Analog SFF, October 2007

by Dell Magazine Authors

  The NGP demonstration experiment, even with the improvements suggested above, is far from the “break-even” point of reliably producing more energy than it consumes. Further, the amount of energy it does produce is very small, and the system reliability for long-duration operation, depending as it does on the robustness of lithium tantalate crystals against radiation damage, is not at all clear. Like any new technology, it needs to be explored further and is likely to encounter unforeseen problems and produce unforeseen applications.

  But in any case, it represents a small, inexpensive, and convenient method of producing a beam of neutrons. This has applications for material studies and for medical cancer treatment and imaging. In the latter context, the NGP group has already demonstrated that it is possible to “tag” the direction of an emerging neutron by measuring the direction of the recoiling 3He nucleus that was produced in the same reaction, since the two particles are emitted back-to-back in the system center of mass frame. Thus, if a neutron was scattered by or produced a nuclear reaction in some material, one would know the direction the neutron was traveling before the event occurred. This could have important element-analyzing imaging applications, both in medicine and in areas like homeland security and nuclear weapons safeguards. A space-based variant of the deuteron-ionizing setup could also provide the basis for a new type of ion thruster.

  Seth Putterman has stated that with this new technology, one could construct a sealed egg-size device, place it in ice water for a while, then hold it in your hand to bring it up to body temperature, and this would cause it to emit enough neutrons to give you a dangerous radiation dose. That does not sound very useful, but it illustrates the power of this new fusion technology.

  Copyright (c) 2007 John. G. Cramer

  * * * *

  AV Columns Online: Electronic reprints of over 130 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: www.npl.washington.edu/av.

  * * * *

  Reference:

  Tabletop Fusion:

  "Observation of nuclear fusion driven by a pyroelectric crystal,” B. Naranjo, J. K. Gimzewski, and S. Putterman, Nature 434, 1115-1117 (2005).

  [Back to Table of Contents]

  ON THE QUANTUM THEORETIC IMPLICATIONS OF NEWTON'S ALCHEMY by ALEX KASMAN

  We're often warned to be careful what we wish for—and the devil is in the details!

  Only the skin around Rick's left eye wrinkled when he gave me the good news. That's a bad sign. Normally, the crow's feet around both eyes become more pronounced when he smiles. They don't make him look old, just extremely happy. But occasionally the wrinkles are only visible on one eye or the other.

  I must have witnessed this event twenty times during the four years that Rick served as my thesis advisor. I also remember a few examples of these one-sided smiles during the previous year, when he taught the Topics in Modern Analysis class I took and was also the professor for the statistics class that I TA'd. Based on this empirical evidence, I developed a theory to explain this “broken symmetry": Rick's non-symmetric, smile-induced wrinkles always indicate that he is lying.

  It gets even more specific than that. I was relatively certain that right side wrinkles suggest that Rick has something extremely positive to say, but feels that he has to restrain himself. For instance, if one of the two really bright students in his statistics class made a particularly insightful remark during class, I think Rick would have liked to have said, “That's fantastic! You're a talented young mathematician. Have you considered majoring in math?” But, worried that saying this would bloat their egos or offend the rest of the students, he would instead just say, “Yes, that's correct.” This sort of remark was generally accompanied by wrinkles around his right eye, and so I was proud to have earned a few right-sided wrinkles during his discussion of my progress on my thesis.

  On the other hand, sometimes he had to smile when he really didn't feel like it. Comments like, “The department has voted to let me serve as chair again starting next semester,” or, “Despite your low grades so far, if you study really hard before the final, you can still earn a good grade in this course,” are the sorts of things he is likely to be saying while smiling with wrinkles around his left eye only.

  So I was a bit concerned when he told me of the job offer from Dr. Stein. On the surface, it really seemed to be good news. Despite the difficult job market, especially for people in my field of non-standard analysis, I had at least one firm job offer.

  But only the skin around Rick's left eye wrinkled when he gave me the good news.

  "What do you think?” he asked me as we walked through the flurry of cherry blossom petals on the central quad. “Does that fit in with your plans?"

  As if I had plans! My plan was to get my degree and get a job. If this was a job, then it fit with my plans. As it was, I received no other job offers, and so had no choices to consider. Not only that, but it was a research post-doc at a mathematics institute! And, from what I've heard, Ann Arbor isn't such a bad place to be either.

  As I said, it seemed to be good news, but the wrinkles got me worrying.

  It was a little bit strange that the job offer came without my even having to send an application. And, I have to admit, I'd never even heard of the “Institute for Mathematical Analysis and Quantum Chemistry,” a research center that seems to have absolutely no web presence at all.

  Perhaps they do government work that is so secret, security precautions prevent them from having a webpage.

  Perhaps the one-sided smile just meant that he was saddened by the thought that I would be leaving soon.

  Perhaps my theory about the symmetry breaking was just plain wrong.

  Or perhaps things were about to take a turn for the worse.

  These were the possibilities I was considering as the train pulled into Ann Arbor. I got out of my seat and started pulling my old green duffel from the rack before we had come to a complete stop. So, when the train finally did stop, the cumbersome bag made me lose my balance and fall on a woman talking on her cell phone. Her eyes narrowed, as if I'd just tried to steal her purse, but her phone conversation continued as if nothing had happened.

  I was still apologizing to her as we entered the terminal building, but I was pulled away by a small man who tugged on my shirtsleeve and meekly asked, “Are you Igor, then?” Raising my hand one more time to try get the attention of the woman who headed for the bathroom, still chatting away on her phone, I recognized the futility of my desire to be forgiven and turned toward the man. My duffel slipped off of my shoulder and fell to the ground, making a sound that would make one think the bag contained a dead body rather than the cheap clothes and toiletries it actually held.

  "Yes,” I said holding out my free hand, “and you are?"

  "I'm Doctor Stein, from the institute."

  Well, I was impressed. The director himself had come to the station to pick me up. That seemed promising. And my first impression of the man was a good one as well. His brown plaid shirt may have clashed a bit with the blue slacks he wore, but he looked friendly. Moreover, although I am not sure exactly what it is about him that gave me the immediate sense that the man was a genius, I was already convinced that Stein was brilliant.

  "But you can call me Frank,” he continued, shaking my hand. “Can I help you with the bag?"

  I suspect that the bag weighed twice as much as Frank, so I just carried it to his gleaming 1972 Ford Country Squire station wagon myself, and we were off.

  At first, we just gossiped about Rick. The two of them had apparently met in grad school and only barely stayed in touch since then. For instance, he didn't know that Rick had married the well known number theorist Lisa Rojahn, or that he had been in a water skiing accident and was confined to a wheel chair for almost a year.

  We also talked about my name, Igor Stravinsky. Everyone asks about it eventually. I began the usual spiel about the famous composer being a distant relative of mine and how my pare
nts, being very fond of music, thought it would be a good idea to name me in his honor.

  But then I noticed a sign indicating that we had entered the city of Ypsilanti, Michigan and I began to ask more pertinent questions about my situation.

  "So, are you taking me to my apartment first? Will I be living in Ypsilanti and commuting to...?"

  "No, no,” he said cheerfully. “You'll be living at the institute with me, and it's in Ypsi.” Then, seeing that I seemed concerned about this bit of geography, he added: “Don't let that worry you, my boy. Did you know that MSRI isn't in Berkeley, but in Oakland?"

  Somewhat comforted by this, I pressed on with my questions. “I did try to read some quantum chemistry papers, you know. There was this cool one where they were trying to predict the color of gold just from the mathematics of it. The funny thing was that because the nucleus is so heavy, they got it all wrong unless they included some relativity in there. Well, I understood that much. But really, the details lost me. I don't get Schrödinger equations and all that stuff about particles. How much of that are you expecting me to learn?"

  "Particles? Don't worry, you won't be needing that. I can do all of the chemistry. You will just be my ‘hired gun,’ handling the Riemann-Hilbert problems that pop up."

  "I didn't see any Riemann-Hilbert problems in what I read. It's too bad, too, because then maybe I would have understood it. So, could you explain to me how..."

  "As I said, Igor, don't worry about it!"

  Finally, I asked a question that I thought would have a simple answer. “Do all of the institute's employees live there, or just me and you?"

  "Yes,” he said, and crow's feet appeared by his right eye. There may also have been some by his left eye, but I couldn't see them from my point of view.

  "I'm sorry, I guess you didn't hear me. I asked whether you and I alone will live at the institute or whether all..."

  "I heard you. I heard you. Now, show me you're as smart as Rick says and tell me why I said simply ‘yes.’”

  It didn't take me long to figure it out, but shock kept me quiet for a bit too long and Frank began to hum the annoying music from the final round of Jeopardy. He really seemed to be enjoying himself.

  "Okay,” I said with a bit too much anger. “I get it! It's not much of an institute is it, if we're the only two people there."

  "It's quite a bit better than it was last week. One hundred percent increase in personnel! Not bad, not bad. And getting better all of the time. Ah ha! And here we are."

  I had not been paying close attention to where we were going during the last bit of conversation, and so I was surprised now to see that we were in a residential neighborhood that had clearly seen better days. The houses were relatively large, with fancy woodwork and reasonably good wooden siding. But they were all in serious need of paint, and grass growing in the many cracks made the sidewalk running in front of them almost invisible.

  The house we had stopped in front of was one of the better looking ones, the weeds having been trimmed back enough that you could see the steps. It had probably been painted some time in the last ten years. Near the porch steps was a little sign that read “Mathematical Analysis/Quantum Chemistry” in gold letters on a black background.

  That pretty much confirmed my theory about Rick's smiles.

  * * * *

  My area of mathematical expertise is solving Riemann-Hilbert problems. I like to think of myself as a wild animal trainer, but rather than making lions jump through hoops, it is complex-valued functions on a Riemann sphere that are doing the jumps for me. Calculus students are used to seeing well-behaved functions: continuous and differentiable everywhere. But in many applications, you not only need functions that have discontinuities, but you need them to jump in rather specific ways at prescribed locations.

  The thing is, it can be pretty difficult to make the functions dance the way you want them to, especially when the moves get fancy. Using the stuff that most mathematicians know, it can appear like a nearly impossible task, giving these sorts of problems a reputation for being onerous. But, I'm lucky that Rick knows the latest mathematical gimmick, a toolbox called “non-standard analysis,” that gives me numbers infinitely smaller and infinitely larger than the usual ones. As it turns out, we can use these as treats to coax the functions to do just what we want. It's still a lot of work, but it is straightforward enough, and not nearly as dangerous as lion taming!

  My job at the institute pretty much consists of using these techniques to solve the Riemann-Hilbert problems that Stein tosses at me. He'll have to carefully describe the jump he wants, where he wants it, and the boundary conditions that cage up the wild function away from the jump so that it is always under control.

  After I had been doing this for just a few days, Rick actually called me to see how I was doing.

  "This job isn't so bad after all,” I told him. “The problem I worked on yesterday was really cool. You should have seen the monodromy that I ended up with! At first I couldn't think of what I could do until I used a Möbius transformation and it all fell into place. You know?"

  "Yes, I know.” Rick sighed and paused. “Has he talked to you about, uh, chemistry?"

  "No. He told me not to worry about that side of it."

  "Okay. Well, keep in touch."

  As I hung up the phone, I had to remind myself of where I was in my latest computation. It was essentially done. So, I finished up what I was doing by writing a brief note to Stein:

  Remember, in the last formula you've got to think of the jump matrix as being an operator on the nonstandard Hilbert space H. Then, using your curve C we can get the answer by using

  X(y)=I—ScF(y) G(u)/(y—u) du

  I'm not sure why Rick seemed so worried about me. I was really beginning to have a great time. Living with Dr. Stein in the old house may have been a little bit unusual, but since he didn't care what I did with my time off, it wasn't like living at home with mom and dad, as I had originally feared.

  In any case, he seemed mostly to approve of what I chose to do with my spare time, which was to hang out on the University of Michigan campus with the math grad students. I attended their colloquia and seminars. I joined them in the U. Club for beers. And I enjoyed a picnic lunch on the Diag with one student in particular, with high hopes of seeing quite a bit more of her.

  Dr. Stein, whom I still cannot quite bring myself to call “Frank,” approved of this because he wanted me to stay connected to the mathematical community. He also seemed to want me to report back to him anything that anyone should say about him. And I did. I told him that his early work in mathematical physics on anti-deSitter spaces (whatever those may be) is apparently still respected, but that he is now considered quite the crackpot. I told him that the department was trying to figure out how to fire him despite his tenure. And I told him that people are very curious to know what we were doing at the institute.

  Since he had not sworn me to secrecy or anything, I was comfortable passing information back the other way as well. I told my friends in Ann Arbor that Dr. Stein was definitely not the craziest person I'd ever met. As far as work goes, I told them that he would frequently give me rather specific Riemann-Hilbert problems, which needed to be solved, and that he was always very grateful and positive when I was able to find solutions relatively quickly. I had no idea what he was doing with my solutions or what it had to do with chemistry.

  * * * *

  On our first official date, Becka and I caught a showing of “How to Steal a Million” with Audrey Hepburn at the Michigan Theater. We had seats right up front by the pipe organ, and somewhere in the middle of the movie her knee rubbed gently against mine and it stayed there.

  Everything was going great. But later, over coffee, she started asking me about my job again. She asked the same questions she had asked at our picnic lunch last month, and I gave her the same answers. I thought I was being romantic when I asked why I should care about Franklin Stein and his micro-institute when all I could th
ink about was her. She didn't agree.

  * * * *

  The next time that Dr. Stein looked over my latest solution, inquiring about the details as usual, I interrupted him with a question of my own.

  "It looks nice,” he was saying. “Yes, very nice. I think we're getting quite close to our goal now, boy. It won't be long now until they see that I'm not such a ‘crackpot’ after all! Just one question: Are the branch cuts double ramified along the..."

  I was barely listening to him. Instead, I was looking over his shoulder at the paper he had been working on. Below some complex analysis that I recognized, large and bold, I saw the expression:

  ff O. + 0(o/) ~ h+O(o^)

  I was thinking, “What is this, astrology?"

  "What is our goal, Frank?” I found myself shouting. I had never taken him up on his offer to call him by his first name before, and so he knew right away that I was annoyed.

  "I will tell you, son.” He spoke calmly, a significant contrast to my agitated state. “You seem pretty bright and may be able to understand the importance of this work more than most of them. But first, are you sure you want to know?"

  Ignoring his polite response, I continued yelling out things I hadn't realized I had been thinking. “You know, I took classes in quantum physics and chemistry in college. I read a few papers on quantum chemistry before coming here. And I never saw any Riemann-Hilbert problems in them. Are you even doing anything with the answers I'm giving you, or do you just go off and come up with another problem for me to work on? Is that what all of this is about, just wasting my time?"

  "We are not wasting anyone's time. We are doing extremely important work here, Igor. The course of history will change.” His voice became deeper and very nearly boomed as he said, “After these many hundreds of years, Isaac Newton's dream will become a reality. By piecing together a bit of this field with a smidgen of that theory, we are resurrecting the greatest scientific achievement of all time, which died a slow and painful death from neglect and misunderstanding."