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.