Quantum Fluctuations of Negative Energy

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It is my understanding that quantum fluctuations arise from implications of the Uncertainty Principle. Specifically:

http://upload.wikimedia.org/math/b/d/1/bd1bb25a5159f9c74803afca6ad65935.png

And that this means that conservation of energy can appear to be violated for a set time "T."

My question is, if we can have a positive change in energy, can we get a negative change?

And if not, why not?
 
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Yes, it can be negative as well. For example, a particle can bounce from a barrier even if its evergy is higher then the barrier.
 
So negative energy is quite plausible?
 
Yes, sure.
Check the Casimir effect for example
The vacuum between the casimir plates has less density then a normal vacuum!
 
Ah, is this what happens in the casimir effect? Negative energy quantum fluctuations?
 
The Casimir effect is supposed to occur because some modes of the EM vacuum are 'short-circuited' by the conducting plates, thereby reducing the vacuum energy density between them.

If negative and positive energy fluctuations were canceled out to the same degree, there would be no energy difference between the plates and outside the plates (?), no Casimir effect.