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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 The Feynman lectures are awesome but definitely outdated in spots.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
    Commented Aug 16, 2022 at 2:57
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    $\begingroup$ @knzhou That explains it, thanks! $\endgroup$ Commented Aug 16, 2022 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. $\endgroup$ Commented Aug 16, 2022 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. $\endgroup$ Commented Aug 16, 2022 at 14:42
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    $\begingroup$ Surely Mr Feynman was joking $\endgroup$
    – jacknad
    Commented Aug 16, 2022 at 20:09

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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. $\endgroup$ Commented Aug 17, 2022 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. $\endgroup$ Commented Aug 17, 2022 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. $\endgroup$ Commented Aug 17, 2022 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. $\endgroup$ Commented Aug 17, 2022 at 16:22
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    $\begingroup$ 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. $\endgroup$ Commented Aug 18, 2022 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. $\endgroup$ Commented Aug 18, 2022 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. $\endgroup$ Commented Aug 18, 2022 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. $\endgroup$ Commented Aug 19, 2022 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. $\endgroup$ Commented Aug 21, 2022 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
    Commented Aug 18, 2022 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
    Commented Aug 18, 2022 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
    Commented Aug 18, 2022 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
    Commented Aug 19, 2022 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. $\endgroup$ Commented Aug 18, 2022 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. $\endgroup$ Commented Aug 18, 2022 at 20:38
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Feynman absolutely was aware of entanglement and also of nonlocality, even without knowing Bell's writings. Entanglement was carved out by Schrödinger and nonlocality by Einstein, Podolski and Rosen decades before Feynman wrote his lectures.

In some way, entanglement is just a consequence of interference, albeit not of interference of partial waves in 3D space. Let me explain. The physical concept of interference, in quantum theory, is described by the mathematical concept of adding vectors in Hilbert space. Now, if you add a concept as to how the Hilbert space of a composite system arises from the Hilbert spaces of the constituents' systems, namely the tensor product, then entanglement in the language of the constituents' systems is just interference (vector addition) in the composite system's description.

So, the way the state spaces of two "simple" systems are combined to the state space of the "combined" state plus interference imply entanglement.

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    $\begingroup$ +1 Thanks, I think this answer is very insightful as well. $\endgroup$ Commented Apr 30, 2023 at 4:37
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I agree with Macro Ocram <31>. Meanwhile we understood more and more the role of Networks in general, and in quantum physics in particular (Quantum Computing etc.). So why hold back and still believe in localized particles and empty ambient Space(Time), only to wonder how waves propagate ("ether", pilot waves of what?)? See my article https://vixra.org/abs/2301.0012

The Network Model provides a unified explanation of "mysterious" quantum phenomena, including a unification of fermions and bosons; in the 2-slit experiment the ``electron'' is a not a point-particle moving etc (why orbitals are sooo different!?), but a fermionic circuit, well characterized by the Schrodinger wave function, on which an excitation travels, literally like a soliton, that splits into an entangled pair of excitations (bilocality), to interfere with "itself" ... The claim is that atomic orbitals, we believe in have analog macroscopic structures: "open orbitals" with non-trivial topology, as connectors of the Quantum Circuit (Corresponds to stationary phase Feynman paths as a "topological skeleton"). The point-electron does not rotate in an atomic orbital (steady-state and bounded), and here the "open orbital" (closed / open structures, e.g. strings etc.) is claimed to be an element of reality, reminiscent of the idea of ether, while the excitation (peek of the Schrodinger wave) travels on it, having bosonic properties ... Bottom line, assume the Schrodinger wave function does model a real structure, i call fermionic channel (network). The later collapses under measurement as a soap bubble would, if you poke it, and we talked about the collapse of the wave function, without believing there is anything real behind this (see The Feynman Legacy in my article: https://arxiv.org/abs/math/0701069) ... etc.

Then the question is "What material is it made off?" ... well, this gets into a different issue (not to discuss here); but are strings real? made of what? What is the quantum "wormhole" in a recent entanglement experiment in a QC (correlated ions! not just a computational simulation ...), made off? etc.

So, "What is a Physics Model anyways!?" If it explains "everything" better (see my article https://arxiv.org/abs/0708.4180), without "patching" particle-wave theories together for instance, EXCEPT for what the quantum connectors are made off (A: what orbitals are made off! Nodes are baryons, S^2 like, with quark structure, yet irreducible ... "Made of what!?" ... "A: Shut-up and MODEL!") I would be satisfied at this stage :) ... and then start the debate: Is the Universe a Simulation?

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    $\begingroup$ Dear Lucian Ionescu. Welcome to Phys.SE. For your information, Physics.SE has a policy that it is OK to cite oneself, but it should be stated clearly and explicitly in the answer itself, not in attached links. $\endgroup$
    – Qmechanic
    Commented Jan 4, 2023 at 13:40
  • $\begingroup$ I apologize; i understand. How should i correct this? "cite oneself, but it should be stated clearly ... not in attached links." So, no links to my work, i guess? $\endgroup$ Commented Jan 4, 2023 at 19:56
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    $\begingroup$ I have now edited your post so that the Phys.SE self-citation policy is fulfilled. $\endgroup$
    – Qmechanic
    Commented Jan 4, 2023 at 20:09

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