Weak Values without State Vectors

After Yakir Aharonov formalized the concept of a ``weak value'', he suggested using them as a guide for what might really be happening in any quantum experiment. But until recently (arXiv:2412.05456) the weak values were always computed from state vectors, and so could only supplement conventional quantum theory. This talk will detail recent progress in deriving local weak value histories throughout any quantum circuit without using state vectors at any point in the analysis. The approach uses an "all-at-once" computational framework where knowledge of the eventual measurement basis is used to eliminate the need for an exponentially large configuration space. The results indicate the plausibility of a full reformulation of quantum theory in terms of locally-defined quantities, compatible with Lorentz covariance, at the expense of a hidden dependence on the future measurement settings.