# Do we not know that momentum is certainly not conserved at single electron double slit experiments?

I am aware that tons of experiments are performed on this topic and the scientists try to be very careful with the experiments and take every possibility into account.

In a single electron double slit experiment, we know the limits to the direction of the electron's momentum since we know the path it travels from the gun to the slits. After the slits, we observe that many electrons go beyond these limits/range in direction, producing an interference pattern on the screen. This phenomena is explained by probability waves.

But, isn't it weird that a particle changes direction (therefore momentum) by itself? It looks like it would be a more robust explanation if something manipulated the electron or transferred energy to it. Ofc, I can say 'well, in the quantum world things are different; follow the formula; think out of the box; etc.', but that is how I feel at the moment.

In summary, what is the possibility that the interaction pattern on the screen is just due to the electrons interacting with the atoms at the edges of the slits? I don't know what causes the periodicity/pattern on the screen but the explanation might be inside the atom, impossible?

• Can the downvoter please explain? I think this is a great question. Sep 22, 2021 at 17:34
• Why do you assume that the barrier in which the slit is made does not feel an impulse equal and opposite to the impulse felt by the electron? Sep 22, 2021 at 18:13
• @SolomonSlow Wow. Maybe I didn't consider this because it is always depicted like an inner action of the electron only. No one talks about the slits' behavior. What you are telling is that the wave function of the electron interacts with the particles on the slit wall (or their wave-functions). But still, there seems to be a connection with the random atomic vibrations on the wall. Sep 22, 2021 at 19:00

The slit is an aperture in a material absorber which is much more massive than the electron. Momentum is conserved: the electron's new momentum is balanced by a reaction in the absorber. The larger the absorber, the harder it is to detect its change in momentum.

[source]

• Thank you. Knowing there is some momentum transfer, should we ignore the possibility that double-slit event might be close to the interactions that we are used to in classical physics? Maybe the actual measurements are almost impossible and maths is just too complicated that -rather than expressing the reality as it is- quantum mechanics provide us a method/tool/model/approximation to deal with the randomness in that scale? But again, I am open to the possibility that in reality it might be just as the quantum mechanics depicts it. Sep 22, 2021 at 16:38
• @rob♦ Can you give justification for your answer or link to a paper? I think that most physicists would find your answer reasonable, but has it been studied? Otherwise I would personally categorize it as "hypothesis" rather than "accepted theory" Sep 22, 2021 at 17:29
• For example, a convincing analysis might solve the Schrödinger equation for the particle-and-slits system. However it is not fully clear to me how exactly to define momentum conservation in this case - expected value does not work since you are comparing to a particular result of the diffracting particle's position. Sep 22, 2021 at 17:33
• @doublefelix There is zero experimental or theoretical support for momentum nonconservation for any isolated system in physics; momentum is the Noether current of translation invariance. The Schrödinger equation with an “external” potential like “an absorber is fixed at this location” describes a non-isolated system and breaks this symmetry. One famous collective interaction is the Mössbauer effect. More relevant for a multi-slit interference context is the widespread use of neutron diffraction to probe the phonon spectrum of a material.
– rob
Sep 22, 2021 at 17:52
• Absence of evidence does not imply evidence of absence. Lack of support for momentum nonconservation does not imply that there is no exception to momentum conservation. And I think that OP makes a good point here - so the burden of proof is on the answerer if he/she believes they have evidence to disprove OP. In this answer I see more of an explanation of a concept than a proof that that concept actually follows directly from the framework of QM to disprove OP's point. Sep 23, 2021 at 5:32

The two slits experiment gives the expected result regardless of whether the particles being sent through the slits are photons, electrons, neutrons, etc, and regardless of whether the barrier into which the slits are let is made of a conductor or an insulator etc.

If the interference pattern on the screen were due to some kind of interaction between the particles being defracted and the particles that formed the boundary of the slits, then you would need to have a convincing theory to account for the fact that the interference pattern seems only to depend on the wavelength associated with the particles being sent through the slits and not on any other factor.

• I think it is not that difficult to observe the effect of the material at the slits. If interference pattern was the result of some classical atomic interaction, then the experiment results would probably vary with the material's atomic weight, heat, density etc. I don't think scientists would miss that. But, I am not sure if they ever get unexpected results and interpret them in a way to fit into the quantum theory, while the actual explanation was different. Sep 22, 2021 at 18:43

Two things:

1. The particles do not interact with the edges of the slits. If they do, they lose coherence and that's that. This has been tested experimentally. Rather, they interact (so to speak) with the paths that are not available to them because of the barrier.

That a path not not-taken, but not available, can affect the the evolution of a wave function may sound like quantum woo...it isn't. It's just linear QM. Further insight can be gathered from the Elitzur-Vaidman bomb-tester, where the lack of an available path (or presence thereof), affects the evolution elsewhere.

1. In the Schrödinger equation set up of this, one would model a slit as a small region of $$V(x)=0$$, $$V(x)=\infty$$ elsewhere ($$x$$ is the transverse direction). With that, the potential lacks symmetry under translations in $$x$$, so that there should be no expectation that $$p_x$$ is conserved.

It's not a bug, it's a feature
It would be indeed a weird behavior for a particle. On the other hand, it is quite usual behavior for a wave - indeed, double slit experiment corresponds to rather usual diffraction phenomena that one can observed for the electromagnetic waves, waves on water, acoustic waves, etc. Thus, double slit experiment demonstrates the wave-like properties of electron (aka wave-partcile duality), which is precisely the point.

• We know that the direction of an electromagnetic wave changes while passing the boundary between two mediums. One possible explanation for refraction is that the electromagnetic wave interacts with the atoms and atoms provide the 'energy' required for the direction change. Maybe something similar is happening with the double slit experiments, i.e. no probability waves. But, it might be vice versa and what we call refraction might actually be some sort of double-slit phenomena occurring at atomic levels. Sep 22, 2021 at 16:12
• @Xfce4 Electron waves are better compared with water waves, since electrons cannot be absorbed and reemitted by screen. But they do interact with the screen, mostly via coulomb forces. Sep 22, 2021 at 16:57