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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?

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    $\begingroup$ That Feynman lecture was given in 1963, and Bell's theorem came out in 1964 (and little attention was paid to it until years later). The Feynman lectures are awesome but definitely outdated in spots. $\endgroup$
    – knzhou
    Aug 16 at 2:57
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    $\begingroup$ @knzhou That explains it, thanks! $\endgroup$ Aug 16 at 3:04
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    $\begingroup$ de Broglie's pilot wave theory is nonlocal, and it allows to describe entangled systems. So your penultimate remark is totally off the mark. $\endgroup$ Aug 16 at 3:57
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    $\begingroup$ @hdhondt Yes I thought so but I was emphasizing the fact that quantum mechanics is more than just unclear when it comes to explaining what’s physically happening. It really shouldn’t even be called incomplete because it doesn’t explain anything. $\endgroup$ Aug 16 at 14:42
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    $\begingroup$ Surely Mr Feynman was joking $\endgroup$
    – jacknad
    Aug 16 at 20:09

4 Answers 4

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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.

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    $\begingroup$ Most of the issues that you list actually can be answered by the current understanding of physics. $\endgroup$ Aug 17 at 1:02
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    $\begingroup$ @flippiefanus Excellent. Perhaps you might like to extend your answer to provide the crystal clear explanation I mistakenly thought we lacked. $\endgroup$ Aug 17 at 5:40
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    $\begingroup$ My thesis advisor and I spent years debating whether (a) the wave function represented the electron or (b) it literally was the electron. By the time I graduated, we could not tell which side of the issue either of us was trying to defend. $\endgroup$ Aug 17 at 15:21
  • $\begingroup$ Ha! I remember the feeling. I did my PhD in the days before the internet, when there were only about three books about quantum mechanics in the library. I remember reading de Broglie's book and Dirac's- I had to send off to another library to borrow them and they took weeks to arrive. $\endgroup$ Aug 17 at 16:22
  • $\begingroup$ Why do you say "imaginary components" as if it is something that can't exist? I guess phase shifts of coherent waves are pretty much real. $\endgroup$ Aug 18 at 10:47
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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.


  1. 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).
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  • $\begingroup$ Feynman's path integral considered all paths which showed that paths of path length that were integer multiples of the wavelength were the paths of highest probability. His motivation for this method was to show how each photon could act on its own. The "superposition of multiple entities" needs to be understood as the whole EM field of the apparatus (all the atoms and all the electrons) interacting with the excited/emitted photon/electron. $\endgroup$ Aug 18 at 20:52
  • $\begingroup$ The superpositions began long before emission, the excited atom is already generating virtual forces in the EM field. Feynman and the scientists at the time assumed the emitted particle had to act on its own without any prior forces.... and this misleading assumption forces us into the mystery. $\endgroup$ Aug 18 at 20:53
  • $\begingroup$ @PhysicsDave: most of what you are saying requires more context to see whether I would agree with it. One thing that I do not agree with is the statement about the path integral. The dominant path requires constructive interference, which does not require an integer multiple for the individual paths. Interference has to do with the relative phase between paths. $\endgroup$ Aug 19 at 7:05
  • $\begingroup$ Yes add all he relative phases per path integral and voila the DSE pattern emerges. Maximums occur at integer multiples of wavelength. $\endgroup$ Aug 21 at 17:43
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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.

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  • $\begingroup$ Whenever you make a measurement, all the other possibilities disappear, whether entanglement is involved or not. Isn't that what any probabilistic theory would predict? $\endgroup$
    – D. Halsey
    Aug 18 at 1:04
  • $\begingroup$ In a usual probabilistic theory I do agree. Like if Alice randomly puts a cake in one of the boxes numbered from 1 to 10. The moment Bob finds the cake in box 6 he knows there is no cake anywhere else. Bob finds nothing strange because he knows the cake can only be in one box. But the double-slit experiment is like a magic world where the cake was in several boxes at once before Bob opens it. And he knows this because he can somehow "interfere" a pair of boxes and verify there have to be some cake-amplitudes in both. I would say the disappearance of the cake-amplitudes involves entanglement. $\endgroup$
    – aystack
    Aug 18 at 12:14
  • $\begingroup$ If you say that disappearance of the amplitudes implies entanglement, don't you have to say that all quantum measurements imply entanglement? $\endgroup$
    – D. Halsey
    Aug 18 at 14:30
  • $\begingroup$ Indeed I would say that all quantum measurements imply entanglement. If I remember correctly, this is also how John von Neumann model quantum measurements. Essentially, a system being measured gets entangled with the measuring device, with different eigenstates entangled to different macroscopically distinguishable states of the device that can then be read out classically. This is mentioned for example in equation (1) of this paper: Zurek, W. H. (2003). "Decoherence, einselection, and the quantum origins of the classical". Reviews of Modern Physics. 75 (3): 715–775. arXiv:quant-ph/0105127 $\endgroup$
    – aystack
    Aug 19 at 10:58
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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.

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  • $\begingroup$ The photon or electron (wave or particle) is interacting with the EM field even before emission (i.e the excited electron in both cases)... the immediate EM field is very dynamic and is influenced by all electrons/atoms in the apparatus ... slit, screen, source, detector. The word "entanglement" is a bit misleading here .... interaction may be more appropriate .... the former typically refers for example to 2 photons created in the same event, the photons have opposite spin properties that are "locked in" or entangled. $\endgroup$ Aug 18 at 20:33
  • $\begingroup$ Feynman's detector experiment was a thought experiment, not one that is possible with photons .... it was performed much later with electrons. $\endgroup$ Aug 18 at 20:38

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