MadSci Network: Physics |
Why are the fundamental laws of physics cast in the form of differntial
equations, not algebraic equations?
Because physics likes to describe changes in properties as functions of other properties or things. This sort of relationship is best described by a differential equation. Once a differential equation is integrated, it becomes an algebraic equation; so one could say that most or all of the fundamental laws of physics can also be stated in simple algebraic form. For example, consider the relationship between position, velocity and acceleration.
But only relationships in which one thing changes with respect to another are stated in terms of differential equations. For example, consider the formula for the energy of a photon, e = hn. The energy e and frequency n of a photon are related by Planck's constant h and do not change.
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