Constraint Counting - Einstein Strength

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

Other articles related to "einstein strength, strength":

Constraint Counting - Einstein Strength - Quasilinear Equations
... The number of these functions is the Einstein strength of the p.d.e ... In the simple example above, the strength is two, although in this case we were able to obtain more precise information ...

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