Light Scattering

In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I often discuss the scattering of light. We mention four types of scattering, each differentiated by the name of the brilliant scientist who first studied it: Compton scattering, Thomson scattering, Rayleigh scattering, and Raman scattering. Let’s see if we can get these all straight.

Compton Scattering

In Chapter 15 (Interaction of Photons and Charged Particles with Matter) of IPMB, Russ and I analyze Compton scattering. This is a particularly simple case: a photon interacts with a free electron, resulting in a scattered photon of lower energy and a recoiling electron. This type of scattering is particularly important for x-rays. You might be wondering how often do we encounter a free electron? Aren’t most electrons bound to atoms? If the incident photon has an energy much greater than the binding energy, then the electron is to a first approximation free and Compton scattering occurs. In the interaction of x-rays with biological tissue, Compton scattering is the dominant mechanism contributing to the interaction cross-section at intermediate energies; say, one tenth to a few MeV. Since the electrons act almost as if they were free, the atomic number of the target atom is unimportant and scattering depends only on how many electrons are present (meaning the mass attenuation coefficient is nearly independent of atomic number). You don’t really want to do imaging of tissue when Compton scattering is the dominate interaction because you don’t get much discrimination between different tissues (the weak dependence on atomic number) and, well, you get a lot of scattering that blurs the image.

Compton scattering is named after Arthur Holly Compton (1892–1962), an American physicist who played a key role in the Manhattan Project. Compton scattering was important in the development of quantum mechanics. The light quanta hypothesis had been developed by Planck and Einstein, but was not widely embraced until 1923, when Compton analyzed his x-ray scattering data by treating the x-ray photon as a particle with energy and momentum, interacting with another particle, the electron. Compton won the 1927 Nobel Prize in Physics for his discovery.

Thomson Scattering

When Compton scattering occurs at such a low energy that we can ignore the difference in energy between the incident and scattered photons, the process is called Thomson scattering. We can analyze Thomson scattering by treating the incident light as an electromagnetic wave rather than a photon. The electric field accelerates the electron, causing it to radiate an electromagnetic wave at the same frequency. The direction of the electric field is important for determining the distribution of the outgoing dipole radiation, so Thomson scattering depends on the polarization of the incident light. This type of scattering is particularly important in plasma physics, where many free charged particles are present. It is not too important in biology and medicine, because usually either the photon energy is so high that Compton scattering occurs, or else the photon energy is so low that one cannot treat the electron as being free. Because the frequency of the light (and therefore the energy of the photons) does not change, Thomson scattering is a type of elastic scattering.

Thomson scattering was first analyzed by, and was named after, J. J. Thomson (1856–1940), the British physicist who discovered the electron, for which he received the Nobel Prize in Physics in 1906. I have my own connection to Thomson: academically speaking, he is my great-great-great-great-great-grandfather.

Rayleigh Scattering

Rather than scattering from a single electron, light can also scatter from an entire atom or molecule, and even larger particles. When the wavelength of the light is much larger than the size of the particle, we get Rayleigh scattering. Like for Thomson scattering, in Rayleigh scattering the light is treated as an electromagnetic wave. However, unlike Thomson scattering, in Rayleigh scattering the scatterer is not a single particle, but instead can be represented by a continuous, polarizable medium. The electric field of the light causes the induced charge distribution to oscillate at the same frequency as the incident light, resulting in the scattered light having the same frequency as the incident light. In IPMB, Russ and I refer to Rayleigh scattering as coherent scattering, because the atom responds coherently as a whole, rather than as individual charged particles. In tissue, coherent scattering dominates Compton scattering at low energies (say, below 1 keV), but such low energy photons also interact by the more important photoelectric effect, so Rayleigh scattering is often not very important. It is crucial for understanding how sunlight scatters off the molecules of the air, causing the blue color of the sky.

When I was an undergraduate at the University of Kansas, I had my first research experience in Professor Wes Unruh’s laboratory studying light scattering off of colloidal impurities in crystals. We were able to determine the size of the impurities by measuring the scattered light as a function of angle. However, these colloids tended to be large, so that you could not ignore interference between light scattered from different parts of the particle. In that case, you must use a more advanced theory, called Mie theory, to calculate the distribution of scattered light. I recall struggling to learn Mie theory from Milton Kerker’s book The Scattering of Light and Other Electromagnetic Radiation. I didn’t work much with Unruh himself, but rather was mentored by then-graduate student Robert Bunch. The first item in my CV is an abstract resulting from that research (Bunch, Roth, and Unruh, 1983, “Size Distributions of Ni and Co Colloids Within MgO,” March Meeting of the American Physical Society).

Rayleigh scattering is named after English physicist John William Strutt (1842-1919), also known as Lord Rayleigh. He was awarded the Nobel Prize for Physics in 1904 for the discovery of argon. Because one of Rayleigh’s students was J. J. Thomson, Rayleigh is my academic great-great-great-great-great-great-grandfather. Rayleigh was the second Cavendish Professor of Physics at the University of Cambridge, following Maxwell and succeeded by J. J. Thomson, Ernest Rutherford, and William Bragg; quite an impressive bunch.

Raman Scattering

In IPMB, Russ and I discuss Raman scattering in Chapter 14 (Atoms and Light). The mechanism of Raman scattering is similar to Rayleigh scattering, in that the scattering occurs off an entire molecule. However, it is unlike Rayleigh scattering in that the scattered light does not have the same frequency as the incident light (inelastic scattering). Instead, some of the energy induces transitions between different vibrational energy levels. These transitions result in the scattered light having a lower energy (Stokes) or a higher energy (Anti-Stokes). Also, because the vibrational energy levels are quantized, the spectrum of Raman scattered light consists of a series of discrete lines. This spectrum contains information about the vibrations within the molecule, and therefore about the chemical bonds.

The description of Raman scattering given above (and in IPMB) is a quantum view that depends on the presence of discrete energy levels. However, one can also develop a classical model of Raman scattering. For instance, treat a simple diatomic molecule as two atoms attached by a spring, so that the molecule has its own natural frequency of oscillation, f_o. If an electric field of frequency f is incident on the atom, it will respond by not only oscillating both at frequency f (Rayleigh scattering) but also at frequencies f+f_o and f-f_o (Raman scattering). The frequency difference between adjacent lines is f_o, which is the same frequency as one would expect in the infrared absorption spectrum. (For those who have read Appendix F of IPMB and are wondering why the the scattered light oscillates with a component at the natural frequency, realize that the charge induced by polarization depends on the electric field, so the force on the charge--charge times electric field--depends on the square of the electric field and the problem is nonlinear.)

Raman scattering was named after Indian physicist C. V. Raman (1888–1970), whose discovery led to the 1930 Nobel Prize for Physics.


Four types of scattering, named after four Nobel Prize winners. Here are some ways to keep them straight: Compton and Thomson scattering is off a single charged particle (usually an electron), whereas Rayleigh and Raman scattering is off an entire atom or molecule or particle. Thomson and Rayleigh scattering are elastic, whereas Compton and Raman scattering are inelastic. Thomson and Rayleigh scattering are most commonly described using the classical wave theory of light, whereas Compton and Raman scattering are typically analyzed using quantum mechanics (although Raman scattering is sometimes analyzed with classical theory).

I admire all four scientists: Compton, Thomson, Rayleigh, and Raman. Who is my favorite? I like Rayleigh best. Love those Victorians.

Letters to a Young Scientist

Letters to a Young Scientist,
by Edward Wilson.

I just finished reading Edward Wilson’s book Letters to a Young Scientist. (I know, I know….I don’t qualify as a young scientist anymore, but I can still enjoy the book.) Wilson is a leading biologist who established two fields of study: island biogeography and sociobiology. He is one of the world’s experts on the taxonomy of ants. Last week’s blog post about the binomial nomenclature for naming animal species was motivated in part from reading this book. You can hardly get further from physics than the taxonomy of ants, so this may seem like an odd topic to discuss in a blog about physics applied to medicine and biology. But the book considers universal themes common to all scientists.

What is Wilson’s main message for young scientists? He writes

First and foremost, I urge you to stay on the path you’ve chosen, and to travel on it as far as you can. The world needs you—badly.

How true. My favorite of Wilson’s letters was number seven, “Most Likely to Succeed.”

Conventional wisdom holds that science of the future will be more and more the product of “teamthink,” multiple minds put in close contact…But is groupthink the best way to create really new science? Risking heresy, I hereby dissent. I believe the creative process usually unfolds in a very different way. It arises and for a while germinates in a solitary brain. It commences as an idea and, equally important, the ambition of a single person who is prepared and strongly motivated to make discoveries in one domain of science or another. The successful innovator is favored by a fortunate combination of talent and circumstance… When prepared by education to conduct research, the most innovative scientists of my experience do so eagerly and with no prompting. The prefer to take first steps alone. They seek a problem to be solved, an important phenomenon previously overlooked, a cause-and-effect connection never imagined. An opportunity to be the first is their smell of blood.

I also liked the point Wilson made in letter three, “The Path to Follow.”

If a subject is already receiving a great deal of attention, if it has a glamorous aura, if its practitioners are prizewinners who receive large grants, stay away from that subject. Listen to the news coming from the current hubbub, learn how and why the subject became prominent, but in making your own long-term plans be aware it is already crowded with talented people… Take a subject instead that interests you and looks promising, and where established experts are not yet conspicuously competing with one another…You may feel lonely and insecure in your first endeavors, but all other things being equal, your best chance to make your mark and to experience the thrill of discovery will be there.

He then states a general principle using a military metaphor.

March away from the sound of the guns. Observe the fray from a distance, and while you are at it, consider making your own fray.

He continues with an observation about big science.

The sequencing of the human genome, the search for life on Mars, and the finding of the Higgs boson were each of profound importance for medicine, biology, and physics, respectively. Each required the work of thousands and cost billions. Each was worth all the trouble and expense. But on a far smaller scale, in fields and subjects less advanced, a small squad of researchers, even a single individual, can with effort devise an important experiment at relatively low cost.

I agree with Wilson on all these points. I think there is a lot to be said for small groups. And I think that too often researchers chase the latest fad. I second Wilson’s advice to march away from the sound of the guns, and to make your own fray instead.

Often those applying physics to biology and medicine are skirmishers whose goal is to probe the unknown searching for vulnerabilities, rather than to join the mass attack. My suggestion is to first get a broad education in both physics and biology, perhaps using a book like the 4th edition of Intermediate Physics for Medicine and Biology (you knew I would get the plug in somewhere), and then find some interesting but little-studied topic, and see where it leads you. And above all, have fun while you are doing it.

But don’t take my word for it. Read the book, or listen to Wilson give his advice to young scientists in his TED talk.

Edward Wilson giving a TED talk about Advice to Young Scientists.

https://www.youtube.com/embed/IzPcu0-ETTU

The Encyclopedia of Life

Although I am a champion of applying physics to biomedicine, physics has little impact on some parts of biology. For instance, much of zoology and botany consist of the identification and naming of different species: taxonomy. Not too much physics there.

A giant in the field of taxonomy is the Sweedish scientist Carl Linnaeus (1707-1778). Linnaeus developed the modern binomial nomenclature to name organisms. Two names are given (often in Latin), genus then species, both italicized with the genus capitalized and the species not. For example, the readers of this blog are Homo sapiens: genus = Homo and species = sapiens. My dog Suki is a member of Canis lupus. Her case is complicated, since the domestic dog is a subspecies of the wolf, Canis lupus familiaris, but because dogs and wolves can interbreed they are considered the same species and to keep things simple (a physicist’s goal, if not a biologist’s) I will just use Canis lupus. Hodgkin and Huxley performed their experiments on the giant axon from the squid, whose binomial name is Loligo forbesi (as reported in Hodgkin and Huxley, J. Physiol., Volume 104, Pages 176–195, 1945; in their later papers they just mention the genus Loligo, and I am not sure what species they used--they might have used several). My daughter Katherine studied yeast when an undergraduate biology major at Vanderbilt University, and the most common yeast species used by biologists is Saccharomyces cerevisiae. The nematode Caenorhabditis elegans is widely used as a model organism when studying the nervous system. You will often see its name shortened to C. elegans (such abbreviations are common in the Linnaean system). Another popular model system is the egg of the frog species Xenopus laevis. The mouse, Mus musculus, is the most common mammal used in biomedical research. I’m not enough of a biologist to know how viruses, such as the tobacco mosaic virus, fit into the binomial nomenclature.

Out of curiosity, I wondered what binomial names Russ hobbie and I mentioned in the 4th edition of Intermediate Physics for Medicine and Biology. It is surprisingly difficult to say. I can’t just search my electronic version of the book, because what keyword would I search for? I skimmed through the text and found these four; there may be others. (Brownie points to any reader who can find one I missed and report it in the comments section of this blog.)

• Escherichia coli (E. coli): the most famous model system in all of biology. The name of this bacteria species appears on page 2 of IPMB, and in Fig. 1.1. Also it appears on pages 29 and 71 (in homework problems), on page 85 in Table 4.2, and on pages 96 and 109. 
• Aquaspirillum magnetotacticum: a type of magnetotactic bacteria, shown in Fig. 8.25 on page 217 of IPMB. Apparently this organism has been reclassified as Magnetospirillum magnetotacticum.
• Chara corallina: I had forgotten about this one until I stumbled upon it as I browsed through the book. In IPMB, it appears on page 225, in the title of a journal article among the list of references for Chapter 8. It’s a type of green algae that produces a biomagnetic signal.
• Drosophila melanogaster was mentioned last month in this blog. It appears on page 239 of IPMB, when discussing potassium channels.

If you want to learn more about any of these species, I suggest going to the fabulous website EOL.org. The site states

The Encyclopedia of Life (EOL) began in 2007 with the bold idea to provide “a webpage for every species.” EOL brings together trusted information from resources across the world such as museums, learned societies, expert scientists, and others into one massive database and a single, easy-to-use online portal at EOL.org.

While the idea to create an online species database had existed prior to 2007, Dr. Edward O. Wilson's 2007 TED Prize speech was the catalyst for the EOL you see today. The site went live in February 2008 to international media attention. …

Today, the Encyclopedia of Life is expanding to become a global community of collaborators and contributors serving the general public, enthusiastic amateurs, educators, students and professional scientists from around the world.

Principles of Musical Acoustics

Principles of Musical Acoustics,
by William Hartmann.

In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I added a new chapter (Chapter 13) about Sound and Ultrasound. This allows us to discuss acoustics and hearing; an interesting mix of physics and physiology. But one aspect of sound we don’t analyze is music. Yet, there is much physics in music. In a previous blog post, I talked about Oliver Sacks’ book Musicophilia, a fascinating story about the neurophysiology of music. Unfortunately, there wasn’t a lot of physics in that work.

Last year, William Hartmann of Michigan State University (where my daughter Kathy is now a graduate student) published a book that provides the missing physics: Principles of Musical Acoustics. The Preface begins

Musical acoustics is a scientific discipline that attempts to put the entire range of human musical activity under the microscope of science. Because science seeks understanding, the goal of musical acoustics is nothing less than to understand how music “works,” physically and psychologically. Accordingly, musical acoustics is multidisciplinary. At a minimum it requires input from physics, physiology, psychology, and several engineering technologies involved in the creation and reproduction of musical sound.

My favorite chapters in Hartmann’s book are Chapter 13 on Pitch, and Chapter 14 on Localization of Sound. Chapter 13 begins

Pitch is the psychological sensation of the highness or the lowness of a tone. Pitch is the basis of melody in music and of emotion in speech. Without pitch, music would consist only of rhythm and loudness. Without pitch, speech would be monotonic—robotic. As human beings, we have astonishingly keen perception of pitch. The principal physical correlate of the psychological sensation of pitch is the physical property of frequency, and our keen perception of pitch allows us to make fine discriminations along a frequency scale. Between 100 and 10,000 Hz we can discriminate more than 2,000 different frequencies!

That is two thousand different pitches within a factor of one hundred in the range of frequencies (over six octaves), meaning we can perceive pitches that differ in frequency by about 0.23 %.  A semitone in music (for example, the difference between a C and a C-sharp) is about 5.9 %. That's pretty good: twenty-five pitches within one semitone. No wonder we have to hire piano tuners.

Pitch is perceived by “place,” different locations in the cochlea (part of the inner ear) respond to different frequencies, and by “timing,” neurons spike in synchrony with the frequency of the sound. For complex sounds, there is also a “template” theory, in which we learn to associate a collection of frequencies with a particular pitch. The perception of pitch is not a simple process.

There are some interesting differences between pitch perception in hearing and color perception in vision. For instance, on a piano play a middle C (262 Hz) and the next E (330 Hz) a factor of 1.25 higher in frequency. What you hear is not a pure tone, but a mixture of frequencies—a chord (albeit a simple one). But if you mix red light (450 THz) and green light (563 THz, again a factor of 1.25 higher in frequency), what you see is yellow, indistinguishable by eye from a single frequency of about 520 THz. I find it interesting and odd that the eye and ear differ so much in their ability to perceive mixtures of frequencies. I suspect it has something to do with the eye needing to be able to form an image, so it does not have the luxury of allocating different locations on the retina to different frequencies. One the other hand, the cochlea does not form images, so it can distribute the frequency response over space to improve pitch discrimination. I suppose if we wanted to form detailed acoustic images with our ear, we would have to give up music.

Hartmann continues, emphasizing that pitch perception is not just physics.

Attempts to build a purely mechanistic theory for pitch perception, like the place theory or the timing theory, frequently encounter problems that point up the advantages of less mechanistic theories, like the template theory. Often, pitch seems to depend on the listener’s interpretation.

Both Sacks and Hartmann discuss the phenomena of absolute, or perfect, pitch (AP). Hartmann offers this observation, which I find amazing, suggesting that we should be training our first graders in pitch recognition.

Less than 1% of the population has AP, and it does not seem possible for adults to learn AP. By contrast, most people with musical skills have RP [relative pitch], and RP can be learned at any time in life. AP is qualitatively different from RP. Because AP tends to run in families, especially musical families, it used to be thought that AP is an inherited characteristic. Most of the modern research, however, indicates that AP is an acquired characteristic, but that it can only be acquired during a brief critical interval in one’s life—a phenomenon known as “imprinting.” Ages 5–6 seem to be the most important.

My sister (who has perfect pitch) and I both started piano lessons in early grade school. I guess she took those lessons more seriously than I did.

In Chapter 14 Hartmann addresses another issue: localization of sound. It is complex, and depends on differences in timing and loudness between the two ears.

The ability to localize the source of a sound is important to the survival of human beings and other animals. Although we regard sound localization as a common, natural ability, it is actually rather complicated. It involves a number of different physical, psychological, and physiological, processes. The processes are different depending on where the sound happens to be with respect to the your head. We begin with sound localization in the horizontal plane.”

Interestingly, localization of sound gets more difficult when echos are present, which has implications for the design of concert halls. He writes

A potential problem occurs when sounds are heard in a room, where the walls and other surfaces in the room lead to reflections. Because each reflection from a surface acts like a new source of sound, the problem of locating a sound in a room has been compared to finding a candle in a dark room where all the walls are entirely covered with mirrors. Sounds come in from all directions and it’s not immediately evident which direction is the direction of the original source.

The way that the human brain copes with the problem of reflections is to perform a localization calculation that gives different weight to localization cues that arrive at different times. Great weight is placed on the information in the onset of the sound. This information arrives directly from the source before the reflections have a chance to get to the listener. The direct sound leads to localization cues such as ILD [interaural level difference], ITD [interaural time difference], and spectral cues that accurately indicate the source position. The brain gives much less weight to the localization cues that arrive later. It has learned that they give unreliable information about the source location. This weighting of localization cues, in favor of the earliest cues, is called the precedence effect.

The enjoyment of music is a truly complicated event, involving much physics and physiology. The Principles of Musical Acoustics is a great place to start learning about it.

Bacterial Decision Making

Medical and biological physics sometimes appear on the cover of Physics Today. For instance, this month (February, 2014) the cover shows E coli. The caption for the cover picture states

Escherichia coli bacteria have served for decades as the “hydrogen atom” of cellular decision making. In that branch of biology, researchers strive to understand the origin of cellular individuality and how a cell decides whether or not to express a particular gene in its DNA. For some of the physics involved, turn to the article by Jané Kondev on page 31.

The article begins with a description of Jacques Monod’s work with the lac operon: a stretch of DNA that regulates the lac genes responsible for lactose digestion. (This story is told in detail in Horace Freeland Judson’s masterpiece The Eighth Day of Creation.) Kondev writes

The key question I’ll address in this article is, What is the molecular basis by which a cell decides to switch a gene on? Although all the cells in figure 1b are genetically identical and experience the same environment, only one appears to be making the protein. As we’ll see, that cellular individuality is a direct consequence of molecular noise that accompanies cellular decision making. The sources of the noise and its biological consequences are currently a hot topic of research. And statistical physics is proving to be an indispensable tool for producing mathematical models capable of explaining data from experiments that look at decisions made by individual cells.

The caption of Fig. 1b reads

In the presence of a lactose surrogate, individual cells can switch from a state in which they are unable to digest lactose to a state in which they are able to consume the secondary sugar. Yellow indicates the amount of a fluorescently labeled protein, lactose permease, which is one of the enzymes needed by the cell to digest lactose.

The article then draws on several physics concepts that Russ Hobbie and I discuss in the 4th edition of Intermediate Physics for Medicine and Biology: the Boltzmann factor, the Gibbs free energy, the Poisson probability distribution, and feedback. The last of these concepts is crucial.

Thanks to that positive feedback, E. coli cells exist in two different steady states—one in which there are many permeases in the cell (the yellow cell in figure 1b), the other in which the number of permeases is low (the dark cells in 1b). Stochastic fluctuations in the expression of the lac genes—fluctuations, for instance, between an on and an off state of the promoter—can flip the switch and turn a lactose noneater to a lactose eater.

The article concludes

Physics-based models are leading to more stringent tests of the molecular mechanisms responsible for gene expression than those provided by the qualitative model presented in biology textbooks. They also pave the way for the design of so-called synthetic genetic circuits, in which the proteins produced by the expression of one gene affect the expression of another. Such circuits hold the promise of bacterial cells capable of producing useful chemicals or combating diseased human cells, including cancerous cells. Whether this foray of physics into biology will lead to fundamentally new biological insights about gene expression remains to be seen.

Kondev’s review offers us one more example of the importance of physics in biology and medicine. And for those of you who think E. coli bacteria is not an appropriate topic for a Valentine’s Day blog post, I say bah humbug.

Distances and Sizes

One of the additions that Russ Hobbie and I made to the 4th edition of Intermediate Physics for Medicine and Biology is an initial section in Chapter 1 about Distances and Sizes.

In biology and medicine, we study objects that span a wide range of sizes: from giant redwood trees to individual molecules. Therefore, we begin with a brief discussion of length scales.

The Machinery of Life,
by David Goodsell.

We then present two illustrations. Figure 1.1 shows objects from a few microns to a few hundred microns in size, including a paramecium, an alveolus, a cardiac cell, red blood cells, and E. coli. Figure 1.2 contains objects from a few to a few hundred nanometers, including HIV, hemoglobin, a cell membrane, DNA, and glucose. Many interesting and important biological structures were left out of these figures.

I admit that our figures are not nearly as well drawn as, say, David Goodsell’s artwork in The Machinery of Life. But, I enjoy creating such drawings, even if I am artistically challenged. So, below are two new illustrations, patterned after Figs. 1.1 and 1.2. Think of them as supplementary figures for readers of this blog.

FIGURE 1.1½. Objects ranging in size from 1 mm down to 1 μm.
(a) Human hair, (b) human egg, or ovum, (c) sperm,
(d) large myelinated nerve axon, (e) skeletal muscle fiber,
(f) capillary, (g) yeast, and (h) mitochondria.

FIGURE 1.2½. Objects ranging in size from 1 μm down to 1 nm.
(a) Ribosomes, (b) nucleosomes, (c) tobacco mosaic virus,
(d) antibodies, and (e) ATP.

Powers of Ten.

When you combine these figures with those in IPMB, you get a nice overview of the important biological objects at these spatial scales. Two things you do not get are a sense of their dynamic behavior (e.g., Brownian motion) at the microscopic scale, and an appreciation for the atomic nature of all objects (you could not detect single atoms in Fig. 1.2½, but they lurk just below the surface; ATP consists of just 47 atoms).

If you like this sort of thing, you will love browsing through The Machinery of Life or Powers of Ten.

The Feynman Lectures on Physics: New Millennium Edition

www.feynmanlectures.info.

Several years ago in this blog, I discussed The Feynman Lectures on Physics. Russ Hobbie and I cite The Feynman Lectures in Chapter 11 of the 4th edition of Intermediate Physics for Medicine and Biology. Recently, a new millennium edition of the Feynman Lectures has been produced and it is fully online: http://www.feynmanlectures.info. If you are reading this blog, you can read The Feynman Lectures, free and open to all. The preface to the millennium edition states

Nearly fifty years have passed since Richard Feynman taught the introductory physics course at Caltech that gave rise to these three volumes, The Feynman Lectures on Physics. In those fifty years our understanding of the physical world has changed greatly, but The Feynman Lectures on Physics has endured. Feynman's lectures are as powerful today as when first published, thanks to Feynman's unique physics insights and pedagogy. They have been studied worldwide by novices and mature physicists alike; they have been translated into at least a dozen languages with more than 1.5 millions copies printed in the English language alone. Perhaps no other set of physics books has had such wide impact, for so long.

This New Millennium Edition ushers in a new era for The Feynman Lectures on Physics (FLP): the twenty-first century era of electronic publishing. FLP has been converted to eFLP, with the text and equations expressed in the LaTeX electronic typesetting language, and all figures redone using modern drawing software.

The consequences for the print version of this edition are not startling; it looks almost the same as the original red books that physics students have known and loved for decades. The main differences are an expanded and improved index, the correction of 885 errata found by readers over the five years since the first printing of the previous edition, and the ease of correcting errata that future readers may find. To this I shall return below.

The eBook Version of this edition, and the Enhanced Electronic Version are electronic innovations. By contrast with most eBook versions of 20th century technical books, whose equations, figures and sometimes even text become pixellated when one tries to enlarge them, the LaTeX manuscript of the New Millennium Edition makes it possible to create eBooks of the highest quality, in which all features on the page (except photographs) can be enlarged without bound and retain their precise shapes and sharpness. And the Enhanced Electronic Version, with its audio and blackboard photos from Feynman's original lectures, and its links to other resources, is an innovation that would have given Feynman great pleasure.”

All three volumes of this classic text are online. There is a lot of extra stuff too, like an errata for each edition, exercises with solutions, stories from many physicists about how The Feynman Lectures influenced their careers, original course handouts, and related links. And did I mention it is available free and open to all?

Enjoy!