A complete(-ish) history of accelerated charges - Westin, Raian Gonçalves (2022)
This dissertation is built out of a collection of works related to one of the most famous problems related to accelerated charges: how does an observer coaccelerated with the charge describes its radiation? I first came across this problem after a Basic-Physics class on electric and magnetic phenomena, in which I tried to connect the radiation emitted by an accelerated charge and the Equivalence Principle; more specifically: \"Would someone accelerated with the charge measure the radiation emitted from it? And how does the answer to this question relate to the Equivalence Principle?\" As a typical second-year physics student, I did not understand either concepts deeply enough to arrive at an answer. It was not until I began my MSc-level studies on this subject that I realized that most of these questions had already been analyzed. Therefore, the main goal of this work is to bring all this knowledge together in a, hopefully, didactic way so that students at the end of their undergraduate studies can understand both the questions and the answers. We present a review of special relativity (with special attention to accelerated frames) and electromagnetism to the extent these subjects are relevant to analyze these questions on radiation emitted by accelerated charges. We perform the classical analysis of the problem (from both inertial- and accelerated-frame perspectives), which for the most part was done by Boulware in 1980. We explain how, from the classical point of view, the whole picture is consistent, with no paradoxes arising. The next step is to introduce the students to quantum field theory in curved spaces in order to present what is probably the first result of this work which is unknown to them: that the very concept of number of particles depends on the reference frame. With this, we revisit the problem using Quantum Field Theory and show that the Unruh radiation plays an essential role in reconciling the observations made by inertial and accelerated observers, which comprises the collection of results that Matsas and collaborators have published over the past years. Finally, I address the problem of the radiation reaction force, a topic which is hardly ever well explained in textbooks and electromagnetism courses due to its many nuances. Here we summarize and sketch the rigorous derivation of this force made by Wald in 2009. Lastly, there is my only original contribution, where I show in both formalisms (classical and quantum), that the EM fields generated by the accelerated electric charge are made entirely by zero-energy Rindler modes, concluding this work which addresses some of the most important classical, quantum, and dynamical aspects related to accelerated charges.