Section 37–6 Watching the electrons

 (Observer effect / Complementarity principle / Complementary descriptions)

 

In this section, Feynman discusses Proposition A, uncertainty principle, and logical tightropes in communicating quantum mechanics. However, the three main points of the section could be observer effect, complementarity principle, and complementary descriptions in quantum mechanics.

 

1. Observer effect:

“Here is what we see: every time that we hear a “click” from our electron detector (at the backstop), we also see a flash of light either near hole 1 or near hole 2, but never both at once! And we observe the same result no matter where we put the detector. From this observation we conclude that when we look at the electrons we find that the electrons go either through one hole or the other. Experimentally, Proposition A is necessarily true (Feynman et al., 1963, p. 37–7).”

 

According to Feynman, Proposition A—"each electron either goes through hole 1 or hole 2"—becomes true only under experimental conditions that forces the electron to choose a definite path. This reveals a deeper truth: the validity of Proposition A is dependent on the act of observation. In the absence of observation, the electron is described by a wavefunction representing a superposition of paths, leading to interference. When an observation is made, the act of measurement restricts the wavefunction to a new quantum state (a different function), allowing the electron to exhibit particle-like behavior and follow a specific path—either through slit 1 or slit 2. This transition from wave-like to particle-like behavior upon observation is often attributed to the observer effect, a concept sometimes linked to Heisenberg’s microscope. It challenges classical notions of objective reality, illustrating that the properties of quantum systems are not pre-determined but emerge through interaction with the apparatus.

 

“You remember that when we discussed the microscope we pointed out that, due to the wave nature of the light, there is a limitation on how close two spots can be and still be seen as two separate spots. This distance is of the order of the wavelength of light. So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons (Feynman et al., 1963, p. 37–9).”

 

Traditionally, physicists would use Heisenberg’s microscope to explain the uncertainty principle involved in the experiment. However, Feynman’s mention of microscope is related to Rayleigh criterion, which states the minimum angular resolution of an image-forming system. Notably, the experiment could be analyzed using the concepts of visibility and distinguishability: 1. Visibility refers to the clarity of the interference pattern, with high visibility indicating sharp fringes and low visibility indicating blurred or no patterns. 2. Distinguishability refers to the ability to determine which hole a particle passed through. There is a quantitative relation, sometimes known as distinguishability-visibility relation, which expresses a trade-off between the visibility of interference pattern and the distinguishability of the particle’s path.

 

2. Complementarity principle:

“He proposed, as a general principle, his uncertainty principle, which we can state in terms of our experiment as follows: ‘It is impossible to design an apparatus to determine which hole the electron passes through, that will not at the same time disturb the electrons enough to destroy the interference pattern’ (Feynman et al., 1963, p. 37–9).”

 

Feynman’s statement of the uncertainty principle suggests that the principle arises from the disturbance caused by the act of measurement. Furthermore, it implies that the main problem is one of apparatus design, but one may consider the possibility of determining the electron’s path using an observation system (instead of physical apparatus). More important, the uncertainty principle is now understood as intrinsic uncertainties of quantum systems, that are independent of any disturbance. Bohr’s complementarity principle offers an alternative explanation: we cannot observe both the wave and particle properties simultaneously. When we observe the electron’s path (particle-like behavior), the interference pattern (wave-like behavior) disappears, and vice versa.

 

Feynman’s perspective is related to Bohr-Einstein debates on the epistemological problems of quantum mechanics. In Bohr’s (1949) words, “[I]t is only the circumstance that we are presented with a choice of either tracing the path of a particle or observing interference effects, which allows us to escape from the paradoxical necessity of concluding that the behavior of an electron or a photon should depend on the presence of a slit in the diaphragm through which it could be proved not to pass. We have here to do with a typical example of how the complementary phenomena appear under mutually exclusive experimental arrangements and are just faced with the impossibility, in the analysis of quantum effects, of drawing any sharp separation between an independent behavior of atomic objects and their interaction with the measuring instruments which serve to define the conditions under which the phenomena occur (p. 46).” Remarkably, Bohr explains the experiment using the complementarity principle. Complementarity is the concept that a single entity can exhibit different (or seemingly contradictory) properties depending on the perspectives or context in which it is observed.

 

Strictly speaking, Feynman’s statement is not a general formulation of the uncertainty principle but rather a specific application to the double-slit experiment. An alternative phrasing of the principle, avoiding terms like “apparatus” and "disturb," might be: It is impossible to determine which hole the electron passes through without affecting the visibility of the interference pattern. Specifically, the distinguishability-visibility relation in a modern double slit experiment may be expressed as: D² + V² ≤ 1 (Jaeger, 2007). This inequality means that as path distinguishability (D) increases, the visibility (V) of the interference pattern must decrease, and vice versa. In the double-slit experiment, when D = 1 (complete distinguishability or complete path knowledge), V = 0, meaning no interference pattern will appear. Conversely, when D = 0 (no path knowledge), V = 1, meaning a full interference pattern.

 

3. Complementary descriptions:

“If one looks at the holes or, more accurately, if one has a piece of apparatus which is capable of determining whether the electrons go through hole 1 or hole 2, then one can say that it goes either through hole 1 or hole 2. But, when one does not try to tell which way the electron goes, when there is nothing in the experiment to disturb the electrons, then one may not say that an electron goes either through hole 1 or hole 2. If one does say that, and starts to make any deductions from the statement, he will make errors in the analysis. This is the logical tightrope on which we must walk if we wish to describe nature successfully (Feynman et al., 1963, p. 37–9).”

 

Feynman’s “logical tightrope” could be related to complementary descriptions, which include classical and quantum descriptions. Proposition A—"each electron either goes through hole 1 or hole 2" is a classical description, which can be determined by an experiment. Perhaps Feynman could have included Proposition B: “each electron exists as a superposition of different states (or possible paths),” which is a quantum description. This describes the electron’s quantum state, where its path remains undefined until measured. In essence, the classical description captures the electron’s particle-like behavior, emphasizing a definite path when observed, while the quantum description highlights its wave-like nature, characterized by an indefinite path when unobserved. This duality illustrates the principle of complementarity, where the wave and particle descriptions are not contradictory but dependent on the experimental setup.

 

In the Audio Recordings* [39 min: 30 sec] of this lecture, Feynman says something like: “The world must be entirely quantum mechanical. It cannot be half classical and half quantum mechanical. If, for example, shmootrinos, a new particle, would all go exactly like waves according to classical physics, we can make any intensity we want. Then, we can just use them to watch electrons, we can cut the intensity down because they don’t have the rules of quantum mechanics, then it would be a paradox...” Feynman also used the word shmootrinos in his lecture on gravitation delivered to advanced graduate students. In Feynman’s (1995) words, “These we might think of as photons or gravitons or neutrinos, or maybe some new particles, some shmootrinos which don't worry about baryon conservation. When they meet another shmootrino dropping in from the other side with opposite momentum, these can have enough energy to create a hydrogen atom.” This playful invention serves to emphasize the necessity of quantum mechanical rules, suggesting the inconsistency that would arise if a new (classical?) particle existed in a quantum world.

*The Feynman Lectures Audio Collection: https://www.feynmanlectures.caltech.edu/flptapes.html

 

“In Fig. 37–5 we have tried to indicate schematically what happens with large-scale objects. Part (a) of the figure shows the probability distribution one might predict for bullets, using quantum mechanics. The rapid wiggles are supposed to represent the interference pattern one gets for waves of very short wavelength. Any physical detector, however, straddles several wiggles of the probability curve, so that the measurements show the smooth curve drawn in part (b) of the figure (Feynman et al., 1963, p. 37–10).”

 

It might seem surprising that the double-slit experiment involving bullets could produce an interference pattern as shown in Fig. 37–5(a). This can be explained by the de Broglie wavelength of bullets, which is extremely small compared to objects like electrons. The rapid wiggles in the interference pattern predicted by quantum mechanics for bullets could be observed if a sufficiently large number of bullets is fired under highly controlled conditions. In practical experiments, however, real-world factors such as slight imperfections in the slit edges (e.g., sharp versus smooth edges) and the granularity of the bullet impacts would likely introduce significant noise, obscuring the interference pattern. If the separation between the two slits were increased, the probability distribution might display two distinct peaks instead of one. Feynman’s analysis also implicitly assumes that the bullets are highly correlated—that is, they possess nearly identical energies or de Broglie wavelengths. Without this assumption, the underlying quantum mechanical effects would be overwhelmed by classical randomness.

Review Questions:

1. Would you explain the uncertainty principle using the observer effect? (Do you agree with Feynman’s statement of uncertainty principle)?

2. Would you explain the double slit experiment using the uncertainty principle or complementarity principle?

3. How would you explain the logical tightrope on which we must walk if we wish to describe nature successfully?

 

The moral of the lesson: The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function (Fitzgerald, 2009).

 

References:

1. Bohr, N. (1949). Discussion with Einstein on Epistemological Problems in Atomic Physics, In N. Bohr, Philosophical Writings of Niels Bohr, 3 vols. Woodbridge: Ox Bow 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. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.

4. Jaeger, G. (2007). Quantum information. New York: Springer.

5. Fitzgerald, F. S. (2009). The crack-up. New Directions Publishing.