B Double slit probability question

[ueit]

Not right. The electron doesn't have any path or position at all except when it is interacting with something else, and that only happens at the source and at the screen.

The electron does interact with the slits. We know that for a fact because its momentum is changed. If the electron only interacts at the source and screen the slits should have no influence on the observed pattern which is not the case.

There is no justification for saying the that electron ever was at or passed through any point in the space between source and screen unless you actually put something (a detector? A random air molecule?. ...) for the electron to interact with at that point.

As I said before, there is something between the source and the screen, the slits.

There is also the point that the electron always interacts with all charged particles in the universe, as a result of it being charged and it always interacts with all massive particles in the universe as a result of it being massive.

An electron never interacts like a bullet, bumping into objects that happen to be in its path, that is a crude approximation.

 

[zonde]

If I understand correctly, yes, I would think so, in the general case, but not in my setup.

Well, but then we would have to extend your model and claim that electron is fired by both sources, right?

 

[Ostrados]

It has to be possible to travel through both slits for a single electron, otherwise I can't explain the possibility of a (possible) interference pattern.

It seems to me that only at detecting the electron it "has travelled" a certain path, right?

In you setup the wave function will not go in both slits it will collapse because the which path info is now revealed due to splitting the paths using a barrier (ex: if particle hits screen A then it came from slit A). Which is equivelent to measurment at slits in normal double slit experiement.

Note: which path info is enough to destroy the interferance even with no direct measurment (see delayed choice experiement).

No puzzle here .. I hope it is clear for you now.

 

[entropy1]

Well, but then we would have to extend your model and claim that electron is fired by both sources, right?

As far as I understand it, you suggest a setup with two sources. In a setup with two slits and one screen, I expect to see interference. In my setup, with two slits and two screens in two separated compartments, there would be two (separated) bulbs (maxima) and no interference pattern. What difference it makes to use two sources instead of one, I can't assess, but it seems to complicate the matter by the possibility of having two particles entering the boxes simultaneously; I don't know if these particles (wavefunctions) blend into one.

 

[mike1000]

Do the slits increase the number of possible paths? The narrower the slit the more undefined the momentum becomes, which I think would translate into an increase in the number of possible paths after the electron passes through the slit.

In other words, the number of possible paths is a function of 1)the number of slits and 2)how wide is each slit. Can I then jump to the conclusion that as the number of possible paths increases we see interference patterns because the electron can (and will) travel any of the possible paths.

 

[DrClaude]

Do the slits increase the number of possible paths? The narrower the slit the more undefined the momentum becomes, which I think would translate into an increase in the number of possible paths after the electron passes through the slit.

In other words, the number of possible paths is a function of 1)the number of slits and 2)how wide is each slit. Can I then jump to the conclusion that as the number of possible paths increases we see interference patterns because the electron can (and will) travel any of the possible paths.

The number of possible paths is always infinite.

 

[entropy1]

The number of possible paths is always infinite.

So what decides which one is actualized?

 

[DrClaude]

So what decides which one is actualized?

We don't know. As far as we understand, the (quantum) world is truly random.

 

[mike1000]

The number of possible paths is always infinite.

Well that kind of takes the uncertainty in momentum, caused by the electron passing through the narrow slit, out of the equation doesn't it? Let me rephrase it this way, passing through the slit causes the uncertainty in momentum which makes certain paths more probable.

 

[DrClaude]

Well that kind of takes the uncertainty in momentum, caused by the electron passing through the narrow slit, out of the equation doesn't it? Let me rephrase it this way, passing through the slit causes the uncertainty in momentum which makes certain paths more probable.

This is where the Feynman path formulation becomes very valuable. What the width of the slits do is change the relative interference of the different paths.

 

[entropy1]

In you setup the wave function will not go in both slits it will collapse because the which path info is now revealed due to splitting the paths using a barrier (ex: if particle hits screen A then it came from slit A). Which is equivelent to measurment at slits in normal double slit experiement.

What I don't get, is how a measurement behind the slits can fix which path the particle must have travelled. This seems a bit retrocausal to me. But maybe it doesn't, for detecting a single particle does not reveal which slit has been passed, right? It is only the emergence of a interference pattern that reveals if both slits were taken, a single particle does not reveal that.

 

[zonde]

What difference it makes to use two sources instead of one, I can't assess, but it seems to complicate the matter by the possibility of having two particles entering the boxes simultaneously; I don't know if these particles (wavefunctions) blend into one.

I proposed to consider two sources in reply to your statement that "The electron goes through both slits."
My intention was to show that while your statement might seem strange but somewhat imaginable with single source, it becomes much more stranger when you consider interference from two sources.
For setup with no interference (like your two boxed screens) it does not add much, of course.

 

[Ostrados]

What I don't get, is how a measurement behind the slits can fix which path the particle must have travelled. This seems a bit retrocausal to me. But maybe it doesn't, for detecting a single particle does not reveal which slit has been passed, right? It is only the emergence of a interference pattern that reveals if both slits were taken, a single particle does not reveal that.

If you look at delayed choice experiement it is even more weird, it truley appears as retro causal. This is the main puzzle in QM nobody has answer to it.

However if you think about it from conservation of energy point of view, then you will discover that what is hapening is a natural thing to happen as a consquence of superposition. It is not easy to explain it but you can think about it that if you can detect the photon at both slits then you will have extra copy of the photon which violates conservation of energy.

 

[entropy1]

We don't know. As far as we understand, the (quantum) world is truly random.

So, when choosing path A or Path B, the choice is truly random? The screens have a different spatial and temporal distance from the source. Which screen is the one that makes de decision to register the impact of the electron? Or: how does the electron 'choose' which slit to take?

 

[Mentz114]

So, when choosing path A or Path B, the choice is truly random? The screens have a different spatial and temporal distance from the source. Which screen is the one that makes de decision to register the impact of the electron? Or: how does the electron 'choose' which slit to take?

In the pilot wave theory the randomness comes from not being able to control the initial conditions. There's cool diagram here of electron trajectories
https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory

 

[BvU]

Screens don't make decisions, electrons don't choose. Why don't you quit trying to make this kind of mental image -- it really restricts you

 

[entropy1]

• So, the electron goes to setting A;
• Or the electron destroys itself on something else before passing a slit;
• Or the electron goes to setting B.

The probability ratios between these depend on the width of the slits in comparison to the size of the rest of the volume.

There is a formula to calculate the probability of every possible path. Which path will be taken is a matter of pure random chance.

Am I right?

 

[StevieTNZ]

I thought the answer is in post #21, confirmed in post #22?

 

[entropy1]

I thought the answer is in post #21, confirmed in post #22?

That was adressed in #35.

 

[bhobba]

I forget if I mentioned it before in the thread but before discussing the double slit plese read:
https://arxiv.org/abs/quant-ph/0703126

Once you understand the above - the question is - why do you think the particle has any properties other than what occurs at observations? Why does it have a path, why is it a wave - indeed anything at all other than something like probability of an observation if you were to do one.

Thanks
Bill

 

[bhobba]

The electron goes through both slits. Why would it go through one slit?

Why would it go through any slit. You are thinking in terms of Feynman's sum over histories approach. Although not usually pointed out it is in fact an interpretation, but of a rather novel kind. But it is still an interpretation - you can't actually say anything apart from an actual observation.

The double slit is simply a demonstration of two important concepts in QM

1. The uncertainty principle
2. The practical application of the principle of superposition.

Thanks
Bill

 

[StevieTNZ]

Then after a while, the the electron could hit screen A. The probability is 50% that it actually does.

If the electron does not impact screen A, the probability it will impact screen B is 100%!

So, what does select which screen, A or B, will be hit? If it is collapse, why does screen A collapse the wavefunction 50% of the time, and when it doesn't, why does it collapse at screen B 100% of the time left? Or do both screens collapse 50% of the time and is there retrocausality from B to A? Or is there no collapse? Is there a non-local effect? Et cetera. Or is it just the way it is (do the math and so forth )

Which-way information is available, so there would be no interference. It has 50% probability of going through slit A, or 50% probability of going through slit B. But then again, screen A is closer than screen B, so... hmmm, interesting question!

 

[BvU]

At the risk of @entropy1 starting this thread from post #1 again:

One thing to consider is that many aspects of "modern physics" are not intuitively obvious
since they may occur at very small or very large scales, high speeds, or many particles (which may not behave like "everyday objects").

This famous lecture by Feynman seems appropriate here.

A fuller reference is below (with an interactive transcript).
This version on YouTube has the intro trimmed and gets right to the lecture.


A useful passage [at about 3m08s above, or 4m12s below]:
For more info on this series of lectures:
http://www.cornell.edu/video/richard-feynman-messenger-lecture-6-probability-uncertainty-quantum-mechanical-view-nature

 

[entropy1]

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.

 

[BvU]

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

It's not the question, it's the anxiety about your mental image of a quantum particle and 'our' trouble shoving you in a particular direction. So just keep going ! You're not the first (witness the double slit threads in PF) and certainly won't be the last.

It turns out to be very difficult to provide assistance at the appropriate level -- appropriate in the sense that it really helps someone to adjust their conception of what's going on. The alleged "shut up and calculate" isn't very useful in this context (you don't want to calculate, you want to understand). But Feynman's lectures are.

 

[bhobba]

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

It's because it's full of implied assumptions all of which are open to question eg you speak of a classical situation controlled by a switch - but in QM we don't have a path little alone anything that controls it.

You have tied yourself into logical knots and confusion by thinking classically - don't do that and your confusion will disappear. It's the hardest thing in the world to do - but to make progress in QM you must.

Have you read the paper I linked to?

Thanks
Bill

 

[entropy1]

Disputed #2 also seems applicable to me in this thread!

 

[entropy1]

Have you read the paper I linked to?

I have downloaded it, but I can't read it overnight; my reading (and interpreting of what I read) capability is very limited currently. So, maybe later and thanks.

UPDATE: Reading it now.

 

[bhobba]

It turns out to be very difficult to provide assistance at the appropriate level -- appropriate in the sense that it really helps someone to adjust their conception of what's going on. The alleged "shut up and calculate" isn't very useful in this context (you don't want to calculate, you want to understand). But Feynman's lectures are.

We all have been through it. I walked around thinking about Schrodinger's cat, double slit, all the stuff that gets asked around here. Then the light slowly dawned and it was so simple - the classical world emerges from the quantum - you can't explain the structure the world is based on by appeals to intuition developed in that structure. Both Bohr and Einstein fell into that trap:
http://physicstoday.scitation.org/doi/pdf/10.1063/1.2155755

So don't feel silly, stupid or any other such response. Simply concentrate on avoiding classical analogies.

Thanks
Bill

 

[entropy1]

Simply concentrate on avoiding classical analogies.

If you replace 'train' by 'particle' (when produced or detected!), you have the quantum version of my question, it seems to me.

It was never my intention to draw classical analogies; if you look around this thread you may find I responded classical to classical questions of participants!

So, correct me if I'm wrong, I think you mean I should SUAC?

Hint: do I have to study states and wavefunctions to understand my question?

 

[entropy1]

Have you read the paper I linked to?

The math is fairly straightforward though I often can't see what the i and ħ and so on do. But I think I get the point.

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

 

[Karolus]

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.

back to the experiment. If I understand the question is, "as a guide mechanism of the electron on the screen" A ", rather than on screen B"? In the case of trains, the answer is: the switch. But in the case of trains there are the tracks, the railroad, in the electron case there is no track, this is where the crucial point, there is not even a "path" that leads to the screen by the electron source. There are not even "trajectories", in the classical sems of the term. Between the source and the two slits, one that propagates is only a wave. Wave of what? A Like it or not, is a wave of probability.

 

[entropy1]

Wave of what? A Like it or not, is a wave of probability.

So, what 'makes' the probability 'collapse' to a detection? You could (would) say: random chance. Then, the total sum of probabilities in the wave would have to be 1, right?

And it has to keep having a total probability of 1 over the time it is evolving?

 

[Ostrados]

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

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]

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"

You might not like these answers, but that doesn't make them wrong.

The correct answer: nobody in the world knows, our understanding and knowledge are limited and our theories are incomplete .. period

No, the correct answer is that the actual world does not behave the way your classical intuition says it ought to behave. Quantum mechanics is an experimentally verified theory within the domain we are discussing. We are not suggesting that you stop thinking classically because of some abstract notion. We are suggesting that you stop thinking classically because the actual world does not work classically. That's what our experiments in the quantum realm have shown us. So if you want to understand how the actual world works, you need to stop thinking classically.

It is true that our theories are incomplete; but that does not mean they contain zero information. We don't have complete knowledge, but we have enough knowledge to know that classical physics doesn't work.

 

[Ostrados]

So, what 'makes' the probability 'collapse' to a detection? You could (would) say: random chance. Then, the total sum of probabilities in the wave would have to be 1, right?

And it has to keep having a total probability of 1 over the time it is evolving?

Probabilty 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)

 

[Ostrados]

No, the correct answer is that the actual world does not behave the way your classical intuition says it ought to behave. Quantum mechanics is an experimentally verified theory within the domain we are discussing.

There is big difference between one thing to be experimentally proven, and to be correctly interpreted. The problem is that we still have no complete satisfying classical or non-classical explanation.

Btw why cannot we have a non-classical explanation that makes sense? Is that too much to ask?!

 

[PeterDonis]

There is big difference between one thing to be experimentally proven, and to be correctly interpreted.

What does "correctly interpreted" mean? Why do you need an interpretation? The theory already tells you how to make predictions, and the predictions are confirmed by experiment. What more do you want?

why cannot we have a non-classical explanation that makes sense?

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.

 

[Karolus]

So, what 'makes' the probability 'collapse' to a detection? You could (would) say: random chance.

Not exactly, what makes "collapse" the wave function, is the detection same!
while the probability of detect the electron at that point, is proportional to the square of the wave function at that point

Then, the total sum of probabilities in the wave would have to be 1, right?
And it has to keep having a total probability of 1 over the time it is evolving?

Yes... before you make a measurement or observation.

 

[entropy1]

Not exactly, what makes "collapse" the wave function, is the detection same!

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.

 

[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]

Probabilty 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 somone and say "look it was a wave but because I watched it the wave collapsed and it became a particle".