[Physics] Can the path of a charged particle under the influence of a magnetic field be considered piecewise linear

electromagnetismmeasurement-problemquantum-electrodynamics

Ordinarily we consider the path of a charged particle under the influence of a magnetic field to be curved. However, in order for the trajectory of the particle to change, it must emit a photon. Therefore, in principle, if we were able to view the path of the particle at sufficiently high resolution, would its path actually be polygonal, with a photon emitted at each vertex?

Best Answer

You're asking what would happen if we could view things with an unlimited high resolution. You view the emissions of the synchotron photons as discrete events and you ask is the path linear between these emissions. The problem is - quantum particles do not have trajectories so it's not meaningful to ask about the actual path followed by the particle. All you can do is make measurements and ask about the sequence of measurement results. There is then a limit on the resolution of what you will find, such as the ~micron limit in the pictures in Anna's answer, where the measurements are the ionization events.