Undoing quantum measurement must violate either determinism, Lorentz invariance or time-symmetry Avshalom C. Elitzur Iyar The Israeli Institute for Advanced Research Rehovot, Israel The peaceful coexistence between quantum mechanics and special relativity is maintained due to the unobservability of hidden variables, and hence the intrinsic unobservability of quantum non-locality in real time. I prove that if time-reversing quantum measurement is possible, this coexistence breaks down. Either Lorentz invariance or time-symmetry must be visibly violated, the more radical option being the inexistence of hidden variables. The EPR argument [1], based on the combined premises of realism, determinism and SR, was in essence an argument for hidden variables (HVs). Then, Bell’s theorem [2] proved that if such HVs exist, they must be nonlocal. Yet even after Bell-inequality violations were demonstrated, the violation of SR remained indirect, as no observable superluminal signal can be sent through the EPR measurements. The proverbial “peaceful coexistence” between QM and SR [3] in due to this very non-signaling. Subsequent theoretical advances related to this issue were relatively minor. Bohm and Hiley [4], seeking to preserve Determinism even under Bell’s proof, imposed another restriction on HVs: They must exert their nonlocal effects in some preferred reference frame. This non-relativistic feature has eventually become (see below) part and parcel of Bohmian mechanics. On the other hand, Elitzur and Dolev [5] derived from SR that hidden variables must remain hidden forever, otherwise their indirect violation of SR would become direct. This restriction, reminiscent of the “cosmic censorship” conjecture [6], equally prohibits the Bohmian preferred reference frame to be ever detected. Apart from these restrictions on HVs, of which [5] renders [4] untestable and leaving Bell’s [2] as the only one of experimental significance, no other restrictions were made. In this article, I derive from these restrictions a few new ones, which add up to a new proof of incompatibility between QM and some basic principles of classical physics.