Einstein Strength
Everyone knows that Albert Einstein said that a physical theory should be as simple as possible, but no simpler. But not everyone knows that he had a quantitative idea in mind.
Consider a second order partial differential equation in three variables, such as the two-dimensional wave equation
It is often profitable to think of such an equation as a rewrite rule allowing us to rewrite arbitrary partial derivatives of the function using fewer partials than would be needed for an arbitrary function. For example, if satisfies the wave equation, we can rewrite
where in the first equality, we appealed to the fact that partial derivatives commute.
Einstein asked: how much redundancy can we eliminate in this fashion, for a given partial differential equation?
Read more about this topic: Constraint Counting
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