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enter image description here Double-slit experiment image source: Wikipedia

The double-slit experiment can be regarded as a demonstration that light and matter can display characteristics of both classically defined waves and particles. It also displays the fundamentally probabilistic nature of quantum mechanical phenomena.

In a double-slit experiment using an electron beam an interference pattern is formed after experimenters record a large amount of electron detections.

I have seen this answer by "anna v" which states an electron never travels through both slits only one slit per electron and the pattern formed is only a statistical probability distribution for the entire accumulation.

But assuming in an experiment in which electrons travel one after the other and each electron travels only through one slit then how could the pattern on the screen be different from the one when we close one slit interchangeably and send electrons only through one slit at a time. (Actual experiments have shown patterns are different indeed)

I think an electron through double-slit as a superposition of probabilities of spatial distribution. Like this picture below:

enter image description here

But according to anna v picture that come to my mind is below (several electrons illustrated):

enter image description here

So I have two related questions:

  1. Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit?

  2. Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations?

Edit: Evidence supporting simultaneous two (path) position:

  1. Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics

  2. One particle on two paths: Quantum physics is right by Vienna University of Technology

  3. Double-slits with single atoms: Selective laser excitation of beams of individual rubidium atoms by Andrew Murray, professor of atomic physics, University of Manchester, UK

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    $\begingroup$ There simply is no "electron" without an electron being detected. An electron is not a thing that has an existence independent of emission and absorption processes. That's the great lesson of quantum mechanics... which is being taught poorly. $\endgroup$ Commented Jun 9, 2023 at 19:08
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    $\begingroup$ No it passes thru one slit ... the EM field that guides it goes thru both. $\endgroup$ Commented Jun 10, 2023 at 0:40
  • $\begingroup$ @FlatterMann I think the mainstream physics POV is that things like particles exist even between the measurements. It is true what you said that we cannot determine the existence of such things outside of measurements or interactions. But as Einstein, they do not like to think the moon is not there when you don't look at it. So the standard is to take measurements as indicators of the real thing (measurement is derived from the real physical thing), not the measurement/interaction itself as the only real thing. $\endgroup$ Commented Jun 10, 2023 at 4:59
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    $\begingroup$ As a general comment: physics is not what the majority believes. It is a collection of facts about nature and their rational explanation. Nowhere in that rational explanation do particles show up. What does show up is exactly what you were told in high school: irreversible energy transfers. Does energy in a system get lost if you don't look at it? Of course not. Does that mean that it is localized in some speck of dust? Of course not. It's that trivially false "logical" step that creates particles in your mind and only in your mind. $\endgroup$ Commented Jun 10, 2023 at 14:13
  • $\begingroup$ Interesting wiki/Dirac note on QFT: “Therefore, even in a perfect vacuum, there remains an oscillating electromagnetic field having zero-point energy. It is this quantum fluctuation of electromagnetic fields in the vacuum that "stimulates" the spontaneous emission of radiation by electrons in atoms. $\endgroup$ Commented Jun 10, 2023 at 16:18

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In general, a different pattern of slits in a single particle interference experiment will result in a different pattern of fringes at the end of the experiment. Consider a point P on the screen that is lit when there is one slit and is dark when there are two slits. If there was one slit an electron might be detected at P, but with two slits the electron won't be detected at P. And if you subject the region after the slit to an electric or magnetic field in general that will change the pattern of fringes. That's not a matter on which physicists disagree, but there is disagreement on what is happening in reality to produce that outcome, or whether such an account is required.

If somebody doesn't have an account of what is happening in the experiment, then they have no account of what is happening in the experiment. So then how could they say whether the experiment has been conducted correctly? If there is no account of what's happening in the experiment, then what is the standard by which the correctness of the setup is judged and what is the explanation for why you adjust the experiment in a particular way to improve it? So we can and should discard the idea that it's acceptable to have no explanation of what's happening in the experiment.

What is the explanation?

The only idea that I think actually works goes like this. The pattern changes if you introduce a second slit, so there must be something coming through the second slit that prevents the electron from arriving at P and that thing is blocked by substances that block electrons, i.e. - the material of the screen. Whatever the thing is that's coming through the second slit it will be affected by magnets and electric fields, just as an electron would be. So it's something that acts like an electron except that we don't detect it. This electron can only be blocked by a portion of a screen or a detector if it interacts with it, but we don't see the result of that interaction, so it must be interacting with an screen or detector that we don't see. That "invisible" screen or detector must have been put there by somebody, so there are "invisible" people too and it must have been manufactured by a factory and so on. There are entire universes full of "invisible" stuff that only interacts with the universe we see around us in such a way that we can exclude other explanations under some limited conditions in labs. And that is what quantum mechanics implies about the world too. This way of looking at quantum mechanics is often called the Everett interpretation, but nobody has proposed another account of what's happening in single particle interference or other quantum mechanical experiments. For more details see "The Fabric of Reality" by David Deutsch and

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

There are other theories whose advocates claim to be able to explain what's happening, such as collapse theories:

https://arxiv.org/abs/1910.00050

that say other versions of the electron are eliminated by some physical process.

One problem with such theories is that saying they have admitted in substance that the electron exists in multiple versions so what are they gaining by adding collapse? There are other criticisms too:

https://arxiv.org/abs/1407.4746

https://arxiv.org/abs/2205.00568

There are other proposed explanations like the pilot wave theory:

https://arxiv.org/abs/2205.13701

which has also been criticised:

https://arxiv.org/abs/quant-ph/0403094

There are other variants too, but there's not much point in listing them all and I guess I've linked enough material above for you to make your own decision.

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  • $\begingroup$ You don't need invisible electrons to explain the change in the pattern. A different geometry of the barrier represents a different charge distribution (the electrons and nuclei in the barrier). A different charge distribution means that the electron would experience a different EM force, hence its trajectory would be different. $\endgroup$
    – Andrei
    Commented Jun 9, 2023 at 7:02
  • $\begingroup$ A photon is a particular kind of state of the EM field. Saying the field guides the photon seems to imply there is a clear separation between the field and the photon, which is false. That state of the EM field has to go through both slits to produce the interference pattern, so the photon goes through both slits. The electron too is a state of a quantum field that is affected by the slit as a result of interacting with it. $\endgroup$
    – alanf
    Commented Jun 9, 2023 at 7:57
  • $\begingroup$ @Andrei A charge distribution is a classical property formed by many electrons (and other charge carrying quanta). It is not something that comes "before" quanta. It is an effect caused by quanta. The same is true for "electromagnetic forces". They are phenomena of the many-quantum system. $\endgroup$ Commented Jun 9, 2023 at 19:10
  • $\begingroup$ @alanf A photon is not a state of the em field. A photon is the irreversible energy transfer between a source and the em field or the em field and an absorber. In the theory it is the physical result AFTER the application of the Born rule. The only "thing" with state in quantum theory is the ensemble of the system and that is not even a thing. The ensemble is an abstract that we write down on paper to calculate the probability estimate for the actual frequentist observations. Physically quanta are irreversible energy exchanges. In the theory they are indices into probability distributions. $\endgroup$ Commented Jun 9, 2023 at 19:16
  • $\begingroup$ @FlatterMann, and how is the fact that charge distribution is a "classical property formed by many electrons" supposed to invalidate my point? A barrier with two slits has a different charge distribution (or if you want, the molecular orbitals associated with the barrier) than a barrier with one slit. So, the incoming electrons would be scattered in a different way. No mystery about that. $\endgroup$
    – Andrei
    Commented Jun 12, 2023 at 7:21
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  1. Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations?

Yes

  1. Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit?

This question is difficult to give a proper answer. The correct course of action is to identify the unequivocal current best theory and the thing they are meant to explain, and so then the mathematical description is exactly the physical reality. i.e. the wavefunction of the single electron in an empty universe is exactly the physical electron itself. Needless to say, this is somewhat interpretation dependent and also hotly debated.

In the double slit experiment, electrons and photons essentially behave the same way, so we can just state it as a general thing for all quantum particles. What we can really conclude from the experiments are that

The excitation in quantum fields get detected like particles but moves like waves.

It is necessary to have some wave parts, because the only way for the isolated single excitations, one-by-one passing through the slits and having interference patterns emerge, the whole "one electron/photon at a time", requires that the wave parts pass through both slits at once. Plenty of people insist that this wave part is not the single electron/photon, but they will not likely disagree that there is this wave part that passes through both. It thus comes down to whether one chooses to include the wave part with the particle part or not. Lots of arguing, very little sense.

There is this little book on some philosophical foundations of quantum theory, and in it, the author covered the fact that you could choose between "the particle passed through slit A AND slit B" and "the particle passed through slit A OR slit B", because as long as you are consistent, these two alternatives are both allowed by quantum theory. I am still searching for the book, though.

Instead, the better argument to have, is to consider that we really ought to stop using the wave-particle concept. Instead, what we have are quantum fields, and what we consider to be waves or particles, are really just excitations on these quantum fields. In that sense, both the wave aspects and the particle aspects come together, and we would sidestep all of these silly arguments.


It is actually rather bad to not include some interpretations business when answering this question. The de Broglie Bohm Pilot Wave Interpretation is rather illuminating here, because if you work out the actual trajectories of a hidden particle riding along the guiding wave, the wave part goes through both slits and causes the interference pattern, but the particle only ever passes through one slit. It is then a very curious thing that the trajectories are separated by the symmetry centre line. That is, it is only after quite a lot of work into Pilot Waves, did we discover that a particle that passes through the bottom slit, will appear on the bottom half of the screen, and never on the top half, and vice versa. It is obvious upon hindsight that such things can occur, but otherwise completely non-trivial.

Alas, that is completely interpretation dependent, and bringing it up is not an endorsement of Pilot Wave Interpretation. It is just fun to consider that there are such interesting things.

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  • $\begingroup$ I'm confused how traversing one or two slits is a matter of personal preference? If we don't try to see which slit is traversed, we see an interference pattern that indicates both slits were traversed. This isn't possible if only one slit is traversed? $\endgroup$ Commented Jun 9, 2023 at 23:34
  • $\begingroup$ @justaphase The physics is the same: if you perform an observation of which slit is traversed, the interference pattern goes away. But when the interference pattern is there, there is a choice of whether to say "it passed through slit A AND slit B" or "it passed through slit A OR slit B". As long as you are internally consistent, it would work out. Reality is often horrible like that. $\endgroup$ Commented Jun 11, 2023 at 0:23
  • $\begingroup$ an interference pattern requires AND though...OR would have no interference? Interference requires both components, so OR would be insufficient? $\endgroup$ Commented Jun 11, 2023 at 17:17
  • $\begingroup$ @justaphase I just told you that someone worked out the maths and proved that OR is also able to get the interference. $\endgroup$ Commented Jun 11, 2023 at 21:37
  • $\begingroup$ @naturallyInconsistent provide a citation to said maths...your answer does not appear rigorous, and anyone can claim that a rigorous justification for their claims exists somewhere in the literature...for example...maybe reveal the title of the "little book" you mentioned? $\endgroup$ Commented Jun 11, 2023 at 23:39
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A helpful fact that few physicists will disagree with is that the wavefunction of the electron certainly goes through both slits. Also, personally I think that describing the whole wavefunction of the electron sufficiently describes that electron.

The origional and simplest model of QM models the electron as follows:

When the electron is not being measured, a "wavefunction" (which moves similarly to a wave) propagates in space. This wave can interfere with itself just like how a wave of water can split into smaller waves and interfere with itself. When the electron is measured, the probability of finding the electron is proportional with how high that wave is at the point in space that wave is located at.

Because the wave is associated with probability of seeing the electron at a specific spot, it's not as if the wave-itself can be seen. Furthermore, because the electron is not seen when it is traveling (since measuring it would stop this wave from existing), we cannot make statements easily about what is happening when it is traveling.

Ultimately though, there is a lot of good conceptual intuition that the electron is going through "Both" slits, simply because it behaves in a way that is different than if it had simply went through either one or the other.

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  • $\begingroup$ So wave-particle duality is the most reasonable approximation according to the standard interpretation of QM? The particle part comes in because when we measure, measurement is in the form of a particle, wave part comes in because its position derives from wave-like properties. $\endgroup$ Commented Jun 15, 2023 at 6:52
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    $\begingroup$ Personally I'm not a big fan of "wave-particle duality" as a concept. I think it just makes things less clear. You are correct though that the position of the particle, when not observed behaves wavelike. When it is observed, it picks a spot and only begins to act like a wave when you stop observing it. The wavelike behavior can happen for any degree of freedom the particle can have, and is not limited to its position. For example, it's "spin-orientation" or which path it takes, or what energy it is in are all things that can act wavelike when not observed. $\endgroup$ Commented Jun 15, 2023 at 19:33
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"But assuming in an experiment in which electrons travel one after the other and each electron travels only through one slit then how could the pattern on the screen be different from the one when we close one slit interchangeably and send electrons only through one slit at a time. (Actual experiments have shown patterns are different indeed)"

Even if we do not understand the details, we know that the reason for the observed pattern is the electromagnetic interaction between the electrons and the barrier. We also know that the forces acting on the electron depend on the distribution of charges (the electrons and nuclei in the barrier). So, it is to be expected that if the charge distribution changes (by adding/removing a slit) the EM force acting on the electron changes as well, leading to a different pattern. I see nothing remarkable/unexpected about that.

Of course, in order to get a detailed understanding one needs to actually simulate the electron/barrier interaction. Unfortunately, due to the large number of charges involved, such a calculation is not possible at this time.

"Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit?"

I think it is only a mathematical model, otherwise, the collapse of the wave to one point would imply faster than light effects which are unlikely.

"Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations?"

Same as above, we have good evidence that nature is local, therefore any explanation that requires non-local effects is unlikely.

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Jun 9, 2023 at 16:57
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This is a long comment about what is an electron as far as particle physics goes.

Here is a bubble chamber photograph of an electron track:

electron

Bubble chamber photograph of an electron knocked out of a hydrogen atom

The curly line was produced by an electron that was struck by one of twelve passing beam $K^-$particles in a liquid hydrogen bubble chamber. It curves in an applied magnetic field and loses energy rapidly, spiraling inward

We have called them elementary particles , because they act like particles , no wave nature is seen within the accuracy of the dots where the particle ionizes (very low energy transfer) the hydrogen atoms and bubbles form in the super-cooled liquid hydrogen, so a picture can be taken. The bubble dots are dimensions of microns.

There is no personal opinion about the size of elementary particles, because the quantum field theory which has been well verified with the particle data , the standard model, axiomatically assumes that elementary particles like the electron are point particles, and that is where mainstream particle physics is now.

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  • $\begingroup$ Comments have been moved to chat; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments. Comments that do not request clarification or suggest improvements usually belong as an answer, on Physics Meta, or in Physics Chat. Comments continuing discussion may be removed. $\endgroup$
    – Buzz
    Commented Jun 12, 2023 at 20:14

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