Double slit probability question

[bahamagreen]

Just to be clear... How does QM view this?

The detector can only indicate the presence of an electron at a place and time - not its motion. So the placement of the detector on either side of a slit does not confirm or deny passage of the electron through the slit; only that an electron was detected at the location of the detector.

Even if the detector was placed within the plane of the slit, not only can the detector not indicate which direction the electron might be presumed to have passed through the slit, but not even that the electron did pass through the slit, for such ideas of "passage" would include a path for the electron that was within the plane of the barrier that has the slits, such a path not going from one side of the slit to the other in either direction.

So all the detector can indicate is "there be an electron at this place at this time", but no information about whether it is moving or which way or how fast, so to speak.

If all this is true, how can there even begin to be any talk about the electron being directed to the slits, approaching the slit barrier, passing through one slit, which slit, both slits, etc?

 

[PeterDonis]

If all this is true, how can there even begin to be any talk about the electron being directed to the slits, approaching the slit barrier, passing through one slit, which slit, both slits, etc?

There can't. Or more precisely, any such talk is interpretation, not physics.

 

[Mentz114]

Just to be clear... How does QM view this?

The detector can only indicate the presence of an electron at a place and time - not its motion. So the placement of the detector on either side of a slit does not confirm or deny passage of the electron through the slit; only that an electron was detected at the location of the detector.
..

It depends on the details of the detector. It can be designed so that it fires only if hit from a certain angle. If there is some knowledge available about the location of the source, then a momentum measurement has been made, because we now have more information about it.
Which path information requires a momentum measurement - and alway disturbs a subsequent position measurement. hence upsetting the interference pattern. I thoght that was QM 101.

 

[bhobba]

It is a pity asking question about this (or any) paper is off topic.

Which paper?

The one I gave?

It most certainly is on topic, so ask away.

In fact its been criticized:
https://arxiv.org/pdf/1009.2408.pdf

But its not at beginner level - start at least an I level thread if you want to discuss the objection.

And even the above objection can be criticized - but that is an A level thread that I will listen to the knowledgeable peoples comments rather than actively participate - Vanhees for example has already in other posts pointed out issues with it.

Unfortunately physics is sometimes like that.

Thanks
Bill

 

[bhobba]

I don't like these answers, typical autoresponse in QM world, "dont think classicaly and confusion will disappear" is no better than saying "shut up and calculate" The correct answer: nobody in the world knows, our understanding and knowledge are limited and our theories are incomplete .. period

PeterDonis gave an EXCELLENT answer .

I just want to point out shut up and calculate is entirely different to a non classical understanding of QM. Many many people, and with all due modesty I believe I am one of then, understands QM - but it can't be done classically. And when you think about it it would be strange if you could - QM explains the classical world - operating in the same way as what it explains would seem rather too convenient and would itself be a strange mystery.

First, to try and understand QM on its own terms study an actual interpretation. A good modern one is Consistent Histories which the textbook on it has kindly been made available for free by the author:
http://quantum.phys.cmu.edu/CQT/index.html

That is just a start - but a good one.

BTW that's the mistake both Einstein and Bohr made in their magnificent debates and alluded to by Weinberg in my link - but that is a whole new story and thread.

Thanks
Bill

 

[bhobba]

probability wave and wave collapse are just part of the standard interpretation for QM not the ultimate truth. There are many other interpretations, if you want a classical interpreration that includes no superposition and no weirdness then look at Pilot Wave theory (however it has the concept of global non localty which is harder to digest)

Pilot wave theory - no weirdness? - eg it pretty much implies a preferred frame that breaks symmetry which QFT has shown is quite fundamental. That is debatable but the topic for another thread.

BTW - that in no way demeans or challenges BM as a legit interpretation - its just all of them have issues.

Also BTW the standard QM formalism does not have wave function collapse - its an interpretation thing. I don't even think BM does - but our resident BM expert Dymystifyer can comment more on that.

Thanks
Bill

 

[bhobba]

If all this is true, how can there even begin to be any talk about the electron being directed to the slits, approaching the slit barrier, passing through one slit, which slit, both slits, etc?

You can't - its all explained in the paper I liked to.

First consider a single slit and a for practical purposes an infinite screen.

Put a detector just behind the slit. The particle will always be detected there - not at some other place on the slit screen. So we know just behind the slit it has a definite position. 100% knowledge of position - zero knowledge of momentum (that's the uncertainty principle), so if you were to measure the momentum of the particle it could be any crazy value ie travel in any direction (note KE has not been changed so only direction is altered). And that is exactly what is found in the single slit experiment - the screen acts as a momentum detector by telling which direction it went in when measured. When not measured - who knows - QM only talks about measurements.

Now let's have two slits. What is the wave function just behind the screen now? Well we know what it is with one slit - a Dirac delta function of position. But QM almost shouts at you the answer - due to the symmetry of the situation its a superposition of two Dirac Delta functions. And low and behold when you work through the math of that you get your interference pattern.

It not wave particle duality, collapse etc etc. Its simply elucidation of two key principles of QM I mentioned before.

Thanks
Bill

 

[Ostrados]

Because your criterion for "makes sense" is "makes sense to me given my existing intuitions". But by that criterion, General Relativity doesn't make sense--to anyone who learned Newtonian physics. Evolution doesn't make sense--to anyone who was taught creationism. And so on. Sometimes your existing intuitions simply don't apply, and you have to learn new ones. Then your definition of what "makes sense" changes. If you don't allow for that possibility, some things will never make sense to you.

You can come up with a logical non-classical interpretation why not?! (There are plenty actually). Why do I have to lock my thinking to old outdated interpretation?

 

[PeterDonis]

You can come up with a logical non-classical interpretation why not?! (There are plenty actually).

Then what's the problem? You were objecting to being told not to think classically, but now you say there are non-classical interpretations, and you are ok with them? Then I don't understand what you're objecting to.

Why do I have to lock my thinking to old outdated interpretation?

Who is saying you do? You were the one objecting to being told to think non-classically.

Also, you don't have to "lock" your thinking to any interpretation. The interpretations aren't the physics. You can use whichever one you want; they all make the same predictions anyway.

 

[Ostrados]

Then what's the problem? You were objecting to being told not to think classically, but now you say there are non-classical interpretations, and you are ok with them? Then I don't understand what you're objecting to.

"dont think classicaly" became autoresponce answer, it is not an answer it is avoiding to answer. I prefer saying the plain truth that our best theories cannot answer this question.

Classical or non-classical I don't mind just give me an explanation that does not make me feel insane when I talk to someone and say "look it was a wave but because I watched it the wave collapsed and it became a particle".

 

[PeterDonis]

I prefer saying the plain truth that our best theories cannot answer this question.

What question?

just give me an explanation that does not make me feel insane when I talk to someone and say "look it was a wave but because I watched it the wave collapsed and it became a particle".

The explanation is the math of QM. Not interpretations. Interpretations don't predict what happens; they just give some people a story to tell after they have already calculated what happens using the math of QM. But the story is not the physics; it's just a crutch some people appear to need because the math of QM and its successful predictions aren't enough for them.

 

[Nugatory]

Classical or non-classical I don't mind just give me an explanation that does not make me feel insane when I talk to someone and say "look it was a wave but because I watched it the wave collapsed and it became a particle".

Pretty much any interpretation that doesn't include collapse will meet that need: MWI, Bohmian, sum-over-paths, minimal statistical all come to mind. MWI might make you feel insane for other reasons... but if it does you have plenty of others to choose from.

 

[Karolus]

I don't entirely understand this sentence. English is not my mother language. In case you made a mistake, would you care to retype it? I almost understand it.

I borrow from wikipedia (I hope that English is clearer):
In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation")

 

[Karolus]

Just to be clear... How does QM view this?

The detector can only indicate the presence of an electron at a place and time - not its motion. So the placement of the detector on either side of a slit does not confirm or deny passage of the electron through the slit; only that an electron was detected at the location of the detector.

Even if the detector was placed within the plane of the slit, not only can the detector not indicate which direction the electron might be presumed to have passed through the slit, but not even that the electron did pass through the slit, for such ideas of "passage" would include a path for the electron that was within the plane of the barrier that has the slits, such a path not going from one side of the slit to the other in either direction.

So all the detector can indicate is "there be an electron at this place at this time", but no information about whether it is moving or which way or how fast, so to speak.

If all this is true, how can there even begin to be any talk about the electron being directed to the slits, approaching the slit barrier, passing through one slit, which slit, both slits, etc?

I am in a sense agree ... In fact the proposed experiment could be equivalent to a source and two detectors (without slits, partitions or other ..)

 

[ueit]

To make this clear: I do not claim that photons or electrons behave like particles or waves at some point; I was just reacting to remarks from others in this thread. So I want to make clear once more what my question is:

Suppose you have a train moving along the railway track X, is passes a switch and ends up at some other track, say track A. Another train on track X passes the same switch and ends up at the alternative track, say track B.

The question would be: what determined on which track the train ends up. The answer would be obvious: the switch!

So, if a train sets off on X, we don't look at any switch, and we 'detect' that a train ended up on track A, what determined we would detect a train on track A rather than track B, or vice-versa? (We could not claim it was the switch)

I am sensing some annoyance over my question but I cannot tell why.

The electron interacts with the material of the slits (electrons and nuclei) via electromagnetic interaction. As a result, a momentum exchange between the electron and the particles in the slits takes place.

In order to understand why an electron goes in one direction or the other you need to know all the details regarding the incoming electron and the microscopic structure of the slits.

 

[BvU]

In order to understand why an electron goes in one direction or the other you need to know all the details regarding the incoming electron and the microscopic structure of the slits.

You wouldn't get a single iota further. Especially not in the context of this thread.

 

[ueit]

You wouldn't get a single iota further. Especially not in the context of this thread.

So you are claiming that understanding the interaction that is responsible with the momentum transfer is irrelevant in understanding the momentum transfer, right?

 

[entropy1]

In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation")

Thank you. So if I understand correctly, the probability (amplitude) of a collapse to occur is given by the wave function?

So it could tick off the detector, but it could also tick the wall of the box the detector is in, and so forth?

Or can a detector 'attract' a detection?

 

[Karolus]

Thank you. So if I understand correctly, the probability (amplitude) of a collapse to occur is given by the wave function?

So it could tick off the detector, but it could also tick the wall of the box the detector is in, and so forth?

Or can a detector 'attract' a detection?

I try to be simple. We have our own wave function, we say that is a function of the x coordinate of the type $f (x) = \cos(x)$. (Not normalizzabile etc, it does not matter) In this state, the electron is "everywhere" in the region$-\infty \leq x \leq \infty$ Where he is exactly, it is a question that has no sense.
I know that the probability that the electron is detected at point $x_0$ is proportional to $|f (x_0)|^2$. Suppose that this value is 0.3 (ie 30%).
Suppose we put the detector at the point $x_0$. The detector can detect the electron (with a click) or not. At the time that the electron has detected electron, f (x) does not exist anymore ... because our electron is so to speak collapsed at the point $x_0$, there where we put our detector.
So there is no attraction or anything, just a probability of detecting the particle at point x.
Things are a little more complex, because in this case, the detector, could be a "shot" photon at point $x_0$. if I have so many electrons equal, with the same wave function, 3/10 the photon will detect the electron at point $x_0$

 

[entropy1]

So, the electron 'is' not anywhere when not detected, but the probability it is detected at some position can be calculated from te wavefunction.

 

[ueit]

So, the electron 'is' not anywhere when not detected, but the probability it is detected at some position can be calculated from te wavefunction.

QM does not say that the electron is not anywhere and it doesn't say there is somewhere either. It just allows you to calculate the probability of detection.

 

[zonde]

You have tied yourself into logical knots and confusion by thinking classically - don't do that and your confusion will disappear.

Getting rid of confusion by all costs is not sensible. Scientific thinking is subset of classical thinking and it is not very sensible idea to get rid of that part of classical thinking. So if you can't be more specific I would say your suggestion is rather useless.

 

[BvU]

Scientific thinking is subset of classical thinking

That wouldn't be good ! Perhaps you meant it the other way around ?

 

[mike1000]

I try to be simple. We have our own wave function, we say that is a function of the x coordinate of the type $f (x) = \cos(x)$. (Not normalizzabile etc, it does not matter) In this state, the electron is "everywhere" in the region$-\infty \leq x \leq \infty$ Where he is exactly, it is a question that has no sense.

I like your example. Let's pretend that the wave function is given by Ψ(x) = cos(x). That is just the probability distribution for the location of the electron. It is a statement of our lack of knowledge of where the electron is located. (I know that cos(x) cannot be a true wave function because it is not square integrable, which is a requirement to have a finite dot product and finite probabilities.) It is not saying the electron is everywhere or no where, it is just the probability distribution associated with the electron at that time.

Position (and momentum) of the electron are random variables in quantum mechanics. As such their possible values are randomly distributed by some, yet to be understood, process.

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable quantity whose possible values depend, in random manner, on a set of random outcomes events.[1] It is common that the outcome depends on some physical variables that are not well understood.

https://en.wikipedia.org/wiki/Random_variable

 

[zonde]

That wouldn't be good ! Perhaps you meant it the other way around ?

No, I meant it the way I wrote it.
There is some basis from which you do any further thinking. You can't start any reasoning from nothing. And in order to have meaningful discussion we have to have common basis. In science this common basis is scientific method and any prerequisites that are required for application of scientific method.

 

[PeterDonis]

the probability (amplitude) of a collapse to occur is given by the wave function?

If you are using a collapse interpretation. But there are interpretations that don't have collapse (such as the MWI).

 

[entropy1]

If you are using a collapse interpretation. But there are interpretations that don't have collapse (such as the MWI).

I ment 'collapse' in the sense of 'detection'.

 

[entropy1]

So, the electron 'is' not anywhere when not detected, but the probability it is detected at some position can be calculated from te wavefunction.

QM does not say that the electron is not anywhere and it doesn't say there is somewhere either. It just allows you to calculate the probability of detection.

I thought it was a fairly straighforward question; but I think we are on the same track here.

 

[PeterDonis]

I ment 'collapse' in the sense of 'detection'.

That clarifies what you meant, but you should realize that this is very confusing terminology, since "collapse" has a precise technical meaning in QM, which is not the same as "detection". It's much better to say "detection" if that's what you mean.

 

[entropy1]

That clarifies what you meant, but you should realize that this is very confusing terminology, since "collapse" has a precise technical meaning in QM, which is not the same as "detection". It's much better to say "detection" if that's what you mean.

I was thinking that a detection and a collapse were similar in the sense that in case of position/momentum uncertainty a detection yields position-information and for that to be possible the wavefuntion has to collapse in a way that the position is known. (sorry for the layman way of expressing this)

I am aware that two different terms usually refer to different concepts.