Problem — Physical law versus correlation

Problem

Explain in five lines the difference between a physical law and a chance correlation. Why is $F=ma$ not just an “observed regularity”?

Solution

Physical law. A physical law is a quantitative and falsifiable relationship, which links to general principles, holds over a wide domain of situations and has predictive power: it allows the outcome of experiments not yet performed to be predicted. It typically expresses a causal link between quantities.

Chance correlation. A correlation, by contrast, is a simple statistical association observed between two quantities. It records that two things “go together”, but guarantees no causal link nor any reliable predictive power: it can arise by chance or from a third confounding variable, and can disappear when the context changes.

Why $F=ma$ is more than an observed regularity. Newton’s second law of dynamics $\vv{F} = m\,\vv{a}$ does not merely note that force and acceleration “go together”: it asserts a causal relationship (force causes acceleration, with mass as the inertial proportionality constant), it is universal (it holds for any body and any force), it fits coherently into the entire edifice of mechanics (principle of inertia, third law, conservation laws) and it yields testable predictions in countless new situations. It is this network of causality, universality and prediction that sets it apart from an empirical correlation.

$\ev{\text{Legge}=\text{causale}+\text{universale}+\text{predittiva}+\text{falsificabile};\quad \text{correlazione}=\text{sola associazione statistica}}$

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Topics: Metodo sperimentale