The Observer Problem

Abstract. Bell's theorem refutes a conjunction of assumptions, and the disagreement of the last sixty years has been about which member to reject. This paper takes the horn Einstein himself identified: separability, the claim that the state of a composite system is fixed by the states of its parts together with their spatiotemporal relations. Following Howard, separability rather than locality is what gave Bell's factorization condition its warrant, and dropping it leaves operational locality and relativity untouched while removing the premise that reality decomposes into parts possessing states of their own. Separability licenses something else as well. Modelling presupposes a position exterior to what is modelled, and only separability makes such a position coherent. Gödel's incompleteness theorems show that a system required to account for itself from outside itself generates a process that does not terminate. Bell refutes the premise; Gödel refutes what the premise licenses. The paper's central claim is that these are one finding rather than two, and that they have not previously been read that way. A third claim follows and is weaker. The same assumption is argued to produce the observed failure of convergence in domains where the modeller is constitutive of what is modelled: the foundations of mathematics and of quantum mechanics do not converge, while astronomy and chemistry do. This is stated as a measurable prediction, nobody has measured it, and the paper identifies where the argument would fail if it is wrong.