Physics is often presented as a set of laws describing reality, but every physical theory also contains elements that are purely about how we describe that reality—coordinates, conventions, and mathematical representations that can change without changing what is actually happening. A natural question follows: how do we separate what is physically real from what is just bookkeeping?
This paper argues that the answer is not a matter of interpretation or preference. There is a simple but powerful principle at work across all of physics: only distinctions that all admissible observers agree on can count as physical content. This is what we call Observer-Invariant Distinguishability (A0). If two equally valid observers can assign different values to something, then that “something” cannot be a physical fact—it is part of the description, not part of the world.
The key result of the paper is that this principle is not optional. We show that if a theory allows observer-dependent facts, it cannot define measurement outcomes in a consistent way. Without that, it cannot define information, and without information it cannot make predictions that different observers can test and agree on. In other words, without A0, a theory stops being physics in the usual sense—it becomes a collection of observer-dependent narratives with no shared empirical meaning.
What makes this especially interesting is that A0 is already quietly built into the theories we trust most. In general relativity, different coordinate descriptions of spacetime are treated as physically equivalent—only invariant geometric quantities matter. In quantum mechanics, different mathematical representations of the same state (for example, differing by a phase) are also treated as equivalent—only relational quantities like probabilities carry physical meaning. These are not arbitrary choices; they are exactly what A0 requires.
Finally, the paper shows how A0 can do more than just clean up our descriptions. When combined with additional assumptions about how physical reality is structured—such as irreversibility in measurement or limits on information—it acts like a filter, eliminating inconsistent possibilities and leaving behind familiar structures like Lorentz invariance or the Hilbert-space framework of quantum theory. A0 doesn’t generate these structures on its own, but it helps explain why only certain kinds of structure survive.
In that sense, A0 is best understood not as a new physical law, but as a condition on what it even means to have a physical law. It draws a sharp line between physics and description—and shows that crossing that line has real consequences.