Double slit experiment and the Uncertainty Principle

[Axel Togawa]

TL;DR Summary

In the double slit experiment, how the uncertainty principle contribute to verify the complementary principle?

With the double slit, experiment we show the double nature of light and matter as wave and particle. In particular, the so called "which way" thought experiment illustrate the complementary principle. In my book, this experiment is analyzed putting a series of particles in front of one of the two slit, so when the electron pass through the slit it scatter with the particles, changing the component of the momentum perpendicular to the direction of motion ΔpyΔpy. Using the uncertainty principle, it's said that the uncertainty on the position of the electron is now Δy<<DΔy<<D with DD the distance between the two slits, and consequently, ΔpyΔpy is so large that the interference pattern is destroyed. But since the uncertainty principle represents an intrinsic property of the electron, independently of the measurement (correct me if I'm wrong), even if I don't alter the state of the electron but can still determine in which slit the electron crosses (I don't know if it's possible), the interference pattern should be destroyed. Doesn't that mean that considering the scattering I should take into consideration the uncertainty principle and the uncertainty due to the scattering?

 

[Nugatory]

But since the uncertainty principle represents an intrinsic property of the electron, independently of the measurement...

It’s not. It’s an inherent property of the state, and an interaction that produces which-way information leads to a different state than an interaction that does not.

 

[DrChinese]

It’s not. It’s an inherent property of the state, and an interaction that produces which-way information leads to a different state than an interaction that does not.

Of course this is absolutely correct. But I thought I would throw this in for the OP to consider:

Use a double slit setup with photons rather than electrons. Place a polarizer over each of the 2 slits.

a. When the 2 polarizers are aligned parallel, there IS interference.
b. When the 2 polarizers are aligned perpendicular (orthogonal), there is NO interference.

In either case, the light is passing through a polarizer. Only their relative orientation changes. Obviously the scattering here is not a factor. The interference disappears when it is possible to determine "which slit" information, regardless of whether one does so or not.

Or you could say it is because the system is placed into a different state.

 

[bhobba]

I think the OP would benefit from reading Demystifier's paper on myths in QM:
https://arxiv.org/abs/quant-ph/0609163

Thanks
Bill

 

[CallMeDirac]

Summary:: In the double slit experiment, how the uncertainty principle contribute to verify the complementary principle?

With the double slit, experiment we show the double nature of light and matter as wave and particle. In particular, the so called "which way" thought experiment illustrate the complementary principle. In my book, this experiment is analyzed putting a series of particles in front of one of the two slit, so when the electron pass through the slit it scatter with the particles, changing the component of the momentum perpendicular to the direction of motion ΔpyΔpy. Using the uncertainty principle, it's said that the uncertainty on the position of the electron is now Δy<<DΔy<<D with DD the distance between the two slits, and consequently, ΔpyΔpy is so large that the interference pattern is destroyed. But since the uncertainty principle represents an intrinsic property of the electron, independently of the measurement (correct me if I'm wrong), even if I don't alter the state of the electron but can still determine in which slit the electron crosses (I don't know if it's possible), the interference pattern should be destroyed. Doesn't that mean that considering the scattering I should take into consideration the uncertainty principle and the uncertainty due to the scattering?

It would be basically impossible to see which slit it went through without altering the state, even that considered it is not the observation that does this.

It is stated in ¨ the grand design¨ by Stephen Hawking ( A great book if you haven't already read it) that the electron takes not one, but all paths through the slit gaining the information that dictates the slit it goes through

 

[PeterDonis]

the grand design¨ by Stephen Hawking

This is a pop science book, not a textbook or peer-reviewed paper, and is not a valid source for PF discussion.

 

[CallMeDirac]

This is a pop science book, not a textbook or peer-reviewed paper, and is not a valid source for PF discussion.

This is a pop science book, not a textbook or peer-reviewed paper, and is not a valid source for PF discussion.

It is a very popular book and it is recognizable. It is more likely someone would recognize that over a 200 page research project behind a $30 paywall.

 

[PeterDonis]

It is a very popular book and it is recognizable.

Which is irrelevant to whether or not it is a valid source for PF discussion. It isn't.

 

[Nugatory]

It is a very popular book and it is recognizable. It is more likely someone would recognize that over a 200 page research project behind a $30 paywall.

Nonetheless it shares the defect of most pop-sci treatments of quantum mechanics: without the math it cannot provide a complete and accurate statement of the theory so cannot be used as the basis for a more complete understanding. In particular, the bit about the electron “taking all paths” is very misleading if taken literally.