Is Single Slit Diffraction Explained by the Heisenberg Uncertainty Principle?

[J O Linton]

TL;DR Summary

Does the quantum mechanical description of single slit diffraction imply randomness?

I have heard it suggested that the random scatter of photons passing through a single slit can be explained by appealing to the HUP. The slit constrains the particle in the Y direction introducing an uncertainty in the Y momentum. A simple calculation leads to a formula which is at least consistent with classical theory. To what extent is this argument valid and what implications does it have for the existence of randomness in nature?

 

[phinds]

I have heard

Just FYI, this is considered a terrible "citation" here on PF. WHERE have you heard? Best to either provide a valid citation or better still, just ask your question directly unless the citation is itself the source of your confusion.

Since there is a pattern that builds up on the receiving plate in the single slit experiment, clearly it is NOT random. It is probabilistic, based on the wave function. Each individual photon is seemingly random but it's really just indeterminate / probabilistic.

 

[PeterDonis]

I have heard it suggested

Where? Please give a specific reference.

 

[Nugatory]

To what extent is this argument valid and what implications does it have for the existence of randomness in nature?

That line of thinking works just fine (assuming it has been presented properly, which we can't tell from "I have heard") and allows us to calculate the probability distribution of photon detections at various points on the screen. To get from that probability distribution to an observed interference pattern we can either:
a) Assume that the probability distribution accurately describes a random process.
b) Assume that there is some deterministic process that we haven't discovered yet which controls where the photons are detected (and presumably if we knew what this process was we would be able to calculate the probability distribution from the first principles of that theory).

#a is quantum mechanics as it is practiced without interpretational baggage.
#b would be a lot more interesting if there were a candidate theory to consider, but so far no one has been able to come up with one.

 

[J O Linton]

I came across the idea a long time ago but a recent post is https://www.physicsforums.com/threa...ble-to-single-slit-diffraction.1060441/unread

In reply to phinds I do not wish to get into an argument over the meaning of the word random - but I hope we can agree that the precise position of an individual photon when it arrives at the screen is unpredicatable. The question is, as Nugatory has so eloquently explained, whether this unpredictability is inherent in the fundamental laws of Nature (i.e. the HUP) or whether it is due to some underlying but as yet unknown deterministic process.

In view of the fact that theorists (including Einstein) have been searching unsuccessfully for such a theory for 100 years now, isn't it time we gave up and admitted that there are events in Nature which inherently unpredictable and only governed by probabilistic laws?

 

[Gary Venter]

There is always measurement error, so the photon does not arrive at a point, but at a distribution. Thus it still has a degree of uncertainty and there is no reason to believe that this uncertainty departs from the mathematics of the wave equation. There is no evidence of a random choice being made.

 

[Vanadium 50]

What are you saying @Gary Venter ? Are you saying if we had better measurements we could beat the HUP? That is not true.

 

[Gary Venter]

No. With not just better but perfect measurement with no uncertainty at all (less than 10^-billion or 10-trillion, etc. cm), we would not have the determinism of the wave equation, and would need randomness. But such measurements are physically impossible so we are always within the realm of the wave equation. HUP would hold either way but wave mechanics would not be able to explain our observations in this impossible case.

 

[PeterDonis]

With not just better but perfect measurement with no uncertainty at all (less than 10^-billion or 10-trillion, etc. cm), we would not have the determinism of the wave equation, and would need randomness.

What are you basing this on? Do you have a reference? Is this a recognized model of some sort?

 

[Gary Venter]

Are you saying we would be able to explain measurement deterministically with the wave equation even if we could measure the location of a particle with zero uncertainty? I don't follow your question. What do you mean by "this?" Are you asking if the particle still follows the wave equation does that require it to be deterministic? Are you asking if the particle's location is uncertain, does that mean it must follow the wave equation?

 

[Vanadium 50]

You came and made a bunch of claims. We're asking you where you got them from.

 

[Gary Venter]

I thought it was well known that the wave equation is deterministic and that measurements always have a distribution. Is any of that new?

 

[PeterDonis]

I thought it was well known that the wave equation is deterministic

It's a deterministic equation for the wave function. The wave function gives proabilities for different possible measurement results. It does not deterministically predict a single measurement result (except in the edge case where the system is already in an eigenstate of the measurement operator).

measurements always have a distribution

A distribution which is predicted by the wave function. You do not appear to be taking into account this extremely important point.

 

[PeterDonis]

Are you saying...Are you asking...Are you asking

We're asking you where all these claims you are making are coming from. Personal theories and personal speculations are off limits here, and that is what your posts look like. If they're not personal speculation, if you are describing some actual theory or model that's in the literature, you need to give a reference.

 

[Gary Venter]

I thought I was just applying logic to known facts. Who are "we" by the way? Is this a committee?

 

[Gary Venter]

predicted by the wave function.

Yes. But the wave function describes a wave that stays a wave.

 

[PeterDonis]

I thought I was just applying logic to known facts.

You thought wrong. Do you have a reference for your claims or don't you?

Who are "we" by the way?

The people who have been asking you to back up your claims in this thread.

 

[Nugatory]

Who are "we" by the way?

So far, "we" is specifically the people who have asked for clarification of

With not just better but perfect measurement with no uncertainty at all (less than 10^-billion or 10-trillion, etc. cm), we would not have the determinism of the wave equation, and would need randomness.

and that is going to include me because I don't understand what you're trying to say here. I understand that the wave function evolves deterministically, I understand that its deterministic evolution lets me calculate a probability distribution for measurement results, I'm willing to accept as a hypithetical the infinitely precise measurement result that you describe (although it is not physically realizable as it would collapse the wave function to a delta function in position space, hence an unnormalizable plane wave in momentum space).
But I don't understand what "we would not have the determinism of the wave function" means, nor why we don't "need randomness" all along when we have a probability distribution of measurement results.

 

[Gary Venter]

Sorry. I was trying to get to the implications of impossible things, which is always a fraught project. Got you now. Forget what I said about what would happen if impossible things were done. I'm just saying that as long as measurements have uncertainty, as predicted by the wave function, and as long as the wave function itself evolves deterministically, we do not need new physics outside of the wave function to explain the results of measurement.

 

[PeterDonis]

as long as measurements have uncertainty, as predicted by the wave function, and as long as the wave function itself evolves deterministically, we do not need new physics outside of the wave function to explain the results of measurement.

In other words, QM works. Yes, it does. But that's a very general observation. What relevance does it have to the specific topic of this thread?

 

[Gary Venter]

Supporting case a mentioned above. The original question seems to imply there is a problem with QM. Also related discussions of "the measurement problem" that assert that QM is not enough are part of the context for the original question..

 

[Vanadium 50]

How does bringing up "impossible things" (especially if you don't immediately describe them that way) help the OP?

 

[PeterDonis]

Supporting case a mentioned above.

Mentioned where? Please quote posts that you are referencing.

The original question seems to imply there is a problem with QM.

Why?

related discussions of "the measurement problem" that assert that QM is not enough

Where? Please give specific references.