Can Complex Systems Lead to Emergent Phenomena?

[Tom McCurdy]

I have been saying it since august that I would get my theory of eveyrthing website going when break started. Well break has arrived and I finally got www.utoe.org properly linked... sort of it will work if you go there but I still need some url masking. Anyway, I need some suggestions on what I should do next with the site. I know for a while Marlon was really excited about starting the site, and Marcus has helped with a lot as well. The site is fully automated right now but needs content. I was hoping to have it become a resource for students to use.

I need to brush up on String theory as well... I have been out for a few monthes... :( Anyway I also am working to get LATEX into a forum... if anyone knows who PLEASE contact me

aim: tm mccurdy 07
email: tom@quantumninja.com
or pm me.

Anyway updates to come... let's see if we can't get this thing off the ground. This also will serve as the location for the LQG forum that we were talking about... I may switch to invision or Vbulletin though sometime... right now its PHPBB, which I have actually come to like.

 

[Tom McCurdy]

I am starting to recollect links about String theory and such... If you have any links please send them to me. Once posted on the site people should be able to rate the usefullness of the site which will help filter out the good from the great.

 

[ZapperZ]

I guess your "content" will never include those articles by Laughlin, Anderson, etc. that challenges the notion of a "theory of everything", will it?

Why do people who barely understand String theory but are obsessed with it often confuses it with the "theory of everything"?

Zz.

 

[arivero]

Besides forums, you could also add a WikiMedia area. It could be useful to bake crude articles. If your site has LaTeX, then WikiMedia provides for inline math. If not, I can provide a mimetex module. My unique doubt is the compatibility of passwords between both systems.

 

[Tom McCurdy]

I guess your "content" will never include those articles by Laughlin, Anderson, etc. that challenges the notion of a "theory of everything", will it?

Why do people who barely understand String theory but are obsessed with it often confuses it with the "theory of everything"?

Zz.

I understand that String theory is not the theory of everything, however it is the most well known theory that many feel may one day lead to the theory of everything. The site is supose to be about everything related to the theory of everything, includding things that challenges it. If you would be kind ennough to provide links I will immediatly add them to the site.

-tom

 

[Tom McCurdy]

Besides forums, you could also add a WikiMedia area. It could be useful to bake crude articles. If your site has LaTeX, then WikiMedia provides for inline math. If not, I can provide a mimetex module. My unique doubt is the compatibility of passwords between both systems.

I am not sure exactly what you mean by adding a wikimedia section. I kind of guess and created this section for the site http://www.quantumninja.com/wiki/ it will be used soley for www.utoe.org and is off my main server. I hope this is what you wanted. I am trying to figure out how to add latex to the forums right now but my php guy has gone on vacation it seems. ... what is a mimetex module?

-tom

 

[Tom McCurdy]

I did some searching on mimetex and found out its site, it seems very nice.

 

[ZapperZ]

I understand that String theory is not the theory of everything, however it is the most well known theory that many feel may one day lead to the theory of everything. The site is supose to be about everything related to the theory of everything, includding things that challenges it. If you would be kind ennough to provide links I will immediatly add them to the site.

-tom

You seem to be confusing the idea of "unification" with "theory of everything". Note that many physicists, especially condensed matter physicists, will point out that "unification" is NOT the same thing as "theory of everything". It may be a TOE for reductionism, but it certainly can't claim to be a TOE for physics.

I have written a lengthy essay on this in my Journal with ample citations to prominent papers.

Zz.

 

[Tom McCurdy]

I understand that unification can happen without a toe... isn't that some goal of LQG? anyway its the only domain name i could get... people steal all the good ones, thanks for the journal I will add it to my site.

 

[Tom McCurdy]

I assume you mean this

There have been frequent claims, both from legitimate sources and quackeries, of the possibility of finding something called the Theory of Everything (TOE). Supposedly, such a theory would contain ALL the necessary interactions that would be able to, in principle, describe ALL the phenomena (at least the existing ones) that we have observed.

We won't talk about the quackery aspect of this. The legitimate aspect of the belief in a TOE is due to the fact that there are only 4 fundamental interactions that are responsible for all the phenomena in our universe that we know of: gravity, electromagnetic, strong, and weak interactions. There is a strong belief (and desire) that all 4 of these fundamental interactions can be unified into a single consistent description. Already the electromagnetic and weak interactions have successfully been unified into an electroweak theory. There are every indication that the strong interaction will be next. Gravity might be the last and most difficult. However, assuming that it can be unified with the others, one then have what is called the Grand Unified Theory (GUT). Most people claim that then, we have achieved the TOE.

The implicit assumption in making such a claim that GUT = TOE is that the principle of Reductionism works. Reductionism is a philosophy which, to state rather crudely, everything in the universe can be reduced to the basic interaction at a single particle case. Then, by simply adding a higher level of complexities, one can then recover all the other more complicated, macroscopic phenomena. So if you know all the interactions that an atom in a human skin has, then by including more and more of the number of atoms/molecules, you will eventually be able to describe all the properties of the human skin. Hence, once you know all there is to know at the single particle scale, then everything else is just a matter of complexities. This then leads to the notion that GUT = TOE.

Most particle and high energy physicists espouse this point of view. I would single out Steven Weinberg as the prominent champion of this school of thought. String theorists have also been known to slip up now and then by claiming that unification of gravity with quantum mechanics is a step towards GUT and TOE.

However, there is another school of thought that would contradict the idea that GUT = TOE. This school of thought is made up of condensed matter physicists, which make up the largest percentage of practicing physicists. The most prominent condensed matter physicists who have stated their opposition to the reductionists idea are Phillip Anderson, Robert Laughlin, and David Pines. They brought up examples that are described as "emergent" phenomena, often seen in condensed matter. These are phenomena that only occurs, or can only be defined, when there are a gazillion interactions occurring. Examples of these are superconductivity, fractional quantum hall effect, magnetism, etc. Laughlin, for example, argued that if you try to write down all the interactions of a single electron in a conductor, no matter how many electrons you add up in your interactions, you will NEVER recover the superconductivity phenomenon. Superconductivity is an emergest phenomenon that is a result of a many-body interaction. The starting point in describing such a phenomenon MUST start not from a single particle scenario, but from a many-body ground state scenario. This effect emergers out of a many-body interaction and will simply disappears if one tries to take it apart to a single-particle level.

What this boils down to is the claim that GUT is the TOE for reductionism, not the TOE for physics. Anyone claiming the existence of any form of TOE will have to seriously address the glaring omission of a huge body of phoenomena from condensed matter physics, which holds some of the most highly verified observations with the highest degree of certainty in any field of physics.

For more resources on emergent phenomena from condensed matter physics and why they contradict the claim of GUT=TOE, read the references below:

1. http://www.pnas.org/cgi/reprint/97/1/28.pdf
2. http://www.pnas.org/cgi/reprint/97/1/32.pdf
3. http://arXiv.org/abs/hep-th/0210162
4. R.B. Laughlin, Rev. Mod. Phys., v.71, p.863 (1999).

 

[Tom McCurdy]

by the way zapper your article has been added to the site... um I just said it was by ZapperZ

 

[marlon]

I understand that unification can happen without a toe... isn't that some goal of LQG? anyway its the only domain name i could get... people steal all the good ones, thanks for the journal I will add it to my site.

If you want/need more clarification on LQG, please feel free to use the introductory post, i wrote in my journal...


regards
marlon

 

[Haelfix]

Here's a simple thought experiment to contradict Laughlin's point of view.

Assume that he is right.

Now, consider a many body system (say an electron gas) with some emergent phenomena. Now, remove one electron from the system. Surely removing one electron amongst gazillions won't affect the statistics of the system or even the notion of an emergent system. Now keep repeating this until you arrive at one of two things.

1) You no longer have the emergent phenomena
2) You no longer have any electrons.

If answer 2 is correct, that implies the dynamics and physics existed in one electron. A contradiction.

If answer1 is correct (say the emergent phenomena is diminished a tiny fraction of a statistic each time you remove an electron), I have just passed a point whereby identically ONE particle effects whether the phenomena exists or not. Since the particle is fundamental, no reduction is possible on that side (I can't slice an electron) ergo the physics must entirely lie within that dynamic. Again a contradiction.

You can make this argument precise, even in the context of a quantum mechanical system (say by the probability of the relevant phenomena occurring), indeed the actual form of the potential typically involved shows that it admits an additive algebra of some kind.

 

[ZapperZ]

Here's a simple thought experiment to contradict Laughlin's point of view.

Assume that he is right.

Now, consider a many body system (say an electron gas) with some emergent phenomena. Now, remove one electron from the system. Surely removing one electron amongst gazillions won't affect the statistics of the system or even the notion of an emergent system. Now keep repeating this until you arrive at one of two things.

1) You no longer have the emergent phenomena
2) You no longer have any electrons.

If answer 2 is correct, that implies the dynamics and physics existed in one electron. A contradiction.

If answer1 is correct (say the emergent phenomena is diminished a tiny fraction of a statistic each time you remove an electron), I have just passed a point whereby identically ONE particle effects whether the phenomena exists or not. Since the particle is fundamental, no reduction is possible on that side (I can't slice an electron) ergo the physics must entirely lie within that dynamic. Again a contradiction.

You can make this argument precise, even in the context of a quantum mechanical system (say by the probability of the relevant phenomena occurring), indeed the actual form of the potential typically involved shows that it admits an additive algebra of some kind.

I think you may have missed his point. It isn't that you start with a physical system one electron at a time. You start with a gazillion electrons at a time, but you try to describe the system by looking at all the interactions on a single electron, and then adding up more and more to the description of the system. What he is saying is that if you already have superconductivity, and then you try to describe this by writing down the equation of motion, or the wavefunction of ALL the electrons in the system (a highly improbable endeavor, at this stage), you can never recover or derive the superconducting effect. This isn't physically adding or taking away one electron at a time.

On a related note, there ARE subject areas that are studying the boundary between collective emergent phenomena and beyond. Such "mesoscopic" research area so far have not found a "phase transition" or a crossover between the two regime.

BTW, in a collective behavior, an electron CAN, in fact, be "chopped up" into a smaller entity - the fractional quantum hall effect and the fractional charge. There has been ZERO attempts to explain this via reductionism because how do you explain that if you have a bunch of stuff coming together, you can get effects the smallest of which is LESS than the individual constitutents within that bunch of stuff. Such fractional effects so far can only be explained using Laughlin's many-particle groundstate wavefunction.

It is always a risk in trying to explain collective emergent phenomena via an analogy. But when I had to do it, I always point out the similarity of a mob behavior. You can have individuals within a group of people being mild-mannered, law-abiding citizens. But somehow, when you put them into a large group of people, be it at sporting events, or public celebrations, the mob mentality takes over and together, they become a loud, obnoxious, rude crowd. You cannot recover this mob behavior if you simply try to look at the behavior of that individual in isolation. This isn't the best analogy to illustrate this phenomena, but it might get the point across.

Zz.

 

[Haelfix]

I simply don't agree.

To use your analogy, I would say its some fundamental property inherent in the individual, that allows for the mob mentality. It is 'turned on' by the presence of others, but using my little gedanken it should imply the relevant details lies hidden in the naive and simple looking interaction with identically one other person. Since we understand the two body problem, we have the full picture even though its beyond our calculational ability to predict the full picture when millions of bodies are present.

I hate to use Wolfram as an analogy, but its fairly easy to show that fairly simple rules can lead to very complicated and chaotic looking end states when iterated. So too is it the case with say an electron gas.

All this is fairly well understood, the example I had in mind was not some cooper pairing, or a fractional quantum hall effect, but rather coulomb screening. Clearly it looks like we have different physics going on, a mode which obeys a different coulombs law... Not good! But actually, in this simple case, you can see how it arises with just a few particles present, and with the aid of a computer the fundamental equations do lead to something like that. In that case its just a bad approximation that naively makes you lose sight of the real analytic picture. Descartes demons strike! Hence, I see no real reason to expect that there is any fundamental obstruction to doing the same for fqhall effects.

If you really want to muck up my point of view, you would argue with quantum field theory. B/c unlike classical mechanics with special relativity, or quantum mechanics without special relativity we have no real way of treating a system with only one or two degrees of freedom... And the obstruction is very severe (not calculational, but rather physical), namely unitarity. Mathematically, its infinite degrees of freedom that we simply *must* consider. So something about subtracting infinite quantities (fields) from other presumably larger infinities makes things completely illdefined and out of our league. Its rather ironic that a theory which is used to describe the ultimate in reductionism, is completely unable to be separated from a many body formalism.

Incidentally the people who work on the intersection between few and many body problems are IMO completely heroic, but probably wasting their time. Their non result isn't too surprising though if you think about it. The order of computation as you add bodies scales as roughly n factorial. For fun, and since we're being inpresice anyway, try expanding sterlings approximation out, and notice all the nontrivial mixings involved.

 

[Tom McCurdy]

Besides forums, you could also add a WikiMedia area. It could be useful to bake crude articles. If your site has LaTeX, then WikiMedia provides for inline math. If not, I can provide a mimetex module. My unique doubt is the compatibility of passwords between both systems.

i had trouble installing laytex we needed my host to install some files that were going to cost money, would you be able to instal your mimetex module? Also what should I do with the wiki page i created..

 

[ZapperZ]

I simply don't agree.

To use your analogy, I would say its some fundamental property inherent in the individual, that allows for the mob mentality. It is 'turned on' by the presence of others, but using my little gedanken it should imply the relevant details lies hidden in the naive and simple looking interaction with identically one other person. Since we understand the two body problem, we have the full picture even though its beyond our calculational ability to predict the full picture when millions of bodies are present.

I hate to use Wolfram as an analogy, but its fairly easy to show that fairly simple rules can lead to very complicated and chaotic looking end states when iterated. So too is it the case with say an electron gas.

Again, as I said, it wasn't a perfect analogy.

As far as Wolfram goes, he has publically stated that he cannot duplicate superconductivity and other emergent phenomena. He said this much when questioned while giving a seminar at Brookhaven a few years ago that I attended. In fact, there are no new physics in his "new physics". So no, we still do not have any evidence that merely by adding complexities, we can obtain these emergent phenomena.

All this is fairly well understood, the example I had in mind was not some cooper pairing, or a fractional quantum hall effect, but rather coulomb screening. Clearly it looks like we have different physics going on, a mode which obeys a different coulombs law... Not good! But actually, in this simple case, you can see how it arises with just a few particles present, and with the aid of a computer the fundamental equations do lead to something like that. In that case its just a bad approximation that naively makes you lose sight of the real analytic picture. Descartes demons strike! Hence, I see no real reason to expect that there is any fundamental obstruction to doing the same for fqhall effects.

Unfortunately, this isn't obvious, at least not to me and to a lot of very knowledgeable people. Fractional quantum hall effect that is also related to the fractional charges have not been "derived" using what you described. This is currently a fact. These effects do not just continuously merge and slowly appear as with your coulomb screening. In many cases, these things are truly a phase transition (such as superconductivity). So no, it is not obvious.

Zz.