Section 8–1 Description of motion

(Motion / Graph of distance versus time / Philosophical questions)

In this chapter, Feynman discusses concepts of kinematics. In this section, the three main points are the nature of motion, graph of distance versus time, and philosophical questions in defining motion. It should be useful to understand these three points from the perspectives of idealizations, approximations, and exceptions.

1. Motion (Idealizations):

“The simplest change to observe in a body is the apparent change in its position with time, which we call motion (Feynman et al., 1963, section 8.1 Description of motion).”

Right at the beginning, Feynman explains motion as “the apparent change in the position of a body with time”. In physics, this involves an idealization of a solid object with a permanent mark, say a point on the object in which we can observe. For example, the “little marker” might be the radiator cap of an automobile or the center of a falling ball. In order to find the kinematical laws governing the changes that take place in the motion of bodies, physicists must be able to describe the changes and have some means to measure them. This is the subject of kinematics which we describe how an object moves but not the cause of its motion.

In short, a body moves in a three (or four) dimensional world. Feynman explains that we can idealize the body as moving in one direction. We shall concentrate on the motion in one direction, as in a car on a flat road instead of a bumpy road. In a sense, it is some kind of trivia, but it allows us to use a graph to illustrate the motion. Essentially, this simplifies the analysis and we can modify it to three dimensions later. It is worth mentioning that Feynman has also explained how 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). To simplify things, the three-dimensional water molecules are sketched in a two-dimensional diagram.

2. Graph of distance versus time (Approximations):

“… but we suppose that the graph means something, that the car has some position at all the intermediate times (Feynman et al., 1963, section 8.1 Description of motion).”

A graph of distance versus time provides approximate information on the motion of an object. It does not give exact numerical values on the time in seconds and distance moved in meters. Feynman explains that as the time increases, the distance moved by a car increases at first very slowly and then more rapidly… If physics teachers are particular about formalities, they may prefer stating a graph of position versus clock reading or using the phrase “distance from the origin.” However, Feynman elaborates that one would have to know where the car is at the half-minute marks for a complete description. In other words, the car has some position at all the intermediate times.

Alternatively, we can describe the graph as a plot of displacement versus clock reading. First, one may prefer the term displacement because positive displacement means moving away from the origin (or toward the right) and negative displacement means moving toward the origin. Next, physics teachers may clarify that if the distance moved increases, the graph should have an upward trend (or rising). However, in his Tips on Physics, he simply states that “[t]he rule is the following: that in the interval Dt = t' – t, the thing has moved from A(t) to A(t') , so the displacement is DA = A(t') – A(t), a difference vector from the old position to the new position (Feynman, Gottlieb, & Leighton, 2006, p. 29).” Feynman did not define displacement nor distinguish distance and displacement.

3. Philosophical questions (Exceptions):

“It turns out that these deep philosophical questions have to be analyzed very carefully in physics, and this is not so easy to do (Feynman et al., 1963, section 3.1 Introduction).”

There are exceptions or limitations in the analysis of motion in physics. In general, they are related to philosophical questions on the meanings of time and space. For example, our concepts of time and space are not simple in the special theory of relativity. This is because Einstein proposes a positivistic perspective on the nature of motion. Furthermore, it turns out that in the motion of atoms, that idea is questionable because we cannot find a marker on an atom and watch it move. This is related to difficulties in determining the exact location of an atom based on the quantum theory. Simply put, the notions of motion are problematic for an object moving at high speed as well as for sub-microscopic objects.

According to Feynman, there are philosophical questions on the difficulties of defining physical concepts precisely. For instance, we may ask “how do you define time?” or “how do you define space?” Interestingly, there are also problems of circularity in defining fundamental physical concepts. For example, “time” is sometimes defined in the dictionary as a period, whereas a period is defined as a duration of time. Similarly, “space” is sometimes defined as an area, whereas an area is defined as an amount of “space.” On the other hand, one may define length in terms of the “time” it takes for light to travel between two points, while “time” can be defined in terms of length which physicists deduce how far light can travel. This is another kind of philosophical question where time is defined in terms of length, and length is defined in terms of time (Wong, Chu, & Yap, 2014).

Questions for discussion:

1. How is the motion of an object idealized in physics?

2. How is the motion of an object approximately represented by a graph of displacement with respect to time?

3. What are the philosophical questions in defining motion?

The moral of the lesson: we should know the idealizations, approximations, and exceptions involved in representing motions.