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One of your sources in this article claims, “After all, even the sacred first law’s conservation of energy breaks down in the quantum realm, albeit in a limited way, he notes. That’s because Heisenberg’s uncertainty principle allows energy momentarily to appear from nothing, although it must be quickly paid back.” This claim is heard occasionally, but I am wondering what the justification for it is, and where it can be found. Many authors emphatically deny that quantum mechanics borrows energy from nothing. Thus, is there a derivation from quantum field theory, or is it time to put to rest a myth?

Paul Merriam
Santa Cruz, Calif.

Quantum systems don’t actually borrow energy from nothing. However, in many cases, their energy values may range widely around a well-defined average. The size of those swings is influenced by Heisenberg’s uncertainty principle. When thinking about those variations, scientists often use metaphors of borrowing and paying back that are, “technically speaking, not completely right,” says Brian R. Greene of Columbia University. However, he adds, “the uncertainty principle can definitely be used in these rough ways to guide our intuition—and it generally does not lead us astray .”—P. Weiss