Double slit experiment confusion regarding "single" electron being shot toward the slit

Question

I have heard many lectures claiming that even a single electron being shot toward the slits will eventually lead to construction of an interference pattern. The rationale for firing one electron at a time is that by using a single electron the possibility of the electron interacting/interfering with other electrons from the electron gun is eliminated. My question is this: The slot is composed of atoms which have electrons. So the fired electron can interfere or interact with anyone or more of the slit electrons thereby nullifying the logic of firing one electron at a time. How does the presence of the slot wall electrons or atoms affect the experiment?

see my answer to a related question here https://physics.stackexchange.com/questions/238855/is-it-wrong-to-say-that-an-electron-can-be-a-wave/238866#238866 . The slits location and width are part of the boundary conditions for the quantum mechanical solution of the system, including the effect of the material of the slits. — anna v, Jan 04 '24 at 06:27

score 1 · Answer 1 · answered Jan 05 '24 at 05:39

Whenever someone investigates the interaction between photons and edges, we interpret the fringes behind an edge as a manifestation of the wave character of the particles. And, at the same time, we always emphasise that these waves are not directly observable. It is therefore only one of the possible interpretations that from fringes with a wavelike intensity distribution behind an edge we can conclude about a wave-particle-duality.

How does the presence of the slot wall electrons or atoms affect the experiment?

The interpretation of the fringes as the result of the interaction between photons (or electrons) and the electric field of the electrons on the edge surface respectively of phonon induction is not common, but has a certain charm. It is no longer necessary to interpret an electron (or photon) interference with itself in single-particle experiments. No more sentences like "we can write it down mathematically, but we can't describe what happens".

The common field between photon and electrons is quantised and the fringes are the manifestation of this quantised field. This must be demonstrated, for example, by changing the electrical potential of the edges.

Yes the quantized field ( or nodal field) like the surface of the drum skin when struck is important. — PhysicsDave, Jan 05 '24 at 15:00

score 0 · Answer 2 · answered Jan 04 '24 at 09:57

As far as I know there is no detailed model about the interaction between the incoming electron and the electrons/nuclei at the slits.

The so-called "classical" prediction for this experiment (two lines behind the slits) is NOT the prediction of the relevant classical theory (classical electromagnetism) but the prediction of Newtonian mechanics for neutral objects interacting only by direct collisions (Feynman's "bullets" example). It is an irrelevant example, as Newtonian mechanics of neutral objects cannot predict electromagnetic induction either.

It would be interesting to model this experiment in the form of charged bullets sent towards a barrier consisting of an equal number of positively and negatively charged bullets. I was unable to find such a treatment.

score 0 · Answer 3 · answered Jan 04 '24 at 10:27

In a real experiment you will have to deal with the effect of charging, so grounded metal is used for the slit system. Any electron reaching the matter is removed.

https://www.hitachi.com/rd/research/materials/quantum/doubleslit/index.html https://www.jeol.com/words/emterms/20121023.070758.php#gsc.tab=0

No undisclosed interests ;-).

score 0 · Answer 4 · answered Jan 04 '24 at 14:40

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You are right that most explanations of the two-slits experiment treat the screen that surrounds the slits as a classical barrier, and neglect the interactions between the individual particles passing through the slits and the individual particles that comprise the screen. The justification is that the nature of those detailed interactions is not the cause of the diffraction pattern that is observed. You can perform experiments with neutrons or even quite large molecules and still get the same diffraction effect, so you can't explain it in terms of electromagnetic interactions with the individual particles comprising the screen.

answered Jan 04 '24 at 14:40

Marco Ocram

26,161

Apparently "Neutrons possess a magnetic dipole moment which makes them sensitive to magnetic fields generated by unpaired electrons in materials." Similarly molecules possess dipole fields .... so I think your conclusion that EM interactions can't explain the observed effects is incorrect. – PhysicsDave Jan 04 '24 at 15:31
@PhysicsDave yes you're right- I should have been clearer and said that the differences between the characteristics of neutrons, molecules etc are such that you can't explain the consistent diffraction pattern in terms of their detailed interactions with the material of the slits. – Marco Ocram Jan 04 '24 at 15:38
@MarcoOcram, do you have any evidence for the above assertion? In the absence of a calculation how would you know what pattern to expect for neutrons or molecules? Why do you think they should be different? – Andrei Jan 05 '24 at 06:48

PhysicsDave · Answer 5 · 2024-01-05T02:30:58.107

The EM field encompasses the entire apparatus and beyond (all space), an excited electron in the electrode is already interacting thru the EM field with all the electrons in the apparatus .... even before emission! However in order to drive the electron to the detector/screen voltage potentials are used (charged slits and screen), the accelerated electron spends little time interacting with slit/apparatus electrons as the strong charges drive it into the screen (although some electrons are likely absorbed at the slit). Most electrons in the slit material are interacting with their nuclei, not so interested in the free electron, however metallic slit material which has free electrons can polarize the photons.

At the screen the very very small "interference" pattern is observed .... this due to the wavelike/resonant nature of the EM field. The EM field governs all interactions in our world/universe (except gravity and forces inside the nucleus), the screen electrons and the traveling electron must obey the EM field "rules" ... the EM field everywhere (even at the screen) was active even as the electron was being emitted ... more resonant pathways in the EM field are higher probability thus the pattern.

score -3 · Answer 6 · answered Jan 04 '24 at 16:21

-3

How does the presence of the slot wall electrons or atoms affect the experiment?

Answer: literally, it makes no significant difference on the important outcome, which is: Is there an interference pattern, or not?

As @Andrei correctly points out: "As far as I know there is no detailed model about the interaction between the incoming electron and the electrons/nuclei at the slits." The reason is simple: Covering one of the slits shouldn't make much difference if the physical edge of the slit was somehow contributing. And of course, there is absolutely no QM theory that would lead us to believe the edge itself interacts with a particle as it passes through the slit (and causing an interference pattern).

If you are willing to consider double slit experimental versions with photons (instead of unwieldy electrons) in one-at-a-time build-up: actual experiments show that the rule - as with electrons or any particle) is that it is the possible knowledge of which path information - and nothing else - that dictates. See the following experiment performed with polarizers in front of each slit. It is the relative orientation of the polarizers that control. If parallel, there is interference. If perpendicular, no interference. In each case, the same apparatus is present at each slit. So it can't have anything to do with a hypothetical interaction with the physical slit edge itself. See:

https://sciencedemonstrations.fas.harvard.edu/files/science-demonstrations/files/single_photon_paper.pdf

Young's double-slit experiment with single photons and quantum eraser

"The which-path marker consists of two, mutually perpendicular, polarizing filters. With one oriented vertically and the other horizontally, they are butted together side-by-side and held in place using a standard lens holder."

Note that in this experiment, the parallel case is emulated by "erasing" the which path markers. The rule being: if it is possible, in principle, to determine which-path information, there will be no interference pattern. If does not matter whether the experimenter extracts that information from the setup, or not.

answered Jan 04 '24 at 16:21

DrChinese

1,036

One call also say the only way to determine which path information is to alter the EM field propagation before or after the slits, whether this field is real, virtual or other form (pilot wave). – PhysicsDave Jan 05 '24 at 02:37
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The electrons do not bump into the atoms at the slits like bullets. The trajectory of the electrons are determined by the electric and magnetic fields associated with all charges in the barrier. If you change the geometry (like closing one slit) you change the charge distribution so you change the fields. different fields would determine different trajectories. So the number of slits is expected to alter the pattern even if the electron only passes through one slit. – Andrei Jan 05 '24 at 06:37
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"there is absolutely no QM theory that would lead us to believe the edge itself interacts with a particle as it passes through the slit" Did you ever solved the hydrogen atom? You need to calculate the Hamiltonian first and since the electron interacts electromagnetically with the electrons/nuclei of the barrier those interactions should be included in that Hamiltonian. The reason this is not done is the complexity of the problem. It cannot be solved, so you use an approximate treatment (boundary conditions). – Andrei Jan 05 '24 at 06:41
Of course, adding polarizers changes again the charge distribution, the fields and the trajectories. You just add more charges to the problem. – Andrei Jan 05 '24 at 06:55
@PhysicsDave If you want to call "anything that happens" (such as re-orienting polarizers) an "alteration of the EM field", then you are correct. However, they don't teach this at universities, nor do they use this idea in actual experiments. I have provided the same reference in discussions with you previously, so I assume by now you should be aware that what you are saying is not a useful description. – DrChinese Jan 05 '24 at 18:11
@Andrei We're discussing the slit wall and double slit particle interactions with same (and not the hydrogen atom). You won't find a reference indicating interference is dependent in any significant way on such interactions. Normally, the relevant parameters in the DS are: wavelength (if a photon); slit width; and distance between slits. And not the components of the slit edges. Adding polarizers (when using photons) does not change any charge distribution. The only significant change with polarizers is their relative orientation. All this is explained precisely in the cited reference. – DrChinese Jan 05 '24 at 18:19
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@DrChinese, the interactions between the particles and the barrier are essential for the experiment. If there is no interaction you get no interference. Neutrinos for example would simply pass through the barrier as if it wasn't there. So, we know for a fact that the particle-barrier interaction is the cause for the observed pattern. Interference is a statistical effect and, indeed, you can describe the pattern without looking at those interactions just like you can describe a water wave without knowing about water molecules. – Andrei Jan 05 '24 at 22:32
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@DrChinese, the polarizers are also made out of atoms, so electrons and protons, so charges. Adding those charges changes, obviously the charge distribution. – Andrei Jan 05 '24 at 22:35
@Andrei Again, whatever change the polarizer makes is obviously measurably insignificant. For all practical purposes, it does nothing. Consequently it's completely ignored in experimental treatments of photons in a DS setup. I am unaware of any similar setups (such as my cited paper with a quantum eraser) that've been done with anything other than photons. When particles with mass and charge (electrons, ions, molecules) are diffracted, there's a lot more complexity to assigning which path markers, I'm not sure it's even feasible. Of course you can diffract such particles and get interference. – DrChinese Jan 06 '24 at 00:01
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@DrChinese, you need to distinguish between a statistical treatment and a microscopic/fundamental treatment. You can describe interference from a statistical/macroscopic point of view. You just specify the macroscopic geometry, you put by hand what the polarizer does, etc. But all those macroscopic properties have a basis in the microscopic interactions. A barrier cannot be a barrier if it does not interact properly with your particles and a polarizer does not do its job either. In principle it should be possible to describe this experiment only in terms of interacting elementary particles. – Andrei Jan 08 '24 at 07:20
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@DrChinese, assuming you have a powerful enough computer to do such a calculation you would need to include those interactions explicitly. If you don't, the calculation would give wrong results - the particles would simply pass through your barrier/polarizer unchanged and you would only get a slightly larger image of the source on the screen, no interference pattern. – Andrei Jan 08 '24 at 07:24

Double slit experiment confusion regarding "single" electron being shot toward the slit

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