The Embedded-Observer No-Go Theorem

We prove that no observer realized as a proper subsystem of a closed, globally unitary quantum system can simultaneously (a) reconstruct the complete global state from its own accessible data and (b) evolve under a fixed, autonomous unitary law, whenever it is genuinely (non-trivially) coupled to the rest of the system. The result follows from four minimal hypotheses - global unitarity, an observer occupying a proper subsystem, a locality structure constraining direct interactions, and a non-fine-tuned interacting boundary - with no further structure assumed. Two of the theorem's three components (a canonical, geometrically forced reduction of the observer's knowledge to a partial trace, and the no-go result itself) require no locality assumption at all and hold for any bipartite split of any unitary quantum system whatsoever. The third component, a causal order controlling when correlations between separated parts of the system can first form, is established in two forms: the standard, approximately-causal Lieb–Robinson bound for any locallyinteracting Hamiltonian system, and a sharper, EXACTLY causal bound proved from scratch and confirmed by explicit numerical example - for the special case of a discrete local quantum circuit. We further show that the theorem's two failure modes are not one fact restated: one is a property of the accumulated history (a “stock”, formalized via the observer's von Neumann entropy) and the other a property of the instantaneous interaction (a “flow”, formalized via the channel unitarity of Wallman, Granade, Harper \& Flammia), and the two are shown, by explicit construction, to be logically separable. The result is situated relative to prior work establishing closely related conclusions by different routes - Wigner's friend (1961), the Page–Wootters mechanism (1983), the Frauchiger–Renner theorem (2018), and the quantum-reference-frame literature - and its specific, narrower technical contribution relative to that literature is stated explicitly.