Engineered Simultaneity: The Physical Impossibility of Consolidated Price Discovery Across Spacelike-Separated Exchanges

TL;DR

This paper demonstrates that the U.S. equity market's NBBO system relies on an impossible simultaneity assumption due to relativistic effects, making true consolidated price discovery across spacelike-separated exchanges fundamentally unachievable.

Contribution

It formalizes the impossibility of consistent price comparison across distant exchanges using relativity and quantum theory, revealing fundamental limits of market microstructure.

Findings

NBBO is an instance of engineered simultaneity

Relativity proves the frame-dependence of event ordering in markets

Approximately $5 billion per year is extracted from this simultaneity gap

Abstract

We define \emph{engineered simultaneity}: the construction of a system that requires temporal comparison of events at spacelike-separated locations, implements this comparison via an implicit simultaneity convention, and represents the result as an objective measurement rather than a conventional choice. We show that the National Best Bid and Offer (NBBO) -- the regulatory cornerstone of U.S. equity markets -- is an instance of engineered simultaneity. The NBBO requires determining ``current'' prices across exchanges whose spatial separation places their price events outside each other's light cones. Special relativity proves that the temporal ordering of such events is frame-dependent: there exist inertial reference frames in which the NBBO differs from the value reported by the Securities Information Processor. The impossibility is not approximate; it is exact and unavoidable within the causal structure of Minkowski spacetime. General relativity compounds the impossibility: gravitational time dilation introduces frame-rate discrepancies between exchanges at different altitudes, and recent work on indefinite causal order in quantum information theory undermines the premise of a fixed causal structure altogether. We formalize the special-relativistic argument using the causal precedence relation, connect it to Lamport's theorem on distributed ordering, and note that approximately \$5~billion per year in latency arbitrage profits are extracted from the gap between the NBBO's implicit simultaneity convention and physical reality.