(Definition of time / Measurement of time / Periodicity of time)
In this section, Dr. Sands discusses a definition of time, measurement of time, and periodicity of time.
1. Definition of time:
“…It would be nice if we could find a good definition of time. Webster defines ‘a time’ as ‘a period,’ and the latter as ‘a time,’ which doesn’t seem to be very useful (Feynman et al., 1963, section 5.2 Time).”
Dr. Sands opines that time is one of the things that we probably cannot define in the dictionary sense. For example, Webster defines time as “a period” and defines the period as “a time.” Thus, it does not provide us with useful information on any characteristics of time. This is similar to a dictionary that defines space as “an area,” and defines the area as “an amount of space.” Essentially, there is a problem of circularity in defining fundamental physical concepts such as space and time. However, physicists could provide a theoretical definition of time or an operational definition of time. For example, Einstein (1905) suggests an operational definition of time when he writes that “a time is to be defined exclusively for the place at which the watch is located (p. 125).”
In physics, time can be defined in terms of characteristics such as “arrows of time.” For example, Gleick (1992) writes that “[p]hysicists had learned to distinguish three arrows of time. Feynman described them: the thermodynamic or ‘accidents of life’ arrow; the radiation or ‘retarded or advanced arrow’; and the cosmological arrow. He suggested keeping in mind three physical pictures: a tank with blue water on one side and clear water on the other; an antenna with a charge moving toward it or away; and distant nebulas moving together or apart (p. 126).” Alternatively, a theoretical definition of time may include the following three characteristics: linear (sequential order), unidirectional (irreversible), and relative (frame-dependent). The concept of time is related to Newtonian mechanics, the second law of thermodynamics, and theory of relativity.
Note: Another possible characteristic of time may be specified as probabilistic (apparent periodicity) from a perspective of quantum mechanics.
2. Measurement of time:
“…One way of measuring time is to utilize something which happens over and over again in a regular fashion — something which is periodic (Feynman et al., 1963, section 5.2 Time).”
Dr. Sands explains that what really matters is not how we define time, but how we measure time. One of the ways to measure time is by utilizing a physical phenomenon (natural or artificial) which happens repeatedly in a regular fashion. For example, a day is related to the relative movement of the earth and the sun. Nevertheless, when Dr. Sands says that days in summer are longer than days in winter, he is referring to the colloquial meaning of day as the time between sunrise and sunset. This is different from the meaning of a day as 24 hours.
In general, a measurement is essentially a comparison process. In other words, every measurement of time is a comparison between a duration of time and a standard unit of time. On the contrary, it is inaccurate to use one’s pulse to measure a pendulum’s period and then to use the period of the pendulum to measure the pulse of another person. Interestingly, an astronomer may measure time in terms of “space” or the distance traveled by light rays from a distant star, and another astronomer may measure space in terms of “time” for light to travel between two points (e.g. light years). This is another kind of circularity where time is defined in terms of space, and space is defined in terms of time. More important, space and time are also defined in terms of the speed of light.
Note: Similarly, in chapter 17, Feynman explains that “nature is telling us that time and space are equivalent; time becomes space; they should be measured in the same units. What distance is a “second”? It is easy to figure out from (17.3) what it is. It is 3×108 meters, the distance that light would go in one second. In other words, if we were to measure all distances and times in the same units, seconds, then our unit of distance would be 3×108 meters, and the equations would be simpler. Or another way that we could make the units equal is to measure time in meters. What is a meter of time? A meter of time is the time it takes for light to go one meter, and is, therefore, 1/3×10−8 sec, or 3.3 billionths of a second! (Feynman et al., 1963, section 17.2 Space-time intervals).”
3. Periodicity of time:
“…We can just say that we base our definition of time on the repetition of some apparently periodic event (Feynman et al., 1963, section 5.2 Time).”
Ideally, we should base our definition of time on the repetitions of a regularly periodic event. However, the concept of astronomical time based on the rotational period of the earth is apparently periodic because there are changes in gravitational fields due to changes in the locations of celestial bodies and changes in the distributions of mass on earth. In a similar sense, the concept of atomic time based on an atomic clock is apparently periodic because it can be changed by slight variations in gravitational fields, electromagnetic fields, motion, temperature or other physical phenomena. Therefore, our definition of “hour” and “day” are based on the repetition of apparently periodic events.
Note: A solar day is a period of time it takes for the earth to rotate about its axis such that the sun appears in the same position in the sky periodically. This is different from a sidereal day that means a period of time it takes for the earth to rotate about its axis such that distant stars appear in the same position in the sky periodically. Furthermore, astronomers define the equation of time as the difference between true solar time (based on the sun’s position in the sky) and mean solar time (related to the time of your watch) (e.g. Sajina, 2008).
Questions for discussion:
1. How would you define time?
2. How should time be measured?
3. Do we have a clock that has regular periodicity?
The moral of the lesson: what really matter is how time can be measured by a clock that has apparent periodicity.
References:
1. Einstein, A. (1905). On the Electrodynamics of Moving Bodies. In J. Stachel (Ed.), Einstein’s Miraculous Year: Five Papers that Changed the Face of Physics (pp. 123-160). Princeton: Princeton University Press.
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. Gleick, J. (1992). Genius: The Life and Science of Richard Feynman. London: Little, Brown and Company.
4. Sajina, A. (2008). On ships, trains, and the equation of time. Physics Today, 61(11), 76-77.
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