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Q & A: can objects touch?

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Most recent answer: 12/04/2012
Q:
In a physics context, things never actually "touch", because in order to actually "touch", there would necessarily be an infinite acceleration. The standard physical explanation for this is: the coulomb repulsion force between electrons will always keep objects from "touching", since this force diverges to infinity as things get very close. I've recently heard several times that this isn't true, but that there is a better (quantum) explanation. I've heard that the reason things can never touch is a consequence of the Pauli Exclusion Principle. For example, if two hydrogen atoms get too close, this would certainly create a situation where the lowest energy potential is that in which both electrons (as indistinguishable particles) share the same wave function. This is a violation of Pauli Exclusion. To me, this seems contradict the former explanation. Which explanation (or both) is correct?
- Jeffrey Burggraf (age 21)
Idaho Falls, ID, USA
A:
I'm not sure that in a modern quantum picture, the old "touch" question is even meaningful anymore. A quantum object's state in space is represented by a spread-out wave. The waves of two objects can and often do overlap. For example, the two electrons in a helium atom in its lowest energy state share the very same spatial wave patterns.
When you consider big classical-like objects, the no-overlap condition starts to emerge. As you say, that's largely because of the Pauli exclusion principle. It turns out that only two electrons, not more, can share the same spatial pattern. The reason is that Pauli says they cannot actually share the same state, but the state includes both the spatial wave pattern and the internal spin property, which has two independent possible states. (You can search this site for more discussion.) That keeps things from collapsing into little condensed balls of equally mixed positive and negative charge.

Still, Coulomb (electrical) force does play a major role. Say you have two deuterium atoms. If they could be fully combined, you'd get a helium nucleus surrounded by those two electrons. Under ordinary conditions this fusion process doesn't happen. The reason is that the positively charged deuterium nuclei have such a strong Coulomb repulsion that they don't get close enough to stick together by the short-range nuclear forces. The negative electron waves are too spread out to help much in this process. Getting that fusion reaction to happen in a controlled way is the goal of fusion energy programs. It's hard because of the strength of the Coulomb repulsion.

Mike W.

(published on 12/04/2012)

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