Section 2–3 Quantum physics

(Uncertainty principle / Particle-wave duality / light-matter interactions)

Feynman clarifies that the concept of a three-dimensional space and of time as a separate thing was changed by Einstein before 1920, first into a combination as space-time, and then further into a curved space-time to represent gravitation. Then, the mechanical rules of “inertia” and “forces” are found to be wrong in the world of atoms. In this section, Feynman discusses at greater length on the uncertainty principle, particle-wave duality, and light-matter interactions.

1. Uncertainty principle:

“… there is a rule in quantum mechanics that says that one cannot know both where something is and how fast it is moving (Feynman et al., 1963, section 2.3 Quantum physics).”

Right at the beginning, Feynman emphasizes that it is wrong to idealize a particle as having a definite location and a definite speed in quantum physics. Simply phrased, one cannot know exactly where an object is and how fast it is moving. The rule can be mathematically expressed as a product of the uncertainty of the momentum and the uncertainty of the position and this product is bounded by a very small constant: ΔxΔp ≥ ℏ/2. According to Feynman, we can use this rule to explain why the size of atoms is larger than the nuclei. This is related to the product of the positional uncertainty and uncertainty in the momentum of nuclei and electrons. However, one may prefer to use the term indeterminacy instead of uncertainty. It helps to avoid a misunderstanding of uncertainty as an error.

Note: During the Pocono Conference 1948, Bohr thought that Feynman did not know the uncertainty principle. In Feynman’s words, “I said that in quantum mechanics one could describe the amplitude of each particle in such and such a way. Bohr got up and said: ‘Already in 1925, 1926, we knew that the classical idea of a trajectory or a path is not legitimate in quantum mechanics; one could not talk about the trajectory of an electron in the atom because it was something not observable.’ In other words, he was telling me about the uncertainty principle. It became clear to me that there was no communication between what I was trying to say and what they were thinking. Bohr thought that I didn’t know the uncertainty principle… (Mehra, 1994, p. 248).” In essence, Bohr’s formulation of quantum theory does not allow an idealization of a path of an electron.

Importantly, one interesting change in the philosophy of science brought about by quantum mechanics is this: it is not possible to predict exactly what will happen in any circumstance. For example, we cannot predict when an atom is going to emit the light and specifically, which atom. Furthermore, it is simply wrong when philosophers say that if an experiment is performed in Stockholm, and then the same experiment is done in Quito, the same results must occur. Feynman cites the example of Foucault pendulum in which the plane of oscillation keeps changing in Stockholm, but the same phenomenon does not happen in Quito. The crux of the matter is we cannot be certain whether we have the same experimental (or environmental) conditions for any experiment.

2. Particle-wave duality:

“… So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one (Feynman et al., 1963, section 2.3 Quantum physics).”

Although Feynman mentions there is no distinction between a wave and a particle, he explains that quantum mechanics unifies the idea of the field, wave, and particle into one. He elaborates that when the frequency of waves is low, the field aspect of the phenomenon is more evident, and it is more useful as an approximate description in terms of everyday experiences. On the other hand, when the frequency of waves increases, the particle aspects of the phenomenon is more evident based on the measuring equipment used. For even higher frequencies of waves, they are deduced from the energy of the particles, by using a rule which assumes the validity of particle-wave duality. Curiously, Feynman does not seem to be thinking only in terms of particle-wave duality, but possibly particle-wave-field trinity.

Note: In this section, there seems to be an editorial error in the statement “no phenomenon directly involving a frequency has yet been detected above approximately 10¹² cycles per second.” It is more likely that Feynman was referring to 10²² Hz (even higher frequencies of waves) instead of 10¹² Hz. If you listen to the CD of this Feynman’s lecture, he says “here” instead of “10¹² cycles per second” while pointing to the blackboard.

Feynman is sometimes known as a “particle guy” rather than “wave guy.” During one of the Alix G. Mautner Lectures, Feynman explains that “[q]uantum electrodynamics ‘resolves’ this wave-particle duality by saying that light is made of particles (as Newton originally thought), but the price of this great advancement of science is a retreat by physics to the position of being able to calculate only the probabilities that a photon will hit a detector, without offering a good model of how it actually happens (Feynman, 1985, p. 37).” In addition, he considers his version of quantum electrodynamics does not need an uncertainty principle. In a footnote of the same lectures, Feynman (1985) states that “[i]f you get rid of all the old-fashioned ideas and instead use the ideas that I’m explaining in these lectures – adding arrows for all the ways an event can happen – there is no need for an uncertainty principle (p. 56)!”

3. Light-matter interactions:

“… This fundamental theory of the interaction of light and matter, or electric field and charges, is our greatest success so far in physics (Feynman et al., 1963, section 2.3 Quantum physics).”

Feynman was awarded the Nobel prize for physics in 1965 for his work in quantum electrodynamics. He mentions that quantum electrodynamics is a theory of the light-matter interactions that has much success in physics. This theory specifies the basic rules for all ordinary phenomena except for gravitational and nuclear processes. Feynman provides the following examples of phenomena: the collision of billiard balls, the motions of wires in magnetic fields, the specific heat of carbon monoxide, the color of neon signs, the density of salt, and the reactions of hydrogen and oxygen to form water. Essentially, if any phenomenon can be idealized as a simple problem, physicists may make approximations and solve it. Feynman claims that no exceptions have been found with quantum electrodynamics outside the nucleus.

Interestingly, Feynman opines that quantum electrodynamics is the theory of all chemistry, and of life if life is ultimately reduced to chemistry and therefore just to physics because chemistry is already reduced. Moreover, it relates the properties of very high-energy photons, gamma rays, and other electromagnetic waves. Next, it has predicted a very remarkable thing: besides the electron, there should be another particle of the same mass, and of opposite charge, called a positron. These two particles may annihilate each other such that there is an emission of light or gamma rays. Thus, physicists generalize that there is an antiparticle for each kind of particle.

The existence of a positron could be predicted by using Dirac’s equation. However, Dirac had reservations on the success of quantum electrodynamics. In the words of Dirac (1951), “Recent work by Lamb, Schwinger, Feynman and others has been very successful in setting up rules for handling the infinities and subtracting them away, so as to leave finite residues which can be compared with experiment, but the resulting theory is an ugly and incomplete one, and cannot be considered as a satisfactory solution of the problem of the electron (p. 291).”

Questions for discussion:

1. Uncertainty principle: what are the implications of Heisenberg’s uncertainty principle?

2. Particle-wave duality: does quantum mechanics unify the idea of the field, wave, and particle, or only explain particle-wave duality?

3. Light-matter interactions: does Feynman’s version of quantum electrodynamics need the idea of uncertainty principle or particle-wave duality?

The moral of the lesson: it is impossible to predict exactly what will happen in any circumstance.

Note: During his Nobel lecture, Feynman (1965) mentions that “my original plan was to describe everything directly in terms of particle motions, it was my desire to represent this new theory without saying anything about fields (p. 14).”

References:

1. Dirac, P. A. M. (1951). A new classical theory of electrons. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 209(1098), 291-296.

2. Feynman, R. P. (1965). The development of the space-time view of quantum electrodynamics. In Brown, L. M. (ed.), Selected papers of Richard Feynman. Singapore: World Scientific.

3. Feynman, R. P. (1985). QED: The Strange Theory of Light and Matter. London: Penguin.

4. 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.

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