In the classical theory of the electromagnetic field (EMF) retarded energies or potentials arise from the study of varying EMF in the presence of moving electric charges. Classical derivations give the scalar retarded potential as the integral of the ratio of the electric charge density measured at the retarded time (t-R/c) over the distance R over the enclosed spherical volume of radius R. In the same token, the retarded vector potential is given by the integral of the electric current density measured at the same retarded time over R over the same enclosed volume divided by the speed of light. See Volume 2, Course of Theoretical Physics, The Classical Theory of Fields, by L. D. Landau, et al, Chapter 8, Pages 171-73, 4th revised English edition, first published by Pergamon Press in 1951.
The term ‘retarded’ is a poor choice as often is the case in the want for more precise descriptive words using the English language among the discourses of the physical sciences. Other examples are the word ‘relative’ for something that is absolute, the word ‘work’ for path independence of kinetic energy, the word ‘power’ for measuring the usage of energy per unit of time, the word ‘phase’ for measuring angular displacement, the word ‘color’ for describing the strong nuclear charges, the word ‘plasma’ for ionized gases, the word ‘gluon’ for directional invariance, and the word ‘hole’ in black holes. The meaning of this cosmological ‘hole’ is really a dimensionless point or zero volume of space-time of infinite mass or infinite energy or infinite density or infinite temperature. For the retarded time (t-R/c), if t=0 at the start of the measurement, it appears that the time is a negative number –R/c. This is physically meaningless without a forgiving reason invoking directional properties. On the other hand, use of incomplete directional properties would still create conceptual confusions as to ‘exact opposite’ or 180°, or orthogonal 90°, or obliqueness arbitrary angles, as well as clockwise or counterclockwise rotations.


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