You raise an important point. The precision of quantum electrodynamics (QED) as a scientific theory refers to its remarkable agreement with experimental observations and its ability to make highly precise predictions within the energy scales where it is applicable. However, it's worth noting that the precision of the entire Standard Model of particle physics, which includes QED along with the weak nuclear force and the strong nuclear force, is collectively evaluated when considering the overall precision of the theory.
Within the framework of the Standard Model, all of its components, including QED, the electroweak theory, and quantum chromodynamics (QCD), are tested and verified to an exceptional degree of precision within their respective energy ranges. These theories have been confirmed by numerous experiments conducted at various particle accelerators and other high-energy physics facilities.
The precision of a theory refers to its ability to make predictions that agree with experimental results to a high degree of accuracy. In this sense, QED is often singled out because it has been tested extensively and shown to agree with experiments with astonishing precision in the energy scales where it is valid.
However, it is indeed important to consider the overall precision of the Standard Model as a unified framework. The Standard Model combines the three fundamental forces—electromagnetism, weak nuclear force, and strong nuclear force—into a single coherent theory that describes the behavior of elementary particles and their interactions. The combined precision of all these components is evaluated to establish the overall accuracy of the theory.
When considering the extremely high-energy scales close to the Planck scale, where quantum gravity becomes significant, the Standard Model is not expected to provide accurate predictions. At these energy scales, the effects of quantum gravity and a more complete theory of quantum mechanics are anticipated to be relevant. The Planck scale represents the energy scale at which the effects of gravity and quantum mechanics are expected to become equally important.
In summary, while QED is often praised for its remarkable precision and agreement with experiments, the overall precision of the Standard Model, incorporating all its components, is considered when evaluating its accuracy. However, it is recognized that at very high-energy scales near the Planck scale, the Standard Model is expected to be incomplete and would require a more comprehensive theory, such as a theory of quantum gravity, to provide accurate predictions.