The Physics of Limits

I spend lots of time thinking - a trance-like state where ideas flow. The feeling is similar when reading about physics, solving problems, doing calculations or randomly following the meanderings of the mind. It brings far greater pleasures than drinking or socializing, though it does not replace the need for human interactions. Exchanging ideas with others is just as fulfilling.

Undoubtedly, the naturally occurring peptide substances in the brain that act as neurotransmitters and appear in abundance while thinking are responsible for the euphoria that is associated with thought. This is augmented by the great satisfaction of new insights that are gained in the process. Strenuous physical activity releases natural endorphins that bring a similar feeling of pleasure. Perhaps these chemical triggers fuel my passion/addiction for physics and ice hockey.

One of our research areas is in fundamental limits of the nonlinear susceptibility. The limits that we calculate follow from the laws of physics. A while back, I got intrigued by the idea that the laws of physics might be derivable from a formulation in terms of limits, or more precisely, constraints. As usual, the idea is not fully original.

In a way, some of the laws of physics are already formulated in this way. For example, the entropy cannot decrease; so, there is a lower limit for the change in entropy. Then there is the upper limit of the speed of light, a crucial constraint from which special relativity follows. The uncertainty principle, which does not allow certain pairs of properties to be simultaneously measured with infinite precision, is yet another constraint. And, that fact that energy is a constant is a very stringent limit; it cannot increase or decrease.

Since physicists have been thinking about these problems for a long time, there are probably few new ideas that would provide a novel approach to physics. However, I still have this gnawing feeling that there is something interesting lurking behind this approach. For example, since the sum rules are a direct consequence of the Schrodinger equation, then perhaps under a constraint, the sum rules could be used to generate general physical principles. Such a formalizing might have unexpected consequences that could lead to the prediction of new and unexpected phenomena.

Since I have been busy with other things, I have not had time to develop this idea, and probably never will. Instead, I will occasionally tinker with paper and pencil to get my neurotransmitters flowing without delusions of success with an occasional vigorous game of hockey to add a tad of spice.

Preparing for class

I am spending large chunks of time preparing for a new class that I am teaching this fall. I never found classical mechanics particularly difficult; but, writing lectures and solving problems is still a challenge.

I devote each Saturday and Tuesday to course development. Though I took a couple of breaks to eat and surf the web, I remained true to my schedule. After grading last week's homework assignment and a quiz on Saturday, I continued to plow through the textbook and organize the material for my lectures.

My serious teaching career (excluding my work as a teaching assistant in grad school and an instructor at a community college) started 20 years ago at Washington State University. Those years have not jaded my enthusiasm for teaching. I continue to make adjustments based on my past successes failures.

But how are improvements possible when good teaching is difficult to define? While there is mounting research on pedagogy, in my mind, many of these studies are inherently flawed. For example, while courses that are based on peer instruction and conceptual problem solving certainly lead to better understanding, it makes it difficult to cover the same amount material. Admittedly, it is wasteful to teach lots of stuff that everyone forgets; but, coverage is also important - especially if a course is a prerequisite in a sequence courses. Such trade-offs must be carefully weighed in an undergraduate curriculum, especially for the student who will take one or two physics classes in a lifetime.

Graduate programs, on the other hand, are populated by motivated students who have both an interest in and an aptitude for physics. PhD programs like ours are based on coursework and research. All students take a set of core classes in their first two years. To become a PhD candidate, they must pass the PhD qualifying exam, which is given at the end of the forth semester.

The qualifier exam committee solicits two problems from each faculty member. A list of topic areas is used as the basis of the solicitation to ensure that the test is well-balanced. Thus, the qualifier exam reflects what the faculty as a whole believe is the core competency of a PhD in physics, and is not necessarily limited to the material covered in class. However, past exams are made available to the students as a study aid.

I find this system to be the ideal game-theoretic approach to ensure buy-in by all parties. It reflects poorly on me as a professor if the students were to do poorly on the part of the exam that is associated with my course. This makes me think very carefully about how to most effectively cover the material to get the optimal balance between breadth and depth. The looming qualifier exam motivates the students to learn the material for long-term understanding, not just for a particular test. Everyone works harder as a result.

My approach is to stress the fundamentals and give lots of examples. I gloss over topics that the students can learn on their own. When preparing a lecture, I first read the material, sometimes many times, until I feel I have a good understanding of the concepts. I then identify what I think are the important points, and use them as anchors in my lectures. I post readings and homework assignments on the web well ahead of the lecture dates so that the students are well prepared for class.

In crafting my lectures, I select problems from the end of the chapter on the basis of how well they complement my notes and whether or not they challenge the student to think more deeply. To select appropriate problems requires me to first suffer through the calculations. This time-consuming task give me ideas on how to fine tune my notes to address potential misunderstandings.

The night before my class, I go over my notes to make sure that I stress the important issues. The morning before my class, I copy my notes to scrap paper, going over in my mind the flow of my presentation. I pay particular attention to the anchor points.

Finally, I reproduce my lecture on scrap paper without looking at my notes. My preparation is complete when I am able to navigate from one anchor point to the next based on general principles of physics and logic.

So to finally get back to my diary entry after this long-winded diversion, I spent most of Saturday reading the textbook, writing notes, and working physics problems. This reminded me of how learning physics requires an intense and prolonged effort. I am thankful to my employer that my teaching responsibilities force me to spend time thinking very deeply about the subject that I love so dearly. And then, I get to share my enjoyment with a group acolytes who share my enthusiasm for learning.