Reduced Mass

In Section 14.4 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss molecular energy levels. In particular, we examine translational, rotational, and vibrational levels. When analyzing rotational levels, we consider a simple diatomic molecule and divide the motion into two parts: a uniform translation of the center of mass, and a rotation about the center of mass. We show that the rotational energy can be written as ½Iω², where ω is the rotational angular frequency and I is the moment of inertia. The moment of inertia is I = [m₁ m₂/(m₁ + m₂)] R², where m₁ and m₂ are the mass of the two atoms making up the diatomic molecule, and R is the distance between them. In quantum mechanics, the spacing of rotational energy levels depends on I.

Later in the same section, Russ and I consider vibrational motion. However, we don’t do a detailed analysis for a diatomic molecule, like we did for rotational motion. In this blog post, I will remedy that situation and present the analysis of vibrations of a diatomic molecule. Our goal is to derive an expression for the vibration frequency in terms of the masses of the two atoms and the spring constant connecting them.

Let’s do the analysis in one dimension. Consider two atoms with mass m₁ and m₂ connected by a spring with spring constant k. The position of m₁ is x₁, and the position of m₂ is x₂.

First, write down Newton’s second law for each atom.

    m₁ d²x₁/dt²  = − k (x₁ − x₂ ) ,

    m₂ d²x₂/dt²  =    k (x₁ − x₂ ) .

Next, define two new variables, as we did for rotational motion: x, the position of the center of mass, and X, the distance between the two masses

     x = [m₁/(m₁+m₂)] x₁ + [m₂/(m₁+m₂)] x₂ ,

    X = x₁ − x₂ .

Then, rewrite Newton’s second law in terms of x and X. After some algebra, we get two equations

     (m₁+m₂) d²x/dt²  =  0 

     [m₁m₂/(m₁+m₂)] d²X/dt²  =   − kX

The first equation represents a free particle of mass M, where

     M = m₁+m₂ ,

and the second equation represents a bound particle with spring constant k and mass m (often called the reduced mass)

     m = m₁m₂/(m₁+m₂) . 

The angular frequency of the vibration is therefore

     ω = √(k/m)

(If you don’t follow that last step, see Appendix F of IPMB).

We have reached our goal: the angular frequency of the vibration, ω, written in terms of k, m₁, and m₂

     ω = √[k (m₁+m₂)/m₁m₂]

In quantum mechanics, the energy levels depend on ω, and therefore on the reduced mass m.

If m₁ >> m₂ then m is approximately m₂. Likewise, if m₂ >> m₁ then m is approximately m₁. For example, if you want the vibration frequency of hydrogen chloride (HCl), the reduced mass is close to the mass of the hydrogen atom.

If m₁ = m₂ = μ (like for molecules such as O₂ and N₂), then the reduced mass m is equal to μ/2. It’s that factor of two in the denominator that’s the surprise.

Quantum Physics of Atoms,
Molecules, Solids, Nuclei and Particles,
by Eisberg and Resnick.

The relationship between m, m₁, and m₂ can be written

    1/m = 1/m₁ + 1/m₂ .

This looks just like the equation for adding resisters in parallel. 

If you want to learn more, I suggest looking at Chapter 12 of Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, by Robert Eisberg and Robert Resnick, often cited in IPMB.

Randy Travis

Forever and Ever, Amen,
by Randy Travis.

I’m a big fan of country music. After all, I was a graduate student in Music City: Nashville. I used to ride my bike down to 16th Avenue by the original Country Music Hall of Fame and listen to the up-and-coming singers perform on the street. During the late 1980s, just as I was finishing my dissertation, the biggest country star was Randy Travis. His debut album, Storms of Life, appeared in 1986, and for the next several years he dominated the country music scene.

I recently listened to Travis’s 2019 autobiography, Forever and Ever, Amen. It tells the story of his glory years, but also covers his troubled youth, his time as the singing cook at the Nashville Palace nightclub, and his tragic health problems.

In 2013 Travis was incapacitated by a massive stroke. The most common type of stroke occurs when a clot blocks the flow of blood to part of the brain. Stroke is ranked as the fifth leading cause of death in the United States; every four minutes someone dies of a stroke. Many of those that survive have brain damage. Following his stroke, Travis suffered from limited use of his right hand and severe speech impairment.

The question for readers of Intermediate Physics for Medicine and Biology is, how can physics address stroke? Two applications that are important for stroke diagnosis and treatment are Diffusion Tensor Imaging and Transcranial Magnetic Stimulation. In diffusion tensor imaging, diffusion in the brain is measured using strong gradient magnetic fields applied during magnetic resonance imaging. Diffusion is anisotropic in the brain’s white matter, with water diffusing faster parallel to nerve axon tracts than perpendicular to them. In IPMB, Russ Hobbie and I write

Diffusion is usually greater along the direction of the nerve or muscle fibers. Since the orientation of the fibers changes throughout the body, the elements of the diffusion tensor vary as well. However, some features of the diffusion tensor, such as the trace (see Prob. 49), are independent of the fiber direction, and are particularly useful when monitoring diffusion in anisotropic tissue, such as the white matter of the brain. In addition, the diffusion tensor contains information about the fiber direction, allowing one to map fiber tract trajectories noninvasively using MRI (Basser et al. 2000).

Diffusion can serve as a biomarker to diagnose stroke and to monitor recovery.

Transcranial magnetic stimulation (TMS) is a method to excite neurons in the brain. Russ and I describe it as

Magnetic stimulation can be used to diagnose central nervous system diseases that slow the conduction velocity in motor nerves without changing the conduction velocity in sensory nerves (Hallett and Cohen 1989). It could be used to monitor motor nerves during spinal cord surgery, and to map motor brain function. Because TMS is noninvasive and nearly painless, it can be used to study learning and plasticity (changes in brain organization over time; Wassermannet al. 2008). Recently, researchers have suggested that repetitive TMS might be useful for treating disorders such as depression (O’Reardon et al. 2007) and Alzheimer’s disease (Freitas et al. 2011).

You could add stroke to the list of disorders that might benefit from repetitive transcranial magnetic stimulation. I say “might” because the technique is still being studied as a stroke therapy, but any method that influences brain plasticity has at least the potential to be useful to stroke victims.

Now, almost ten years after his stroke, Travis continues to slowly recover. Although he has not yet been able to return to a singing career, in 2016 he did lead his fans in singing Amazing Grace when he was inducted into the Country Music Hall of Fame. His autobiography is captivating and inspiring. The courage and tenacity of stroke victims should motivate us all to use our science to address this devastating illness.

Randy Travis sings Amazing Grace at his induction into the Country Music Hall of Fame.

https://www.youtube.com/watch?v=11bgiJH1zhA

Randy Travis singing his signature song, Forever and Ever, Amen.

https://www.youtube.com/watch?v=KtKXc_v2iLE

Randy Travis singing Storms of Life.

https://www.youtube.com/watch?v=piTt6zu2FKs

The Intellectual Immigration That Has Mattered Most to Biology

The Eighth Day of Creation,
by Horace Freeland Judson.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I analyze the role physics plays in the biological sciences. What is that role, and how did it begin? Insight can be found in Horace Freeland Judson’s classic book The Eighth Day of Creation: The Makers of the Revolution in Biology. The development of molecular biology occurred in the mid-twentieth century and was spurred in part by immigrant physicists escaping central Europe before the start of World War II. Judson describes this intellectual exodus from physics to biology.

The mass intellectual emigration from continental Europe in the 1930s, which so stimulated physical science in the United States and England, also had profound consequences for biology, even though the men involved were fewer and younger, with their reputations still to make. They included [Max] Perutz, who left Austria for England in 1936, and [Erwin] Chargaff, also an Austrian, who emigrated to the United States in 1934. A less direct influence was the distinguished and passionately intelligent Hungarian physicist Leo Szilard, who in the 1930s had been the first to envision the possibility that sustained nuclear fission, a chain reaction, would work and cause an explosion, and the first to urge that the United States should try to make an atomic bomb. Szilard wrote the letter about the idea that [Albert] Einstein signed and that was read to [President Franklin] Roosevelt in 1939. Szilard worked on the atomic project at the University of Chicago through the war; afterwards, in reaction against the weapons and against the big-money, big-team physics he had been instrumental in creating, he turned to biology and also to campaigning within the international scientific community for disarmament—for example, through the Pugwash conferences, which he helped to found. In 1947, [University of Chicago chancellor Robert] Hutchins gave Szilard the physicist an appointment as professor of biology and sociology. In the early years of molecular biology, Szilard was an erratic if interesting experimenter and theorist, a cross-pollinator of ideas and an effective critic of others’ work, an intellectual and ethical inspiration to younger scientists. 

The most important immigrant to biology, however, was Max Delbrück. Delbrück was German, born to the aristocracy of the intellect—his father was the professor of history and his uncle the professor of theology in the University of Berlin—and trained as a quantum physicist. His mind and style had been formed by Niels Bohr, the physicist, philosopher, poet, and incessant Socratic questioner who made Copenhagen one of the capital cities of science between the wars. Delbrück_’s ideas about the physical properties of the gene, in a youthful paper of 1935, had led [Austrian physicist Erwin] Schrödinger to write [the influential book] What Is Life? Delbrück was perhaps the earliest of the theoretical physicists who have crossed over to biology; Szilard, [Francis] Crick, Maurice Wilkins were others, while Linus Pauling, arriving at biology from a different tangent, was a physical chemist whose strength was founded in quantum mechanics. The move from physics has been the intellectual immigration that has mattered most to biology [my italics].

Each of us who has emigrated from physics to biology has followed in the footsteps of giants such as Szilard and Delbrück. We each follow our own individual path, but share a common bond. Physicists have played key roles in biology, and will continue to do so.  

The International Day of Medical Physics, Held on Marie Curie's Birthday

The poster for the 2022
International Day of Medical Physics

Monday, November 7, is the International Day of Medical Physics. The purpose of this annual event, organized by the International Organization for Medical Physics, is to raise awareness about the role that medical physics plays in our lives. The date coincides with the birthday of Marie Curie.

The Search for the Elements,
by Isaac Asimov.

To celebrate the International Day of Medical Physics, I quote an excerpt from Isaac Asimov’s book The Search for the Elements that describes Curie’s discovery of the elements polonium and radium.

Thomson, Roentgen, Becquerel, and Rutherford all received Nobel prizes for their work. But the most glamorous of all the Nobel laureates of the turn of the century was Marie Curie, born Marja Sklodowska in Poland in 1867. Marie went to Paris to get an education (at the Sorbonne), and there she met and married a French chemist, Pierre Curie.

Becquerel’s discovery of the radiations from uranium fascinated Marie; it was she who suggested the term “radioactivity.” With enthusiasm and imagination, she plunged into a career of investigating this phenomenon. Marie began by trying to measure the strength of radioactivity. As the instrument of measurement she used the phenomenon of piezoelectricity, involving the electrical behaviors of crystals, which had been discovered by Pierre Curie. Pierre, realizing perhaps that his wife was a greater scientist than he was, abandoned his own research and joined her.

As they measured the radioactivity of samples of uranium ore, they found to their surprise that some samples were many times more radioactive than could be accounted for by the uranium content. This could only mean that other radioactive elements also were present. But if so, the amount must be extremely small, because the Curies were unable to detect any by ordinary chemical analysis. So they decided they would have to collect huge quantities of the ore to get enough of the trace material to analyze. They managed to get tons of ore from the mines in Bohemia; the Austrian government had no use for it and was glad to give it away, provided the Curies paid for the transportation. This took almost all their life savings.

They set up shop in a little unheated shed and went to work on their mounds and mounds of uranium ore. Year after year they kept concentrating the radioactivity, discarding inactive material and working with the active. (Marie took time out to have a baby, Irene, who later turned out to be a great scientist on her own.) At last, in July 1898, they succeeded in boiling down their tons of ore to a highly radioactive residue. What they had was a pinch of black powder which was 400 times more radioactive than the same quantity of pure uranium would have been. In this bit of stuff they found a new element resembling tellurium. Mendeleev might have named it “eka-tellurium.” The Curies called it “polonium,” after Marie’s native land.

This element didn’t account for all the radioactivity, however. A still more active element must be hiding in their ore. Six months later they finally concentrated that element. Its properties were like those of barium. The element fitted into row IIa in the seventh period of Mendeleev’s table. It was the first new element discovered in the seventh period since Berzelius had found thorium 60 years before.

The Curies called the new element “radium,” because of its powerful radioactivity.

Pierre Curie died in 1906 as the result of a traffic accident (involving a horse-drawn cab, not one of the new-fangled motor cars). Marie took over his professorship at the Sorbonne and carried on alone. She was the first woman professor in the history of that proud institution. Moreover, she was the only scientist in history to receive two Nobel prizes—one in physics (shared with her husband and Becquerel) for their accurate measurements of radioactivity, and one in chemistry for the discovery of polonium and radium.

International Organization of Medical Physics President Message on the International Day of Medical Physics 2022. 

https://www.youtube.com/watch?v=LZcEZYkUsCo

Marie Curie: Scientist

https://www.youtube.com/watch?v=ZEV4KJBJvEg

The Boundary Layer

In Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce a concept from fluid dynamics called the boundary layer.

The behavior of a sphere moving through a fluid illustrates how flow behavior depends on Reynolds number... At very high Reynolds number, viscosity is small but still plays a role because of the no-slip boundary condition at the sphere surface. A thin layer of fluid, called the boundary layer, sticks to the solid surface, causing a large velocity gradient and therefore significant viscous drag.

Life in Moving Fluids,
by Steven Vogel.

For readers who want to know more about the boundary layer, let me quote the start of Chapter 8 of Steven Vogel’s masterpiece Life in Moving Fluids.

At the interface between a stationary solid and a moving fluid, the velocity of the fluid is zero. This, of course, defines the no-slip condition… The immediate corollary of the no-slip condition is that near every such surface is a gradient in the speed of flow. Entirely within the fluid, speed changes from that of the solid to what we call the “free stream” velocity some distance away. Shearing motion is inescapably associated with a gradient in speed, so in these gradients near surfaces, viscosity, fluids’ antipathy to shear, works its mischief, giving rise to skin friction and consequent power consumption. The gradient region is associated with the term “boundary layer”…

The boundary layer… wasn’t so much discovered as it was invented, in the early part of this century, as a great stroke of genius of Ludwig Prandtl. Recognizing the origin of this notion is crucial. In the basic differential equations for moving fluids, the Navier-Stokes equations, some terms result from the inertia of fluids and some from their viscosity… The Reynolds number gives an indication of the relative importance of inertia and viscosity… At Reynolds numbers below unity, inertia can be ignored and nicely predictive rules nonetheless derived—[such as] Stokes’ law for the drag of a sphere… At high Reynolds number, one might expect to get away with neglecting viscosity… It may sound neat, but it all too commonly gets us in trouble—results diverge from physical reality, drag vanishes, and d’Alembert has his paradox.

Prandtl reconciled practical and theoretical fluid mechanics at high Reynolds numbers by recognizing that viscosity could never be totally ignored. What changes with Reynolds number was where it had to be taken into account; initially it mattered everywhere, but as the Reynolds number increased well above unity, viscosity made a difference only in the gradient regions near surfaces. These regions might be small, and they might get ever smaller… as the Reynolds number increased; but as long as the no-slip condition held, a place had to exist where shear rates were high and viscosity was significant. Prandtl called the place in question… the “boundary layer.” In general, a higher Reynolds number implies a thinner boundary layer but a higher shear rate in that boundary layer.

To learn more about the biological significance of the boundary layer see the Chapter 9 in Life in Moving Fluids, which is all about “Life in Velocity Gradients.”

Boundary Layer Theory,
by Schlichting and Gersten

If you want a more rigorous and mathematical analysis of boundary layers, I recommend Boundary Layer Theory by Hermann Schlichting and his student Klaus Gersten. The eighth edition of this book (2000) is cited in IPMB; a revised and updated ninth edition was published in 2017. Schlichting and Gersten write

At the end of the 19th century, fluid mechanics had split into two different directions which hardly had anything more in common. On one side was the science of theoretical hydrodynamics, emanating from Euler’s equations of motion and which had been developed to great perfection. However this had very little practical importance, since the results of this so-called classical hydrodynamics were in glaring contradiction to everyday experience. This was particularly true in the very important case of pressure loss in tubes and channels, as well as that of the drag experienced by a body moved through a fluid. For this reason, engineers, on the other side, confronted by the practical problems of fluid mechanics, developed their own strongly empirical science, hydraulics. This relied upon a large amount of experimental data and differed greatly from theoretical hydrodynamics in both methods and goals.

It is the great achievement of [German scientist] Ludwig Prandtl [1875–1953] which, at the beginning of this century, set forth the way in which these two diverging directions of fluid mechanics could be unified. He achieved a high degree of correlation between theory and experiment, which, in the first half of this century, has led to unimagined successes in modern fluid mechanics. It was already known then that the great discrepancy between the results in classical hydrodynamics and reality was, in many cases, due to neglecting the viscosity effects in the theory. Now the complete equations of motion of viscous flows (the Navier Stokes equations) had been known for some time. However, due to the great mathematical difficulty of these equations, no approach had been found to the mathematical treatment of viscous flows (except in a few special cases). For technically important fluids such as water and air, the viscosity is very small, and thus the resulting viscous forces are small compared to the remaining forces (gravitational force, pressure force). For this reason it took a long time to see why the viscous forces ignored in the classical theory should have an important effect on the motion of the flow.

In his lecture on “Über Flüssigkeitbewegung bei sehr kleiner Reibung” (On Fluid Motion with Very Small Friction) at the Heidelberg mathematical congress in 1904, L. Prandtl... showed how a theoretical treatment could be used on viscous flows in cases of great practical importance. Using theoretical considerations together with some simple experiments, Prandtl showed that the flow past a body can be divided into two regions: a very thin layer close to the body (boundary layer) where the viscosity is important, and the remaining region outside this layer where the viscosity can be neglected. With the help of this concept, not only was a physically convincing explanation of the importance of the viscosity in the drag problem given, but simultaneously, by hugely reducing the mathematical difficulty, a path was set for the theoretical treatment of viscous flows. Prandtl supported his theoretical work by some very simple experiments in a small, self–built water channel, and in doing this reinitiated the lost connection between theory and practice. The theory of the Prandtl boundary layer or the frictional layer has proved to be exceptionally useful and has given considerable stimulation to research into fluid mechanics since the beginning of this century. Under the influence of a thriving flight technology, the new theory developed quickly and soon became, along with other important advances—airfoil theory and gas dynamics—a keystone of modern fluid mechanics.

Introductory Fluid Mechanics L19 p2 — The Boundary Layer Concept.

https://www.youtube.com/watch?v=k37vPSA3E1g

 

E. Bodenschatz — Ludwig Prandtl (1875–1953)

https://www.youtube.com/watch?v=cv952Nhc_vs

Maurice de Broglie and the First Observation of an X-ray Absorption Edge

If you shine x-rays through a material and measure the number absorbed by it, you create an x-ray absorption spectrum. The absorption is related to the cross section; the bigger the cross section, the more the x-rays are absorbed. Figure 15.2 from Intermediate Physics for Medicine and Biology is shown below, where the cross section for carbon is plotted as a function of the x-ray energy. I’ve drawn an oval around what’s the most interesting feature of the plot, the jump in the cross section at an energy of about 0.28 keV. This abrupt rise is known as the K edge, and is an example of an absorption edge. 

A slightly modified version of Figure 15.2 from
Intermediate Physics for Medicine and Biology.

The cross section jumps up when the photon’s energy rises above the binding energy of a K-shell electron [an electron in the innermost energy level]. It’s not a small effect; the cross section increases by more than a factor of ten at the K edge (note that this is a log-log plot). 

When I see such a dramatic effect, I imagine how surprising it must have been for the person who observed it first. Who was the person who discovered the K edge? Maurice de Broglie.

Maurice de Broglie in 1932.

Maurice was the elder brother of the more-famous Louis de Broglie, who Russ Hobbie and I mention when talking about electron waves and the electron microscope. Maurice was born in Paris in 1875. After more than a decade in the French navy, he left the military to study physics. He was interested in x-rays, which were discovered by Wilhelm Röntgen in 1895. In 1913, Maurice published the first observation of an absorption edge (Comptes Rendus, Volume 157, Pages 924–926). When World War I began, he went back to the navy to do research on detecting U-boats (German submarines). After a long career in science, including being awarded the Hughes Medal by the Royal Society of London, he died in 1960 at the age of 85.

Farrel Lytle, an x-ray spectroscopy pioneer, tells Maurice’s story in his review article (Journal of Synchrotron Radiation, Volume 6, Pages 123–134, 1999).

Although Röntgen represents the beginning of X-ray science, the remarkable de Broglie royal family has been significant in both the world of science and the history of France. It has been said that if Maurice did nothing more than convince his younger brother, Louis, to drop his study of history and begin a career in science, he should be memorialized for that alone. But he did considerably more than that. His work in X-ray and atomic physics was innovative and important. Maurice had begun a career as a naval officer, but became interested in the exciting new world of X-rays and physics and resigned his commission. Beginning in the laboratory of Paul Langevin working on the ionization of gases by X-rays, he later built his own laboratory in his personal mansion on rue Châteaubriand. There he became the first in France to work with X-ray diffraction. During these experiments he invented X-ray spectroscopy. The experimental innovation came about when he mounted a single crystal on the cylinder of a recording barometer where the clockwork mechanism rotated it around its vertical axis at 2° h⁻¹. As the crystal rotated, all angles between the incident beam and the diffraction planes (hence, all X-ray energies) were recorded on a photographic plate. In this way he obtained an X-ray line spectrum from the tube with sharp and diffuse lines, bands etc. Two of the absorption bands proved to be the K edges of Ag and Br in the photographic emulsion. This was the first observation of an absorption edge (de Broglie, 1913). It took a few more experiments to reach the correct interpretation of the absorption edges. After the end of the First World War, Maurice gathered a large group of young scientists, all working on X-ray diffraction or X-ray spectroscopy, at the laboratory in his home. Joining him in his work were, among others, Alexandre Dauvillier, Jean Thibaud, Jean-Jacques Trillat, Louis Leprince-Ringuet (all were major contributors to the field of X-ray science) and his young brother, Louis. Maurice’s scientific work and his social position soon made him a major player in the science world.

Apparently it took a while to figure out that the absorption edges belonged to materials in the photographic film and not the x-ray tube or the crystal, but eventually it was all sorted out. A German scientist, Julius Hedwig (1879–1936), independently studied x-ray spectroscopy, and may have observed an x-ray absorption edge before Maurice, but he soon abandoned the work while Maurice pursued it further, becoming the father of x-ray spectroscopy.

Paul Horowitz Discusses The Art of Electronics

The Art of Electronics,
by Horowitz and Hill.

Nine years ago I wrote in this blog about the second edition of Horowtiz and Hill’s textbook The Art of Electronics. At the end of that post I hinted that a new edition of their book was in the works. The third edition of The Art of Electronics appeared in 2015, just in time for Russ Hobbie and me to cite it in the fifth edition of Intermediate Physics for Medicine and Biology.

Recently, I stumbled upon a delightful YouTube video of an interview with Paul Horowitz, explaining how The Art of Electronics began. I’ll keep this post brief, so you’ll have time to watch the video. The host is Limor Fried, who goes by the moniker Ladyada in honor of computer programing pioneer Ada Lovelace. Fried owns the electronics company Adafruit Industries, which is a cross between a business and an educational organization. Notice that during the interview Fried wears a “transistor man” tee shirt; I remember reading about transistor man in The Art of Electronics when I was designing a circuit in John Wikswo’s lab during graduate school.

Enjoy the video, and make The Art of Electronics your go-to book for designing circuits; or, just read it for fun.

Ladyada interview with Paul Horowitz, author of The Art of Electronics.
  https://www.youtube.com/watch?v=iCI3B5eT9NA

 

Meet Limor “Ladyada” Fried at Adafruit Industries.
  https://www.youtube.com/watch?v=SpYMgScKRwk

Thomas Young, Biological Physicist

The Last Man Who Knew Everything,
by Andrew Robinson.

Almost ten years ago in this blog, I speculated about who was the greatest biological physicist of all time, and suggested that it was the German scientist Hermann von Helmholtz. Today, I present another candidate for GOAT: the English physicist and physician Thomas Young. Young’s life is described in Andrew Robinson’s biography The Last Man Who Knew Everything.

Young (1773–1829) went to medical school and was a practicing physician. How did he learn enough math and physics to become a biological physicist? In Young’s case, it was easy. He was a child prodigy and a polymath who learned more through private study than in a classroom. As an adolescent he was studying optics and building telescopes and microscopes. As a teenager he taught himself calculus. By the age of 17 was reading Newton’s Principia. By 21 he was a Fellow of the Royal Society.

Some of his most significant contributions to biological physics were his investigations into physiological optics, including accommodation and astigmatism. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I state that the “ability of the lens to change shape and provide additional converging power is called accommodation.” Robinson describes Young’s experiments that proved the changing shape of the lens of the eye is the mechanism for accommodation. For instance, he was able to rule out a mechanism based on changes in the length of the eyeball by making careful and somewhat gruesome measurements on his own eye as he changed his focus. He showed that patients whose lens had been removed, perhaps because of a cataract, could no longer adjust their focus. He also was one of the first to identify astigmatism, which Russ and I describe as “images of objects oriented at different angles… form at different distances from the lens.”

Young’s name is mentioned in IPMB once, when analyzing the wave nature of light: “Thomas Young performed some interference experiments that could be explained only by assuming that light is a wave.” The Last Man Who Knew Everything describes Young’s initial experiment, where he split a beam of light by letting it pass on each side of a thin card, with the beams recombining to form an interference pattern on a screen. Young presents his famous double-slit experiment in his book A Course of Lectures on Natural Philosophy and the Mechanical Arts. Robinson debates if Young actually performed the double-slit experiment or if for him it was just a thought experiment. In any case, Young’s hypothesis about interference fringes was correct. I’ve performed Young’s double-slit experiment many times in front of introductory physics classes. It establishes that light is a wave and allows students to measure its wavelength. Interference underlies an important technique in medical and biological physics described in IPMB: Optical Coherence Tomography. 

A green laser passing through two slits 0.1 mm apart produces an interference pattern.
Photo by Graham Beards, published in Wikipedia.

Young also studied color vision based on the idea that the retina can detect three primary colors. This work was rediscovered and further developed by Helmholtz fifty years later. Young was also one of the first to suggest that light is a transverse wave and therefore can be polarized.

In Chapter 1 of IPMB, Russ and I define the Young’s modulus, which relates stress to strain in elasticity and plays a key role in biomechanics. Young also studied capillary action and surface tension, two critical phenomena in biology.

Was Young a better biological physicist than Helmholtz? Probably not. Was Young a better scientist? It’s a close call, but I would say yes (Helmholtz had nothing as influential as the double slit experiment). Was Young a better scholar? Almost certainly. In addition to his scientific contributions, he had an extensive knowledge of languages and helped decipher the Rosetta Stone that allowed us to understand Egyptian hieroglyphics. He really was a man who knew everything.

Radiofrequency Radiation and Cancer, by David Robert Grimes

Grimes DR (2021)
Radiofrequency Radiation and Cancer,
JAMA Oncology, 8:456–461.

In my book Are Electromagnetic Fields Making Me Ill? I discussed the danger of cell phone radiation. Recently David Robert Grimes wrote his own review about this topic—Radiofrequency Radiation and Cancer—which appeared in JAMA Oncology (Volume 8, Pages 456–461, 2021). Below is his abstract.

Importance Concerns over radiofrequency radiation (RFR) and carcinogenesis have long existed, and the advent of 5G mobile technology has seen a deluge of claims asserting that the new standard and RFR in general may be carcinogenic. For clinicians and researchers in the field, it is critical to address patient concerns on the topic and to be familiar with the existent evidence base.

Observations This review considers potential biophysical mechanisms of cancer induction, elucidating mechanisms of electromagnetically induced DNA damage and placing RFR in appropriate context on the electromagnetic spectrum. The existent epidemiological evidence in humans and laboratory animals to date on the topic is also reviewed and discussed.

Conclusions and Relevance The evidence from these combined strands strongly indicates that claims of an RFR–cancer link are not supported by the current evidence base. Much of the research to date, however, has been undermined by methodological shortcomings, and there is a need for higher-quality future research endeavors. Finally, the role of fringe science and unsubstantiated claims in patient and public perception on this topic is highly relevant and must be carefully considered.

Many of Grimes’s conclusions are similar to those in Are Electromagnetic Fields Making Me Ill? and in Intermediate Physics for Medicine and Biology. I was particularly interested in the last few paragraphs of his discussion, where he examines the public perception of cell phone radiation health risks.

Public perception is also an important consideration, especially in the context of addressing patient fears. Given the combined biophysical and epidemiological evidence base to date against the proposition that RFR is carcinogenic, it might seem surprising that this belief is so widely evangelized and propagated relentlessly. A major and unedifying part of the reason for this is the noxious influence of fringe science on confounding public understanding; the BioInitiative Report, a nonscholarly [non-peer reviewed] work that insists that RFR causes many harms from cancer to autism, has been widely circulated since 2007. Despite its popularity, it has been repeatedly debunked by health bodies worldwide, and the attempts to treat its unsubstantiated assertions as equivalent to the weight of peer-reviewed weight of scientific evidence are archetypical false balance.

Tellingly perhaps, the recent misinformation propagated around 5G is not even new—the same grave claims were made about prior mobile technologies for decades and were equally unsupported. Their renaissance now is underpinned by disinformation perpetuated across social media and a microcosm of a greater problem with online disinformation. There is, for example, a thriving online market for dubious devices that promise to protect consumers from RFR, furthering a likely misguided perception of harm. Cancer is an emotive topic, which undoubtedly increases the virulence of misguided assertions. It is accordingly important to be cognizant of the fact that while the issue may be strictly academic to researchers, it is a source of anxiety and apprehension to patients and the general public, and there is an onus on scientists to both convey the scientific consensus and to ensure that future work is conducted to a high standard.

The International Agency for Research on Cancer designation of RFR as a group 2B agent (a possible carcinogen) in 2011 is also frequently misunderstood as implying evidence of harm. However, such an interpretation is incorrect, as reiterated in the most recent International Agency for Research on Cancer communication in 2020, which stated that “despite considerable research efforts, no mechanism relevant for carcinogenesis has been consistently identified to date. In the past 5 years, epidemiological research on mobile phone use and tumours occurring in the head has slowed down compared with the previous decade. Most new and previous case-control studies do not indicate an association between mobile phone use and risk of glioma, meningioma, acoustic neuroma, pituitary tumours, or salivary gland tumours.”

It is worthwhile too to acknowledge a potentially political dimension to the propagation of falsehoods on 5G in particular; a New York Times investigation found that Russian state forces were complicit in spreading falsehoods, with the European Commission finding the fingerprints of both Russian and Chinese health disinformation rising with the advent of COVID-19, including false claims linking cancer to RFR. All of this undermines collective understanding and makes it imperative that scientists be at the vanguard of communicating the evidence to prevent detrimental misconceptions [my italics].

Grimes has taken much criticism for his article, all of which, in my opinion, is undeserved. See, for example, this website containing an attack titled “Why did JAMA Oncology publish a paper written by a Telecom industry spokesperson?” by Joel Moskowitz (JAMA Oncology did no such thing). Several groups called for JAMA Oncology to retract Grimes’s article, but the journal refused (I’m proud of them). My advice for Grimes is to just be happy that people are paying attention to his work. Are Electromagnetic Fields Making Me Ill?, which covers much of the same ground and comes to similar conclusions, has not been similarly criticized, apparently because the critics are either unaware of it or don’t think it’s important enough to bother with.

Grimes is an Irish scientist and science writer who won the 2014 John Maddox Prize for standing up for science and was elected a fellow of the Committee for Skeptical Inquiry. If you want to read more by him, I suggest his excellent book Good Thinking: Why Flawed Logic Puts Us All at Risk and How Critical Thinking Can Save the World.

Michael Joy (1940–2020)

This week I belatedly learned that Mike Joy died. This was sad news indeed. Joy was a Canadian electrical engineer who measured current density in the body using magnetic resonance imaging. In Chapter 8 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I include a homework problem in which the magnetic field throughout the body is known and the student’s task is to determine the current density.

Section 8.6 

Problem 24. The differential form of Ampere’s law, Eq. 8.24, provides a relationship between the current density j and the magnetic field B that allows you to measure biological current with magnetic resonance imaging (see, for example, Scott et al. (1991)). Suppose you use MRI and find the distribution of magnetic field to be 

B_x = C(yz² − yx²) 

B_y = C(xz² − xy²) 

B_z = C4xyz 

where C is a constant with the units of T m⁻³. Determine the current density. Assume the current varies slowly enough that the displacement current can be neglected.

To solve this homework problem, calculate the curl of the magnetic field to get, within a proportionality constant, the current density. By the way, the problem doesn’t ask you to do this, but you might want to verify that the divergence of B is zero as it must be according to Maxwell’s equations, and that the divergence of j is zero (conservation of current).

Scott et al. (1991)
IEEE Trans Med Imaging
10:362–374.

The article we cite in IPMB is a beautiful paper by Greig Scott, Robin Armstrong, Mark Henkelman, and Joy. At that time Scott was Joy’s graduate student at the University of Toronto.

Scott GC, Joy MLG, Armstrong RL, Henkelman RM (1991) Measurement of nonuniform current density by magnetic resonance. IEEE Transactions on Medical Imaging Volume 10, Pages 362–374.

Using MRI to measure current density was one of those ideas I wish I’d thought of, but I didn’t. When Peter Basser and I wrote a paper analyzing an alternative (and less successful) method to detect action currents using MRI, we cited four of Joy’s articles in our very first sentence! I first met Joy when we co-chaired a session at the 2009 IEEE Engineering in Medicine and Biology Society Conference in Minneapolis. I had the honor of being the external examiner for one of Joy’s graduate students, Nahla Elsaid, at her 2016 dissertation defense. Joy was a delightful guy, and a joy to work with. I’ll miss him.

Below is Joy’s obituary.

MICHAEL LAWRENCE GRAHAME JOY (July 31, 1940–July 5, 2020) was born in Toronto and died at Drynoch Farm in Caledon, on his own terms, in his own time. He was predeceased by his wife Jane (née Andras) and will be dearly missed by his wife Carol Fanning, his son Rob, his daughters Gwen and Ellen, their partners, his grandchildren (Asha, Nel, Tallulah, Freya, Kelvin, and Skyler) and generations of nieces, nephews, cousins, former students, friends and colleagues.

Mike was professor emeritus at the University of Toronto; Institute of Biomaterials & Biomedical Engineering; Department of Electrical & Computer Engineering. He was a pioneer in the development of Magnetic Resonance and Electric Current Density Imaging and earned numerous significant grants, awards and citations.

Mike, (Muncle Ike, Zeepa) was truly a unique individual. He was a man of many interests who always had time for the numerous children who would follow him like shadows as he puttered on his latest amazing project. He could turn the most mundane chore into both an adventure and a learning experience. He imparted his love of nature, enquiry and adventure on his young assistants, whether tinkering on his jet boat Feeble, constructing a zip line, building model rockets, fishing, or going on long walks where “getting lost” was all part of the fun.

Mike enjoyed being surrounded by those he loved. His birthday parties at the Bay were the highlight of the summer while the Christmas tree parties at the Farm kicked off the festive season. Whether at summer picnics, Church, dinners, gatherings, bridge games, visiting family at Nares Inlet or summer afternoons on the side porch, he was always at the center of things with his distinctive laugh and quick sense of humour.

Mike left his imprint on so many. His was a life well lived and well loved. In lieu of flowers, please consider a donation to the Georgian Bay Land Trust, one of the many conservation projects Mike supported.