Section 1–4 Chemical reactions

(Simple molecules / Special molecules / Human molecules)

According to Feynman, a chemical reaction is an atomic process in which there is a rearrangement of atomic partners. Furthermore, there is no sharp distinction between chemical reactions and physical processes. In this section, Feynman discusses chemical reactions that are related to simple molecules, special molecules, and human molecules.

1. Simple molecules (Carbon burning in oxygen):

“the oxygen may arrive with only a little energy, but the oxygen and carbon will snap together with a tremendous vengeance and commotion, and everything near them will pick up the energy (Feynman et al., 1963, section 1.4 Chemical reactions).”

Feynman begins with a simple chemical reaction pertaining to “carbon burning in oxygen.” Initially, a carbon atom can combine with an oxygen atom to form a molecule that is called carbon monoxide. He explains that atoms are very special and they tend to attract certain particular atomic partners: “carbon attracts oxygen” much more than “oxygen attracts oxygen” and “carbon attracts carbon.” Interestingly, he describes an oxygen atom and a carbon atom can snap together with a tremendous vengeance and commotion even though the oxygen atom had only a little energy. That is, chemical reactions generate additional kinetic energy of atoms (or thermal energy) and increase the temperature of the surrounding. In certain circumstances, it can result in flames and generate light.

In a sense, Feynman seems to suggest that the carbon atom in the carbon monoxide molecule is not satisfied with having one partner (oxygen atom). It is possible to have another chemical reaction when a carbon monoxide molecule collides with another oxygen atom. A carbon monoxide molecule can combine with another oxygen atom to form a molecule that is called carbon dioxide. Feynman adds that in a very rapid reaction where the explosion is very fast, more carbon monoxide molecules are formed instead of carbon dioxide. This can be related to an automobile engine or car when a very large amount of energy is released during these chemical reactions. However, “forming carbon dioxide” nowadays can be closely related to global warming and economic prosperity.

You may like Feynman’s further explanation of this chemical reaction during a British Broadcasting Corporation interview: “Atoms like each other to different degrees. Oxygen, for instance in the air, would like to be next to carbon, and if they get near to each other, they snap together. If they’re not too close though, they repel and they go apart, so they don’t know that they could snap together. It’s just as if you had a ball, it was trying to climb a hill and there was a hole it could go into, like a volcano hole, a deep one. It’s rolling along, it doesn’t go down in the deep hole, because if it starts to climb the hill and then rolls away again. But if you made it go fast enough, it will fall into the hole… (Feynman, 1994, p.128).”

2. Special Molecules (Odor of Violets):

“If we go into a field of small violets, we know what “that smell” is. It is some kind of molecule, or arrangement of atoms, that has worked its way into our noses (Feynman et al., 1963, section 1.4 Chemical reactions).”

Unlike the “carbon burning in oxygen,” there is no explanation on the formation of the “odor of violets.” Instead, Feynman mainly discusses the chemical structure of α-irone and how chemists find out the arrangement of atoms in special molecules by using chemical reactions. Essentially, they mix the special molecules with some known chemicals to find out whether the color of which changes to red or blue. During the British Broadcasting Corporation interview mentioned earlier, Feynman replies that, “the smell of violets is very similar to the chemical that's used by a certain butterfly … to attract all its mates? It turns out that this chemical is exactly the smell of violets with a small change of a few molecules (Feynman, 1994, p.107).” His main intention in this interview is to show that the smell of violets is still beautiful when we understand the special molecules in terms of atoms.

You can trust Feynman on chemistry because he had a great deal of experience as a working chemist when he was young. Interested students should read the section “The Chief Research Chemist of the Metaplast Corporation” in his autobiography, Surely You’re joking, Mr. Feynman! When Feynman asked Frederic de Hoffman to give his impression of the Metaplast Corporation, Hoffman guessed that it must have twenty-five or fifty chemists, and the chief research chemist has his own office (Feynman, 1997). Thus, Hoffman believed that his laboratory having only six chemists were unable to compete with the Metaplast Corporation. Hoffman might be shocked when he realized that Feynman was the chief research chemist of the Metaplast Corporation, whose staff consisted of only a bottle-washer (Feynman’s friend’s brother).

3. Human Molecules:

“all the life of a stream of water, can be nothing but a pile of atoms… When we say we are a pile of atoms, we do not mean we are merely a pile of atoms… (Feynman et al., 1963, section 1.4 Chemical reactions).”

It is controversial whether life can be essentially explained by a pile of atoms. Feynman primarily explains that atoms exist based on physicists’ deductions from Brownian motion and x-ray analysis. To be precise, Einstein’s (1905) derivation of diffusion coefficient of spherical particles (e.g. sugar) through a liquid and Perrin’s experiments in the determination of Avogadro’s number help to calculate the number of atoms. In addition, Max von Laue’s discovery of diffraction of X-rays in crystals shows that a crystal is a periodic array of atoms in 1912. Curiously, Feynman mentions that we cannot see atoms by using a light microscope or an electron microscope. However, Erwin Müller’s field ion microscope made history in “seeing” atoms on Oct 11, 1955.

Currently, biologists do not agree that behaviors of human beings (or human molecules) can be merely explained by a pile of atoms. Interestingly, Feynman asks us to imagine how a human being walking back and forth in front of us, talking to us, is a great glob of atoms in a very complex arrangement. He even ends the chapter with an intriguing statement: “[w]hen we say we are a pile of atoms, we do not mean we are merely a pile of atoms, because a pile of atoms which is not repeated from one to the other might well have the possibilities which you see before you in the mirror.” In a sense, this suggests the possibility of unique human molecules (e.g. a girl) looking into a mirror, but we should expect chemical reactions to occur during this process.

Feynman opines that the most important hypothesis in biology is “everything that animals do, atoms do.” This is sometimes known as a reductionist view in which the behavior of living things can be completely understood in terms of atoms according to the laws of physics. On the contrary, biologists would disagree with Feynman because they adopt an emergentist view in which a different property (or trait) of a composite system can be emerged from its smaller systems or constituents. In other words, they do not agree that all biological phenomena can be explained in terms of chemistry and physics. Simply put, reductionism means that the whole can be explained totally by its parts (or atoms), whereas emergentism means that the whole cannot be simply explained by the properties of its parts.

Questions for discussion:

1. Explain the phenomenon carbon burning in oxygen in terms of simple molecules.

2. Explain how scientists determine the chemical structure of special molecules (e.g. the odor of violets).

3. Explain whether chemical reactions occur when human molecules (male or female) look into a mirror.

The moral of the lesson: Life is nothing but a pile of atoms such as methane and ammonia, in which there is a continuous rearrangement of the atomic partners (or simply chemical reactions).

References:

1. Einstein, A. (1905). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der physik, 322(8), 549-560.

2. Feynman, R. P. (1994). No Ordinary Genius: The Illustrated Richard Feynman. New York: W. W. Norton & Company.

3. Feynman, R. P. (1997). Surely you’re Joking, Mr. Feynman. New York: Norton.

4. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley. 

Section 1–3 Atomic processes

(Evaporation of water / Dissolution of salt / Equilibrium)

In this section, Feynman describes two atomic processes: water evaporating in air and salt dissolving in water. In addition, he explains the meaning of equilibrium and discusses liquid-vapor equilibrium during the evaporation of water and solid-liquid equilibrium during the dissolution of salt.

1. Water evaporating in air:

“From time to time, one on the surface happens to be hit a little harder than usual, and gets knocked away (Feynman et al., 1963, section 1.3 Atomic processes).”

Feynman mentions that air consists of oxygen (two oxygen atoms stuck together to form one oxygen molecule), nitrogen (two nitrogen atoms stuck together to form one nitrogen molecule), as well as lesser amounts of carbon dioxide, argon, and others. Next, there are also water vapor molecules above the liquid water. More important, the main process for the evaporation of water is that a water molecule on the surface of water happens to be hit slightly harder than usual, and gets ejected from the surface to the air. In short, it is similar to a sufficiently energetic ball hits another less energetic ball. However, there is a problem of representation in Figure 1–5 (Water evaporating in air): the dynamic process of evaporation cannot be clearly shown by the static figure.

Essentially, water evaporates when water molecules gain sufficient kinetic energy from random collisions such that they can break away from the attractions of previously nearby water molecules. Furthermore, water molecules that leave tend to have more kinetic energy than the average water molecules, whereas water molecules that stay tend to have lesser kinetic energy. Thus, the liquid gradually cools due to evaporation because the remaining water molecules have lesser average motion than what they had earlier. Nevertheless, the real process is slightly more complicated when it involves other impurities such as nitrogen molecules that “join in” or “dive in,” and “get lost” among the water molecules.

On the other hand, Feynman provides a real life example that may happen to divers. There could be some elaborations because he simply states that “the air molecules leave more rapidly than they come in, and in doing so will make bubbles.” As a suggestion, we can explain that it is about the decompression sickness and the process is similar to what happens when you open a can of coke. Simply phrased, the pressure surrounding the drink is decreased, which causes the carbon dioxide gas to come out of the liquid coke in the form of bubbles. Similarly, if excessive nitrogen bubbles are formed in your blood, they can damage blood vessels and even obstruct the flow of blood. It is the formation of nitrogen bubbles that causes decompression sickness or nitrogen narcosis.

2. Salt dissolving in water:

“If there is almost no salt in the water, more atoms leave than return, and the salt dissolves. If, on the other hand, there are too many “salt atoms,” more return than leave, and the salt is crystallizing (Feynman et al., 1963, section 1.3 Atomic processes).”

According to Feynman, salt is a solid that has an organized arrangement of “salt atoms,” or to be more precise, it is made of sodium ions and chlorine ions. He elaborates that an ion is an atom which either has a few extra electrons or has lost a few electrons. In a salt crystal, chlorine ions (chlorine atoms with an extra electron) and sodium ions (sodium atoms with one electron missing) are stick together by electrical attraction. Interestingly, they are separated in the water due to the attractions of the negative oxygen atoms and positive hydrogen atoms for the ions. The hydrogen ends of the water molecules are more likely nearer to the chlorine ions, while the oxygen ends are likely nearer to the sodium ions. This is because the sodium ion is positive and the oxygen end of the water is negative, and they attract electrically.

There is also a problem of representation in Figure 1–6 (Salt dissolving into water). Feynman asks whether we can tell from this figure that the salt is dissolving into water or it is crystallizing out of the water. It is unclear whether the figure represents the dissolution of salt because some of the salt atoms are leaving the crystal and the other salt atoms are rejoining it at the same time. If there are almost no salt atoms in the water, more salt atoms are likely to leave (dissolve) than to return (crystallize) and the salt is dissolving. If there are too many salt atoms in the water, more salt atoms are likely to return than to leave and the salt is crystallizing.

Feynman ends the section by saying that it is very difficult to predict which way the process will go, that is, whether more or less salt will dissolve. He could have related this process to another real life example. For instance, there could be an elaboration on the impurities in common salt or the salt in Dead sea. Better still, Feynman should discuss the following anecdote: Mrs. Eisenhart asked him, “Would you like cream or lemon in your tea, Mr. Feynman?” Interestingly, Feynman’s answer was “I'll have both, thank you.” However, her response was “Heh-heh-heh-heh-heh. Surely you're joking, Mr. Feynman (Feynman, 1997, p. 60).” The atomic processes involved in mixing (or dissolving) cream and lemon with tea should be more complicated. But, another question is “Would you drink Feynman’s tea?”

3. Equilibrium (similarities and differences):

“By equilibrium we mean that situation in which the rate at which atoms are leaving just matches the rate at which they are coming back (Feynman et al., 1963, section 1.3 Atomic processes).”

There are different kinds of equilibrium in the two atomic processes: liquid-vapor equilibrium during the evaporation of water and solid-liquid equilibrium during the dissolution of salt. When water is evaporating in air, it reaches a phase equilibrium in which the rate of evaporation and the rate of condensation are the same. (Feynman’s use of the term equilibrium is vague because phase equilibrium is closely related to thermal equilibrium, mechanical equilibrium, and chemical equilibrium.) When a salt crystal is dissolving in water, it reaches a solubility equilibrium in which a chemical compound such as salt in the solid state is in chemical equilibrium with a solution such as water. During this equilibrium, the rate of dissolution is equal to the rate of precipitation.

Feynman explains that the word equilibrium simply means the situation in which the rate of atoms moving away is equal to the rate of atoms coming back. Although both processes appear to be in static equilibrium according to our eyes, they are actually in dynamic equilibrium under a powerful microscope. In short, this equilibrium is macroscopically static and microscopically dynamic. Importantly, we have used the term atoms instead of molecules during the dissolution of salt. Feynman clarifies that the concept of a molecule of a substance is only approximate and exists only for certain substances. More appropriately, he describes salt in terms of an arrangement of sodium and chlorine ions in a cubic pattern and explains that it is not natural to group them as “molecules of salt.”

Questions for discussion:

1. Explain the evaporation of water in terms of atoms or molecules.

2. Explain the dissolution of salt in terms of atoms or ions.

3. Compare the two atomic processes: liquid-vapor equilibrium during the evaporation of water and solid-liquid equilibrium during the dissolution of salt.

The moral of the lesson: Phase equilibrium and solubility equilibrium are reversible atomic processes that are macroscopically static, but microscopically dynamic.

References:

1. Feynman, R. P. (1997). Surely, you’re Joking, Mr. Feynman. New York: Norton.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

Section 1–2 Matter is made of atoms

(Solid / Liquid / Gas)

Feynman states the atomic hypothesis as all things are made of atoms that are moving perpetually, attracting each other when they are in a relatively short distance apart, and repelling upon being squeezed into one another. Currently, this is a fact because we can “see” individual atoms by using a scanning tunneling microscope and move them from one location to another. Importantly, atoms were initially defined as indivisible and indestructible fundamental entities, but they are reformulated as systems of nucleons that are made of quarks. In a sense, quarks are now the fundamental physical entities and have the traditional meaning of “atoms.” However, we explain properties of water, steam, and ice in terms of atoms instead of quarks.

Note: In volume 2, chapter 6 of The Feynman Lectures, he mentions that the field-ion microscope provided human beings with the means of seeing atoms for the first time.

1. Properties of water (liquid):

“… a picture of water magnified a billion times, but idealized in several ways (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Feynman describes the use of best optical microscope available, roughly 2000 times, to magnify a water drop. He would revise this section considerably because scanning tunneling microscopes are now available. Donald Eigler of IBM’s Almaden Research Centre is the first person to manipulate an individual atom in a controlled way such that we can “see” atoms. This technical achievement was predicted by Feynman in a lecture titled There’s Plenty of Room at the Bottom given at an American Physical Society meeting at California Institute of Technology on December 29, 1959. In Feynman’s words, “[t]he principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom. It is not an attempt to violate any laws; it is something, in principle, that can be done; but in practice, it has not been done because we are too big (Feynman, 1999, p. 137).”

Interestingly, Feynman mentions three limitations of Figure 1–1 (Water magnified one billion times). First, the particles are idealized in the figure as having sharp edges. As an alternative, the edges could be blurred because the particles are almost everywhere in the sense that they may be found in locations further away with lower probabilities as predicted by quantum mechanics. Second, the particles are sketched in a two-dimensional figure. Therefore, the figure does not show possible three-dimensional arrangements of particles. Third, the figure is a static representation of water molecules. Currently, the movements of water molecules can be illustrated in e-books by using applets that can represent concepts dynamically.

On the other hand, Feynman states that “the jiggling motion is what we represent as heat: when we increase the temperature, we increase the motion (Feynman et al., 1963, section 1–2 Matter is made of atoms).” This statement of heat as jiggling motion can be confusing to students. If heat (Q) is defined as the kinetic energy of molecules in a body, it causes confusion because it has a similar meaning as the term “internal energy” (U) in the equation, ΔU = Q + W. Thus, it is not a surprise that students have confusion with the term heat and internal energy (e.g. Kautz, Heron, Loverude, & McDermott, 2005). Although Feynman also uses the term heat as a verb, this is different from physicists and physics educators who define heat as a process of energy transfer. The definition of heat as a process clearly means that it is not a form of substance or fluid.

2. Properties of steam (gas):

“… to an excellent approximation, if the density is low enough that there are not many atoms, the pressure is proportional to the density (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Students may not understand why Feynman uses the word approximation to explain that the pressure of a gas is proportional to the density of the gas. This relationship is exact if we apply the ideal gas equation, PV/T = NkT. To be more accurate, we use the van der Waals equation of state, [p + a(N²/V²)](V – Nb) = NkT. Feynman has this equation in mind when he says that “if we consider the true nature of the forces between the atoms, we would expect a slight decrease in pressure because of the attraction between the atoms… (Feynman et al., 1963, section 1.2 Matter is made of atoms).” The term a(N²/V²) is needed to correct the effect due to the attractive intermolecular forces which become stronger as the molecules get closer. Next, the volume for a random molecular motion to take place is lesser by Nb because gas molecules are not point particles and have finite volume. (The constants a and b can be determined experimentally depending on the gas selected.)

Curiously, Feynman explains that Figure 1–2 (Steam) fails in one respect because there would not be as many as three water molecules at ordinary atmospheric pressure. However, this is not definitely incorrect, but it is a matter of probability. In general, most figures having the same size are likely not to have even one molecule. Perhaps it should be emphasized that the figure does not give the idea of random motion of particles. On the other hand, he simply mentions that there is a 105^o 3′ angle between the hydrogen atoms. Alternatively, we can explain that a water molecule has a tetrahedron shape in which two of the “attachments” are electron clouds containing two electrons each, and the other two “attachments” are a hydrogen atom each sharing two electrons with the oxygen atom. Moreover, the hydrogen atoms are 104.5^o from each other because of the greater repulsion between the two electron clouds that force the hydrogen atoms slightly closer together.

3. Properties of ice (solid):

“… minimum amount of motion that atoms can have is not enough to melt a substance, with one exception: helium (Feynman et al., 1963, section 1.2 Matter is made of atoms).”

Feynman mentions that Figure 1–4 (Ice) is wrong because it is drawn in two dimensions. In addition, he states that the material has a definite place for every atom. However, the figure does not show that the atoms are vibrating “in place” or oscillating in fixed locations. That is, the picture is a static representation of water molecules. Interestingly, as we decrease the temperature, the vibration decreases until it reaches near absolute zero; there is a minimum amount of vibration that the atoms can have, but not zero based on quantum physics. Thus, we explain that ice has thermal energy because the atoms have kinetic energy. (As mentioned earlier, physicists and physics educators may not agree with the phrase “ice has heat” that was used by Feynman.)

According to Feynman, helium is an exception among atoms because it does not freeze at absolute zero unless we increase the pressure high enough to make it solidify. Physicists may question Feynman how it is possible to achieve absolute zero according to Nernst’s theorem. The temperature “absolute zero” is a theoretical concept and it is practically impossible to cool an object to absolute zero within a finite number of steps in an experiment. Thus, it is more appropriate to use the phrase “near absolute zero” instead of “at absolute zero.” 

More important, there are reports that helium may behave like a supersolid, another state of matter that has the crystalline structure of a solid, and it flows like a liquid. Nevertheless, definitions of solid, liquid, and gas are usually simplistic. Strictly speaking, it is possible to have intermediate states between solids and liquids: e.g. liquid crystals. It is worth mentioning that glass is sometimes known as an amorphous solid or a supercooled liquid. There is also research on two different states of liquid water.

Questions for discussion:

1. Explain properties of water in terms of atoms and discuss limitations of figure 1–1 in representing a liquid.

2. Explain properties of steam in terms of atoms and discuss limitations of figure 1–2 in representing a gas.

3. Explain properties of ice in terms of atoms and discuss limitations of figure 1–4 in representing a solid.

The moral of the lesson: Do not be confused by misleading figures in textbooks that represent solid, liquid, and gas.

References:

1. Feynman, R. P. (1999). The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. Cambridge, MA: Perseus.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Kautz, C. H., Heron, P. R. L., Loverude, M. E. & McDermott, L. C. (2005). Student understanding of the ideal gas law, Part I: A macroscopic perspective. American Journal of Physics, 73(11), 1055-63.

Section 1–1 Introduction

(Learning physical laws / Guessing physical laws / Changing physical laws)

In section 1–1 introduction of The Feynman Lectures on Physics, there are three important points: difficulties in learning physics (learning physical laws), scientific method (guessing physical laws), and tentative nature of science (changing physical laws).

1. Difficulties in learning physics (Learning physical laws): 

“… one needs a considerable amount of preparatory training even to learn what the words mean (Feynman et al., 1963, section 1–1 Introduction).”

Feynman provides only two reasons that the process of learning physics cannot be shortened from four years to four minutes. Firstly, we still do not know all fundamental physical laws. With more discoveries in science, physicists realize increasing areas in physics that our scientific knowledge could be incorrect or incomplete. Secondly, statements of physical laws are expressed using scientific terms and advanced mathematics. Thus, it is not sufficient to learn physics by simply mastering mathematical skills. Furthermore, physics students will continue to learn and unlearn physics concepts because many physical laws are merely approximations to the complete truth.

Importantly, physics students require a considerable amount of preparatory training to learn the meaning of many scientific terms or words. We cannot simply learn many physics concepts by reading the definitions. Note that Feynman has the tendency of mentioning the word “define” or “definition” in his lectures and discussing many problems of definitions. Thus, there could be more explanations why it is not easy to learn what the words mean. In general, definitions of physics concepts are often inadequate because there are definitional problems such as incorrect, incomplete, and ambiguous. For example, Feynman mentions that “[b]y definition, light is unpolarized if we are unable to find out whether it is polarized or not. The polarization may change more rapidly than we can detect (Feynman et al., 1963, section 33-2).” These discussions of definitions are insightful, and physics teachers can use them to correct students’ preconceived notions of many physics concepts.

2. Scientific method (Guessing physical laws): 

“…there are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce, and guess (Feynman et al., 1963, section 1–1 Introduction).”

According to Feynman, an important process of scientific method involves the use of experiment to check the correctness of scientific knowledge. Although he mentions that the test of all knowledge is experiment, this principle is based on the assumption that the experiment is correctly executed without careless mistakes. Of course, this assumption is not necessarily always correct because experimental physicists might make mistakes in interpreting experimental results or fudging some data. In an address titled Cargo Cult Science, Feynman (1974) questions the measurements of the electron’s charge shortly after Millikan because the experimental results seem to be manipulated such that they were slowly increased over a period of time. Importantly, Feynman suggests that experimental physicists should also report everything that might invalidate the experiment.

Essentially, both theoretical physicists and experimental physicists need to guess new physical laws. However, Feynman (1965) gives a better description of the scientific method in a Messenger lecture: “we look for a new law by the following process. First, we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the results of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works (p. 156).” Interestingly, the audience laughed out loud when he mentioned the word “guess.” Nevertheless, Feynman advised them not to laugh and explained that “guessing” is truly an important process in science. In short, the scientific method is about making our best guess.

3. Tentative nature of science (Changing physical laws): 

“…So a ‘law’ was invented: mass is constant, independent of speed. That ‘law’ is now found to be incorrect. Mass is found to increase with velocity, but appreciable increases require velocities near that of light (Feynman et al., 1963, section 1–1 Introduction).”

Physicists (especially particle physicists) may disagree with Feynman and explain that the correct law should be stated as the mass of an object is constant and it is independent of velocity. For instance, Hecht (2009) writes that Einstein did not derive an equation for relativistic mass. However, Einstein (1905) proposed the concept of transverse mass = μ/(1 – v²/c²) and longitudinal mass = μ/(1 – v²/c²)^3/2 in which μ is the electron’s mass; these two concepts of mass are velocity-dependent. Subsequently, Einstein changed his position on the concept of mass. In a letter to Barnett, Einstein (1948) proposes that “It is not good to introduce the concept of the mass, m = m₀/(1 – v²/c²)^–1/2 of a moving body for which no clear definition can be given.” Some physics teachers have cited this letter of Einstein to support the concept of invariant mass.

More important, in his Autobiographical notes, Einstein (1949/1979) writes that “…it was clear that the inert mass of a physical system increases with the total energy (therefore, e.g., with the kinetic energy) (p. 61).” In other words, the mass of a physical system increases if the total kinetic energy of its constituents increases. For example, the mass of a cup of water increases with temperature because the water molecules move with higher speeds. In essence, we should distinguish mass of a particle and mass of a physical system. Moreover, there is no agreement on the use of terms such as mass, rest mass, and relativistic mass among physicists. Mathematically, the relativistic mass of an object may be defined as m = E/c² instead of m = m₀/(1 – v²/c²)^–1/2. However, physical laws related to the concept of mass may continue to change.

In an article titled Mass versus relativistic and rest masses, Okun (2009) argues that Feynman’s use of velocity-dependent mass is confusing. Feynman’s approach is based on the principle of mass-energy equivalence, or simply energy has mass. That is, the mass of an object or a physical system is dependent on its total energy, including its kinetic energy. On the contrary, Okun disagrees that there is a complete equivalence of mass and energy that is suggested by the famous equation, E = mc². Perhaps Feynman would propose to resolve the disagreement as follows: “The question is: which one is right? If these various alternatives are not exactly equivalent mathematically, if for certain ones there will be different consequences than for others, then all we have to do is to experiment to find out which way nature actually chooses to do it… (Feynman, 1965, p. 53).”

Questions for discussion: 

Physics teachers could discuss the following questions with their students if this section is a required reading for their introductory physics module. 

1. How would you learn physical laws? 

2. What do you understand by the term “scientific method”? 

3. Are physical laws always correct? 

The moral of the lesson: while students are learning physical laws, physicists are guessing and changing physical laws. 

References: 

1. Einstein, A. (1905/1952). On the electrodynamics of moving bodies. In The Principle of Relativity, a collection of originals papers on the special and general theory of relativity. New York: Dover. 

2. Einstein, A. (1948). Letter to Lincoln Barnett, 19 June 1948. In L. B. Okun (1989) The concept of mass. Physics Today, 42(6), 31–36. 

3. Einstein, A. (1949/1979). Autographical notes (Translated by Schilpp). La Salle, Illinois: Open court. 

4. Feynman, R. P. (1965). The character of physical law. Cambridge: MIT Press. 

5. Feynman, R. P. (1974). Cargo Cult Science. In R. P. Feynman, (1997). Surely, you’re Joking, Mr. Feynman. New York: Norton.

6. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley. 

7. Hecht, E. (2009). Einstein never approved of relativistic mass. The Physics Teacher, 47(6), 336–341. 

8. Okun, L. B. (2009). Mass versus relativistic and rest masses. American Journal of Physics, 77(5), 430–431.