Section 2–4 Nuclei and particles

(Nuclear force / Elementary particles / Elementary interactions)

Feynman starts this section by explaining how a bigger explosion is due to smaller particles, nuclei. That is, a greater amount of nuclear energy released in an atomic bomb has to with changes inside the nucleus, whereas a relatively lesser amount of chemical energy released in a TNT explosion has to do with changes of electrons on the outside of the atoms. This is related to stable nuclei that are held together by enormous nuclear forces. In this section, the three main ideas discussed are the nuclear force, elementary particles, and elementary interactions.

1. Nuclear force:

“… The question is, what are the forces which hold the protons and neutrons together in the nucleus? (Feynman et al., 1963, section 2.4 Nuclei and particles).”

According to Feynman, Yukawa suggested that forces between neutrons and protons have a field that behaves like a particle when it “shakes.” In 1935, Yukawa predicted that the particle should have a mass of two or three hundred times of an electron, and it could be discovered in cosmic rays. The first candidate for Yukawa’s prediction, initially called a μ-meson, was discovered in 1936 by Carl David Anderson and others through cosmic rays interactions. This particle was later proved to have the wrong properties and it is later renamed as a muon. (Note: Feynman’s statement “it was called a μ-meson, or muon” is potentially confusing.)

In 1947, Powell, Lattes, and Occhialini discover pion (previously known as π-meson) in products of cosmic rays that satisfied Yukawa’s criterion. The delay in discovery is due to the World War II that ended in August 1945 as physicists gradually returned to research. However, calculations involved in the theory of quantum nucleodynamics are so difficult that no one was able to figure out the consequences of the theory and to check them against experiments for almost twenty years. Although Feynman mentions quantum nucleodynamics which could be appropriate to describe the theory of nuclear force, it has been replaced by the term quantum chromodynamics (QCD).

Yukawa’s idea of a new particle was novel because it was thought that the nuclear force could be resulted from the exchange of electron and neutrino. The situation was also messy in the 1930s because Bohr proposed that energy is not conserved and Heisenberg thought that electron might be the particle involved in the nuclear force. Furthermore, it was unclear whether the nuclear force is a fundamental force or a secondary force that can be derived from the electromagnetic force. Importantly, Yukawa (1982) explains that “I had this idea of a nuclear force field very early. Looked at from the quantum mechanical viewpoint, a field of force, almost by necessity, implies that there is a particle accompanying that field. We actually infer the existence of the photon as the particle accompanying the electromagnetic field… (p. 194).” Yukawa was awarded the Nobel Prize in Physics in 1949 for the prediction of pions.

2. Elementary particles:

“… Several particles have been omitted from the table. These include the important zero-mass, zero-charge particles, the photon and the graviton, which do not fall into the baryon-meson-lepton classification scheme… (Feynman et al., 1963, section 2.4 Nuclei and particles).”

Feynman has discussed problems in defining elementary particles. First, he asks whether new particles discovered in 1961 are really particles because their lifetimes are very short and they could be considered as some kind of “resonance” interaction of a certain definite energy. Next, the photon and the graviton do not fall into the baryon-meson-lepton classification scheme, however, there are also problems in defining baryon, meson, and lepton. Originally, baryon, meson, and lepton mean “heavy-weight particle,” “middle-weight particle,” and “light-weight particle” respectively. Moreover, Okun (1962) introduces the term hadrons that mean strongly interacting particles. Currently, hadrons are classified as two families: baryons as bound states of three quarks and mesons as bound states of a quark and an anti-quark. The term lepton is a misnomer because a muon (a member of the lepton family) is relatively heavy.

Historically speaking, Feynman (1948) writes that “it appeared that we now know, with varying degrees of certainty, of at least eleven so-called elementary particles. First, there are the familiar electrons, neutrons, protons, and photons… (p. 8).” In addition, in an article titled partons, Feynman suggests that “[w]e need a name for what one would call the ‘elementary particles’ of the theory. We do not know if there are any such particles in the end, but we will start by supposing that there are because otherwise we would have no field theory at all. I will call these things ‘partons’ (Feynman, 1970, p. 519).” On the other hand, Gell-Mann received the Nobel Prize in physics in 1969 for his work on the theory of elementary particles and he coins the term quarks which mean the fundamental building blocks for particles such as neutron and proton.

Note: Gell-Mann does not agree with Feynman’s theory of “partons” and rename them as “put-ons” because Gell-Mann reasons that these particles do not obey quantum field theory (Wilczek, 2008). Interestingly, Gell-Mann is an enthusiastic bird-watcher and has learned many languages such as Latin, French, and Spanish. However, one of Feynman’s stories about his father is that the name of a bird does not matter: “You can know the name of a bird in all the languages of the world, but when you’re finished, you'll know absolutely nothing whatever about the bird... So let’s look at the bird and see what it’s doing – that’s what counts. I learned very early the difference between knowing the name of something and knowing something (Feynman, 1988, p. 14).”

3. Elementary interactions:

“… there seem to be just four kinds of interaction between particles which, in the order of decreasing strength, are the nuclear force, electrical interactions, the beta-decay interaction, and gravity (Feynman et al., 1963, section 2.4 Nuclei and particles).”

Feynman states that the four kinds of interaction between particles which, in the order of decreasing strength, are the nuclear force, electrical interactions, the beta-decay interaction, and gravity. In addition, he mentions that the photon is coupled to all charged particles, gravity is coupled to all energy, and provides a table that compares the strength of the four interactions. However, physicists currently describe the four interactions as the strong force, electromagnetic force, weak force, and gravitational force; the strong force is mediated by gluons and weak force is mediated by W bosons and Z bosons. More important, we can compare the strengths of the four forces by using a graph instead of a table because the strengths of these forces are distance-dependent.

Feynman summarizes that all the rules outside the nucleus seem to be known, whereas inside the nucleus, the principles of quantum mechanics are still valid. He adds that the rules of the game are the quantum-mechanical principles, and those principles apply to the new particles as well as to the old. Importantly, Feynman admits that physicists have limited understanding of the nuclear (strong) force. Recently, Wilczek (2007) explains that “[i]n principle, the equations of QCD contain all the physics of strong internucleon forces. But in practice, it is extremely difficult to solve the equations and calculate those forces (p. 156).” He clarifies that nucleons are complicated objects and the statement “protons and neutrons are made from three quarks” contains an oversimplified truth.

It is worthwhile to ponder Yukawa’s thinking process pertaining to the nature and strength of nuclear force as follows, “[i]s the new nuclear force a primary one? Or is it a secondary one, derived from the gravitational and electromagnetic forces? That is the fundamental question. Now, gravity cannot be applicable in this case, because the gravitational force between such minuscule objects as protons and neutrons is unimaginably small. It is much too weak to bind together such a compact and strongly aggregated composite as a nucleus. Electromagnetic forces, on the other hand, are much stronger than gravitation; but they are still too weak to be the source of the nuclear force. Not only that: electromagnetism appears to give only forces of repulsion, rather than attraction. Because the neutron is electrically neutral, there should not be any large electrical force between it and other particles; and protons repel each other (Yukawa, 1982, p. 194)!”

Questions for discussion:

1. Is the nuclear force a fundamental force or can it be derived from the gravitational or/and electromagnetic forces?

2. What are the elementary particles?

3. How do physicists compare the relative strengths of the four fundamental interactions?

The moral of the lesson: there is a Mendeleev-type chart for the so-called new elementary particles, but the next question is whether these so-called elementary particles are made of sub-quarks, preons, or new fundamental building blocks.

References:

1. Feynman, R. P. (1948). Pocono Conference. Physics Today, 1(2), 8-10.

2. Feynman, R. P. (1973). Partons. In Brown, L. M. (ed.), Selected papers of Richard Feynman (pp. 519-559). Singapore: World Scientific.

3. Feynman, R. P. (1988). What Do You Care What Other People Think? New York: W W 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.

5. Okun, L. B. (1962). The Theory of Weak Interaction. Proceedings of 1962 International Conference on High-Energy Physics at CERN. Geneva.

6. Wilczek, F. (2007). Particle physics: Hard-core revelations. Nature, 445(7124), 156-157.

7. Yukawa, H. (1982). Tabibito “The Traveler” (Translated by L. Brown & R. Yoshida). Singapore: World scientific.

Section 2–3 Quantum physics

(Uncertainty principle / Particle-wave duality / light-matter interactions)

Feynman clarifies that the concept of a three-dimensional space and of time as a separate thing was changed by Einstein before 1920, first into a combination as space-time, and then further into a curved space-time to represent gravitation. Then, the mechanical rules of “inertia” and “forces” are found to be wrong in the world of atoms. In this section, Feynman discusses at greater length on the uncertainty principle, particle-wave duality, and light-matter interactions.

1. Uncertainty principle:

“… there is a rule in quantum mechanics that says that one cannot know both where something is and how fast it is moving (Feynman et al., 1963, section 2.3 Quantum physics).”

Right at the beginning, Feynman emphasizes that it is wrong to idealize a particle as having a definite location and a definite speed in quantum physics. Simply phrased, one cannot know exactly where an object is and how fast it is moving. The rule can be mathematically expressed as a product of the uncertainty of the momentum and the uncertainty of the position and this product is bounded by a very small constant: ΔxΔp ≥ ℏ/2. According to Feynman, we can use this rule to explain why the size of atoms is larger than the nuclei. This is related to the product of the positional uncertainty and uncertainty in the momentum of nuclei and electrons. However, one may prefer to use the term indeterminacy instead of uncertainty. It helps to avoid a misunderstanding of uncertainty as an error.

Note: During the Pocono Conference 1948, Bohr thought that Feynman did not know the uncertainty principle. In Feynman’s words, “I said that in quantum mechanics one could describe the amplitude of each particle in such and such a way. Bohr got up and said: ‘Already in 1925, 1926, we knew that the classical idea of a trajectory or a path is not legitimate in quantum mechanics; one could not talk about the trajectory of an electron in the atom because it was something not observable.’ In other words, he was telling me about the uncertainty principle. It became clear to me that there was no communication between what I was trying to say and what they were thinking. Bohr thought that I didn’t know the uncertainty principle… (Mehra, 1994, p. 248).” In essence, Bohr’s formulation of quantum theory does not allow an idealization of a path of an electron.

Importantly, one interesting change in the philosophy of science brought about by quantum mechanics is this: it is not possible to predict exactly what will happen in any circumstance. For example, we cannot predict when an atom is going to emit the light and specifically, which atom. Furthermore, it is simply wrong when philosophers say that if an experiment is performed in Stockholm, and then the same experiment is done in Quito, the same results must occur. Feynman cites the example of Foucault pendulum in which the plane of oscillation keeps changing in Stockholm, but the same phenomenon does not happen in Quito. The crux of the matter is we cannot be certain whether we have the same experimental (or environmental) conditions for any experiment.

2. Particle-wave duality:

“… So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one (Feynman et al., 1963, section 2.3 Quantum physics).”

Although Feynman mentions there is no distinction between a wave and a particle, he explains that quantum mechanics unifies the idea of the field, wave, and particle into one. He elaborates that when the frequency of waves is low, the field aspect of the phenomenon is more evident, and it is more useful as an approximate description in terms of everyday experiences. On the other hand, when the frequency of waves increases, the particle aspects of the phenomenon is more evident based on the measuring equipment used. For even higher frequencies of waves, they are deduced from the energy of the particles, by using a rule which assumes the validity of particle-wave duality. Curiously, Feynman does not seem to be thinking only in terms of particle-wave duality, but possibly particle-wave-field trinity.

Note: In this section, there seems to be an editorial error in the statement “no phenomenon directly involving a frequency has yet been detected above approximately 10¹² cycles per second.” It is more likely that Feynman was referring to 10²² Hz (even higher frequencies of waves) instead of 10¹² Hz. If you listen to the CD of this Feynman’s lecture, he says “here” instead of “10¹² cycles per second” while pointing to the blackboard.

Feynman is sometimes known as a “particle guy” rather than “wave guy.” During one of the Alix G. Mautner Lectures, Feynman explains that “[q]uantum electrodynamics ‘resolves’ this wave-particle duality by saying that light is made of particles (as Newton originally thought), but the price of this great advancement of science is a retreat by physics to the position of being able to calculate only the probabilities that a photon will hit a detector, without offering a good model of how it actually happens (Feynman, 1985, p. 37).” In addition, he considers his version of quantum electrodynamics does not need an uncertainty principle. In a footnote of the same lectures, Feynman (1985) states that “[i]f you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows for all the ways an event can happen – there is no need for an uncertainty principle (p. 56)!”

3. Light-matter interactions:

“… This fundamental theory of the interaction of light and matter, or electric field and charges, is our greatest success so far in physics (Feynman et al., 1963, section 2.3 Quantum physics).”

Feynman was awarded the Nobel prize for physics in 1965 for his work in quantum electrodynamics. He mentions that quantum electrodynamics is a theory of the light-matter interactions that has much success in physics. This theory specifies the basic rules for all ordinary phenomena except for gravitational and nuclear processes. Feynman provides the following examples of phenomena: the collision of billiard balls, the motions of wires in magnetic fields, the specific heat of carbon monoxide, the color of neon signs, the density of salt, and the reactions of hydrogen and oxygen to form water. Essentially, if any phenomenon can be idealized as a simple problem, physicists may make approximations and solve it. Feynman claims that no exceptions have been found with quantum electrodynamics outside the nucleus.

Interestingly, Feynman opines that quantum electrodynamics is the theory of all chemistry, and of life if life is ultimately reduced to chemistry and therefore just to physics because chemistry is already reduced. Moreover, it relates the properties of very high-energy photons, gamma rays, and other electromagnetic waves. Next, it has predicted a very remarkable thing: besides the electron, there should be another particle of the same mass, and of opposite charge, called a positron. These two particles may annihilate each other such that there is an emission of light or gamma rays. Thus, physicists generalize that there is an antiparticle for each kind of particle.

The existence of a positron could be predicted by using Dirac’s equation. However, Dirac had reservations on the success of quantum electrodynamics. In the words of Dirac (1951), “Recent work by Lamb, Schwinger, Feynman and others has been very successful in setting up rules for handling the infinities and subtracting them away, so as to leave finite residues which can be compared with experiment, but the resulting theory is an ugly and incomplete one, and cannot be considered as a satisfactory solution of the problem of the electron (p. 291).”

Questions for discussion:

1. Uncertainty principle: what are the implications of Heisenberg’s uncertainty principle?

2. Particle-wave duality: does quantum mechanics unify the idea of the field, wave, and particle, or only explain particle-wave duality?

3. Light-matter interactions: does Feynman’s version of quantum electrodynamics need the idea of uncertainty principle or particle-wave duality?

The moral of the lesson: it is impossible to predict exactly what will happen in any circumstance.

Note: During his Nobel lecture, Feynman (1965) mentions that “my original plan was to describe everything directly in terms of particle motions, it was my desire to represent this new theory without saying anything about fields (p. 14).”

References:

1. Dirac, P. A. M. (1951). A new classical theory of electrons. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 209(1098), 291-296.

2. Feynman, R. P. (1965). The development of the space-time view of quantum electrodynamics. In Brown, L. M. (ed.), Selected papers of Richard Feynman. Singapore: World Scientific.

3. Feynman, R. P. (1985). QED: The Strange Theory of Light and Matter. London: Penguin.

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.

5. Mehra, J. (1994). The Beat of a Different Drum: The life and science of Richard Feynman. Oxford: Oxford University Press.

Section 2–2 Physics before 1920

(Electrical force / Electric field / Electromagnetic waves)

In this section, Feynman briefly discusses classical physics. He pictures physics before 1920 as something like this: First, the universe is in a three-dimensional space of Euclidean geometry and another dimension called time. Second, the elements in physics include particles and there are 92 kinds of atoms, which have different properties. Third, particles have properties such as inertia and there are two kinds of force (electrical and gravitational). However, Feynman discusses at greater length on the electrical force, electric field, and electromagnetic waves.

Note: According to Feynman, quantum mechanics was discovered just after 1920.

1. Electrical force:

“… this new force (which is the electrical force, of course) has the property that likes repel but unlikes attract. The “thing” that carries this strong interaction is called charge (Feynman et al., 1963, section 2.2 Physics before 1920).”

Typical physics textbook authors simply write that “like charges repel and unlike charges attract.” Although Feynman shortens it to “likes repel but unlikes attract,” he elaborates the situation when a negative charge carrier is placed at an appreciable distance away from two oppositely charged particles that are very close together. He explains that the negative charge carrier would feel practically no electrical force because the attraction from a positively charged particle and the repulsion from a negatively charged particle balance out. Currently, some physicists explain that electric charge refers to an attribute or property of an object. They prefer not to use the term electric charge as an object, and state that there are two common kinds of charge particles in daily life: electrons (negative) and protons (positive).

On the other hand, if a positively charged particle is placed nearer to a large neutral object, it is possible that attraction arises because protons are repelled to the other end of the neutral object, whereas electrons are attracted to the positively charged particle and move closer to this particle. Thus, the repulsion is less than the attraction because the electrical force between the positively charged particle and electrons is relatively stronger when they are closer to each other. Simply put, when they come closer together, the protons and electrons are rearranged such that they have a stronger interaction. However, in Feynman words, “the thing that carries this strong interaction is called charge.” This description is potentially confusing because the term strong interaction means meson-baryon interaction in section 2.4 of this chapter. Section 2.2 is mainly about the electromagnetic interaction that is mediated by photons.

Importantly, Feynman adds that all things including human beings are made of strongly interacting positive charge carriers and negative charge carriers. In daily life, we may accidentally rub off electrons from our clothes such that there are attractions and repulsions among these charge carriers. This may more likely happen if we wear wool sweaters or sit on a chair that is made of certain fabric during the dry winter. As a result, “mini lightning” and “mini thunder” occur at home. Physics teachers should discuss how to avoid these static electricity problems by wearing cotton clothes, using antistatic sprays, or other ways.

2. Electric field:

“… This potentiality for producing a force is called an electric field. When we put an electron in an electric field, we say it is ‘pulled’ (Feynman et al., 1963, section 2.2 Physics before 1920).”

Feynman visualizes a charged particle creates (or distorts) a “condition” in space, such that when we put another charged particle there, it feels a force. The condition in space that produces an electrical force is called an electric field. In short, there are two rules: (a) a charged particle creates an electric field, and (b) additional charged particle that is placed in the electric field experiences a “pull” and move. Furthermore, the moving charged particle also experiences a magnetic field. To be more precise, the charged particle is not under the influence of electric field that exactly follows the inverse square law. This is due to a delay in action because the influence cannot travel faster than the speed of light. However, some textbook authors only define an electric field as a region in space in which a charge experiences an electric force.

Feynman has an insight analogy that further explains the nature of electric field: In a pool of water that has two floating corks, we can push a cork by giving another cork a push. If we look only at the two corks, we can see one cork “directly” moves in response to the motion of the other cork. Physicists explain that there is a disturbance in the water caused by a cork, and the water then disturbs the other cork. One may develop a “law” on how the water causes the motion of an object nearby. If the first cork is farther away, then the second cork would appear stationary because we move the water locally (no distant influences). If we oscillate the cork continuously, a new phenomenon is involved in which water waves travel a much longer distance. This oscillatory influence is different from the idea of direct interaction between the two floating corks. We can replace the term “direct interaction” by the existence of a pool of water or specifically, the electromagnetic field.

On the contrary, Feynman has developed quantum electrodynamics by using the concept of “particle” instead of “field.” During his Nobel lecture, Feynman (1965) explains that “electrons cannot act on themselves, they can only act on other electrons. That means there is no field at all. You see, if all charges contribute to making a single common field, and if that common field acts back on all the charges, then each charge must act back on itself. Well, that was where the mistake was, there was no field. It was just that when you shook one charge, another would shake later. There was a direct interaction between charges, albeit with a delay. The law of force connecting the motion of one charge with another would just involve a delay. Shake this one, that one shakes later. The sun atom shakes; my eye electron shakes eight minutes later, because of a direct interaction across (p. 10).” The direct (inter-particle) interaction between two charged particles can be mediated by a photon (particle).

3. Electromagnetic waves:

“… The electromagnetic field can carry waves; some of these waves are light, others are used in radio broadcasts, but the general name is electromagnetic waves (Feynman et al., 1963, section 2.2 Physics before 1920).”

Electromagnetic waves may be distinguished as radio waves, light waves, ultraviolet waves, infrared waves, X-rays, and gamma rays. The main difference between light and oscillatory electromagnetic waves such as those used in radio broadcasts is in the frequency of oscillation. In other words, if we shake a charge carrier more and more rapidly, we can pick up a whole series of different kinds of effects, which are all unified by specifying only one number: the number of oscillations per second. Interestingly, Feynman considers electromagnetic waves that oscillate at a very low frequency behave like a field because they are almost not oscillating. Thus, he identifies three rough behaviors in the electromagnetic spectrum: field (very low frequency of oscillation), waves, and particle (very high frequency of oscillation).

During a British Broadcasting Corporation interview, Feynman (1994) explains that “[t]he radio waves are just the same kind of waves, only much longer waves. Then there’s the radar from the airplane which is looking at the ground to figure out where it is, which is coming through this room too, plus X-rays, cosmic rays, all these other things which are exactly the same kind of waves, just shorter and faster, or longer and slower - it’s all the same thing. So this big field, this big area of irregular motions, this electric field, this vibration contains a tremendous information (p. 132).” However, Feynman may be perceived as sloppy because he uses the terms longer waves and electric field instead of longer wavelengths and electromagnetic field.

Questions for discussion:

1. Electrical force: What happen if a positive charge carrier is placed considerably nearer to a large neutral object?

2. Electric field: What is the nature of electric field?

3. Electromagnetic waves: How do the behaviors of electromagnetic waves change from very low frequency of oscillation to very high frequency?

The moral of the lesson: an electric field is a condition in space that can produce an electrical force, whereas the electromagnetic field can carry electromagnetic waves.

References:

1. Feynman, R. P. (1965). The development of the space-time view of quantum electrodynamics. In Brown, L. M. (ed.), Selected papers of Richard Feynman. Singapore: World Scientific.

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

3. 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 2–1 Introduction

(Idealization / Exception / Approximation)

According to Feynman, the scientific method includes observation, reason, and experiment. This is similar to Bacon’s scientific method that proposes testing and refining hypotheses by observing, measuring, and experimenting. During an address titled What is Science?, Feynman slightly disagrees with Bacon’s method and explains that “He [Bacon] spoke of making observations, but omitted the vital factor of judgment about what to observe and what to pay attention to (Feynman, 1999, p. 173).” Feynman points out that we do not merely observe because there is also judgment or reasoning involved. In this section, Feynman suggests three ways in understanding physical laws: idealization (or simplification), exception (or violation), and approximation (or imprecision).

1. Idealization (or simplification):

“First, there may be situations where nature has arranged, or we arrange nature, to be simple and to have so few parts that we can predict exactly what will happen, and thus we can check how our rules work (Feynman et al., 1963, section 2.1 Introduction).”

Feynman imagines the physical world to be like a great chess game being played by the gods, and physicists are observers of the game. Although they do not know the rules of the game, they would like to deduce and understand the rules. To understand the rules or physical laws, he provides the following analogy: In one corner of the chess board that has only a few chess pieces, we can deduce the rules exactly. This first way of understanding physical laws may be described as idealization or simplification when physicists focus on a simple phenomenon or problem having only a few physical variables. Similarly, in Newton’s first law of motion, we idealize a physical world in which there is no resultant external force acting on an object. Physicists imagine the object to be under ideal conditions such that they can solve the problem exactly.

In the previous lecture, Feynman has explained that a picture of water that is magnified a billion times could be idealized in several ways (Feynman et al., 1963, section 1.2 Matter is made of atoms). First, the water molecules in the picture are simplified by having sharp edges. To be more accurate, the edges could be blurred because the particles are almost everywhere and they may be found in locations further away having lower probabilities as predicted by quantum mechanics. Next, for the reason of simplicity, the water molecules are sketched in a two-dimensional arrangement instead of three dimensions. To be more realistic, one may also use an animation that shows the motion of particles in a three-dimensional world.

Historically speaking, Galileo’s method of idealization in experiment marks an important milestone in modern science. For example, Galileo states four claims on the period of simple pendulum: (1) The law of length: the period varies with the square of its length, (2) the law of amplitude independence: the period is independent of its amplitude, (3) the law of weight independence: the period is independent of its weight, and (4) the law of isochrony: all periods are the same if the length is the same. However, we should not expect empirical data to exactly fit these physical laws because they are based on simplifying assumptions such as an ideal world that has no friction. Galilean idealization is the practice of introducing assumptions in physical models with the goal of simplifying theories such that exact calculations are possible.

2. Exception (or violation):

“A second good way to check rules is in terms of less specific rules derived from them. For example, the rule on the move of a bishop on a chessboard is that it moves only on the diagonal… the most interesting phenomena are of course in the new places, the places where the rules do not work — not the places where they do work! (Feynman et al., 1963, section 2.1 Introduction).”

It is possible that a rule that works well for a long time until we discover an exception to this rule. In general, the most interesting phenomena are not those that obey rules, but rather the exceptions or violations that lead physicists to develop new rules that are even more fundamental. In his autobiography Surely you’re Joking, Mr. Feynman, Feynman writes that “the discovery of parity law violation was made, experimentally, by Wu, and this opened up a whole bunch of new possibilities for beta decay theory (Feynman, 1997, p. 248).” Simply put, the violation of parity law implies that there is yet another fundamental law of physics to be discovered. In fact, this violation contributes to an understanding of another new rule: the law of weak interactions.

The exceptions or violations in classical physics have also resulted in revolutions in understanding physics. For example, the wave theory of light fails to account for the blackbody spectrum and the stability of atoms accurately. These failures led to the development of new rules that are now known as quantum mechanics of atoms. In other words, it is important to identify the exceptions or limitations of classical physics and understand to what extent the physical laws are applicable in most physical phenomena. On the other hand, the failure of Newtonian mechanics to account for the null results of the Michelson-Morley experiment has helped Einstein to develop a new rule, the special theory of relativity. Furthermore, the failure of the special theory of relativity to account for the precession of Mercury’s orbit has prompted Einstein to develop another new rule, the general theory of relativity.

Note: If you listen to the CD of this Feynman’s lecture, he did mention the word “violation,” but this word is omitted in this section of The Feynman Lectures. Of course, you can find this word in other chapters of the book.

3. Approximation (or imprecision):“The third way to tell whether our ideas are right is relatively crude but probably the most powerful of them all. That is, by rough approximation (Feynman et al., 1963, section 2.1 Introduction).”

Interestingly, Feynman has cited Alexander Aleksandrovich Alekhine, a world class chess champion because it is difficult to completely understand his reasons for moving a particular chess piece. In a general sense, one may roughly guess his motive is to protect the king during the game. Similarly, it is difficult to have a physical model that describes the motion of a complicated object exactly. As an example, physicists may apply Newton’s second law of motion that is approximately correct to describe the motion of a spacecraft. A prediction of the spacecraft’s motion by using the equation F = ma has a greater magnitude of error if its speed is higher or approaching the speed of light.

Similarly, the mass of a chair can be defined only approximately. Feynman explains that some atoms evaporate from the chair and sometimes a few atoms (such as dirt) fall on it and get mixed with the paint. Strictly speaking, it is difficult to define a chair precisely because we are unable to tell exactly which atoms are chair, which atoms are air, which atoms are dirt, or which atoms are paint that belongs to the chair. Feynman imagines that a student may object because he does not like this imprecision, and he prefers to define everything exactly. Importantly, Feynman explains that “[i]f you insist upon a precise definition of force, you will never get it! First, because Newton’s Second Law is not exact, and second, because in order to understand physical laws you must understand that they are all some kind of approximation (Feynman et al., 1963, section 12–1 What is a force?).”

Questions for discussion:

Physics teachers may discuss the idea of idealization (or simplification), exception, and approximation in understanding physics as found in the following passages in section 1.2 Matter is made of atoms (Feynman et al., 1963).

1. “… This is a picture of water magnified a billion times but idealized in several ways. In the first place, the particles are drawn in a simple manner with sharp edges, which is inaccurate.”

2. “… This minimum amount of motion that atoms can have is not enough to melt a substance, with one exception: helium.”

3. “… Nevertheless, to an excellent approximation, if the density is low enough that there are not many atoms, the pressure is proportional to the density.”

The moral of the lesson: Physical laws are formulated by using idealizations and approximations, but physicists should be cognizant of exceptions or violations in these laws. 

In other words, physicists need to cheat (idealizing assumptions), tweak (approximating answers), and confess their sins whether intentional (idealizations and approximations) or unintentional (exceptions or violations).

Note: For those who are interested in the differences between approximation and idealization, they may want to read this article: Norton, J. D. (2012). Approximation and idealization: Why the difference matters. Philosophy of Science, 79(2), 207-232.

References:

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

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

3. 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.

About the author

I am a fan of Feynman, with over ten years of experience teaching introductory physics. I don’t really like travelling, but I visited the following countries/places: Australia (Perth), Austria (Salzburg, Vienna), Bosnia, Brunei, China (Guangzhou, Hong Kong, Macau), Croatia (Split), Egypt (Cairo, Mount Sinai), France (Toulouse, Marseille, Nice, Paris), Germany (Frankfurt), Indonesia (Batam, Jakarta, Pulau Bintan), Israel (Mount Carmel, Golan Heights, Jerusalem), Italy (Assisi, Milan, Rome, Venice), Japan (Tokyo), Malaysia (Kenyir Lake, Kuala Lumpur, Malacca, Pulau Redang, Pulau Pemanggil), Portugal, South Korea (Gwangju, Mokpo, Seoul), Spain (Barcelona), Switzerland (Bern, Interlaken, Jungfrau), Taiwan (Taipei, Mount Alishan, Kaohsiung), Thailand, United Kingdom (London), United States (Hawaii, Pittsburgh), Vatican, and Vietnam (Ho Chi Minh, Quảng Trị).

My blogs:

Meditating Feynman’s Lectures
How would Feynman answer examination questions?

Problems of physics assessment

Selected Publications:

1. Wong, C. L., Chu, H. E., & Yap, K. C. (2016). Are Alternative Conceptions dependent on Researchers’ Methodology and Definition? : A Review of Empirical Studies related to Concepts of Heat. International Journal of Science and Mathematics Education. 14(3), 499-526.

2. Wong, C. L., Chu, H. E., & Yap, K. C. (2014). Developing a Framework for analyzing definitions: A Study of The Feynman Lectures. International Journal of Science Education. 36(15), 2481-2513.

3. Wong, C. L. (2013). Is there a best definition of weight? The Physics Teacher, 51(9), 516-7.

4. Lim, K. M., Lee, G. C. F., Sheppard, C. J. R., Phang, J. C. H., Wong, C. L., & Chen, X. (2011). Effect of polarization on a solid immersion lens of arbitrary thickness. Journal of the Optical Society of America A, 28(5), 903-911.

5. Yap, K. C., & Wong, C. L. (2007). Assessing conceptual learning from quantitative problem solving of a plane mirror problem. Physics Education, 42(1), 50-55.