Can virtual particles break the law that energy cannot be created or destroyed?

In summary, Virtual Particles do not break the law that energy cannot be created or destroyed, as they only "borrow" energy for a very short amount of time and quickly annihilate each other. This arises from the time/energy uncertainty principle and does not violate energy-momentum conservation in the bigger picture. The Casimir Effect is considered as the most straightforward experimental evidence for this. However, when considering a small region of space, it may appear as if energy conservation is momentarily violated, but this is not the case when looking at the entire system. While quantum fluctuations and non-zero energy fluctuations do occur, they still follow the operator identity of <\partial_0 H> = 0. There is some confusion about virtual pair creation via
  • #36
"Not really (afaik)."

Well, there is a trivial way. Namely by changing regularization and renormalization schemes.

Both series could sum to infinity but *naively* differ term by term. Changing renormalization schemes will typically rearrange the kth and (k+1) terms. So they are in effect equivalent, but it might look at first glance like they are not.
 
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  • #37
Good point! One should add this to the list I compiled
 

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