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What I read on Wikipedia is

… quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.

Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like the anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen.

Following Wikipedia

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle.

From this I understood that the deviation from the magnetic moment of the electron is calculated by QED. But, how the magnetic moment by itself of subatomic particles is a prediction of QED?

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From this I understood that the deviation from the magnetic moment of the electron is calculated by QED. But, how the magnetic moment of subatomic particles is a prediction of QED?

A prediction is anything that comes out of a theory. Here, the theory (the calculation) predicts what the value of a particular quantity should be - you don't know in advance if this value is correct until you check experimentally. It predicts what the experiment will show.

If the experimental result is in agreement (within the experimental error), you gain some confidence that the theory is correct. If it turns out that the prediction isn't experimentally supported (and if this isn't due to bad data or human error), well then some aspect of the theory is wrong.

In this lingo, predictions can ostensibly be about the past; e.g. a theory can "predict" something about the state of the early universe (so, something in the past), and then extrapolate from there an inference about what we should expect to see through our telescopes now (so it's, again, really a prediction about what data to expect if the theory is true).

A prediction can be about something that hasn't been measured yet (either at all, or hasn't been measured as precisely as needed to differentiate between competing candidate theories). Or it can be about things that have already been observed, but for which there's currently no accepted theoretical explanation. Or it can be about known things; any prediction about known phenomena must be in agreement with data already collected, to the extent that it has been established as certain.

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