally). Initial data are specified, and then appropriate evolution equations are used to find what happens in the future (or past). The set of all possible initial data sets is usually extremely nontrivial. The laws of physics impose constraints on what is allowable even at one instant in time. Are you taking this into account?

If I'm still misunderstanding you, maybe you could point to one these Laughlin-Anderson-Weinberg debates. Google didn't turn up anything useful.

 

[vanesch]

Look at the behavior of a crowd at a sporting game. I don't know about you, but being near the Chicago Cubs baseball field (Wrigley Field), I've seen some "interesting" fan behavior when they're in a large group of people. Yet, if you simply take that person out, analyze his behavior, you could get a mild-mannered, law-abiding citizen. Yet, put him in a group of people at a baseball game, and he's a foul-mouthed maniac. The individual behavior cannot explain the "collective" behavior.

This would mean that if I only have one individual, I cannot obtain a behaviour that is observed in the crowd. But let us now take our single individual, and put 3D goggles and earphones on his head, and (very important !) fill his belly with 4 cans of beer. Now let us play the movie of a crowd in a stadium on his 3D headset, in such a way that our individual is convinced to be sitting on his chair in the stadium. I'm pretty sure we will now observe similar "interesting" behaviour!
But that would then mean that this behaviour is "reductionist-wise" encoded into his individual behaviour, and can be displayed given the right visual, alcoholic and auditory stimuli, even if those stimuli are normally not present in every-day situations (and hence the behaviour seems to be different: we're simply exploring a different input-output range of the model of behaviour in every - day situations and in the stadium). And I'm pretty sure that when writing out the statistical physics model of several such individuals, in a relationship as is the case in a stadium, the collective behaviour comes out as one of the solutions.

In condensed matter, there are "higher order" collective behavior that simply do not emerge out of looking at all the interactions at the individual particle level. Does that mean the interactions at the individual particle level are completely irrelevant (your Point 2)? No.

I didn't mean to say that they are completely irrelevant. I just meant that point 2 indicated that they are not the cause of the collective behaviour. In that if you could calculate, without any un-allowed for approximation, the expected collective behaviour purely based upon the "reductionist" model, but taking into account all interactions, you would find a DIFFERENT behaviour than what is the true behaviour. I have to say I find it extremely difficult to believe that there are many physicists out there holding such a view.
Of course, as it has been pointed out, there are often different cases possible, depending on initial conditions.

For CM physicists, what additionally indicates that this is the case is the so-called "quantum protectorate"[1], in which the "uneveness" and disorder at the individual particle scale do NOT play any role in various collective behavior such as superconductivity. These emergent phenomena are immune to such details.

That, by itself (universality and so on) is not an argument for point 2). You can indeed have universality emerging from big classes of underlying reductionist models, as long as they satisfy some broad properties. This is indeed, as has been pointed out, of a similar behaviour as the law of large numbers: many different "reductionist" distributions, when added together, result in a gaussian distribution.
But that doesn't mean that you cannot obtain that gaussian starting with a given reductionist distribution ! Indeed, the gaussian is very well simulated if you do a monte carlo simulation.

However, it is a clear indication of the opposite claim: in certain cases, the collective behaviour is so universal, that it doesn't contain much information anymore of the underlying reductionist model. So you cannot use these data to deduce the reductionist model of individual behaviour out of the collective behaviour. This is what puts "barriers" between different scales of observation, and it is at the same time a curse and a blessing. It is a blessing, because it allows you to forget about the individual behaviour, and start from scratch from the collective behaviour, and it is a curse because the information of the individual behaviour is largely lost, and you can only do "elementary particle" experiments to find out precisely the individual behaviour.
But again, this is NOT point 2).
Point 2 says: "reductionist behaviour" NOT -> "collective behaviour"
Universality says: "collective behaviour" NOT -> "reductionist behaviour" because MANY reductionist behaviours lead to the same collective behaviour.

cheers,
Patrick.

 

[selfAdjoint]

In the examples in the paper, it seemed to me that the emergent symmetries were already present in the high-energy short scale primary phenomena, but hidden or broken by the intense short range interactions. It was only by "integrating out" those short range effects that the symmetries became visible. But when you integrate out the individual behaviors, what you get are the collective behaviors, and so it is these that exhibit the symmetries.

Information has not been gained by this integration, rather the contrary, but something that was obscured has been made plain, like squinting your eyes to see a shape in the bushes.