Today I started writing a short piece on the early universe for kids; maybe eight year-olds? I am not sure I have what it takes, but I thought I would give it a shot. No wonder I never get anything done!
The tiny keyboard is going to take some practice! Here is a shot of me reflected in my office window, taken with the OLPC camera.
I finished assigning grades. I was nice. I would love to teach classes without grades; I think that grading only interferes with the educational channel between students and teachers. The only educational advantages (forget institutional advantages) of grading that I can see are the following:
(1) Graded assignments are much more likely to be taken seriously and completed. This consideration is paternalistic but it may have some force in the
real world. (2) Graded assignments give the students low-bandwidth but high-impact feedback on their knowledge and gaps in that knowledge. This consideration is also paternalistic, since verbal analysis of student performance contains far more information, but it is true in my experience that a low grade (on, say, a mid-term) is much more likely to inspire hard work than a verbal suggestion.
That said, grading makes my relationship with the students somewhat adversarial. It also discourages students (especially those with performance-based financial support) from taking risks with their course selection. This point, maybe the most important, is the one that clearly shows grading to be incompatible with the (important) mission of the University.
On the final exam, I asked the following:
Explain why the astronauts in the Space Shuttle are weightless.
I was lenient in grading. But my position is actually at odds with most of the textbooks. Here's why.
The standard textbook answer is something like
Actually, the astronauts on the Shuttle still have weight, since there are still gravitational forces acting on them. However, they feel like they are weightless because they are in an accelerating reference frame that is accelerating at the acceleration that the gravitational force is providing. This will be followed with various things about equivalence and plummeting elevators and non-inertial forces and so on.
My explanation is that the gravitational force on an object is not the weight of the object, when the word
weight is properly understood. The weight of an object is not the gravitational force but rather the contact force that holds the object up against gravity (and non-inertial forces). It is this contact force, after all, that a spring scale measures, because a spring scale does its job by providing a contact force. It is also this contact force, after all, that you perceive by having your feet pressed onto the floor or behind pressed into the seat of your chair. Indeed, gravitational forces can never be measured locally or internally (that's equivalence!), all you can measure is the stresses and strains required to oppose them in our non-inertial (by GR standards) frame.
My view makes the astronauts not misled but truly weightless. It also makes it true, not apparent, that one is lighter at the top of a hill and heavier at the bottom of a hill on a roller-coaster, and same for the related changes you experience in an elevator.
Since my last post I thought of many things I would like to have included but didn't. I guess the biggest is that I got two questions near the end that were effectively about Coriolis force. I did no non-inertial forces and/or accelerated reference frames. And this would have been fun to bring up in the context of Galileo, because there is a non-trivial Coriolis effect on his (apocryphal) experiment at the leaning tower of Pisa. It also is a nice use of cross products and pseudo-vectors.
I gave my last class today; still have to prepare a final. It has been a fun semester, and the students have performed well with a set of extremely difficult problems in lectures and recitations and problem sets, including ill-posed problems, approximate problems, and numerical problems. I ran out of time at the end, as I always do. Many subjects were not covered. Perhaps my biggest regret is not making it to the analysis of non-circular orbits using the effective one-dimensional radial potential. This analysis takes a long time to set up and then solve, but it is so damned beautiful.
In class today, I said that the biggest impacts of physics on society have been (1) the Brahe, Kepler, Galileo, Newton understanding of celestial mechanics, and (2) the development of the atomic bomb. The former was the beginning of precise, quantitative science (I think), undermining the authority of non-empirical scholarship in areas of natural philosophy, and establishing calculus and quantitative observation as the key tools of physics. The latter created an ability to (trivially and unilaterally) destroy ourselves and pushed all of world politics to global mutual destruction brinksmanship. After these two I might put the discoveries of AC and DC electricity (and batteries and the like), and the optimization of steam engines (and the discovery of thermodynamics and the like).
At the suggestion of my pedagogy mentor Sanjoy Mahajan (MIT), I assign
reading memos, to be turned in before the class in which I expect the reading to be done. This encourages the students to do the reading (I give a small fraction of the grade for doing the memos), and it also gives me some exceedingly insightful feedback about what works and what doesn't in the book I am using (Chabay & Sherwood).
In Chapter 11 (this week's chapter), the book makes the requisite notes about the increase in entropy possibly having something to do with the advance of time, a subject I avoid for its capability of generating enormous quantities of speculation. In the reading memos, one of my students (John Morrow) asked:
A closed system will tend toward maximum entropy. Is it possible for it to reach maximum entropy before the rest of the universe? And if so wouldn't that imply that time would stop for the closed system?
Beautiful question! This either throws doubt on that whole crazy idea, or else implies that all systems that have or perceive time must be out of equilibrium? Insane! But of course that would be some of that speculation I abhor.
I spoke yesterday in class about rotating solid bodies, in particular when the object is spinning around an axis not aligned with one of the principal axes of the moment of inertia tensor. The challenging point is that if you fix the axis of rotation then you get bearing forces or torques, but if you spin torque-free then the axis of rotation necessarily precesses. Of course the details are pretty hard for a student seeing this material for the first time; many of my colleagues would drop this from an intro course. But I love mechanical engineering, and this particular process comes up just about everywhere in our every-day experience. I can't help but talk about it!