The Supreme Court of Science

I recently read a short article in The Economist on the topic of fairness. The gist of the piece was that fairness depends on the perspective of the observer. For example, a conservative may argue that an entrepreneur is entitled to keep the proceeds resulting from hard work provided that the rules ensure a level playing field. If all individuals have an equal opportunity to participate, and the rewards are in proportion to the effort, then any redistribution would be unfair. Even under such idealized conditions, a liberal might argue that it is unfair for someone to keep all the profits because the resources would be better spent by a benevolent government on projects that are more noble than the greedy and wasteful accumulation of wealth by an individual.

Imagine a sporting event where two teams battle for a couple hours before throngs of cheering fans. At the end of the contest, the winning team is required to donate points to the opponents to force a tie. Now would this be fair? Clearly, this solution would anger all parties. Such analogies gloss over the nuances and complexities of the real issues, and are the staple of spin doctors that make for hyper-actively-delivered sound bites on Fox News. This is not to say that a Utopian society run by a benevolent government is a viable alternative to the unscrupulous industrialists portrayed by liberals.

Members of a free society are entitled to jabber nonsense and to exercise personal preferences in private or with like-minded (or mindless) individuals. However, when such nonsense finds its ways into politics and fills the halls of power, government becomes dysfunctional. The problems are compounded by politicians who are forced to pander to the masses. Many of us complain that politicians all lie. The root of the problem resides in the stupidity of the electorate, not in the politicians who must walk a fine line that avoids the minefield of our dogmatic sensitivities yet satisfies our contradictory demands.

This craziness originates in the way our neurons are hard-wired. Scientific evidence has documented all sorts of peculiar but fascinating traits of the human brain such as confirmation bias, which selectively reinforces beliefs based on dubious evidence and ignores floods of data to the contrary. We fool ourselves into believing all kinds of wacky ideas while easily detecting the folly in the conviction of others. We do not hesitate to accept contradictory concepts of truth. All this leads to vigorous ideological wars. The scientific method is designed to minimize these biases when seeking the truth.

Consider the irrational protest against childhood vaccinations. While nothing is totally risk free, the benefits of inoculations far exceed the risks. In addition to a growing swell in deniers of the efficacy of all vaccinations, some individuals believe that some vaccines cause autism. There is no scientific evidence that shows autism to result from the mercury compound used to preserve vaccinations (the rate of autism is no different with and without the mercury compound), but large numbers of people don't buy it and are applying political pressure to remove the important preservative. Though it is one of the most powerful theories in all of science, there are large numbers of people that do not believe in evolution. Similarly, many people can't seem to shake the belief that power lines and cell phones cause brain tumors.

False beliefs are innocent enough, but when these beliefs lead to action - such as forcing teachers to give equal weight to evolution and creationism/intelligent design or withholding inoculations from children - humanity suffers. Real children die and the power of ignorance fuels further disinformation that leads to a decrease in the quality of life.

The supreme court weighs in on legal matters, so why not assemble a group of unbiased and open-minded scientists to rule on the veracity of issues that can be resolved with evidence-based methods? The patent office automatically rejects perpetual motion machine filings, so why not automatically disallow a bogus settlement against a defendant who has science on her side? Empower science court to strike down a proposed curriculum that teaches religion under the guise of science, to veto consumer pressure to force insurance payments to alternative medical practices whose methods are baseless, and to disallow lawsuits that break the laws of physics.

Legal courts arbitrate disputes between parties using the law of the land as the basis of a decision. When science becomes an integral part of a case, the courts rely on expert witnesses. Unfortunately, it is always possible to find an "expert" with seemingly acceptable credentials who will contradict the scientific consensus. In these cases, jurors may end up returning verdicts based on the way the testimony is extracted rather than on the weight of the evidence. This method of interrogation may be the best available when deciding whose side of the story to accept, but scientific truth is best gleaned by a careful analysis of the evidence in the absence of theatrics and emotions.

For example, there is no evidence linking brain tumors to electromagnetic radiation from power lines and cell phones. Not only is there no statistically significant correlation between the two, but all plausible mechanisms of electromagnetically-induced tumor growth are inconsistent with the laws of physics describing the interactions of electromagnetic waves with matter. Suits against power companies for causing brain tumors should not be permitted to be brought to trial when the best scientific evidence shows the accusation baseless. That such cases are even heard implies ignorance of the facts; or, perhaps the courts believe that they can determine the veracity of the underlying science in lieu of the well-established body of literature.

In the absence of evidence, a typical vacuous argument posits that there might be a connection based on unknown science. This is equivalent to stating that unicorns cause sexual dysfunction. We would chuckle if an individual brought a case against a supermarket for allowing invisible unicorns to roam its isles, endangering the reproductive ability of its shoppers. The electromagnetic suits are scientifically equally ridiculous, but are not met with the incredulity they deserve.

A science court would make rulings based on the best available scientific evidence - the statutes being the laws of physics, chemistry, biology, etc. If an electromagnetic tumor case were to be filed, it would be dismissed before wasting society's resources. A suit against a pharmaceutical company for causing autism would also be dismissed as would a suit to force feed creationism in public schools under the guise of science.

Science evolves to accommodate new evidence. The guiding principles used by the judges of science court would be adjusted to take into account new discoveries. In short, science court would provide the most current and up-to-date information to ensure that judgments are made on the basis of the best available evidence rather than emotional bias or political philosophy. Judges, who are experts in the law, are well qualified to deliver verdicts pertaining to legal matters. Individuals who are well versed in the scientific method should rule on issues that are based on scientific principles, and to set precedents that would be used by the legal system. It is time that we recognize that science is not legislated, but discovered as a result of carefully-designed experiments that minimize bias.

Bias colors the perceived fairness of an outcome, even when each party draws on the same facts. To be ignorant of the established scientific consensus when deliberating a settlement is unconscionable. To purposefully ignore or obfuscate the facts to obtain a favorable outcome is criminal, especially when championing an ideology . To me, fairness starts with a process of evaluating and accepting the scientific consensus and using it as the bedrock of the laws. The establishment of an independent judicial branch that codifies the best science into a practical form is a necessary step for moving forward into a future that is both dependent upon and threatened by the technologies that science has enabled.

An overwhelming Friday

The summer is a wonderful season to get lots of work completed in preparation for the daily grind of the semester. But its duration is much too short to accomplish all that was intended at its start.

Papers take a back seat to teaching and service during the academic year, so writing manuscripts is one of my summer priorities. Unfortunately, I have more than half a dozen projects with results that need to be published. Even if I devoted the rest of the summer to writing papers, most would be left undone by the start of classes. Getting ready for a trip to present an invited talk in San Diego in a week and a Plenary talk in three weeks in Budapest is also occupying lots of time and energy. Coupled to daily visits to the lab and dealing with the constant challenges of building new experiments and fixing old ones, time is scare. I will be satisfied with the completion of two papers.

My afternoon rounds in the lab continue to be satisfying, with new results daily. In addition, I look forward to Xavi's 6 week visit, which starts next week. We have high expectations for cracking two problems that have been haunting us for many years. There are other problems, potentially with very significant consequences, which have been relegated to the back burner. Unfortunately, they may need to simmer for yet another year before I begin to work on them in earnest.

Being preoccupied with all these activities, I am concerned that I will be unprepared for the new class that I will be teaching this fall. Preparation for a graduate class suffers from a huge multiplier effect. A one hour lecture may take 15 hours of prep time. In addition to developing pedagogical strategies, I spend lots of time solving potential homework problems. It is hard to assess the pedagogical value of a problem unless one struggles through it from the perspective of a student. Problems that take lots of time due to their mathematical challenge are sometimes appropriate, especially if the mathematical technique is useful for a broad range of problems. On the other hand, mathematically simple problems with seeming paradoxes that result from misconceptions force the students out of their cognitive comfort zones. The struggle to conquer such problems leads to a deeper understating. One of the wonderful perks of my job is that I am continually intellectually stimulated and am always learning new things.

Often, I have not seen the material that I will be teaching since graduate school, so when preparing my lectures, I fall into the same traps and make the same blunders as the students. It takes lots of work to put the state of confusion behind me so that I can be in a position to teach the material. It is a great asset as a teacher to have had experienced the same difficulties that the students will experience. The most horrible teachers are the ones that cannot understand why the students are confused, and are therefore unable to be helpful.

I look forward to the weekend to get lots of work behind me. I will undoubtedly be disappointed with my progress, but the time we have is always insufficient for our plans. The summer is whizzing by, as is this weekend. I need to get back to work.

Recent paper accepted

All papers are written with expectations that they will be appreciated by the scientific community. That's why authors are indignant when a manuscript gets rejected by reviewers before it can see the light of day in a scientific journal.

Recently, Shoresh submitted a manuscript to JOSA B (see http://lanl.arxiv.org/PS_cache/arxiv/pdf/1006/1006.1320v2.pdf for a preprint). In this work, he used Monte Carlo calculations, which were first implemented by my son, to let the computer role the dice to randomly determine transition moments and matrix elements of a hypothetical quantum system. To make the results consistent with quantum mechanics, we used a procedure that constrains the choices to be consistent with the sum rules. By rolling the dice millions of times, we can get a feeling for the properties of a much broader range of systems than one could synthesize in the laboratory.

In a paper that we published three years ago, we used this approach to study the hyperpolarizability. In the recent work, we aplied the approach to the second hyperpolarizability. The calculations yielded the same kind of surprising result, which this time around were a tad bit less unexpected, and that is that the Monte Carlo approach seems to give certain properties that are not observed experimentally nor predicted theoretically using standard Hamiltonians. The upshot is that some very exotic systems with a large second hyperpolarizabilities may be lurking out there - yet to be discovered.

Every time I submit a new paper, I fret that my long string of acceptances will come to an end. Sure, I have had manuscripts that got rejected, but eventually they get published once I fix some relatively minor error. W were delighted to have another acceptance. The reviewers' summaries follow this post. The detailed comments are technical in nature and have been omitted. The bottom line is that the paper is slated to be published in the next couple of months. While we are pleased, we are already working on the next two papers, each which extend our work to the next level. The more we learn, the longer term our goals become.

Reviewer comments appear here:

Reviewer 1
This manuscript is closely related to similar work on the first
hyperpolarizability by two of the authors (ref. 13) which sought
to understand the gap between the theoretical maximum
hyperpolarizability and the highest values measured experimentally.
The present paper extends this approach to the second
hyperpolarizability, γ, whose theoretical maximum value was derived
in ref. 2. In theory, the second hyperpolarizability in the zero-
frequency limit depends only upon the energies of the excited
states of the system and the transition dipole moments connecting
these states with each other and with the ground state. (Actually
the usual expression involves both transition dipole moments and
permanent dipole moments, but it can be transformed to one that
involves only transition dipoles as shown in ref. 19.)  There are
also fundamental sum rules that relate these quantities.  In this
manuscript, the authors use a Monte Carlo method to randomly sample
different combinations of excited state energies and transition
dipole moments, always requiring that they be constrained by the
general sum rules. The goal is to gain some insight into the
physical parameters needed to produce γ values near the theoretical
limit. The largest second hyperpolarizabilities found by this method
do approach the analytically calculated theoretical maximum.
Furthermore, these results indicate that the largest γ values are
found when only three states—the ground state and two excited
states dominate.

The manuscript is clearly written and well motivated.  While the
derivations refer to much previous work from the corresponding
author and his co-workers, it is not necessary to have read those
papers to understand the results presented here.  The results do
not provide much help to those trying to design real molecules with
large second hyperpolarizabilities.  However, they are certainly
interesting and this is a worthwhile addition to the literature of
this field from one of its
most original thinkers.

There are a few typos/misspellings/grammatical errors that do not
interfere with the readability of the paper.

Reviewer 2
This article presents very interesting new results and should
be published as soon as possible provided that some minor
changes/clarifications are addressed...

Sum Rules

I just skimmed over the paper by Stavros Fallieros. In those 15 minutes, I learned something new, which I shared in an email to my students. Below is the email, with typos and all.


I have just read the papers sent to me by Shoresh on the rigid rotator. My analysis of those papers in light of our work is as follows.

These papers show that the sum rules cannot be violated. As we know, for a given potential, there can be both bound states and free states. Since the sum rules require one to sum over all these states, summing over just a subset gives the wrong result.

In the case of a rigid rotator, the wavefunctions are confined to a wire loop (or attached with a rigid rod, the problem is equivalent). If one starts with a wire loop that is represented by a non-infinite potential so that the wavefunction can spill out of the loop, there are free and bound states. In this case, it is simple to sum over all states and the sum rules are obeyed yielding unity for the (0,0) sum rule.

When the electron is confined to the wire, which can be approximated as the limiting case of a delta function shell, the free states are pushed away to infinite energy. If one includes these infinite-energy states in the sum rules, all is well and the (0,0) sum rule is still obeyed. However, when not accounting for the free states by use of the limiting case, the free states are missed and the sum rules give 2/3 instead of 1. So, the problem is not that the sum rules need to be generalized or that they are being violated, but that we are not taking into account all the states as required by the sum rules. The easiest way to deal with this issue is to just throw in the factor of 1/3 to account for the bound states at infinite energy, which are otherwise difficult determine when starting from the idealized quantum wire.

Now to Shoresh's problem. In our calculations, we get the result that just two terms exceed the sum rules. Since all of the terms are positive definitive, there is no way that missed states can fix the problem. They will only make the sum rule violation problem bigger. So, I still think that there is a problem with the calculation that needs to be traced. In the end, when applying the sum rules, we should get a result that is less than unity.

Once we are certain that our formulation is correct, it will be interesting to see how the issues with infinite energy states affect the off-diagonal sum rules. The upshot is that if the off-diagonal sum rules give nonzero sums, then the dipole-free expression will give the wrong result. However, if we can determine the effect of the infinite energy states on the sum rules, we can reformulate the dipole-free form to make it work in these special cases.

We still need to fix the betaDF and betaSOS code. Perhaps Julian can concentrate on this problem while Shoresh works on the sum rules.

The consistency of physics

Most of my entries are not quite in the form of a diary as I had planned. However, my posts reflect the fact that I spend lots of time thinking about things, so I argue that these are genuine diary entries. But at least for today, my entry will be more diary-like

When I made my rounds in the lab this afternoon, I noticed a common theme in my discussions with the students -- the amazing consistency of physics. Physics covers a broad range of phenomena (everything in the universe obeys the laws of physics!) that mesh together in the most beautiful ways.

My first stop was the department office on the 12th floor to sign paperwork. In the most recent power change, I once again avoided chairing the department, but as a comprise, I agreed to be the associate chair for a year -- the same deal I had made 8 years ago. But, my true pleasures awaited me on the 7th floor, the location of my labs.

First, I spent time talking with Julian, an undergraduate student, and Shoresh, a graduate student, who are using sum rules as a guide to developing theories of the relationship between the geometry of quantum nanowires and their nonlinear-optical properties. What started out as a simple class project has evolved into a huge undertaking. New subtleties keep popping up. Last week we had to revisit the basics of expectation values of quantum mechanics when applied to loops of wires. The fact that the answers that we are getting continue to be inconstant with the sum rules is a sure sign that we are getting something wrong.

Since sum rules are derived directly from the Schrodinger equation with no approximation, they cannot be violated. About an hour of discussions on the topic led to some new ideas and new approaches that will help us better understand our problems, which hopefully will lead to a solution. While constantly tracing errors in theoretical models is highly unpleasant, the exhilaration of learning makes it all worthwhile. Michael Cohen, a student of Feynman's and a professor of mine at U Penn showed me the value of going back to the basics and testing the assumptions, no matter how trivial. The process always leads to a deeper understanding.

Next I went to Nathan's office, a student who is doing work that we hope will someday lead to ultra-smart materials. After I helped him and Xianjun clean some laser optics, Nathan described his ambiguous experimental results of the previous evening. Then we returned to his office to discuss another project that we had started in nonlinear optics class. He and two of his classmates did calculations to understand if the process of cascading could be used to break the fundamental limits of the nonlinear optical response that I had calculated 10 years prior. Since my calculations were fairly general, I did not believe this to be possible; but, we are obligated to test the hypothesis. Cascading appears to be a topic of growing interest in the nonlinear optics community because of the new avenues it may provide for making better materials. Our work will assess its usefulness and may lead to design guidelines for new nonlinear-optical material paradigms.

There were several false starts - calculations that gave infinities or calculations that yielded limiting cases that were inconsistent with known physics. After a couple of weeks, and many discussions, we finally converged to what appeared to be a robust theory of cascading. After receiving a draft manuscript from the students, I spent several days adding lots of new material, expanding the bibliography, as well as correcting lots of little errors. Just as I was applying the finishing touches in smug satisfaction of the beauty of the final product, I noticed that we failed to consider one important case. So, I sent Nathan an email, and he went back to the drawing board.

Again, the infinities reared their ugly heads. Luckily, my 2006 paper provided us with some guidance. Nathan concluded that indeed, he could remove the infinities with this method; but, again, there are many subtleties and ambiguities regarding the formulation of the model. After a brief discussion, we agreed on an approach and Nathan immediately began implementing the calculations.

Almost 10 years ago, one of my students and I discovered that some materials self heal after photodegradation. This was an exciting discovery because of the apparent reversal of the arrow of time. The result is yet to be fully understood. Three students are presently working on the project. This work requires lots of samples to be made, long experiments that can take several days of continuous operation, and complex analysis of huge data files. Some of these experiments are currently up and running while we are in the planning phases of building a new instrument and upgrading some older experiments.

The experimental results are encouraging but continue to throw more puzzles our way than providing reliable tests of our hypotheses. But, I have a good feeling that we are expanding into new experimental techniques that will hopefully provide lots of answers as well enabling us to pose more interesting new questions.

When I got home from the lab, my inbox had a message labeled "important." Shoresh had found a paper that shed light on our observation of sum rule violation. The paper's abstract was short but to the point, "We discuss application of the Thomas-Reiche-Kuhn sum rule to simple quantum-mechanical models and its apparent violation by the rigid rotator."

Scanning through the paper, I noticed that the first reference in the bibliography was coauthored by Stavros Fallieros -- an incredible coincidence considering that my parents bought his house in 1968 when I was 10 years old. There must have been the essence of sum rules in the walls that were infused into my being during adolescence.

As it turns out, my in-laws were good friends with the Fallieros family, and continued to remain in touch. Several years after I wrote my 2000 paper on fundamental limits, my wife was visiting her mother in a suburb of Philadelphia, where she ran into Stavros. During the exchange of pleasantries, he learned about our common interest in sum rules, and relayed through my wife the message that he wanted a copy of my paper, which I happily mailed to him. Unfortunately, he passed away soon after, and we never had a chance to discuss the work. Ironically, the sum rule paper that he wrote, and which I recently found, was his last journal publication. With the perfect symmetry not often found in life, one of the last papers that he had in his possession was my paper on sum rules.

The interconnectedness of science is mirrored in the relationships between scientists. We are each small cogs in a gargantuan machine that produces new knowledge. One of my former graduate students, Xavi (PhD in 2007), who was the first person to appreciate my use of the sum rules in nonlinear optics will be visiting my group for 6 weeks this summer. Later in the summer, his co-advisor will also be visitng from Belgium. This combination of our two visitors, a new student in my group, Sengting, who is following in the footsteps of Xavi in his pursuit of a joint PhD degree between WSU and the University of Leuven, along with Shoresh and Julian provides us with a formidable crew that will undoubtedly add to the knowledge base of science.

As I sit here at my computer in this small pocket of nostalgic bliss, thinking about international collaborations and our connections with past and future science, I am looking forward to the satisfaction of learning new things as well as tracking divergences in calculations, fixing lasers, and deficit spending to buy components for a new experiments. Another typical day begins!