Continuity as Possibility: A Methodological Distinction for Physics

## Abstract Physics uses continuous mathematics - fields, manifolds, wave functions, differential equations - to make predictions. Physical observations are recorded as discrete events: detector clicks, particle counts, energy transitions. This paper argues that this is not an accident to be explained away, but a structural fact that should be treated as a working principle. The claim: continuous mathematical objects describe distributions over possible outcomes. They are not physical entities occupying space. Discrete events are what physically happens. Confusing these two produces recurring conceptual difficulties—most visibly in the quantum measurement problem and in spacetime singularities. This distinction reframes, but does not solve, several open problems. It does not derive the Born rule, does not specify a concrete discrete causal structure, and does not yield new experimental predictions. Its value is diagnostic: it identifies where existing puzzles are category errors versus where they are genuine open technical problems, and it identifies a specific reframing of how discrete causal models (such as causal set theory) might recover Lorentz-invariant physics.