# Double slit experiment

I think I am on the right track in understanding QM because I am very confused

Few questions:

1. Lets say electrons are emitted from the electron gun towards a slit. Do the electrons display the wave property even before passing through the slit right after leaving the electron gun or does it happen only after they pass through the slit?

2. If wave function is a probability of finding a particle, doesn't that mean particle is actually there somewhere or does it mean the probability of "it" getting manifested into a particle if observed/measured at the point?

Thanks

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jfizzix
Gold Member
Electrons always behave like waves. Their wavelength is so small though that beams of electrons don't spread much on their own, but if they pass through a slit small enough compared to their wavelength they diffract and interfere just like light does.

The wavefunction is an amplitude; the square of the wavefunction gives you the probability distribution.

Whether or not this means that the particle is actually there somewhere, or if it "manifests itself" upon measurement is actually an open question in quantum physics.

What can be said is that we only measure the probability by looking at the results of measuring lots of particles, and everyone agrees on what the probabilities ought to be. How these probabilities actually come from measuring single particles is an unanswered question, though.

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If the experiment is done in a medium then do we know when the wave function collapses related to the optical density of the medium? I mean, we know that we see the interference pattern on an high density receiving object when light goes through medium like air. Apparently the wave function does not collapse when "un-manifested particle" is passing through a less denser medium probably even interacting with it. So, what is the relation (mathematical hopefully) between the wave function and the density of the medium?

bhobba
Mentor
If the experiment is done in a medium then do we know when the wave function collapses related to the optical density of the medium?

The situation in a medium is quite complex:

Also understand the situation with wave-function collapse is also quite complex - its very interpretation dependent - some interpretations don't even have it, while with others its a big problem - at least some think so anyway - others think its a bit of a non issue.

My advice is put these questions to one side right now and proceed to learn about QM.

Eventually, and hopefully, you can work you way through Ballentine which is the best book I have found:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20
http://www-dft.ts.infn.it/~resta/fismat/ballentine.pdf

Here it is developed from two axioms and you can see precisely what the fundamental assumptions really are - I should really say assumption because the second axiom follows from the first from a beautiful piece of math known as Gleason Theorem - well not strictly which is why it really a second axiom - but it strongly suggests it:
http://en.wikipedia.org/wiki/Gleason's_theorem

Anyway that's for the future - for now simply accept a full understanding of what the central issues are needs a bit of further study and don't get too caught up in interpretational issues at the start.

Thanks
Bill

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And, as usual, I would suggest Feynman Lectures Vol III chapter 1, 2 and 3.

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I am bit confused with the explanations given for not seeing interference pattern in much bigger objects when passed through the slits.

So, the explanation is that the wavelength is so small for big objects that interference pattern become indecipherable hence rendering it useless to differentiate the maxima and minima. But this statement also means that interference pattern is very much there, only that it cannot be seen. This understanding leads us to following combination of explanations that are contradictory

1. Interference pattern is there for quantum objects even when observed but they become indecipherable which also means that the quantum objects are indeed going through only one slit at a time and producing indecipherable interference pattern only when observed. So, the wave nature is always present for an object irrespective of its size.

2. Interference pattern is there only for quantum objects and not for bigger objects which means there is a certain wavelength beyond which interference pattern is not seen and hence the above statement is false.

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bhobba
Mentor
I am bit confused with the explanations given for not seeing interference pattern in much bigger objects when passed through the slits.

The real explanation, as well as how classicality emerges involves decoherence.

For example a few stray photons from the CBMR is enough to decohere a dust particle and give it a definite position.

Einstein once asked Bohr 'Do you really think the moon isn't there if you aren't looking at it?' Bohr, in response, said, Einstein, don't tell God what to do'. But the jokes on both of them - the moon is never not looked at - it is constantly observed by its environment all the time, and that is in fact what gives objects its commonsense everyday behavior.

Remove it, and while a technical tour de-force doing it, it can be done, and some very weird behavior emerges:
http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

However the jig is up in explaining that in layman's terms - you need to consult tomes on it for the detail.

Thanks
Bill

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1. Interference pattern is there for quantum objects even when observed but they become indecipherable which also means that the quantum objects are indeed going through only one slit at a time and producing indecipherable interference pattern only when observed. So, the wave nature is always present for an object irrespective of its size.
Yes, interference pattern is there for quantum objects even when they are observed. The question now is, "how much interference is there?". You may read the third chapter of Feynman lectures, where he quantitatively shows the formation of fringes and gives you some numbers to play with. You can actually see interference disappearing as you go from one extreme to another by varying parameters.

2. Interference pattern is there only for quantum objects and not for bigger objects which means there is a certain wavelength beyond which interference pattern is not seen and hence the above statement is false.
What is a quantum object? This world is Quantum Mechanical (starting from electron, molecules through you and me upto big galaxies) and hence all the objects are quantum objects. All objects have the property to interfere. For big objects, interference is less apparent and we say "interference pattern is absent".

EDIT:
I shouldn't say apparent. Interference is less.

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Yes, interference pattern is there for quantum objects even when they are observed.

Isn't interference supposed to be "destroyed/lost" when the quantum particles are measured/observed? So, are you saying the pattern we see when quantum particles are measured/observed is also an interference pattern as compared to the pattern produced when the quantum particles are not measured/observed?

Well it depends on the wavelength of the photons used for detection. So we have two extremes, in one extreme the wavelength is very long which results in no change in interference pattern (long wavelength is not good for detection) and on other extreme wavelength is extremely small and we see no interference (and in principle you can make it zero). And then we have actual situations which is between these extremes (in which we do see interference pattern but not similar to the case without photons).
This demonstrated in Feynman lectures Vol III, chapter 3 with diagrams and equations.

bhobba
Mentor
1 person