Section 4–1 What is energy?

(Conserved quantity / Indestructible blocks / Abstract quantity)

In this chapter, Feynman says that we have no knowledge of what energy is and we do not understand the conservation of energy. In this section, he discusses the concepts of energy as a conserved quantity, indestructible blocks, and abstract quantity.

1. Conserved quantity:

“…The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes (Feynman et al., 1963, section 4.1 What is energy?).”

According to Feynman, the law of conservation of energy governs all natural phenomena. Remarkably, there is no known exception to this law within experimental accuracy. Based on this law, the amount of energy does not change in the manifold changes which nature undergoes. In short, it states that there is a numerical quantity that remains the same even when something happens. However, the law does not provide a description of a mechanism behind the natural phenomena. It seems a strange fact that the total amount of energy of a system must always be the same whenever we calculate some number by using various formulae of energy.

Importantly, Feynman advocates strict conservation of energy instead of statistical conservation of energy. During a Messenger Lecture, Feynman elaborates that “[i]t might have been that the law of energy conservation was not right; in fact, it was proposed by Bohr for a while that perhaps the conservation law worked only statistically, on the average. But it turns out now that the other possibility is the correct one (Feynman, 1965, p. 75).” Simply put, Bohr was willing to give up the law of conservation of energy during a beta decay. On the contrary, a firm belief in the strict conservation of energy has led to the discovery of neutrinos (Dennis’ blocks under the rug).

Note: In a paper titled The quantum theory of radiation, Bohr, Kramers, and Slater (1924) write that “a statistical conservation of momentum is secured in a way quite analogous to the statistical conservation of energy in the phenomena of absorption of light (p. 174).”

2. Indestructible blocks:

“…Imagine a child, perhaps ‘Dennis the Menace,’ who has blocks which are absolutely indestructible, and cannot be divided into pieces (Feynman et al., 1963, section 4.1 What is energy?).”

Feynman distinguishes the energy in an isolated system and real system by using Dennis’ block and Bruce’s block respectively. Initially, he illustrates the law of conservation of energy by using Dennis’ indestructible blocks. Being curious, Dennis’ mother discovers the law of conservation of blocks in which the number of blocks remains the same though some could be hiding under a rug. As an exception, the increase in the number of blocks may be explained by the additional blocks that Bruce brings in. This problem can be resolved by defining an isolated system, for example, Dennis’ mother closes the window and does not let Bruce in anymore. Nevertheless, the most remarkable fact is that there are no blocks because energy is not a material substance, but it is given meaning in mathematical calculations.

Some physics teachers explain the concept of energy by using Feynman’s blocks and consider energy as a quasi-material or pseudo-substance. On the contrary, Wilhelm Ostwald regards energy as a form of substance. For instance, Ostwald (1910/2013) writes that “we may call energy a substance unqualifiedly, since in every instance of which we know the principle has been maintained that a quantity of any energy never disappears unless an equivalent quantity of another energy arises (p. 136).” He was awarded Nobel Prize in Chemistry in 1909 for his work on catalysis and for his investigations into the fundamental principles governing chemical equilibria and rates of reaction.

Note: The law of conservation of energy is only applicable to an isolated system instead of a real system. Thus, Planck (1945) clarifies that “[a] system which changes without being acted on by external agents is called a perfect or isolated system. Strictly speaking, no perfect system can be found in nature, since there is constant interaction between all material bodies of the universe, and the law of the conservation of energy cannot be rigorously applied to any real system (p. 46).” Interestingly, Feynman uses Bruce’s blocks to illustrate how the total energy in a real system could be increased.

3. Abstract quantity:

“…It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas (Feynman et al., 1963, section 4.1 What is energy?).”

When Feynman says that we have no knowledge of what energy is, it does not mean that we know absolutely nothing about the nature of energy. Essentially, he considers energy as an abstract quantity and prefers to be open minded in the understanding of the mechanism behind the various mathematical formulae for different forms of energy. Furthermore, Feynman does not visualize energy as little blobs of a definite amount. In the last section of this chapter, Feynman explains that the frequency of light can be anything, and thus, there is no law that says that energy must always be quantized as a certain definite amount or come in lumps.

Physicists commonly cite Feynman and claim that there is no good definition of energy. Historically, Poincare (1906/1952) writes that “[a]s we cannot give a general definition of energy, the principle of the conservation of energy simply signifies that there is a something which remains constant (p. 166).” Currently, physics teachers may argue that we should clearly define the concept of energy and it is inappropriate to say we have not knowledge of what energy is. However, a definition of energy as “the capacity (or ability) to perform work” mainly states the effect of energy as work. This general definition still does not tell us about the nature of energy.

Note: Sir James Jeans explains that energy is a mathematical abstraction as follows: “the attempt to regard the flow of energy as a concrete stream always defeats itself… The concept of energy flowing about through space is useful as a picture, but leads to absurdities and contradictions if we treat it as a reality. Professor Poynting gave a well-known formula which tells us how energy may be pictured as flowing in a certain way, but this picture is far too artificial to be treated as a reality; for instance, if an ordinary bar-magnet is electrified and left standing at rest, the formula pictures energy flowing endlessly round and round the magnet… The mathematician brings the whole problem back to reality by treating this flow of energy as a mere mathematical abstraction (James, 1932, p. 129).”

Questions for discussion:

1. What does the law of conservation of energy really mean?

2. What is the most remarkable aspect of energy that must be abstracted from Dennis’ blocks?

3. Is it true that there is no good definition of energy?

The moral of the lesson: energy is an abstract quantity that is conserved and indestructible.

References:

1. Bohr, N., Kramers, H. A., & Slater, J. C. (1924). The quantum theory of radiation. In B. L. Van Der Waerden (Ed.). Sources of Quantum Mechanics. New York: Dover.

2. Feynman, R. P. (1965). The character of physical law. Cambridge: MIT Press.

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.

4. Jeans, J. H. (1932). The Mysterious Universe. New York: Macmillan.

5. Ostwald, W. (1910/2013). Natural Philosophy. Auckland: The Floating Press.

6. Planck, M. (1945). Treatise on Thermodynamics. New York: Dover.

7. Poincare, H. (1906/1952). Science and hypothesis. New York: Dover.