For those who know quantum mechanics or physical chemistry

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biostructure
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14 Feb 2009, 6:41 am

I just thought of this analogy a few days ago, and neither of the people I told it to has taken quantum mechanics, so they didn't really get it. The analogy relates to how socially highly involved people connect with the world around them.

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Most anyone who has studied quantum mechanics has looked at the “particle in a box”, i.e. a particle confined within a “square well” that is bounded by discontinuous jumps on either side. The wave function is zero everywhere outside the well but non-zero at most points inside.

Many of you will also have looked at the case of two separate square wells separated bya barrier of finite height and width, and what happens as they are brought together. If the wells are far enough apart, there are two wave functions that look for all intents and purposes like those for the single square well, one centered in each well. As the two wells approach each other, the two wave functions start to “mix”, and the relevant states of the system no longer consist of separate functions for each well, but rather of a symmetric function and an anti-symmetric function of different energies that look rather like the sum and difference, respectively, of the separate well wave functions. The original functions corresponding to each single well in some sense cease to exist. The amount of “mixing” depends on how similar in energy the bottoms of the two wells are.

Now for the mental stretch, imagine each person’s identity, or concept of self, as a wave function that corresponds to the well that is that person’s brain. Then, imagine two people in a room together in a social situation being like energy wells that are close enough that the wave functions overlap. Then, there is a new pair of wave functions that forms from this overlap, one of which corresponds to a shared identity and one that corresponds to deviation from that shared identity. For many people these seem to, for the duration of that encounter, replace the pure individual identities of the two parties.

For those who have studied molecular orbital theory, it’s obvious how this extends to larger groups. In a molecule, electrons no longer “belong” to individual atoms, but are theoretically delocalized over all atoms. When two molecules react (think cycloaddition, you O-chem buffs), the energy levels of each reacting molecule can be split again by the new interactions. By the time you put a large molecule together, the molecular orbitals look nothing like the original atomic orbitals.

So applying that to the social world, during the process of growing up, social groups join, fragment, and shift alignment in many different ways, and for people who are integrally a part of this structure, their “identity orbitals” are split and re-combined so many times by adulthood that it becomes very difficult to separate their identities from the larger society anymore. Part of each person’s characteristics are transferred from him to the rest of the group while part of the group is transferred back, just like each carbon atom in a benzene ring provides some electron density to the ring yet owes much of its reactivity to the rest of that ring. The entire group is not best described by the set of individual identities (which by now are in some sense hypothetical, as nobody knows what the members WOULD be like had they lived in isolation), but by a new shifted set that takes into account the mixing due to the overlap.
*********************************************************

This is an analogy I came up with for why I think many socially highly involved people seem to lack a well defined, distinct personality when looked at in isolation, and why they seem to be unable to see their feelings without reference to the norms of the society in which they live.



ruveyn
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14 Feb 2009, 12:23 pm

What does consciousness have to do with square wells?

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biostructure
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14 Feb 2009, 4:06 pm

ruveyn wrote:
What does consciousness have to do with square wells?

ruveyn


Nothing. They are only relevant in the sense that I figured the case of a square well was the one that most people would have looked at. The analogy I came up with has nothing to do with the shape of any particular wave function or the potential well that it corresponds to, but with the operation of how two or more states are "mixed". If this operation is not familiar to you (in a conceptual sense--actually computing it is very non-trivial and cannot be done exactly even in quite simple cases) then you probably won't get anything from the analogy.



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15 Feb 2009, 1:25 am

I can visualize your analogy, and believe it holds some merit.


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15 Feb 2009, 2:06 am

Yup, that'll work. Though, unless you're with fellow nerds, it seems less like a viable analogy than a way of trying to prove to other people that you think you're smarter than them. Not saying that's what you're doing, it works as a way for you to weed out who's more like you, but that's probably what the average person will think you're doing.



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12 Mar 2009, 5:04 pm

I agree fully with your analogy. I have a tendency to construct similar analogies myself and I have in fact done the same trio you mentioned. Do not worry, the phenomenon is well known and carefully covered within psycology. It is mostly used when an individual is moved from a familiar enviroment into another enviroment. After some time the new enviroment shows some characteristics of the old enviroment and the individual show a significant relatedness with its new enviroment. We can take this a bit further: If the individual is moved back to its orginal enviroment, the original enviroment will be affected while the individual regains some of its original characteristics. Both enviroments will have changed irreversibly, which only occurs in psycology and sociology.

Be careful. The converse of your analogy is not necessarily true. Stockholms syndrome is not applicable to physical chemistry. This is due to the (assumption) of using a state space, in which history has no meaning.



ruveyn
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12 Mar 2009, 6:39 pm

QuantumCowboy wrote:
I can visualize your analogy, and believe it holds some merit.


no ket should go out without a bra

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12 Aug 2009, 7:46 am

biostructure wrote:
Most anyone who has studied quantum mechanics has looked at the “particle in a box”, i.e. a particle confined within a “square well” that is bounded by discontinuous jumps on either side. The wave function is zero everywhere outside the well but non-zero at most points inside.

Many of you will also have looked at the case of two separate square wells separated bya barrier of finite height and width, and what happens as they are brought together. If the wells are far enough apart, there are two wave functions that look for all intents and purposes like those for the single square well, one centered in each well. As the two wells approach each other, the two wave functions start to “mix”, and the relevant states of the system no longer consist of separate functions for each well, but rather of a symmetric function and an anti-symmetric function of different energies that look rather like the sum and difference, respectively, of the separate well wave functions. The original functions corresponding to each single well in some sense cease to exist. The amount of “mixing” depends on how similar in energy the bottoms of the two wells are.

Now for the mental stretch, imagine each person’s identity, or concept of self, as a wave function that corresponds to the well that is that person’s brain. Then, imagine two people in a room together in a social situation being like energy wells that are close enough that the wave functions overlap. Then, there is a new pair of wave functions that forms from this overlap, one of which corresponds to a shared identity and one that corresponds to deviation from that shared identity. For many people these seem to, for the duration of that encounter, replace the pure individual identities of the two parties.

For those who have studied molecular orbital theory, it’s obvious how this extends to larger groups. In a molecule, electrons no longer “belong” to individual atoms, but are theoretically delocalized over all atoms. When two molecules react (think cycloaddition, you O-chem buffs), the energy levels of each reacting molecule can be split again by the new interactions. By the time you put a large molecule together, the molecular orbitals look nothing like the original atomic orbitals.

So applying that to the social world, during the process of growing up, social groups join, fragment, and shift alignment in many different ways, and for people who are integrally a part of this structure, their “identity orbitals” are split and re-combined so many times by adulthood that it becomes very difficult to separate their identities from the larger society anymore. Part of each person’s characteristics are transferred from him to the rest of the group while part of the group is transferred back, just like each carbon atom in a benzene ring provides some electron density to the ring yet owes much of its reactivity to the rest of that ring. The entire group is not best described by the set of individual identities (which by now are in some sense hypothetical, as nobody knows what the members WOULD be like had they lived in isolation), but by a new shifted set that takes into account the mixing due to the overlap.


Very interesting. It's almost like I have watched this sort of thing in action. I was trying to explain this sort of perspective to a friend a few weeks ago, but couldn't get it out right. I can't remember my quantum mechanics clearly, is the two well case caused by tunneling or entanglement? Or both?

The description of the benzene ring reminds me of what happens in conducting polymers but there it happens on a much larger scale. In conducting polymers though, the electrons stay localized and the polymer is non-conductive until radicals are introduced. At that point the wave functions spread and the remarkable properties of the macromolecules emerge.


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CaroleTucson
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12 Aug 2009, 9:15 am

All I know of quantum mechanics is a few things I've read here and there, but if I understand what you're getting at ... what you mean is that when people come together in a group, the whole of the group dynamic is more than the sum of the parts.

I think that's definitely true.

I hope I haven't grossly misunderstood what you were saying ...



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12 Aug 2009, 11:45 pm

This is a brilliant analogy; it definitely works since when people are together, they are under the influence of each other and their "energies" overlap; for example, if one person feels sad while the other person feels very hyper and they are together, the happy/hyper person would put themselves in the other person's shoes and become more calm and thoughtful, while the sad person would be cheered up by the happy person and become less sad. In social situations, everything usually tends towards the equilibrium, just like waves interacting with each other. When a person walks into a room full of serious people and lights the room with a wide smile, everyone in the room instantly becomes happier and the person who walks inside instantly feels the serious atmosphere and is influenced by it as well.
Actually, the combination of quantum physics and psychology might be significant at some level, but again it might not. If you have watched the movie What The Bleep Do We Know, you might find it either proposing an interesting theory or being complete bulls**t. It talks about how everyone's minds may be connected on a quantum level. One might argue that this is true, because there are social phenomena that prove the existence of a collective consciousness, such as the Bystander Effect, or even the fact that coincidences where people seem to know what others are thinking/experiencing. For example, it often happens that a person thinks about calling their friend and is about to pick up the phone when the phone rings and that same friend they were just about to call is on the line. But one might also argue that it is a ridiculous idea, and that all of the above is either pure coincidence, is a result or logical reasoning, or is a result of how people have been conditioned to respond to certain situations. But, after all, why do people get an emotional boost after interacting with others? Where do they get this emotional energy from?
So, by connecting quantum energy to human interactions, you might be onto something there.


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ruveyn
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13 Aug 2009, 4:28 am

MathGirl wrote:
This is a brilliant analogy; it definitely works since when people are together, they are under the influence of each other and their "energies" overlap; for example, if one person feels sad while the other person feels very hyper and they are together, the happy/hyper person would put themselves in the other person's shoes and become more calm and thoughtful, while the sad person would be cheered up by the happy person and become less sad. In social situations, everything usually tends towards the equilibrium, just like waves interacting with each other. When a person walks into a room full of serious people and lights the room with a wide smile, everyone in the room instantly becomes happier and the person who walks inside instantly feels the serious atmosphere and is influenced by it as well.
Actually, the combination of quantum physics and psychology might be significant at some level, but again it might not. If you have watched the movie What The Bleep Do We Know, you might find it either proposing an interesting theory or being complete bulls**t. It talks about how everyone's minds may be connected on a quantum level. One might argue that this is true, because there are social phenomena that prove the existence of a collective consciousness, such as the Bystander Effect, or even the fact that coincidences where people seem to know what others are thinking/experiencing. For example, it often happens that a person thinks about calling their friend and is about to pick up the phone when the phone rings and that same friend they were just about to call is on the line. But one might also argue that it is a ridiculous idea, and that all of the above is either pure coincidence, is a result or logical reasoning, or is a result of how people have been conditioned to respond to certain situations. But, after all, why do people get an emotional boost after interacting with others? Where do they get this emotional energy from?
So, by connecting quantum energy to human interactions, you might be onto something there.


I think you may be conflating emergent behavior with quantum effects.

Even in a purely deterministic regime, a complex system will manifest emergent and non-linear behavior. A very frequent confusion is the conflation of chaotic dynamics with quantum effects. In point of fact, Schroedinger's Equation is as linear and well behaved as can be as are all Hermitean operators are in Hilbert Space.

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13 Aug 2009, 5:41 pm

I can appreciate the intellectual elements that have gone into this analogy, but I do not feel it is a good representation.

An important aspect of humans is their interdependency. Note that this analogy posits an initial identity prior to overlap, but this is wrong. There is no identity prior to overlap, the state of overlap is necessary to life (newborns readily die without intervention, they are quite incapable of non overlapping/dependent survival), and the overlap is often posited as necessary to the development of identity.

The impression the analogy gives is quite contrary to this. It reads as though there is some initial state of identity that is transformed by interactions with other humans, whereas even before birth there is such interaction, and prior to anything that we would consider identity (in the sense of personal identity), such interaction is persistent and pervasive.



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14 Aug 2009, 7:45 am

What is this weird thing you people have with resurrecting long-dead threads?

It's interesting, though, that a book I read recently (Can the World Afford Autistic Spectrum Disorder?: Nonverbal Communication, Asperger Syndrome and the Interbrain) calls on a lot of fairly recent looking research to reach the same sorts of conclusions.



azulene
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17 Aug 2009, 12:09 pm

peterd wrote:
What is this weird thing you people have with resurrecting long-dead threads?


Why keep the threads if they are long-dead? Isn't this better than starting the same topic again?

peterd wrote:
It's interesting, though, that a book I read recently (Can the World Afford Autistic Spectrum Disorder?: Nonverbal Communication, Asperger Syndrome and the Interbrain) calls on a lot of fairly recent looking research to reach the same sorts of conclusions.


That book you read looks very interesting. What exactly does the author they mean by afford? Are they saying ASDs are a drain on the world?


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