Section 4–4 Other forms of energy

(Forms of energy / Independence of time / Available energy)

Feynman relates the law of conservation of energy to the symmetry of time-displacement that was commonly discussed during advanced graduate courses on physics instead of introductory courses. In this section, the three interesting concepts discussed are forms of energy, independence of time, and available energy.

Note: If you listen to the audio CD of this lecture, Feynman says that “we know that it is not electrical, not gravitational, and not purely kinetic (not chemical), but we do not know what it is.” Currently, we know that nuclear force is a residual effect of the strong force or gluon field.

1. Forms of energy:

“There are many other forms of energy, and of course, we cannot describe them in any more detail just now … (Feynman et al., 1963, section 4.4 Other forms of energy).”

In general, different forms of energy include gravitational potential energy, kinetic energy, elastic potential energy, thermal energy, electrical energy, light energy, chemical energy, nuclear energy and mass energy. For example, elastic potential energy can be illustrated by pulling down a spring that can later lift a weight. As the spring passes through the equilibrium point, its elastic potential energy is converted into kinetic energy. If the spring is mounted vertically, there is also a transfer of some gravitational potential energy either going in or out of the spring. There is no change in gravitational potential energy if this experiment is performed “sideways” or horizontally.

Feynman also clarifies that there are not really many different forms of energy. Firstly, heat energy is essentially kinetic energy of atoms in random motion. Secondly, chemical energy can be understood as due to the kinetic energy of the electrons inside the atoms as well as the electrical energy of interaction of the electrons and the protons. Next, elastic potential energy is similar to the chemical energy because these two forms of energy are mainly the electrical energy of the attraction of the atoms. However, the gravitational potential energy of an object can be explained as field energy of a system because it is stored in the gravitational field instead of the object. Moreover, mass energy is now understood as contributed by the Higgs field. In short, we may replace potential energy by field energy (with the support of field theories).

Note: From a perspective of pedagogy, some physics educators suggest to teach students that there are different kinds of transfer of energy instead of different forms of energy (Falk, Herrmann, & Schmid, 1983). Similarly, we do not speak about different forms of electric charge. In other words, it is confusing to introduce different forms of electric charge, such as “electronic charge,” “protonic charge,” “Cl-ionic charge,” according to the charge carrier involved during a transfer of charge.

2. Independence of time:

“As independence in space has to do with the conservation of momentum, independence of time has to do with the conservation of energy… (Feynman et al., 1963, section 4.4 Other forms of energy).”

Feynman explains that the conservation of energy is very closely related to an important property of the world, things do not depend on the absolute time. Simply phrased, when we perform an experiment at a given moment and carry out the same experiment at a later moment, the laws of physics remain unchanged. If we assume that this is true, and add the principles of quantum mechanics, then we can deduce the law of the conservation of energy. This is related to Noether’s theorem in which conservation laws are related to symmetry principles: for example, time translation symmetry gives conservation of energy, space translation symmetry gives conservation of momentum, and rotation symmetry gives conservation of angular momentum.

One may wonder why Feynman states that the law of conservation of energy is closely related to the symmetry of time in quantum mechanics. This could be related to his proof of conservation of energy by using a transformation of time-displacement in his Ph.D. thesis titled A New Approach to Quantum Theory. Interestingly, based on an interview with Feynman in Austin, Mehra (1994) writes that “Feynman’s approach could be used in the theories with advanced and retarded interactions, where Noether’s theorem does not work without proper modifications. Feynman ‘proved a thing called Noether’s theorem, not knowing that it was known’ (p. 132).”

3. Available energy:

“With regard to the conservation of energy, we should note that available energy is another matter… (Feynman et al., 1963, section 4.4 Other forms of energy).”

It is important to distinguish “conservation of energy” and “energy conservation.” Although there is a law of conservation of energy, there is a problem of “energy conservation” because the available energy for human utility is not conserved easily. The laws which govern available energy are called the laws of thermodynamics and they involve a concept called entropy. Thus, a pertinent question is how we can continue to get our supplies of energy every day. Interestingly, we may say that our supplies of energy are from the sun, rain, coal, uranium, and hydrogen, but it is the sun that makes the rain and coal such that they all come from the sun.

Feynman also predicts that energy can be obtained from water if it can be controlled in thermonuclear reactions. However, scientists are developing hydrogen fuel cell cars that can run by water, and a design involves electrolysis a splitting of water into hydrogen and oxygen. The main problem is still about energy conversion efficiency that is a ratio of energy output to energy input.

Note: When Feynman says that “she liberates a lot of energy from the sun, but only one part in two billion falls on the earth,” it is based on a quick approximate by calculating the square of ratio of the earth’s radius to the distance between the earth and sun: (r/R)². To be more accurate, one may use the ratio (pr²/4pR²). Note that the radius of the earth (r) is approximately 6,371 km, whereas the distance between the earth and the sun (R) is approximately 149, 597, 870 km.

Questions for discussion:

1. What are the different forms (or types) of energy?

2. Why does an independence of time have to do with the law of conservation of energy in quantum physics?

3. Why does the available energy for human utility is not conserved easily?

The moral of the lesson: the law of conservation of energy is related to the symmetry of time translation.

References:

1. 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.

2. Falk, G., Herrmann, F., & Schmid, G. B. (1983). Energy forms or energy carriers?. American Journal of Physics, 51(12), 1074-1077.

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