What is physics?

According to the Oxford Languages Dictionary, physics is “the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.”

What do physicists do?

• They teach in secondary schools, universities, and other venues such as teachers’ colleges.

• They do research, both pure and applied. (I’m not crazy about the adjective “pure”; it makes it sound like applied physics is impure. But we’re stuck with it.) AI: “‘Pure and applied physics’ refers to two complementary approaches to the study of physics. Pure physics focuses on understanding the fundamental laws of nature, while applied physics focuses on using those laws to develop practical technologies and solve real-world problems.” For example, studying the basic structure of atoms led to the laser. But the lines are not always clear. Sometimes both are going on simultaneouly, and even in the same research group.

Teaching

Let’s start with the negative. “Physics avoidance” is common for example, in US high schools, sometimes aided and abetted by making it non-required. Of US university students, only one third of one percent are studying physics as their major subject. Even among the STEM (Science, Technology, Engineering, and Mathematics) students, only two percent are majoring in physics.

Why? Several reasons; inter alia,

media misrepresentation;

humanities’ physics envy: trying to make STEM into STEAM: (Science, Technology, Engineering, Arts, and Mathematics);

political bias: “Physics is a weapon of white male oppression of females and minorities” (more about this in the section Science Anxiety.);

stereotyping and mockery: “Geek”, “Built any bombs lately?”.

In horror films, mad physicists play a prominent role:

• The Invisible Ray: “A scientist becomes murderous after discovering, and being exposed to the radiation of, a powerful new element called Radium X.”

• Man Made Monster: “A mad scientist turns a man into an electrically-controlled monster to do his bidding.”

• The Fly: “A scientist has a horrific accident when he tries to use his newly invented teleportation device.”

• Monster of Terror: “A young man visits his fiancée’s estate to discover that her wheelchair-bound scientist father has discovered a meteorite that emits mutating radiation rays that have turned the plants in his greenhouse to giants.”

• Last, but surely not least, Stanley Kubrick’s Dr. Strangelove. (“Mein Führer, I can valk!”)

Even the good guys, such as Spiderman and the Hulk, gained their powers by exposure to radioactivity.

To be fair, Dr. Frankenstein was a biologist. And although it is not related to physics, who can resist The Devil Bat? “A mad scientist develops an aftershave lotion that causes his gigantic bats to kill anyone who wears it.”

That’s a lot to combat. But inarguably, the best weapon is education.

Teaching methods

The traditional method has been the lecture, known variously as “chalk and talk” and “the sage on the stage”. It need not be abandoned, but over the last few decades, various teaching strategies have been shown to aid science learning. These include:

• The implementation of teacher–student and student–student interaction in lieu of straight lecturing.

• The design of laboratories to elicit creativity in approaches to problem definition and solution, in lieu of “cookbook” instructions. “Show that the period of a pendulum doesn’t depend on its mass” versus “On what does the period of a pendulum depend?”

• The recommendation of alternative presentations of materials from other textbooks, journals, and popular expositions

My own career consisted of both teaching and research, as well as naming, studying, and reducing science anxiety.

Courses

Check pretty much any university physics syllabus, and it will include

• a course for social science and humanities students, alternately called Liberal Arts Physics or more cutely, Physics for Poets.

• several introductory courses for physics majors and others who need it for various requirements, such as chemistry majors and pre-medical/dental aspirants.

• intermediate and advanced courses for physics majors, including specialties such as Pre-engineering and Biophysics.

I have taught most of those. Instead of a long description, I will describe my favorite: Liberal Arts Physics, then mention a course for physics students.

Liberal Arts Physics

It’s one thing to teach majors’ courses, where the students think like us; it’s quite another to teach students who think differently. I employed various techniques. One I call the modified Socratic method. I briefly lectured on the subject at hand. Then I asked a question about the material I just chalked and talked. I didn’t ask for hands. To do so favors the quick and the glib. Instead, I chose a student at random and asked them the question. Then I waited. Either the student would answer in a reasonable time, or coudn’t. If the latter, I followed up with a question whose answer led up to it. If the student still couldn’t answer, I went back further. In my experience, almost all students will reach a point, perhaps several questions back, when they can answer. Then I brought them forward.

There are two ostensible difficulties with this method. First is the time consumed. Second is the possibility of provoking the student’s anxiety. For the first, the time used acts as a review of the subject for the other students, some of whom are unsure of the various answers. For the second, I praised the student as they answered each of the questions in the process. I also reassured the student—and all the others—that the selection of each student will be random and involve all of them over the semester.

I also used in-class group exercises in lieu of labs, which are not usually part of the liberal arts physics course. For example, when we were studying circular motion, I divided the class into groups; one set of groups examined how a clothes washer works; the other set, a clothes dryer.

One method that has proved particularly effective is group project work. Group methods have been shown to be pedagogically effective. One of the greatest virtues of group work is that it levels the playing field, especially for females and less confident students. Here is an article I wrote about it, describing group work in Denmark, where it has a long history, and the ways it can be adapted for the US.

Physics students’ group project work

For freshman physics students, we instituted group projects. These were semester-long, and met several hours a week. Students selected projects and chose an instructor as adviser. Here are some examples:

High friction surfaces

Dynamics of motion in vertical circles

Seismological models in the laboratory

Friction on ice

Analysis of pianos

Investigation of wind turbines and solar cells

At the conclusion of the course, each group made a presentation to faculty and any students who wish to attend. These were twelve minutes long: ten for presentation, two for questions and comments. (The proportions were fexible.) Each of the group members presented part of the report. Grading by the adviser was for each individual student and for the group as a whole. Our freshman project course was just one of many examples of group project work.

Much more can be said about pedagogy, but this shall suffice. You can find more in Helge Kastrup’s and my book, Fear of Physics .

Research

Here I describe some research projects in which I was involved. All of my work has been collaborative.

Physics of the eye

In 1980, my Loyola colleague, Professor of Psychology Richard Bowen discovered that if you shine a bright light for a brief time into the eye, and follow it with another, you will see the second one flickering, despite the fact that the light itself doesn’t. From this he concluded that the flickering is generated in the eye.

Rich asked me what in physics could help in understanding the phenomenon. Since the bright square-shaped “inducing” pulse” causes flicker of the “response pulse”, I proposed that we make the inducer flicker and see what the response does. Are there inducer frequencies that produce brighter and/or more flickers? We found the answer to be yes. This was an example of an effect called resonance, which occurs in many phenomena. (For example, it’s what you get when you tune in a radio station.) At certain frequencies of the inducer, we saw the flicker light intensity become higher and generally produce more flickers. This occurred at more than one inducer frequency – more complicated that the single-resonance effect. Let’s turn to a musical instrument for an analogy. For any but the flute, which produces a single fundamental, there appear ultraharmonics: overtones. Its name gives the information: in addition to the fundamental, higher frequencies appear: those tell you what the instrument is. But there are also lower frequencies appearing: so-called subharmonics or undertones (really–that’s the word). Here is an example. And both over-and undertones of flickers were what we saw. Altogether, we saw three resonances: the fundamental, one overtone, and one undertone. The fundamental resonance appeared at a somewhat different frequency than that predicted by the simple one-resonance physical model; one overtone (the ultraharmonic) appeared at three times that frequency; one undertone (the subharmonic) at 1/3 of it. Another Loyola colleague, Professor of Mathematics Rich Lucas and I examined these effects and found that they were described by a formula called the Duffing Equation. (See Duffing Equation if you’re interested.)

We don’t know the biology of the eye : that’s not our expertise. But the mathematics and physics we do. Perhaps someday it will all be explained by the biology.

Physics of the atmosphere

 Fog

By Carl Sandburg

The fog comes
on little cat feet.

It sits looking
over harbor and city
on silent haunches
and then moves on.

It actually sits perfectly still on its haunches for a pretty long time before it moves on. How do we know? From lidar. Taking its name from radar: radio detection and ranging, lidar is light detection and ranging. A radio wavelength of an FM station at 100 million Hertz (your radio reads “100”) moving at the speed of light: 300 million meters per second, is 300/100: three meters. Lidar detects much shorter wavelengths than radar: it requires the use of a laser. The wavelength of green light is of order five 10 millionths of a meter. It can therefore probe much smaller objects than can radar. Radar and lidar work the same way: the simplest design consists of a transmitter and a detector at the same place. A pulse is sent out; it collides with and scatters back from an object to the detector. The total round trip time gives the distance to the object. For radar it could be an airplane. For lidar it can be something much smaller, such as a fog droplet.

I was part of a group that studied fog by lidar, using a pulsed ruby laser as the transmitter and the telescope at Northwestern University's Lindheimer Astrophysical Research Center (LARC) as the detector. We fired a pulse into a fog and found that the backscattered signal to the telescope from the fog was unchanged over a period of hours, which we had not expected. I also undertook to analyze the "distribution function" of fog droplets; i.e., how many of each size there might be. I chose reasonable guesses for the smallest and the largest droplets. Their radii are on the order of micrometers: millionths of a meter. Droplets of that size scatter light, making it hard to drive in fog. Not so for rain, whose droplets are much larger, and less susceptible to light scattering.

Physics of the atom

When we look at a rainbow or through a prism, we see light as a continuous spectrum. Until the twentieth century, why this was so was unclear. So physicists looked for a simple system, as is their wont. They chose hydrogen gas. It emitted a line spectrum; that is, only certain wavelengths showed up when it was heated, as in Figure 1. But that too, despite being ostensibly simple, was not understood. Enter Niels Bohr, a young Danish physicist, who provided an answer in 1913– by breaking the rules of classical physics. He adopted the model of electrons circling a nucleus, like planets circling the Sun. But here’s the difference. Planets can take any orbit they like. If the same were true for electrons, then the energy given off if they dropped from higher to lower orbits could be anything–a continuous spectrum! Bohr got around this by postulating–contra classical physics–that the electrons, unlike the planets, were constrained to certain orbits, as in Figure 2. Thus, the output of light when an electron dropped from one orbit to a lower one could only have certain energies; viz., a line spectrum. Conversely, input light at that wavelength causes the electron to jump from the lower to the higher orbit. The color of the line was determined by the size of the quantum leap in energy, as in Figure 3.

Figure 1 - Visible part of the emission spectrum of hydrogen

Figure 2 - Bohr model of the atom

Figure 3 - Atomic energy levels

Over the next few years, Bohr’s model was modified; for example, the orbits were shown to be elliptical rather than circular. But then came a model of the atom that overthrew Bohr’s, relegating to it the sobriquet “The old quantum mechanics”. The new quantum mechanics, which we have to this day, is based on the premise that an electron (and any other particle) is also a wave. The breakthrough was provided by Erwin Schrodinger (he of feline fame), with his equation linking wave and particle properties. To give two concrete examples, if you look through a screen door at a streetlight, it will appear to have alternating light and dark sections; this is proof of the wave nature of light. On the other hand,when a closing elevator door reopens as you leap in (if you’re lucky), that’s because you are interrupting an invisible beam of light, which triggers a circuit which reopens the door. That beam can only be explained by light being made up of particles.

Good to know, but let’s stick with Bohr’s particle model for convenience. The first element in the periodic table is hydrogen. Hydrogen gas in its simplest form consists of two particles: a heavy, positively charged nucleus and a light, negatively charged electron circling it, as in Figure 2.

The next element is helium, which in its simplest form is a nucleus four times as heavy and twice as charged as hydrogen’s, with two electrons circling it, as in Figure 4. (Two important properties of helium. First, it is used in balloons, because it is lighter than air and thus floats. Second, if you breathe it, you can sound like Donald Duck.)

Figure 4 - Helium atom structure

Here’s the problem: the structure of the hydrogen gas can be obtained by exact calculation. The spectrum of helium and all the other elements can only be obtained approximately. This has nothing to do with quantum physics. It turns out, as was proved mathematically centuries ago, that the “two-body problem” is the only one that can be solved exactly. And hydrogen gas is the only case of this for the elements. So physicists have constructed elaborate schemes to get good approximate results for the others; viz., those that match experiment–in our case, spectra. The one I worked with is called “self consistent field theory”. By “field” we mean what is commonly called “force field”, like, say, the gravitational field of the Earth, or in the case of atoms, the electromagnetic field: the field of electricity and magnetism it produces. Imagine an atom with a few electrons, and one in a larger orbit than all the rest. What does that one see? It sees the nucleus surrounded by a sort of cloud of the others. Sodium is an example, as in Figure 5. (Note: The orbits at not really equally spaced. The real picture would be hard to fit on the page.)

Figure 5 - Sodium atom energy levels

It has a nucleus of charge +11, and circling it, eleven electrons, each of charge -1, as in the figure. The eleventh electron is in a larger orbit than the others. (Chemists call this the valence electron.) So it sees a “quasi-nucleus” (for want of a better term): the actual nucleus surrounded by a sort of cloud of 10 electrons. Thus, total charge (11-10): 1. The two-body hydrogen-like problem! So it can be solved exactly. Well, not quite. That cloud isn’t really a cloud, it’s ten electrons zipping along in their orbits around the nucleus. Counting the nucleus and the valence electron, that’s a 12-body problem! So now the self-consistency kicks in. The problem as, we said, can only be solved numerically. (When I started in the late 60’s, the input consisted of stacks of cards. Now I could do it on my Mac.) So we start with the valence-electron-quasi-nucleus cloud model and do a hydrogen-like calculation. But then we have to do it for all the other electrons. The lucky valence electron sees an approximately spherical cloud between it and the nucleus. Each of the others, however, is embedded in a cloud that surrounds it. The computer then calculates the approximate orbit of each of the electrons in turn. It does it repeatedly, until the final iteration is the one that gives the same answer as the one before it. A good way to think of it is that at the end, each electron contributes to the field just what it gets from the field. That’s what we mean by “self-consistent”.The criterion for judging if a step is better than the one before it is that the energy of the whole system gets lowered. That’s a general rule, not restricted to quantum physics. Balls roll downhill. And keep in mind: All of these calculations are not actually dealing with electrons as pure particles; they also have wave properties, as we saw.

I got into this business serendipitously. I was working on my Ph.D. in experimental physics (in which I later realized I was a disaster). The money of my then-adviser ran out, and I was left high and dry. So I threw myself at the feet of Art Freeman, then chair of the Northwestern physics department. Art, a theoretical physicist, changed my life: He said “Would you like to work for me?” That’s where I learned self-consistent field theory, on which I spent a great part of my research life. I owe my career to Art, who passed away a few years ago at age 88. We became much more than teacher-student. He was my son’s godfather and a witness to the signing of my wedding document.

Once Art had taught me the rudiments of self-consistent field theory, he sent me to the person who would become my Ph.D. mentor, Paul Bagus. It turned out that he and I had both gone to the Bronx High School of Science! Paul taught me the tricks of the trade and saw me through the theoretical part of my dissertation, using the results of self consistent theory to obtain transition probabilities (which comprise the next section). He and I have stayed in contact over the years, calculating various properties of atoms. Our latest collaboration was a pedagogical review of the theory, which resulted in a presentation by me to the Chicago chapter of the American Association of Physics Teachers. We have also become good friends.

Here are some of the research problems in this area that I have worked on.

How bright is a star really? Transition probabililties.

Ordinary stars are mostly hydrogen. So we might expect to see spectral lines as in Figure 1, due to the transition of an electron from one orbit’s energy level to a lower one, as in Figure 2. Astrophysicists have determined what the intrinsic brighness of each type of star would be. You would think that these values would tell you how far away the star is by what brightness you observe. Not quite. In addition to the size of the energy jump (Figure 3) , there is the question of its likelihood of making that jump. That has to be factored in. We call that the “transition probability”. That’s what we can calculate using self-consistent field theory, and that was the subject of my Ph.D. dissertation. I did it for carbon, nitrogen, and oxygen. Why? Because astrophysicists have found some in stars, albeit in much lower amounts than hydrogen. So there it stood. But now came another problem: their spectra were mostly at wavelengths in the ultraviolet range. Think sunburn. Luckily the Earth’s atmosphere blocks most of that out. But then the only way to use my results would be for measurements made outside the Earth’s atmosphere. So my work was relegated to obscure journals, from 1971–until the early 1990’s, when a colleague came up to me, excitedly announcing that my work was now being cited. In a word (well, two words): Hubble Telescope! Not exactly the text on my T-shirt: “I BECAME A PHYSICIST FOR THE FAME AND THE MONEY” but gratifying nonetheless, to have made a contribution to scientific knowledge.

Sneaking a peek at the nucleus. Muonic atoms.

Look again at the diagram of the Bohr atom for sodium in Figure 5. Other atoms look about the same: a heavy compact nucleus and lightweight electrons revolving around it from considerable distance, again like the solar system. How much can we know about the structure of the nucleus if the only possible probes, the electrons, are so far away? Not a whole lot. But one way to find out is to see if we can find electron-like particles that can get closer in. We can. They are called muons. They have the same charge as electrons: -1, but have 207 times the mass. Doing the math (trust me), that puts them 207 times closer to the nucleus than are electrons. With them, we can probe features of the nucleus that would otherwise be invisible. One such is its internal magnetism. Without going into detail, that’s what we did.

Here’s a partial title of one of our papers: “Muonic Hyperfine Anomalies: Large but not Giant”. Never mind what “Hyperfine Anomaly “means; it’s a magnetic feature of the nucleus. Focus on “Large but not Giant”. Why such a title? Because an experimental group had claimed that the effect was huge. Our calculations showed that it was big, but nowhere as big as they claimed. So who was wrong? They were. Why? Since they had their muons in a crystal, they blew the hell out of it when measuring the effect.

Now a word about the politics of science–and don’t let anyone tell you there isn’t any.

First example. There was an international conference on muonic atoms in Canada. Art Freeman sent me, then in my callow thirties, to give a paper. I talked with the leader of the experimental group, a lot older and more famous than I, and we agreed to modify our comments to reflect what had been done. I spoke first, politely saying the the experimental and theoretical results differed, a far cry from “You screwed up”. He followed–giving a talk extolling their work and never mentioning ours.

Second example. They had published their work in a very prestigious journal. We sent our work showing our calculations and their error to the same journal. It was rejected. Why? Because journal editors don’t like egg on their face. So we published it in another journal, but people who only read the original would never know that the experimental results were wrong and our theoretical ones were right One of our team jokingly proposed that we should not have shown that they were wrong, just have said that the disagreement between experiment and theory was a conundrum. Of course we gladly paid the price for integrity.

SUSYQM

Most of my research activity from 1995 on involved what is called “supersymmetric quantum mechanics”, abbreviated “SUSYQM” and pronounced “Susiecue em”. It sounds daunting; it was indeed, sitting on the interface of physics and mathematics. But I think I can explain the idea without using either.

First of all, credit where credit is due. The leader of our group was Asim Gangopadyaya, my colleague and friend. The ideas poured out of him–often in the middle of the night. I would sometimes check my email in the morning and receive a message from him sent at four AM. (When did the guy sleep?)

In Figure 3 we saw energy levels for hydrogen. The difference between levels gave the spectrum. As we mentioned above, we could calculate the energies by solving that old workhorse, the Schrodinger Equation–possible, but tedious. There’s another way, called (you guessed it) SUSYQM. If you could somehow find the energy of the lowest state: the so-called ground state, you could get all the others. Not only that, you could find all the energy levels of related ones, which we call partners. Here’s a graph of one and some its partners (Figure 6). Notice that the ground state of each is the next state up; i.e., the first excited state of its partner. Here’s a good analogy. Take the four stringed instruments. Tune them so that the differences in pitch are the same for each instrument. Now make the lowest pitch of the cello the same as the second lowest of the bass, the lowest pitch of the viola the same as the second lowest of the cello, and the lowest pitch of the violin the same as the second lowest pitch of the viola, as in Figure 6 . (The Ill-tempered Strings?) There you have it. If you know the notes of the bass, you can get all the others.

Figure 6 - Partner energy levels

We found that there are a dozen such systems. One is the hydrogen atom. Another works for diatomic (two-atom) molecules. A third is the quantum version of the harmonic oscillator. (The macroscopic version is a vertical pendulum as in a grandfather clock, or a mass oscillating on a spring, as in Figure 7.) The others are for more arcane systems.

Figure 7 - Harmonic oscillator model of a mass on a spring

Our harmonic oscillator calculations led to another example of scientific politics. Asim found a paper by a prominent physicist in a prominent journal on the “half-harmonic oscillator”: the mass crashing into the floor. I looked at the paper and saw that it was wrong. We figured out why, and sent a paper to the same journal. Rejected. So we wrote a second version. Rejected. Finally, we wrote a third version, spelling out all the details. You guessed it: rejected. Asim is a soft-spoken, well-mannered fellow. Not so yours truly. I wrote them back, “The minimum requirement of a theory is that it get the right answer.” They wrote back the equivalent of “Never darken our doorstep again.”

Eventually, we put our correct solution for the half-harmonic oscillator in a book written by Asim and me and a third colleague, Constantin Rasinariu: Supersymmetric Quantum Mechanics, An Introduction. By the way, I had proposed that instead of our photos on the back cover flap of the book, we do a centerfold. I even convinced them to photoshop our heads onto muscular bodies in bathing suits. But in the long run they chickened out. I still have the pictures. “Blackmail” is such an ugly word….

Publications

Here are some of my research publications in the three areas I have discussed.

“Multiple Resonances in the Double-Flash Effect”, J. V. Mallow and R. J. Lucas, J. Opt. Soc. Amer. A9, 2105 (1992). URL

“Fog Droplet Distribution Functions for Lidar,” J. V. Mallow, Applied Optics, 21, 95 (1983). URL

“Experimental and Theoretical Investigation of Astrophysically Important Ultraviolet Transition Probabilities,” J. V. Mallow. In Atoms and Molecules in Astrophysics , ed. N. Roberts and T. Carson, Academic Press, London, 347-352 (1972). URL

“Dirac-Fock Method for Muonic Atoms: Transition Energies, Wave Functions, and Charge Densities,” J. V. Mallow, J.P. Desclaux and A.J. Freeman, Phys. Rev. A17, 1804 (1978). URL.

“Breit Interaction Determination of Muonic Hyperfine Anomalies: Large but not Giant,” A.J. Freeman, M. Weinert, J.P. Desclaux and J. V. Mallow, J. Mag. and Mag. Mat. 22 L1 (1980). URL

Supersymmetric Quantum Mechanics: An Introduction, A. Gangopadhyaya, J. V. Mallow, and C. Rasinariu, Singapore: World Scientific Publications. (1st edition 2011; 2nd edition 2018). URL