boring science

When asked about the usefulness of electricity, "Of what use is a newborn baby?"
--- Michael Faraday (or maybe Benjamin Franklin about balloon flight)

Have you ever gotten the impression that the introductory physics textbook you are forced to use is a charlatan, that maybe it was designed by physicians and engineers purposely to make physics look boring, so that anyone with any imagination would be driven away? Science is about nature; but almost all of the examples described in these courses are artificial (man-made).

This type of approach has important drawbacks, even for non-physicists. College degrees have breadth requirements for a good reason. Breadth does not mean teaching outside topics as if they were inside.


"Those who cannot learn from history are doomed to repeat it."
--- common paraphrase of George Santayana

Generally such a book looks much more like a history book, and apparently the authors thinks that the only way to learn from the mistakes of history is to repeat them. (Let's hope they didn't write the lab manual, too.) Or maybe they are just disgruntled physicists, who think that, well, they had to learn it that way, so, by golly, that's the way you're going to have to learn it, too.

The science of tomorrow is not the science of yesterday. Even biologists should know quantum mechanics and special relativity, which are not only the most interesting parts of physics to laymen, but relevant to things like molecular biology and particle-beam cancer treatment. The new ideas of tomorrow, in any branch of science, will not come from just old physics.


"Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime."
--- common paraphrase of Anne Isabella Thackeray Ritchie

Such books give no hint of how a scientist really thinks. If you learn anything in school, it should be how to think. Memorization is less useful: You can always look it up.

The course is taught basically like this:

  1. Give a few examples in class.
  2. Give the same examples on homework.
  3. Discuss the same examples in recitation sections. (I.e., do the homework problems for them. In grade school this is called "cheating".)
  4. Give the same examples on the exam.
This has the consequences: This problem is much more extreme than it might sound: Most of the 2nd-semester students can't This includes students who get 100% on the exams. Essentially, the students can't solve problems, they can only memorize the solutions. They are just photocopiers, without even optical character recognition.

I almost forgot the most important point: Every problem gives numerical values to all quantities, and answers must be given in numerical values. So every problem is not only a test on units, but also on how well one can use a calculator, which on an exam means a hand-held calculator (but not a smartphone, which is too smart). This teaches every student:

  1. Arithmetic is more important than algebra. Plug in numbers as soon as possible so you can lose sight of what you're doing. (Something similar is happening to grad students, who now use Mathematica™ to do all algebra & integrals.)
  2. Use only 1970's technology. 1960's technology (slide rules) or worse yet, doing arithmetic in your head, is obsolete. But 1980's technology (personal computers) is cheating.


Here is a list of some of the things I have found in such books given to me as the "TA" of such courses:

1st semester

  1. The concept of symmetry as an invariance of nature is nowhere even mentioned. Symmetry appears only as a property of particular solutions or problems. Linear symmetry is not distinguished from cylindrical symmetry. Rotations as transformations are thus not given, not even when discussing angular momentum. No indication is given how dot products and cross products relate to rotational invariance.
  2. The introductory chapter of the book includes a discussion of units, but nowhere is mentioned the fact that the whole point of units is that you can choose whatever units are most convenient, such as using the (reduced) mass of the electron as a unit of mass in atomic physics.
  3. The book begins with "handyman physics": fulcrums, pulleys, etc. Who are we trying to attract to physics, carpenters? (This is why I didn't get interested in physics until I was 8, instead of at 5. By then I learned from Crackerjacks and cereal that the good stuff is at the back, not in the front. But you can't teach a course that way.)
  4. Vectors are done with unit vectors "i, j, k" (even in upper-division undergraduate courses), which are really quaternions. Why are we teaching them quaternions when we haven't even taught them complex numbers yet? Does anybody really use them anymore? If so, what is the unit vector for time in 4-vectors? (In this old quaternion notation it would be 1, but I'm sure nobody has used that since Maxwell.) Obviously this notation was already out of date in 1905, so why do we still teach 19th-century notation in the 21st century?
  5. Newton's laws are discussed before conservation of energy and momentum. Ironically, conservation of energy is used before Newton's laws for the special case of constant acceleration (i.e., gravity), but only as a subsidiary condition and not by name.
  6. Centrifugal force is said to be misleading or incorrect, as demonstrated by a drawing of what would happen if an object were released from circular motion. In fact, the drawing is incorrect, since it illustrates only the centrifugal force, and ignores conservation of angular momentum, as if there were an angular friction. No wonder it took so long for Einstein to invent general relativity.
  7. Scattering is discussed, and later the center of mass, but nowhere is the center-of-mass frame discussed! (I guess you can ignore most modern accelerators.)

2nd semester

  1. Electrodynamics is apparently about circuitry. (What are these stupid constants "ε0" and "μ0"?)
  2. Ampere's law is given first in its original incorrect form (with little hint given that it is wrong), then corrected much later.
  3. Maxwell's equations appear in full only in integral form, in spite of the fact they can only be applied in the 5 cases of maximal symmetry (3 for charge, 2 for current). So they're taught 4 equations are only good for 5 examples. (& they aren't taught that these are actually 2 much simpler equations, since no special relativity.)
  4. They don't appear in differential form (except in an appendix), even though a partial version of the differential equations is applied to radiation. The gradient appears only in a footnote (the divergence & curl only in the appendix).
  5. Refraction of light is claimed to have no explanation in terms of particles, quoting Newton's failure. Of course it does: As we know from quantum mechanics, Newton's mistake was to confuse phase and group velocities. Galilean relativity isn't covered until just before special relativity. So students never get a chance to learn about symmetry.
  6. Special relativity appears near the end, if at all, and after electromagnetism and optics. (Ever hear of nonrelativistic light?) Of course, that means in practice it won't be covered in the course.
  7. Lorentz transformations come before 4-vectors. Minkowski space isn't even mentioned.
  8. Complex numbers don't appear till the end of quantum mechanics (itself toward the end of the book). Sin's, cos's, and complicated trigonometric identities abound, especially for electromagnetism. (On the other hand, quaternions are OK? See above.)
  9. Planck's constant is introduced in its original form, as "h"; " ħ" does not even appear.
  10. Particle physics is tacked on the end (although a few particles themselves appear earlier, and collide).


  1. Although forces are often given as vectors, only the magnitude of the force is given in the equation for Coulomb's law: The radial unit vector never appears; it is only described in words. (Who wrote the textbook, Faraday?)
  2. Derivatives & integrals are repeatedly used, but almost never by name. "Δ" is always used instead of "d", and "∑" instead of "∫". Solutions to differential equations are given (e.g., for circuits) without the equations.
  3. Dot products and cross products are frequently used, but never by name. In specific applications, dot products are written either with cos θ or with the projection of one vector on the other, but never with both, nor is the equivalence indicated. The right-hand rule appears to work differently in different cases.
  4. Maxwell's equations are called "Maxwell's predictions", and written only in words. Ampere's law is never corrected.
  5. A relativistic cube is said to appear "rectangular". If they had even only watched a little popular science on TV, they would know it appears as a rotated cube.