Date of Submission

Fall 2024

Academic Program

Physics

Project Advisor 1

Paul Cadden-Zimansky

Abstract/Artist's Statement

This paper presents a novel geometric approach to visualize Electromagnetic Fields using Minkowski diagrams. Traditionally, Minkowski diagrams have been used to represent spacetime coordinates under Lorentz transformations. We extend this framework to EM fields, developing a structure that we refer to as "squishy" Minkowski diagrams that showcase how the electric and magnetic fields transform between reference frames. By examining the geometric and mathematical properties of both types of diagrams, we find several key symmetries and analogies between spacetime and field transformations, such as their causal structure, their metric, and certain invariant intervals. In particular, we find that area transformations are invariant under both types of Minkowski diagrams and that energy density transforms following patterns that are closely related to the relativistic Doppler effect, as Einstein predicted in 1905. The geometry framework presented in this paper provides invaluable insights into the connection between EM fields and spacetime and offers valuable visualizations for better understanding relativistic electromagnetism. In addition to this, we present an open-source web application created specifically as a tool for education and visualization of the geometric properties and transformations discussed in this paper.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.

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