How Precise Can QED Predict the Motion of Charged Particles?

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Discussion Overview

The discussion revolves around the precision of Quantum Electrodynamics (QED) in predicting the motion of charged particles within electromagnetic fields. Participants explore the scope of QED's predictive capabilities, particularly regarding its limitations and the conditions under which it achieves high precision.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether QED can predict the entire arbitrary motion of charged particles with high precision or if its predictions are limited to specific cases, such as the Lamb shift and magnetic moment of the electron.
  • Another participant asserts that QED's applicability is restricted to "bound problems" and "scattering problems," suggesting that while QED can yield precise numerical predictions, these are confined to a limited spectrum of motions due to the slow divergence of the perturbative expansion of the S-matrix elements.
  • A follow-up inquiry asks if there are other types of motions to which QED does not apply, indicating a search for clarity on the boundaries of QED's predictive power.
  • Another participant argues that achieving 12-digit accuracy in predicting motion requires corresponding accuracy in the electromagnetic field, which they claim is not feasible with current technology.

Areas of Agreement / Disagreement

Participants express differing views on the extent to which QED can predict the motion of charged particles, with some emphasizing its limitations and others questioning the nature of those limitations. The discussion remains unresolved regarding the full scope of QED's predictive capabilities.

Contextual Notes

Participants highlight the dependence of QED's predictions on specific types of problems and the technological limitations in achieving high precision in measurements of electromagnetic fields.

goran d
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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?
 
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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".
 
dextercioby said:
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?
 
goran d said:
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.
 

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