The double-slit experiment requires wave-like interference of possible paths according to the quantum action principle, but it doesn't require entanglement since it's a single-particle phenomenon. Isn't entanglement arguably even more mysterious, since it violates local realism and thus can't be explained by de Broglie's pilot wave theory? Is there some reason Feynman wasn't concerned by entanglement?
I think what he was getting at is that we don't yet have a single agreed interpretation of what is 'really' happening at a quantum level, and the two-slits experiment typifies the nature of the conceptual gap we have yet to fill. Entanglement in that context can be considered as 'just' another example of the strange effects that arise from the quantum nature of matter.
The fundamental issue with the two slits experiment- and all the other experiments that exhibit quantum interference effects- is that we don't really understand the link between a particle and its associated wave function. We know the wave function tells us probabilistically where the particle might be found, and we know that if we model the two slits experiment by assuming that the wave function of an incident electron interferes with itself, then we get a result that agrees with experiment. But why should the wave function behave in that way? What causes the wave function to be blocked by the screen and pass only through the slits, given that: a) the screen is in any case largely empty space at a microscopic level; b) it doesn't seem to matter what the screen is made of; c) the effect happens whether the incident particle is electrically charged or a neutron, say; and d) quite large objects with hundreds of atoms can be diffracted. So why, in all those disparate cases, can we model what happens simply by assuming that the inbound object has an associated wavelength and the screen blocks the propagation of the incident wave in exactly the same way that a macroscopic screen with two slits would affect a water wave? And bear in mind that wave-functions are abstract mathematical entities with imaginary components, so why should they be physically diffracted?
I think that when we have a crystal clear and universally agreed answer to questions like that, we will also know how best to conceptualize entanglement.
The concept of entanglement was introduced by Schrödinger.1 So the idea must have been known to Feynman.
However, entanglement is a consequence of a deeper concept associated with the way quantum system can form superpositions of multiple entities (particles). I guess that Feynman understood that this is the essential property of quantum physics that sets it apart from what we call "classical" physics.
This superposition principle is actually a consequence of something even deeper, namely the fact that interactions are quantized and localized, which was already reveal in the work of Planck and de Broglie. Such interaction would inevitably give rise to superpositions of multiple entities. These properties of interactions are revealed in the double slit experiment. Although the field of the particle interferes due to the slits, the observation involves localized quantized detections.
I don't think that quantum physics is today still as "mysterious" as Feynman thought it was. Many very clever people have thought about it from various perspectives. As a result, we have a very good idea about what is going on. It is just that the concepts are counter intuitive.
- E. Schrödinger, "Discussion of probability relations between separated systems". Mathematical Proceedings of the Cambridge Philosophical Society, 31, 555–563 (1935); E. Schrödinger "Probability relations between separated systems". Mathematical Proceedings of the Cambridge Philosophical Society, 32, 446–452 (1936).
I would say there is entanglement involved in the double slit experiment. By entanglement I mean some kind of "spooky action" at a distance, as in the EPR paper, though not necessarily in the sense of Bell inequality violation.
Consider the situation that there is always at most one particle in the double slit apparatus. Although before detection the wave function of the particle spread over the whole detection screen, at the moment one detects a particle somewhere on the screen, one knows for sure there cannot be detections anywhere else, as if all the wave function elsewhere suddenly spookily disappears.
I am not sure if this is what Mr Feynman had in mind, but here are some thoughts of mine.
The particle interacts with the plate containing the slits, and this interaction results in entanglement between atoms in the plate and the states of the particle. The resulting combined state is a superposition of "basic combined states", where each individual "basic combined state" already contains the information where the particle will land on the screen (in this sense, maybe we can say the particle "bounces off"). Upon measuring on the detection screen, the resulting state is a "basic combined state", one part of it contains the position of the particle. Theoretically, this also gives information one the state of particles in the plate (the ones with which the interaction took place). However, the experiment does not care about that other part of the state.
We have no information about the state of the particle when it reaches the plate, the wave function describes the uncertainty on how the particle has spread out in space. This results in the superposition pattern of "basic combined states". Now, there is another variant of the double slit experiment where (due to Feynman btw) you place detectors immediately before or after the slits. Then the interference pattern vanishes (or is reduced), as the measurement gives information about the combined state and results in a collapse of the wave function ("forces one reality for the particle").
Theoretically, with this explanation, it might make a difference how close or far away the detectors are placed. Moving the detectors modulates the intensity of the interference pattern. I am not sure if this is true, as I have not done this experiment.