Preface to June 2004 Edition

This text has developed out of an alternate beginning physics course at New Mexico Tech designed for those students with a strong interest in physics. The course includes students intending to major in physics, but is not limited to them. The idea for a ``radically modern'' course arose out of frustration with the standard two-semester treatment. It is basically impossible to incorporate a significant amount of ``modern physics'' (meaning post-19th century!) in that format. Furthermore, the standard course would seem to be specifically designed to discourage any but the most intrepid students from continuing their studies in this area -- students don't go into physics to learn about balls rolling down inclined planes -- they are (rightly) interested in quarks and black holes and quantum computing, and at this stage they are largely unable to make the connection between such mundane topics and the exciting things that they have read about in popular books and magazines.

It would, of course, be easy to pander to students -- teach them superficially about the things they find interesting, while skipping the ``hard stuff''. However, I am convinced that they would ultimately find such an approach as unsatisfying as would the educated physicist.

The idea for this course came from reading Louis de Broglie's Nobel Prize address.^1.1De Broglie's work is a masterpiece based on the principles of optics and special relativity, which qualitatively foresees the path taken by Schrödinger and others in the development of quantum mechanics. It thus dawned on me that perhaps optics and waves together with relativity could form a better foundation for all of physics than does classical mechanics.

Whether this is so or not is still a matter of debate, but it is indisputable that such a path is much more fascinating to most college freshmen interested in pursing studies in physics -- especially those who have been through the usual high school treatment of classical mechanics. I am also convinced that the development of physics in these terms, though not historical, is at least as rigorous and coherent as the classical approach.

The course is tightly structured, and it contains little or nothing that can be omitted. However, it is designed to fit into the usual one year slot typically allocated to introductory physics. In broad outline form, the structure is as follows:

• Optics and waves occur first on the menu. The idea of group velocity is central to the entire course, and is introduced in the first chapter. This is a difficult topic, but repeated reviews through the year cause it to eventually sink in. Interference and diffraction are done in a reasonably conventional manner. Geometrical optics is introduced, not only for its practical importance, but also because classical mechanics is later introduced as the geometrical optics limit of quantum mechanics.
• Relativity is treated totally in terms of space-time diagrams -- the Lorentz transformations seem to me to be quite confusing to students at this level (``Does gamma go upstairs or downstairs?''), and all desired results can be obtained by using the ``space-time Pythagorean theorem'' instead, with much better effect.
• Relativity plus waves leads to a dispersion relation for free matter waves. Optics in a region of variable refractive index provides a powerful analogy for the quantum mechanics of a particle subject to potential energy. The group velocity of waves is equated to the particle velocity, leading to the classical limit and Newton's equations. The basic topics of classical mechanics are then done in a more or less conventional, though abbreviated fashion.
• Gravity is treated conventionally, except that Gauss's law is introduced for the gravitational field. This is useful in and of itself, but also provides a preview of its deployment in electromagnetism. The repetition is useful pedagogically.
• Electromagnetism is treated in a highly unconventional way, though the endpoint is Maxwell's equations in their usual integral form. The seemingly simple question of how potential energy can be extended to the relativistic context gives rise to the idea of potential momentum. The potential energy and potential momentum together form a four-vector which is closely related to the scalar and vector potential of electromagnetism. The Aharonov-Bohm effect is easily explained using the idea of potential momentum in one dimension, while extension to three dimensions results in an extension of Snell's law valid for matter waves, from which the Lorentz force law is derived.
• The generation of electromagnetic fields comes from Coulomb's law plus relativity, with the scalar and vector potential being used to produce a much more straightforward treatment than is possible with electric and magnetic fields. Electromagnetic radiation is a lot simpler in terms of the potential fields as well.
• Resistors, capacitors, and inductors are treated for their practical value, but also because their consideration leads to an understanding of energy in electromagnetic fields.
• At this point the book shifts to a more qualitative treatment of atoms, atomic nuclei, the standard model of elementary particles, and techniques for observing the very small. Ideas from optics, waves, and relativity reappear here.
• The final section of the course deals with heat and statistical mechanics. Only at this point do non-conservative forces appear in the context of classical mechanics. Counting as a way to compute the entropy is introduced, and is applied to the Einstein model of a collection of harmonic oscillators (conceptualized as a ``brick''), and in a limited way to an ideal gas. The second law of thermodynamics follows. The book ends with a fairly conventional treatment of heat engines.

A few words about how I have taught the course at New Mexico Tech are in order. As with our standard course, each week contains three lecture hours and a two-hour recitation. The book contains little in the way of examples of the type normally provided by a conventional physics text, and the style of writing is quite terse. Furthermore, the problems are few in number and generally quite challenging -- there aren't many ``plug-in'' problems. The recitation is the key to making the course accessible to the students. I generally have small groups of students working on assigned homework problems during recitation while I wander around giving hints. After all groups have completed their work, a representative from each group explains their problem to the class. The students are then required to write up the problems on their own and hand them in at a later date. In addition, reading summaries are required, with questions about material in the text which gave difficulties. Many lectures are taken up answering these questions. Students tend to do the summaries, as their lowest test grade is dropped if they complete a reasonable fraction of them. The summaries and the associated questions have been quite helpful to me in indicating parts of the text which need clarification.

I freely acknowledge stealing ideas from Edwin Taylor, Archibald Wheeler, Thomas Moore, Robert Mills, Bruce Sherwood, and many other creative physicists, and I owe a great debt to them. My colleagues Alan Blyth and David Westpfahl were brave enough to teach this course at various stages of its development, and I welcome the feedback I have received from them. Finally, my humble thanks go out to the students who have enthusiastically (or on occasion unenthusiastically) responded to this course. It is much, much better as a result of their input.

There is still a fair bit to do in improving the text at this point, such as rewriting various sections and adding an index ...

Finally, a word about the copyright, which is actually the GNU ``copyleft''. The intention is to make the text freely available for downloading, modification (while maintaining proper attribution), and printing in as many copies as is needed, for commercial or non-commercial use. I solicit comments, corrections, and additions, though I will be the ultimate judge as to whether to add them to my version of the text. You may of course do what you please to your version, provided you stay within the limitations of the copyright!

David J. Raymond

New Mexico Tech

Socorro, NM, USA

raymond@kestrel.nmt.edu