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It is often stated that QED makes predictions correct up to many decimal places.

What are the experiments that show this? And all have to provide measurements up to 12 decimal places?

To my understanding you need at least two experiments with that precision, because first you need to determine the fine-structure constant and only then you can plug it in into the formula for predictions?

And technically, it would only show consistency between those two experiments with QED, but does not exclude that measuring another property is not predicted by QED?

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    $\begingroup$ Precision tests of QED $\endgroup$ Commented Aug 11, 2022 at 9:16
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    $\begingroup$ This question (v2) seems quite broad. $\endgroup$
    – Qmechanic
    Commented Aug 11, 2022 at 13:54

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Some famous experiments that supported QFT are

  • Lamb–Retherford experiment: In 1947 this experiment showed physics beyond the relativistic quantum mechanics (RQM) founded by Dirac. In that same year, Hans Bethe explained this phenomenon using some new techniques. Interestingly Weisskopf derived it before Bethe but because of his insecurity about his mathematical abilities, he did not publish his results (which turned out to be correct). What's even more interesting is that when these people derived it QED was not yet known. Inspired by these techniques Tomonaga, Schwinger, Feynman, and Dyson later formulated QED. Lamb shift can be used to measure the fine-structure constant.
  • Electron g-factor: It is exactly $-2$ in Diracs RQM. But QED predicts to a very great precision the experimental value which is $−2.00231930436256(35)\pm 1.7×10^{−13}$.
  • Existence of Higgs boson: Because naively including mass in a gauge theory violates the gauge invariance, Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and 't Hooft have found an intelligent way (called Higgs mechanism) to give masses to gauge bosons using spontaneous symmetry breaking. This prediction was verified in 2012.

These are the most famous experiments. You can read the Precision tests of QED etc for less popular ones.

It is often stated that QFT makes predictions correct up to many decimal places.

This is not always true. In fact in the cosmological constant problem the prediction of $\Lambda$ is "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics". Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude.

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  • $\begingroup$ Doesn't the g-factor prediction need a measured value for the fine-structure constant from another experiment first? Which experiment would that be? Does the Lamb experiment give 12 decimal places of the fine-structure constant? $\endgroup$
    – Gere
    Commented Aug 11, 2022 at 9:26
  • $\begingroup$ @Gerenuk currently it is the opposite. They use the electron g-factor for the most precise measurement of $\alpha$. Read here. But historically, first they used $\alpha$ from other experiments to explain the g-factor. $\endgroup$ Commented Aug 11, 2022 at 9:30
  • $\begingroup$ I see. But what is that "other experiment" (Lamb?) and more importantly does it give 12 decimal places of α? I mean it's not meaningful to use g-factor alone to fix α and then use that α to predict the g-factor. $\endgroup$
    – Gere
    Commented Aug 11, 2022 at 9:35
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    $\begingroup$ Oh, come on. If you want to parrot this statement about the cosmological constant, at least go to the end. This is not a prediction, this is a naive estimate. You can always subtract out this huge contribution to the cosmological constant without any known problem. $\endgroup$
    – OON
    Commented Aug 11, 2022 at 9:48
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    $\begingroup$ In fact the dependence on the cutoff is showing that you are not talking yet about physical quantities. This is a greatly simplified way to demonstrate the apparent sensitivity of the parameter to the physics at the very high scales $\endgroup$
    – OON
    Commented Aug 11, 2022 at 9:51

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