Undergrad Can Quantized Momentum Transfer Explain Double-Slit Interference Patterns?

[Ali Lavasani]

In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron. Here, the whole slit structure is regarded as a quantum object with several eigenstates, which transfers a quantized momentum to the incident particle. Momentum quantization is a result of the "Duane's quantization rule".

My question is, how come can a large macroscopic object like the slit structure be a quantum object? What determines what eigenstate it's in (the configuration of its atoms or something else for example)? The author admits that the mechanism of the momentum transfer is unknown, so isn't such an explanation weird, and why should it be considered?

 

[jambaugh]

Ali, all objects are quantum. objects. Most are just so big that we can use a gross classical description.

As to Duane's quantization rule, in the original paper: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1085314/pdf/pnas01878-0020.pdf see section 5, where he points out: "The reasoning by which we have deduced Braggs' law [...] cannot be considered a logical demonstration. We may regard the reasoning, however as a means of suggesting equations to be tested[empirically]."

In reading the paper you can see that he is working heuristically, starting with the hypothesis of quantized momentum exchange and pulling relevant parameters such as atomic spacing an Plank's constant to assign a value to this quantum of momentum exchanged. There is not attempt to claim any further mechanism in this. It is not an explanatory hypothesis but rather merely a derivational one. I am not inclined to pay to see this recent article since the abstract does not suggest she has added anything significant to Duane's 1923 paper.

 

[DrChinese]

... the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron. Here, the whole slit structure is regarded as a quantum object ... The author admits that the mechanism of the momentum transfer is unknown, so isn't such an explanation weird, and why should it be considered?

If the interference pattern was due to the slits, how is it that covering one up does not produce an interference pattern? There's still a slit!

I looked, but could not locate a free version of her work to read. So I could not determine the reasoning. However, the slit itself would not be the source of interference. It is instead responsible for the shape of the interference bands.

I would not consider this a suitable article to base any conclusion on.

 

[lodbrok]

In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron. Here, the whole slit structure is regarded as a quantum object with several eigenstates, which transfers a quantized momentum to the incident particle. Momentum quantization is a result of the "Duane's quantization rule".

The fact that there is momentum transfer in diffraction should not be surprising. You can't have change of direction without momentum transfer. Therefore it is obvious that all particles going through slits change direction due to momentum transfer. But why does this transfer exhibit the pattern observed in diffraction and interference patterns? (ASIDE: Note that diffraction and interference patterns are physically the same phenomena). I think Duane's original paper and the paper you cited are trying to answer this question.

It is interesting that momentum transfer is already used in standard treatments of diffraction from more complex systems such as crystals, where reciprocal space (really momentum space) is used to describe and represent the diffraction pattern. Where the reciprocal lattice vector corresponds to the momentum transfer vector. In this sense it is commonly understood that the momentum is transferred to crystal momentum. (See for example https://en.wikipedia.org/wiki/Ewald's_sphere)

See also this paper https://doi.org/10.1016/j.cis.2013.10.025

 

[Ali Lavasani]

The fact that there is momentum transfer in diffraction should not be surprising. You can't have change of direction without momentum transfer. Therefore it is obvious that all particles going through slits change direction due to momentum transfer. But why does this transfer exhibit the pattern observed in diffraction and interference patterns? (ASIDE: Note that diffraction and interference patterns are physically the same phenomena). I think Duane's original paper and the paper you cited are trying to answer this question.

It is interesting that momentum transfer is already used in standard treatments of diffraction from more complex systems such as crystals, where reciprocal space (really momentum space) is used to describe and represent the diffraction pattern. Where the reciprocal lattice vector corresponds to the momentum transfer vector. In this sense it is commonly understood that the momentum is transferred to crystal momentum. (See for example https://en.wikipedia.org/wiki/Ewald's_sphere)

See also this paper https://doi.org/10.1016/j.cis.2013.10.025

In the paper I cited, the interference pattern is justified using the "momentum transfer". The author herself admits that "the mechanism of the momentum transfer is unknown". She just removes the probability wave and replaces it with "momentum transfer from the slits to the particle", where the particle is equally probable to go throw each of the slits, and also equally probable to go toward any direction after passing one of the slits. Basically, the math is equivalent to the orthodox Copenhagen interpretation using probability wavefunction, and that's why I'm asking why one should consider this model.

 

[Ali Lavasani]

If the interference pattern was due to the slits, how is it that covering one up does not produce an interference pattern? There's still a slit!

I looked, but could not locate a free version of her work to read. So I could not determine the reasoning. However, the slit itself would not be the source of interference. It is instead responsible for the shape of the interference bands.

I would not consider this a suitable article to base any conclusion on.

The math is kinda equivalent to that of the orthodox explanation. The author considers equal probabilities for the particle passing throw each slit (kinda superposition), and when a slit is chosen, the particle can go toward any direction with equal probabilities depending on the transferred momentum which is stochastic (kinda equivalent to the spherical wave math), and then somehow proves that the pattern would be proportional to the Fourier transform of the slit structure's geometry. I think the theory is mathematically equivalent to the orthodox theory, with just a different interpretation, of course a weird one, invoking an "unknown" momentum transfer mechanism. The author has in fact gotten rid of "wave-particle duality" with invoking other weird things (unknown momentum transfer mechanism, nonlocality because of the need for the periodicity of the slit structure, etc.). This is why I don't get the point of this paper.