On the strength of Maxwell’s equations

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Abstract
The ‘‘strength’’ of a set of field equations (first defined by Einstein as the number of Taylor coefficients of field variables that could be chosen arbitrarily) is used to show that the amount of initial data required by the electromagnetic formulation of Maxwell’s theory in free space is equal, without approximation, to that required by the potential formulation. In each formulation, the strength is interpreted in terms of the amount of initial data required to provide a solution of the Cauchy initial-value problem and in terms of the invariance properties of the formulation. Equality of the strengths of the two formulations of Maxwell’s theory is used to support the assertion that knowledge of the strengths of other established field theories provides a means for predicting the possible existence of unknown formulations of the theories.

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