Michael Fowler's Home Page
University of Virginia Physics Old home page
Michael Fowler's Lecture Notes Online.
Galileo and Einstein
The course follows the development of ideas approximately in the historical sequence. After looking over the first recorded real mathematics, that of the Babylonians, we review some of the Greek contributions to math and science, which were essential to both Galileo and Einstein in their work. We shall prove and find very useful Pythagoras theorem, and a few other ideas about triangles. We'll also look at Greek ideas about the Solar System, and how they measured the distance to the Moon quite accurately (using the ideas about triangles!). We will examine how these ideas reached western Europe by way of the Arab world.
We'll do some of Galileo s actual experiments that led to understanding motions of projectiles, and show how Newton connected these results with the motion of the Moon, and then to all the planets. Next, we'll examine the nature of light, for this is what led Einstein to question the traditional concepts of space and time. Finally, we'll develop the theory of Special Relativity, including time dilation, relativistic mass increase, and E = mc2.
Modern Physics
Modern physics means physics based on the two major breakthroughs of the early the twentieth century: relativity and quantum mechanics. Physics based on what was known before then (Newton s laws, Maxwell s equations, thermodynamics) is called classical physics. This course traces in some detail just how the new ideas developed. We examine the experimental and theoretical paradoxes that forced thinking out of the traditional path. This is a valuable exercise the classical ideas are in much better accord with common sense (defined by Einstein as the layer of prejudices in place by age eighteen), so seeing how the new physics came about is helpful in overcoming that common sense and getting a better understanding of nature. But this is not just a course on concepts: the lectures and homework are sufficient to give the student a basic technical grasp of special relativity, and of Schr dinger s quantum mechanics.
Graduate Quantum Mechanics
Graduate Electricity and Magnetism
A new set of notes, based on Jackson, but with some additions (and subtractions). Sufficient notes for the two-semester course, but I plan to add a few topics to give extra flexibility.
Physics 152: Gravity, Fluids, Waves, Heat
This grab bag of physics topics formed the second semester of our four-semester introductory physics course designed for physics majors. I've also added material which isn't in the standard textbooks, especially on fluids, to give a more complete picture.
Some PowerPoint Slides for Introductory Physics
The ones above open in .pdf: to get the actual PowerPoint files, after opening change .pdf to .pptx
...and Applets!
News!
UVa Physics Department History
I'm currently putting together some documents about our Department's history.
Prequel: The UVa Physics Department, like Modern Physics itself, emerged in recognizable form in the years around 1900. In fact, though, there was earlier science in Virginia, both research and teaching, so we will mention a few early contributors to set the stage for subsequent development.
1. Here's the prequel.
2. A history written in 1968 by Prof. Fred Brown.
3. *Our most important document*:
ANNUAL REPORT OF THE SCHOOL OF PHYSICS FOR THE FISCAL YEAR 1947-48
Llewellyn G. Hoxton, Chairman, School of Physics, University of Virginia, March 25, 1948.
Introductory Comments and Summary:
Does not sound like a promising title for an important document: but this one is much much more than just an annual report!
In 1948, Hoxton was retiring after more than forty years at UVa. This document was his attempt to make clear to the incoming University President, Colgate Darden, how and why the Department developed as it did over those forty plus years, and what would be needed to continue successful development.
In other words, how did UVa science go from mental asphyxiation (Rogers phrase) in the 1840s to the Manhattan Project in the 1940s? And how best to continue?
To sketch the context, it helps to start a little earlier, back in the 1820s. Jefferson wanted to create a university following the European model, and in particular the sciences should include ongoing significant research as well as teaching. Hoxton makes clear how and why the University fell short of Jefferson's vision for much of the past, and how things might be improved in the future. One recurring problem in Hoxton's time was that in contrast to its competitors (Harvard, then Hopkins) UVa's budget was set by state legislators, who mostly wanted a straight teaching college for their children. So allocations for any kind of science research were minimal (unless there was obvious commercial or military importance, such as geology or meteorology.) Furthermore, building up the University by bringing in top European academics proved more difficult than Jefferson anticipated, at least in part because of slavery.
Perhaps the most important science faculty member in the first half century after founding was William Barton Rogers (at UVa 1835 to 1853), a nationally eminent scientist. He tried to persuade the Virginia legislature to think bigger about science. This did lead to the beginning of the School of Engineering (only the fourth in the country) but in the end Rogers found Massachusetts more receptive, so he left Virginia, went there, and founded MIT. Happily, that turned out to be very successful!
After Rogers left, Francis H. Smith became Chairman, 1853 to 1907. (Note: Hoxton was here as a student 1896 to 1900, then as faculty from 1906 on, so from this point on Hoxton is writing from direct experience.) Smith followed Rogers in giving excellent lectures, but he had little interest in research. Nevertheless, important original work was done here in 1897-1905, by Instructor W. J. Humphreys (Ph. D. Hopkins), who raised the necessary money himself, including that for an excellent shop. He later became an eminent meteorologist (but not at UVa).
To summarize: from 1853 to 1897 Virginia physics (perhaps we should say pre-physics) was moving very slowly, and was way underfunded by the state. Humphreys stirred things somewhat until 1905, but then little further happened until 1928, when a miracle occurred: a multiyear grant of tens of thousand of dollars a year for science at UVa from the General Education Board. To modern ears, that might sound like some government department, but in fact it was Rockefeller philanthropy. At almost the same time, the duPont corporation gave significant money for graduate student support, and finally even the state was shamed into contributing reasonable annual amounts.
But none of this largesse would have gotten us to the Manhattan Project without a further coincidence: Jesse Wakefield Beams earned his Ph. D. here in 1925, became a postdoc at Yale, then in 1929 joined the UVa faculty. His thesis research had been on finding the photoelectric delay time, using high speed rotating mirrors (this led eventually to centrifuges), but he had wide interests and his enthusiasm plus the influx of new students changed the atmosphere completely: there were suddenly around a dozen graduate students, and, for example in summer 1935 seven Ph.D.'s were awarded. Furthermore, things were changing nationally by that point: the switch to war work. Beams and UVa responded, establishing research not only on uranium separation but also on missile guidance and detection, with now many more graduate students, and Navy funding. The Department had become modern.
Hoxton's 1948 Annual Report: Our Version.
The original document (one of the carbon copies) resides in the UVa Library Special Collections. You will be allowed to inspect it, with supervision. It is not conveniently readable. The library can also provide copies, but these are also not too easily useable.In contrast, our transcription here is standard searchable text. This is new, so there may be errors, please let us know. The main work was done by the formidable team of Chat GPT and Lou Bloomfield. Thanks, Lou!
How Creating a USEM Led to a Long-Lost Telescope
Michael Fowler, UVa 08/29/2025
In the late 1980 s, the University expanded its teaching offerings by introducing University Seminars, USEMs. They re still with us: one-semester two-credit courses for typically a dozen students (max 18). The aim was (and is) to develop critical thinking interactively, avoiding any form of rote learning. In the fall of 1990 I taught a USEM I called Galileo. It consisted of going through Galileo s rather short book, Two New Sciences, a book he wrote for a general audience, so in colloquial Italian, not Latin (of course we read it in English). The text is a conversation between three friends (one religious, one a skeptic, one in the middle) who perform many simple science experiments together with pendulums, rolling balls, floating objects, etc., testing their preconceived notions. Galileo gives detailed instructions, with diagrams, and in class we reenacted some of their demonstrations, including those which historically led to the first clear understanding of acceleration.
Virginia has a long tradition of excellent physics teaching at all levels, and a wonderful collection of physics demonstrations, many handmade and some a century (or more!) old. We tried a few of the old ones in the USEM, the whole class taking part, and mostly they worked fine. However, as the semester went on, I kept looking for something a little different, and one day my search led to an extra small room at one end of the Physics Department s demo lab (the room no longer exists in the newly reconfigured building). This dusty room was evidently rarely used. In one corner, beneath some stairs there was a pile of what appeared to be physics demo junk, long abandoned. I got down, dug in, and pulling aside a covering of cobwebs and dust, among other things a rather large brass telescope emerged! I was elated. It had likely been there for decades.
The telescope was just what I needed to strengthen my Galileo course. He himself had built the first really good telescope in 1609. Just before that, around 1603, some telescopes were made in Holland, with magnification 3x. But Galileo s was 20x, and that was a game changer powerful enough to see the moons of Jupiter (previously unknown) and to reveal that our own Moon was just a big sunlit rock, not some magic stuff as had been widely believed. Both these observations were foundational to modern astronomy.
I have to admit that the students were not as excited as I was by the old telescope. It had a very narrow field of vision compared with the binoculars they were used to, the image quality wasn t great, and at four feet long it was a bit unwieldy. So after the first year I decided not to use it in class. Instead I put it on display in my office, on top of a big bookcase, where it remained from 1990 until the Physics Building reconstruction in 2023, when it moved with me to a smaller office.
To brighten up my new small office I polished the telescope lightly with Brasso. Much crud was removed but more importantly the telescope maker s name was revealed: W&T Gilbert (see illustration). I promptly googled W&T Gilbert to discover their telescopes weren t that good (no surprise) and consequently they went bankrupt in 1828! UVa bought the telescope shortly after Jefferson died in 1826. In fact, he had a very similar (but better) telescope, his was made by the Dollonds, another London firm, around 1790.
At this point, I realized the telescope might be interesting to a wider audience, so I got in touch with Meg Kennedy, Curator of Material Culture at the UVa Small Special Collections Library, and her colleague Ricky Patterson. It happened that they were about to open an exhibition on early astronomy at the University, and when I told her about my telescope, they were anxious to include it.
It turned out that the key to identifying the telescope was a letter written in 1830 from Robert Maskell Patterson (Professor of Natural Philosophy, hired in 1828 to replace Charles Bonnycastle who himself became Professor of Mathematics) to Ferdinand Hassler (Head of US Coast and Geodetic Survey) planning a National Observatory. Maskell Patterson lists the astronomical equipment he has to hand (including some from Bonnycastle s original small observatory, designed by Jefferson). Predictably, Maskell Patterson was not impressed with our telescope, I quote from the 1830 letter:
But of the most important instrument, I have to complain greatly. Our best telescope, is a four feet refractor, by W.+T. Gilbert, and a very inferior instrument even of its class The Board has authorized the purchase of a fine telescope as soon as the funds will permit.
So the old telescope, after thirty-five years as a teaching tool and accent piece in my physics office, is finally recognized as having been at the University from the start. Perhaps such remarkable longevity deserves recognition, despite admittedly mediocre quality? In any case, the telescope will have a new home as part of Special Collections.