Not Every Defect Is in the Law

Systems for discovering physical laws usually search over equations while fixing the experimental representation: what quantities exist, what instruments measure, and what experimenters control. We show that defects can instead lie elsewhere in the theory, and that law search can hide this distinction even with a perfect fit. We call this failure mode absorption: a discrepancy originating in the experimental representation is reproduced by rewritten physical laws. In a mass–spring system with a delayed sensor, two law edits reproduce the recorded channel to \(5.1\times10^{-16}\) relative error while leaving the incorrect measurement model unchanged. For linear systems, absorption occurs when the theory matches the apparatus's direct input–output feedthrough, has enough states to realize the observed dynamics, and can express those dynamics with its declared dimensions and parameters. Across 100 drawn linear systems, law-only accounts exist in all 100 cases. Additional drives resolve none of these ambiguities, whereas an added measurement resolves every case; independently constructed systems and established law-discovery methods show the same qualitative behavior. These results explain the title's central claim: $\text{not every defect is in the law}$. A perfect law fit can recover observable behavior without identifying its physical origin, making the choice of what to measure part of scientific discovery itself.