atoms hopping around

Barbara Capogrosso-Sansone defended her dissertation this summer, and I was lucky enough to wangle an invitation. What follows are the thoughts of a wannabe social scientist/activist who imagines significant connections between the languages of math (especially quantum physics) and human words as they are spoken and written in intentional conversation with one another. You may decide that the t-shirt John wore for the event describes me perfectly:

“I live in my own little world, but its ok … they know me there.”

On the off chance that I might be on to something, well, you’ll read what a mishmash I’ve made of Barbara’s quantum Monte Carlo study of ultracold bosons in optical lattices. My attention was captured immediately because she’s working with a Bose-Einstein condensate (BEC). Some folks have suggested that something like a BEC might be responsible for consciousness. (It can’t be an actual BEC, because our brains – let alone the rest of our rather incredible bodies – cannot live at the supercold temperature involved.)
The general thing that I’m thinking, as I mentioned to Don in my exuberance that day, is that we are all really talking about the same thing, we’re just using different languages to do the talking. “We” who? What “same thing”? Ah. I can’t quite answer that, yet. The “what” is something along the lines of spirit – but it goes by many, many names: energy, power, life, creativity, inspiration, vision, to name those that leap to mind today. Perhaps it is the answer E.O. Wilson seeks, a theory of consilience. Perhaps it is the miracle Wendell Berry argues can never, ever, be captured by any equation humans are able to devise. Berry, btw, is also a fantastic resource on living in the presence of fear.
As to the “we” – I’ve got a rather broad criteria that includes anyone/everyone trying to find solutions to the challenges that face humanity today. Specifically, though, I aim to include the people I’ve met at UMass Amherst, in all our varied fields and disparate ambitions. In the midst of Barbara’s exegesis on the dipole interaction and quantum phase transitions, she said there’s something intriguing occurring in these optical lattices:

atoms hop around

Mathematicians (perhaps more than any other kind of physical scientist?) deal with the observable, the measurable, the essentially reliable. Social scientists, on the other hand, strive for the predictable but are constantly having to engage the sheer diversity of actual human responses to living, i.e., the social implies the unbounded. There may be parameters to the “hopping” we can do, but the rules that determine these parameters are not yet known.
Honestly, I’m not sure I want those parameters defined too accurately, but I do think we (humanity) need to figure out the forces that can be used to alter the realities we live in, largely because the current conditions are frightening to those of us with relative privilege and still totally suck for the majority of the world’s population. My basic thesis is that language is the tool.
k through the trees.jpg

The secondary thesis (if you’ll just go along with the first one for awhile), technically an hypothesis, is that language is energy – quantum energy, in fact, full of potential that can be experientially realized. The energy is in the transformations created through the assignment of meaning – both to things said and to things perceived but unsaid. Barbara spoke of the Bose-Hubbard model (1989), and mentioned a kinetic energy term, “hopping matrix element” (“t”). Does it work as an analogy? Language operates within fields of understanding and mis- or non-understanding. We in the West, especially) tend to privilege “understanding,” but misunderstanding is a potent space in-and-of-itself (see Chang).
Listening carefully to the language of math (especially by teachers of math and scientists using math), I hear metaphors of social interaction: “onsite repulsion” (e.g., prejudice?) “localized atoms” (e.g., jargon, culturally-specific terminology?), “zero compressibility” (no range of possible interpretation?), superfluid state (meanings in flux?) “Each line,” Barbara explained a graph, “represents a particle, [these are] world-lines.” Sounds like discourse trajectories to me! There are “hopping events” and “periodic boundary conditions in time.” Could these be akin to particular complexities in conflict negotiation and other difficult forms of problem-solving?
What I find most instructive concerning the language of math that I think social scientists could learn from, is that when mathematicians come up against a dilemma, they invent a way to deal with it. Tell me the truth, what is the correlate in real life of imaginary numbers? Barbara’s work goes even further than imaginary numbers, she is working with imaginary time.* Her atoms, somehow inversed in temperature, move in imaginary time, then hop to their nearest neighbor even though they could go somewhere else. Now, I do not know the significance of this in terms of physics, but if I extrapolate to the ways that discourse works, I would say something is indicated to the effect that simply reversing the conditions leads to a similar effect. Am I interpreting accurately enough? Flip the dynamics of oppression, it’s still an equation of privilege/disadvantage. I know I am reaching here, so some of you that KNOW the math might explain how well the analogy does or doesn’t hold. Basically, (it seems) some attractive force remains at work and effectively reduces the range of possibility to only that which is closest, even though more distant positions are possible (and, socially at least, probably more desirable).
Ok, I admit I’m straining a bit since so much time has passed since the event. My thoughts now are based on interpreting my notes, rather than recalling what excited me in the actual moment. Still, Barbara is working with mechanisms (a worm algorithm, winding numbers, superfluid stiffness) that enable the sampling of topologically different configurations, generating “a mass in order to calculate superfluid stateness.” Again, it seems there is a calculation occurring across time and space that allows the identification of relativistic behavior, specifically, particle-hole symmetry.
Let me return to language, meaning, understanding and its opposite. What I say (these words I type) could be imagined as “particles”; they can only be understood if a suitable “hole” exists for reception. Gaps are crucial, of course, and low energy levels always seem a good idea (especially as we enter the age of conservation). Which means, as Barbara says,

We need to create particles and holes at the same time.

If I wasn’t excited before (i.e., driven to a higher energy state!), I got moreso as Barbara continued. Because even though the work begins in imaginary time, “the system of effective action” is translated into real time. Keep in mind that I am not making an atom-person comparison, but an atom-language comparison. “The transition,” continues Barbara, “is driven by adding or subtracting a small number of particles…[This is a] different physics – quantum fluctuations, at some point it becomes more favorable for the system to delocalize.” In other words (I think!), it becomes possible for atoms not to choose their nearest neighbor, but to behave in a truly alternative fashion. Amazing transformations then occur, such as the velocity of sound replacing the speed of light!
A bunch of people had questions at this point in the presentation; which was only (!) laying the groundwork for the discussion of results. Somehow along the way Barbara established a three-dimensional description of ground state properties, coming up with a phase diagram, information about strong coupling expansion, and a surprising finding concerning the critical region – which was bigger than predicted. What happens is a special kind of symmetry – based on the numbers (visible by graphing) and the relativistic behavior of sound itself. The symmetry is the crux (if I’ve got this right) of the transition from the mathematical world of the imaginary to the real, physical world.
The math and physics proper implications are far beyond me, but the pieces I grasp for language involve the importance of temperature (emotion may serve as the social science equivalent?), the changes from a homogenous to non-homogenous system (monocultural to mixed/multicultural?), and this discovery: “two bosons cannot occupy the same site.” Again, a reach, but no two words – even the same word – can never occupy the precise same spacetime with exactly equivalent momentum. “This model,” Barbara concludes, “is different than before, [which was] hard-core = only one (_____?) per site, and the interaction is long ranged.” The gist I took away from the presentation is that added dimensionality matters. The parameters of various electric fields (imagine the matrix of social/cultural factors that generate belonging or identity or community) can be tuned independently, via this knowledge about the hopping matrix element, such that “there is only a three-body repulsion…. [in this] system, meanfield predictions show the system undergoes a solid-superfluid quantum phase transition, [which effects the]
• Charge density wave, and the
• Bond order.”
Stick with me – or rip me to shreds! We’re witnessing (and probably participating in) huge “charges” of social density in waves (dare I say) of anti-Palinism (to give the most prominent current example). A transition resulting from this wave would be most welcome, would it not? (Well, if it goes the way we desire – I’m not sure the model provides the tools to predict which way a wave may break, yet.) But such a transformation will alter the social order – the relational bonds that tie us into certain elemental states will be disrupted, allowing the possibility for new and different bonds to form.
A Footnote:
*Stephen Hawking describes imaginary time as a “kind of time in the vertical direction,” which is “not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.” The Beginning of Time, a public lecture by Dr. Stephen Hawking.

The Last Section of My Original Notes (for kicks and grins):
Particle doesn’t want to stay “here” because a very big _____ of energy. A filling factor of 2/3 for the charge density wave, we have a packet hopping back and forth between the _____ affecting the algebraic long-range order of

One thought on “atoms hopping around”

  1. “Meaning” is the point I didn’t articulate! Or, meaningfulness. Those holes and particles that need to be co-created are a metaphor (if not the actual mechanism) of the stuff that enables “understanding.”
    Or so I suggest ­čÖé

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