Symmetries for the Mind’s Eye: The Far-Reaching Significance of Lorentz and Gauge Invariance

Background to the Essay

In the 1980’s and 1990’s I was an active contributor to the AAPT journal The Physics Teacher (TPT) as an author, member of the editorial board, and for a while something of a “sounding board” to Clifford Swartz, the editor of TPT for nearly 30 years. During one phone call between us in 1998, he said he would like to have an article explaining the basic idea of gauge theory and how this concept unifies physics. I suggested some notable physicists to contact, but he said that all the articles he saw so far were beyond the level of TPT. He asked if I would write one. My first book of personal researches, And Yet It Moves: Strange Systems and Subtle Questions in Physics, had been published by Cambridge a few years earlier (1993) and was receiving favourable comments for its clear discussion of complex issues, including the Aharonov-Bohm effect, which is illustrative of gauge theory in the realm of quantum physics and electromagnetism. I agreed and produced this paper.

The reviewers to whom the paper was sent liked the paper, but concluded that it was more suitable for another journal than TPT. The collective arguments of the reviewers were that the subject matter was too abstract, a high school teacher could not follow all of it, and a high school teacher could not use the contents in a classroom. I pointed out in response that the subject was indeed abstract, but so are all the laws of physics to one degree of another. And in any event, “you knew the material is abstract; that is why you asked me to write the article.” Moreover, an article of this kind does not have to be “used” in class at all. Surely there are TPT readers who have heard of the importance of gauge symmetry and simply want to know more about it. Self-instruction is an important part of education for both teachers and students. Furthermore, those who do want to know more should be able to follow the principle ideas of the paper and come away with a better understanding. After all, it is not necessary to understand everything in order to learn something. But in the end, Dr Swartz regretted that he would not be able to publish the piece.

Now—more than a quarter century later—I still believe that readers, especially those who have studied calculus, can benefit from the discussion of gauge symmetry presented in this essay. And since 2025 is the centennial year of the creation of quantum mechanics, it is ideal reading material for the International Year of Quantum Science and Technology (IYQ).

Read Symmetries for the Mind’s Eye. (PDF)