How Precise Can QED Predict the Motion of Charged Particles?

[goran d]

It is claimed that QED could predict certain quantities, like the lamb shift and magnetic moment of electron with astonishing precision of 12 digits. My question is the following: does QED predict only a few things to this precision, or does it predict, this precisely, the entire arbitrary motion of charged particles in electromagnetic fields, in all situations? To what does such precision apply?

 

[dextercioby]

What you call "the entire arbitrary motion of charged particles in electromagnetic fields, in all situations" is really limited in Quantum Electrodynamics. It's either that one deals with so-called "bound problems" or "scattering problems". Due to the slow divergence of the perturbative expansion of the S-matrix elements, one can get very good numerical predictions. But only under this limited spectrum of "motions".

 

[atyy]

What you call "the entire arbitrary motion of charged particles in electromagnetic fields, in all situations" is really limited in Quantum Electrodynamics. It's either that one deals with so-called "bound problems" or "scattering problems". Due to the slow divergence of the perturbative expansion of the S-matrix elements, one can get very good numerical predictions. But only under this limited spectrum of "motions".

Are there other types of motions to which QED does not apply?

 

[Vanadium 50]

the entire arbitrary motion of charged particles in electromagnetic fields

To get 12 digit accuracy of the motion, you need 12 digit accuracy of the field. This is not possible with today's technology.