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

Paul Borrill

Abstract

We introduce the concept of engineered simultaneity: a system design that (1) requires comparing events at spacelike-separated locations, (2) implements this comparison via an implicit simultaneity convention, and (3) represents the result as objective rather than conventional. The United States National Best Bid and Offer (NBBO), mandated by SEC Regulation NMS Rule 611, is shown to be an instance of engineered simultaneity. We prove that the NBBO is frame-dependent: its value depends on the reference frame in which "current" prices are defined. Since the exchanges that generate quote data are separated by distances of 43-1,180 km, light-travel times of 143-3,940 microseconds create unavoidable windows during which no frame-independent price ordering exists. High-frequency trading firms exploit this window by accessing exchange data via direct feeds (latency ~tens of microseconds) while the consolidated Securities Information Processor operates at ~1,128 microseconds -- a ratio exceeding 50:1. We demonstrate that this constitutes a category mistake in the sense of Ryle: the NBBO applies the concept of "simultaneity" in a domain where it has no frame-independent meaning. The resulting information asymmetry extracts approximately $5 billion annually from other market participants.

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

Abstract

We introduce the concept of engineered simultaneity: a system design that (1) requires comparing events at spacelike-separated locations, (2) implements this comparison via an implicit simultaneity convention, and (3) represents the result as objective rather than conventional. The United States National Best Bid and Offer (NBBO), mandated by SEC Regulation NMS Rule 611, is shown to be an instance of engineered simultaneity. We prove that the NBBO is frame-dependent: its value depends on the reference frame in which "current" prices are defined. Since the exchanges that generate quote data are separated by distances of 43-1,180 km, light-travel times of 143-3,940 microseconds create unavoidable windows during which no frame-independent price ordering exists. High-frequency trading firms exploit this window by accessing exchange data via direct feeds (latency ~tens of microseconds) while the consolidated Securities Information Processor operates at ~1,128 microseconds -- a ratio exceeding 50:1. We demonstrate that this constitutes a category mistake in the sense of Ryle: the NBBO applies the concept of "simultaneity" in a domain where it has no frame-independent meaning. The resulting information asymmetry extracts approximately $5 billion annually from other market participants.
Paper Structure (13 sections, 3 theorems, 3 equations, 2 figures, 2 tables)

This paper contains 13 sections, 3 theorems, 3 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The NBBO as a Simultaneity Claim
  3. Regulatory Definition
  4. The Consolidation Process
  5. Formal Definition
  6. Causal Structure of the U.S. Exchange Network
  7. Exchange Locations
  8. Minkowski Analysis
  9. Connection to Distributed Systems Theory
  10. Quantifying the Exploitation
  11. The Magnitude Counterargument
  12. Discussion
  13. Conclusion

Key Result

Theorem 1

Let $E_A$ and $E_B$ be exchanges separated by distance $d > 0$. Let $\alpha$ and $\beta$ be quote events at $E_A$ and $E_B$ respectively, with $|t_\alpha - t_\beta| < d/c$. Then there exist inertial frames $S$ and $S'$ such that the NBBO computed from $\{\alpha, \beta\}$ differs between $S$ and $S'$

Figures (2)

  • Figure 1: Minkowski diagram of the U.S. exchange network. Events $\alpha$ (NYSE quote) and $\beta$ (CME quote) are spacelike-separated: no light signal from $\alpha$ can reach $\beta$ before $\beta$ occurs. Their temporal ordering is frame-dependent. The SIP, located near the NJ cluster, receives both events and computes an NBBO---but this NBBO reflects arrival order at the SIP, not any frame-independent temporal ordering.
  • Figure 2: Timescales in the U.S. exchange network. The orange dashed line marks the light-time separation $d/c$: events closer in time than this are spacelike-separated. HFT execution times ($<$10 $\mu$s) and direct feed latencies ($\mathcal{O}(10)\,\mu$s) operate far below the light-time for the NJ--Chicago corridor (3,940 $\mu$s), while even within the NJ cluster (143 $\mu$s) they approach the boundary. The $>$50$\times$ gap between direct feeds and the SIP consolidated feed (right edge annotation) defines the exploitable asymmetry.

Theorems & Definitions (5)

  • Definition 1: Engineered Simultaneity
  • Theorem 1: Frame-Dependence of the NBBO
  • proof
  • Corollary 1
  • Proposition 1