ABSTRACT
CONTENTS 22.1 Introduction ...............................................................................................334 22.2 Physical Contents of Maxwell’s Equations............................................336 22.3 Electromagnetism and Geometry ..........................................................340 22.4 Perception of Space and Time .................................................................344 Acknowledgments ..............................................................................................347 References ............................................................................................................347
We reconstruct Maxwell’s equations showing that a major part of the information encoded in them is taken from topological properties of spacetime. The residual information, divorced from geometry, which represents the physical contents of electrodynamics, translates into four assumptions: (i) locality; (ii) linearity; (iii) identity of the charge source and the charge coupling; and (iv) lack of magnetic monopoles. However, a closer inspection of symmetries peculiar to electrodynamics shows that these assumptions may have much to do with geometry. Maxwell’s equations tell us that we live in a three-dimensional space with trivial (Euclidean) topology; time is a one-dimensional unidirectional and noncompact continuum; and spacetime is endowed with a light cone structure readable in conformal invariance of electrodynamics. Our geometric feelings relate to the fact that Maxwell’s equations are built in our brain. Hence our space and time orientation, our visualization and imagination capabilities are ensured by unceasing instinctive processes of solving Maxwell’s equations. People usually agree in their observations of angle relations. For example, a right angle is never confused with an angle slightly different from right. By contrast, we may disagree in metric issues, say, a colour-blind person finds the light wave lengths quite
