What is quantum tunnelling?

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On the sitcom 'The Big Bang Theory', one of the jokes goes:

"A physicist walks into an ice cream parlor and orders an ice cream for himself and one for the empty seat next to him. He does this for weeks until the owner asks him what he's doing. The physicist says, "well, I'm a physicist, and quantum mechanics tells us that the matter above this stool to spontaneously change into a beautiful woman, who might accept my offer and fall in love with me. The owner says that lots of beautiful women come in here. Why not buy an ice cream for them? The physicist says, "yeah, but what are the odds of that happening?"

In the DVD feature, the science consultant says that it's based on quantum tunnelling...could someone explain it a bit more in layman's terms? Sounds really interesting

Thanks
 

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  • #2
K^2
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That's not exactly correct. The materialization of a beautiful woman has more to do with uncertainty principle and wave function collapse. Related concepts, but not the same thing.

At any rate, tunneling is what allows a particle to cross from point A to point B even if it does not have enough energy to be between these two points. For example, in a tunneling microscope, there is a voltage applied between the needle and the sample, but it's not high enough to overcome attraction between electrons and atoms in the needle, so an electron cannot classically cross the gap between needle and sample. However, if you get the needle sufficiently close, the current still flows, as electrons tunnel from needle to sample. Because probability of tunneling decreases exponentially with distance, the tunneling current is extremely sensitive to the distance, allowing tunneling microscope to map out the surface of the sample.
 
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A more simpler way to envision it is to imagine trying to walk from A to B, but you reach a hill. If you decide to walk over that hill, it will cost you more energy than taking the shortcut, which would be a tunnel straight through it.
 
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