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Does the Pauli exclusion principle instantaneously affect distant electrons?

If this rule works, could you not set up an experiment to test the theory (as described by Brian Cox in his A Night with the Stars lecture$^1$) and monitor another piece of diamond to see if the electrons change levels in time with the changes in energy of the electrons in the heated piece? If you used a pin point heating element that could change temperature at different frequencies, would you detect the frequency change in the monitored piece?


$^1$ The Youtube link keeps breaking, so here is a search on Youtube for Brian Cox' A Night with the Stars lecture.

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Related question physics.stackexchange.com/questions/21677/… –  twistor59 Jan 28 '13 at 14:18
Also of relevance is this blog discussion and this one –  twistor59 Jan 28 '13 at 14:22
This question is incomplete without state exactly what behavior you are asking about--we haven't all watched the same show. In any case, you can expect Dr. Cox to know the basics pretty well, but in the show he likes to push things for dramatic effect. –  dmckee Jan 28 '13 at 15:43
Possible duplicate: physics.stackexchange.com/q/18527/2451 –  Qmechanic Jan 28 '13 at 17:18
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marked as duplicate by Manishearth Jan 28 '13 at 19:25

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Brian Cox's statements can be paraphrased as 'no two electrons can be in the same energy level, so if we change the energy level of any electron in the Universe, then all the other electrons will change energy levels - so we are all connected'.

This is essentially true except that he said "energy level" instead of "quantum state" (which for some reason caused a lot of controversy on Twitter). See this video, which is called "Was Brian Cox wrong?".

Pauli's exclusion principle has, I assume, been measured. Although, I don't know if you could measure it in the way you suggested.

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