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In the double slit interference pattern for the wave of an electron, what will happen if I make the slits to be smaller than the size of an electron ? Will I still observe an interference pattern on the opposite side of the screen or no electron will be able to cross the slit?

If no, then how can a quantum prisoner escape ?

Isomorphic
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  • The thing with the electron is: up to our current measuring accuracy, it has no dimensions. It's a point particle. See also this wikipage. If you do the experiment with, say, protons, you do theoretically have the possibility of making the slit smaller than the particle size. Although such a slit would be mighty difficult to fabricate. Apparently, the largest particles used in this sort of experiment are Buckminsterfullerenes (see here). It might be possible there. – Wouter Nov 16 '13 at 10:03
  • Well, Iota, I daresay that is precisely what means "not to have a slit"! So I'd guess electrons would never cross this hypothetical setup.

    Moreover: What do you mean by "size of an electron"? As far as I can remember from my undergrad course in particle physics, electrons have a trivial form factor that comes from their point particle nature.

    Form factors in scattering setups are an evidence that electrons behave as point particles (at least as far as our current technologies allow us, which is down to the fm-GeV scale).

    Besides, how would you fabricate such a small slit!?

     – user17581 Nov 16 '13 at 10:09

2 Answers2

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Size is a nebulous concept when you get down to the quantum domain. All you can do is measure the interaction potential of your particle with whatever it's hitting. If there is a hard core to the potential then you can take this as a measure of the size, but unless the potential goes to infinity at the hard core the particle will still be able to get through slits that are too small for it by tunneling.

As the comments have said, electrons don't have a hard core, or at least none that we've been able to measure (the current limit is about $10^{-18}$ m or about a thousand times smaller than the size of a proton).

So when diffracting electrons reducing the slit size just reduces the probablility of the electron passing through the slit and makes the final diffraction image fainter. Protons do have a hard core, which gives them an effective diameter of about $1.6 \times 10^{-15}$ m. If you make the slit size smaller than this then you will drastically decrease the probability of the proton passing through the slit, but there is still a non-zero probability that it will tunnel through so you will still get an interference pattern but it will be extremely faint.

We'll gloss over the practical problems of making the slit size smaller than a proton!

John Rennie
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Nothing teaches like experimental observation. So I would suggest to iota, that (s)he should do the experiment, then come back and report the observed result. so what is the size of an electron ?