Suppose an electron is producing an electric field by emission of virtual photons and interacting with other particles. What parameters determine the probability that it will emit at least one virtual photon in a time period of length $T$? What is the formula for this probability?
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The famously dimensionless fine-structure constant
$$\alpha=\frac{1}{4\pi\epsilon_0}\frac{e^2}{\hbar c}\approx\frac{1}{137.036}$$
is the probability that an electron or positron emits or absorbs a photon, when one calculates Feynman diagrams.
G. Smith
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