A signature achievement of twentieth-century science was the development and spectacular success of quantum electrodynamics in explaining the energy difference (called the Lamb shift) between the 2s1/2 and 2p1/2 states with the same total angular momentum, and the anomalous intrinsic spin magnetic moment of the electron due to vacuum fluctuations of the electromagnetic field. However, it is not a theory relegated to a few historically celebrated experiments. It generally applies to ordinary nonlinear optical phenomena and lasers, and the applications of quantum electrodynamics are expanding to the nascent fields of quantum information and quantum cryptography. The effects of vacuum fluctuations are ...
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