# B Double slit probability question

#### PeterDonis

Mentor
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 somone 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

Mentor
Classical or non-classical I dont 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")

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#### 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

Homework Helper
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

Gold Member
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

Gold Member
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

Gold Member
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

Homework Helper
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. Lets 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

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#### zonde

Gold Member
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

Mentor
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

Gold Member
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

Gold Member
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

Mentor
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

Gold Member
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.

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#### PeterDonis

Mentor
I was thinking that a detection and a collapse were similar
No, they're not, because "detection" is interpretation-independent: it's something that's directly observed. "Collapse" is interpretation-dependent: some interpretations of QM have collapse, some don't, and we don't directly observe collapse, we only directly observe detection.

in case of position/momentum uncertainty a detection yields position-information and for that to be possible the wavefuntion has to collapse
Only in collapse interpretations. In no collapse interpretations (the MWI, for example), it doesn't.

#### Nugatory

Mentor
n case of position/momentum uncertainty a detection yields position-information and for that to be possible the wavefunction has to collapse in a way that the position is known.
That cannot be right.... It sounds as if you are saying that we cannot make a position measurement if there is no collapse. But we already know that quantum mechanics works just fine, for measurements of position as well as everything else, without introducing the concept of collapse.

#### bhobba

Mentor
So you are claiming that understanding the interaction that is responsible with the momentum transfer is irrelevant in understanding the momentum transfer, right?
No - he is claiming what the formalism of QM says.

Its simple - so simple many don't get it. It took me a while to get it - but that's just because its in plain sight and you gloss over the obvious.

The formalism is a theory about observations that occur in a common-sense classical world. Whats going on when not observed - momentum transfer yada yada yada the theory is silent on.

This raises the legit issue of QM - the issue ignored by Einstein and Bohr which is why they both have issues (I wont say wrong - its simply a blemish that's best fixed - Weinberg is a bit more prosaic). How does a theory that assumes a classical world from the start explain that world. Great progress has been made in fixing that up, but some problems remain. What those issues are (the factorization problem, key theorems elucidating the problem, and other key theorems associated with decoherence - there are others as well) are (at least in part) detailed here:
https://www.amazon.com/Understanding-Quantum-Mechanics-Roland-Omnès/dp/0691004358

Thanks
Bill

#### bhobba

Mentor
No, they're not, because "detection" is interpretation-independent: it's something that's directly observed. "Collapse" is interpretation-dependent: some interpretations of QM have collapse, some don't, and we don't directly observe collapse, we only directly observe detection.
Go to a library, or in some other way, get a copy of Ballentine.

QM is based 2 axioms - none of which includes collapse.

I know this can be confusing because some texts have it as an actual axiom - it isn't. I remember having a long 'conversation' with the author of such a book. But he remained unconvinced despite pointing him to Ballentine.

But you can take it as a given there is no collapse in the formalism of QM - I know of no expert here (and many are professors who teach it) that says so. The author of the textbook simply has not thought it through carefully enough eg there is obvious no collapse in MW - if collapse was an axiom you wouldn't have that interpretation.

Thanks
Bill

#### PeterDonis

Mentor
QM is based 2 axioms - none of which includes collapse.
Yes, I know, but there are interpretations of QM which have "collapse" in them. I was pointing out the same thing you are: "collapse" is not part of the actual theory of QM, it's only part of certain interpretations.