Section 14–4 Nonconservative forces

(Globular star cluster / Atomic level / Energy of light)

In this section, Feynman discusses non-conservative forces from the perspectives of a globular star cluster, atomic level, and energy of light. Physics teachers may change the sequence of teaching by discussing frictional forces at the atomic level (a concept that students are likely more familiar) followed by the globular star cluster.

1. Globular star cluster:

“…we analyze a system like that great globular star cluster that we saw a picture of, with the thousands of stars all interacting… (Feynman et al., 1963, section 14–4 Nonconservative forces).”

Feynman explains that friction is apparently a non-conservative force because it has been discovered that the fundamental forces between the particles are conservative. He suggests that we can analyze a system such as a star cluster that is drifting in space. The star cluster can be conceptualized as a single object if we do not have a powerful telescope to see the details. Gravitational forces are still responsible (or “wasted”) for increasing the kinetic or potential energies of the stars inside the star cluster. Strictly speaking, the total energy of the star cluster is still conserved, but it is our inability to see the detailed motions inside that suggest the energy of the star cluster is not conserved. However, Feynman could have explained the apparent loss of kinetic energy of the star cluster using the concept of friction.

In astrophysics, dynamical friction (or gravitational drag) causes a loss of kinetic energy of celestial bodies through gravitational forces with matters in space (Chandrasekhar, 1943). Similarly, a rocket may accelerate and gain kinetic energy through the slingshot effect (or gravity assist). Simply put, this is accomplished via gravitational interactions and it results in a loss of kinetic energy in a large celestial body such as a planet. Importantly, the total energy of the rocket and the celestial body remain constant. Using the law of conservation of energy, we can conclude that a loss of kinetic energy of a massive body is compensated by an increase in a less massive body. In short, a star cluster loses kinetic energy because of dynamical friction or Chandrasekhar friction.

2. Atomic level:

“When we study matter in the finest detail at the atomic level, it is not always easy to separate the total energy of a thing into two parts, kinetic energy, and potential energy… (Feynman et al., 1963, section 14–4 Nonconservative forces).”

According to Feynman, it is not always easy to separate the total energy of a thing into kinetic energy and potential energy at the atomic level. He elaborates that it is not strictly possible to treat heat and chemical energy as being pure kinetic energy or pure potential energy. In a sense, he was inconsistent in using the term heat that could mean “primarily kinetic energy” or “a mixture of kinetic and potential energy.” Physicists prefer to define heat as a process (Romer, 2001) and sometimes use the term internal energy instead of heat. In general, “internal energy of a real gas” can be expressed as a sum of the potential and kinetic energies of the molecules of a system. On the other hand, “internal energy of an ideal gas” does not include potential energy because we assume there are no interactions between molecules.

From a microscopic perspective, frictional forces (or electromagnetic forces) cause a loss of kinetic energy of a large object via electromagnetic forces between charges in the atoms. For example, an atom may accelerate and gain kinetic energy through a collision. This is accomplished through electromagnetic interactions and it results in a loss of kinetic energy in the large object. Importantly, the total energy of the large object and atoms (including electrons) remain constant. Using the law of conservation of energy, we can conclude that a loss of kinetic energy of the large object is compensated by an increase in kinetic energy of atoms. This is similar to how a star cluster loses kinetic energy because of friction as mentioned earlier.

3. Energy of light:

“Light, for example, would involve a new form of energy in the classical theory, but we can also, if we want to, imagine that the energy of light is the kinetic energy of a photon… (Feynman et al., 1963, section 14–4 Nonconservative forces).”

Feynman says that the law of conservation of energy will appear to be incorrect if we neglect to take interactions into account. (In biology, the law of conservation of energy may appear incorrect because biology students study open systems instead of isolated systems). Generally speaking, the kinetic energy of an object is not really lost because the atoms inside are jiggling with a greater amount of kinetic energy. In addition, he clarifies that the formula T + U = constant (14.2) would still be right if we conceptualize the energy of light as the kinetic energy of photons. However, there is also a continuous loss of light energy from the object that is in the form of infrared radiation. Physicists may add that the object would emit even more photons if its temperature is higher.

The emission of light energy can be related to the oscillations of charged particles. In Chapter 28, Feynman explains that light was recognized as electromagnetic influences extending over long distances and generated by an almost incredibly rapid oscillation of the electrons in the atoms (light has both particle and wave properties). Essentially, the fundamental mechanism for the emission of photons is due to the acceleration of charges (e.g., electrons). Furthermore, Feynman adds that “the charge moves around, the unit vector wiggles, and the acceleration of that unit vector is what we are looking for. That is all. Thus E = (−q/4πϵ₀c²)(d²e_r′/dt²) is a statement of the laws of radiation…(Feynman et al., 1963, section 28–2 Radiation).” However, there is also an apparent loss of light energy in the universe that is known as redshift.

Questions for discussion:

1. How would a globular star cluster lose kinetic energy as a result of friction?

2. Is it always easy to separate the total energy of a thing into two parts: kinetic energy and potential energy (at the atomic level)?

3. How does the energy of light help to maintain the law of conservation of energy?

The moral of the lesson: Non-conservative forces (e.g., frictional forces) appear only because we neglect microscopic complications.

References:

1. Chandrasekhar, S. (1943). Dynamical Friction. I. General Considerations: the Coefficient of Dynamical Friction. The Astrophysical Journal, 97, 255–262.

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. Romer, R. H. (2001). Heat is not a noun. American Journal of Physics, 69(2), 107–9.