🔬 physics

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

This paper argues that the National Best Bid and Offer (NBBO) is a physically impossible construct because it enforces an arbitrary simultaneity convention on spacelike-separated price events, creating a fundamental conflict with the frame-dependent nature of time in special relativity and resulting in approximately $5 billion annually in latency arbitrage profits.

Original authors: Paul Borrill

Published 2026-03-04

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Paul Borrill

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Core Idea: The "Universal Now" is a Lie

Imagine you are watching a live sports game on TV. The announcer says, "At this exact moment, the quarterback throws the ball!"

In our daily lives, we assume there is one single "now" that everyone in the universe shares. If the quarterback throws the ball in New York, and a fan in Chicago sees it, we think they are seeing the same "moment."

This paper argues that in the world of high-speed stock trading, this assumption is physically impossible.

The author, Paul Borrill, uses the laws of physics (specifically Einstein's Special Relativity) to prove that because the stock exchanges are far apart (separated by hundreds of miles), there is no such thing as a single, universal "now" for them.

The Analogy: The Race of Light

Imagine two runners, Runner A in New Jersey and Runner B in Chicago. They are 1,000 miles apart.

The Rule: To decide who is the "fastest" runner, we need to know who started running first.
The Problem: Light (and information) takes time to travel. It takes about 5 milliseconds for a signal to go from New Jersey to Chicago.
The Scenario:
- Runner A starts running.
- 1 millisecond later, Runner B starts running.
- Because they are so far apart, a person standing in New Jersey sees Runner A start first.
- But, if you were moving very fast in a spaceship, you might see Runner B start before Runner A.

In physics, both observers are right. There is no "true" order to who started first. The order depends entirely on where you are standing and how fast you are moving.

The Stock Market Problem: The "Best Price" Myth

The U.S. stock market is regulated by a rule called NBBO (National Best Bid and Offer). This rule says: "At any given moment, the price of a stock must be the best price available across all exchanges."

To do this, a central computer (called the SIP) collects price updates from 16 different exchanges scattered across the country. It tries to create a single list of "current" prices.

The Paper's Argument:

The Distance: The exchanges are too far apart. A price update from New York and a price update from Chicago happen at "spacelike-separated" locations. This means light cannot travel between them fast enough to connect the two events.
The Physics: Because of this distance, physics says there is no objective way to say which price update happened "first."
The Trick: The SIP (the central computer) just picks an order based on when the messages arrive at its own door. It says, "I got the New York message at 10:00:01 and the Chicago message at 10:00:02, so New York was first."
The Lie: The paper calls this "Engineered Simultaneity." It is a system that pretends to measure an objective "best price," but it is actually just measuring "which message got to our specific computer first."

The Metaphor: The "Phantom" Clock

Imagine a town where everyone has a different clock, and the clocks are not synchronized.

The Mayor (the SIP) says, "We will declare it 12:00 PM for the whole town when my clock hits 12:00 PM."
The baker in the next town says, "But my clock says it's 11:59 AM!"
The baker in the town across the river says, "My clock says it's 12:01 PM!"

The Mayor creates a rule: "We will ignore the other clocks. When my clock says 12:00, it is 12:00 for everyone."

The paper argues that the stock market is doing exactly this. It is forcing a single time on a system where physics says time is relative. It's like trying to measure the temperature of a room using a thermometer that is calibrated to a theory of heat that doesn't exist (like "phlogiston," an old, debunked theory).

The Consequence: The $5 Billion "Frame" Advantage

Because the "official" price (the NBBO) is based on a fake, arbitrary order of events, some people can exploit it.

The Insiders: High-frequency traders (HFTs) have their computers physically located right next to the stock exchanges. They see the price updates almost instantly (in microseconds).
The Outsiders: Regular investors and the SIP see the price updates much later (after the signal travels through cables).

The "Race":
Imagine a price drops in New York.

The HFT in New Jersey sees it instantly.
The HFT buys the stock in New York.
The HFT sells it in Chicago before the "official" price update from New York even arrives at the central computer.
The central computer (SIP) still thinks the price is high, so it tells everyone else to buy at the old, high price.

The HFT makes a profit by trading on information that the "official" system hasn't acknowledged yet. The paper estimates this "time-travel" advantage costs the market about $5 billion a year.

Why This Matters

The author isn't just saying, "Hey, the system is slow." He is saying, "The system is built on a physical impossibility."

It's not a bug: You can't fix this with faster computers or better cables. The speed of light is a hard limit.
It's a category mistake: We are treating a "convention" (an arbitrary rule we made up) as if it were a "measurement" (a fact of nature).
The Solution: The paper suggests we need to admit that the "Best Price" is just a local opinion, not a universal truth. We need to design systems that acknowledge the uncertainty, rather than pretending we have a perfect, universal clock.

Summary in One Sentence

The U.S. stock market tries to create a single, perfect "current price" for stocks across the country, but because of the speed of light, physics proves that such a thing is impossible, and the gap between this fake reality and the real world is being exploited to steal billions of dollars.

1. Problem Statement

The paper addresses a fundamental contradiction between the regulatory architecture of U.S. equity markets and the laws of physics.

The Regulatory Premise: Regulation NMS (2005) mandates the National Best Bid and Offer (NBBO), a consolidated price representing the "best available" bid and offer across all 16 U.S. exchanges "at any given time." This relies on the assumption that a single, objective "current" time exists simultaneously across geographically separated data centers (e.g., New Jersey to Chicago).
The Physical Reality: According to Einstein's Special Theory of Relativity, simultaneity is not absolute. For events separated by a spacelike interval (where the distance is too great for light to travel in the elapsed time), the temporal ordering of events is frame-dependent. There is no unique answer to "which event happened first" for spacelike-separated events; different inertial observers will disagree on the order.
The Conflict: The NBBO requires a total order (a definitive sequence of prices) for events that physics dictates can only have a partial order (some events are unordered/concurrent). The paper argues that the market treats a conventional choice (arrival time at a specific server) as an objective physical measurement, creating a "category mistake."

2. Methodology

The author employs a rigorous interdisciplinary approach combining Special Relativity, Distributed Systems Theory, and Market Microstructure Analysis.

Formal Definition (Engineered Simultaneity): The paper defines "Engineered Simultaneity" as a system satisfying three conditions:
1. It requires temporal comparison of events at spacelike-separated locations.
2. It implements this comparison via an implicit convention (e.g., order of arrival at a central processor).
3. It represents the result as an objective system property rather than a consequence of the convention.
Minkowski Spacetime Analysis: The author models the U.S. exchange network (New Jersey clusters vs. Chicago) using Minkowski diagrams.
- It calculates light-travel times ( $d/c$ ) and fiber propagation delays between exchanges.
- It applies the Lorentz transformation to prove that for quote updates occurring within the light-travel time of the distance between exchanges, there exist inertial frames where the temporal order of quotes is reversed.
Distributed Systems Mapping: The paper connects the physical problem to Lamport's Theorem on distributed ordering.
- It establishes that the "happened-before" relation ( $\to$ ) is the only physically meaningful ordering.
- It demonstrates that quote events at spacelike-separated exchanges are "concurrent" in Lamport's sense, meaning no causal ordering exists between them until communication occurs.
Economic Quantification: The paper analyzes latency arbitrage data to quantify the economic exploitation of this physical gap, comparing direct exchange feeds (low latency) against the Securities Information Processor (SIP) consolidated feed (high latency).

3. Key Contributions

Theorem 1 (Frame-Dependence of the NBBO): The paper formally proves that the NBBO is not a frame-independent measurement. If two quote events are spacelike-separated, there exist inertial reference frames where the "Best Bid" reported by the SIP differs from the "Best Bid" calculated in another frame.
Concept of "Engineered Simultaneity": The author introduces this term to describe the systematic construction of systems that treat impossible temporal comparisons as objective facts. This provides a precise descriptor for the mechanism behind the NBBO.
Distinction Between Convention and Reality: The paper clarifies that the SIP does not measure the market state; it measures the arrival time of data at a specific location. The "NBBO" is an artifact of the specific simultaneity convention (arrival at the SIP), not a universal truth.
Comparison to Google Spanner: The paper contrasts the financial system's approach with Google's Spanner database, which uses "TrueTime" to acknowledge uncertainty intervals. The financial system, conversely, pretends the uncertainty (the light-speed delay) does not exist.

4. Results

Physical Impossibility: The impossibility of a unique NBBO is exact and unavoidable within the causal structure of Minkowski spacetime. It is not a technical limitation that can be solved by faster clocks or better synchronization; it is a law of physics.
The Latency Gap:
- Direct proprietary feeds receive data in $\approx 10$ microseconds.
- The SIP consolidated feed introduces a delay of $\approx 1,128$ microseconds (for the NJ-Chicago corridor).
- This creates a >50:1 ratio in latency, allowing direct-feed participants to inhabit a reference frame closer to the exchange's local frame, while SIP users inhabit a displaced frame.
Economic Extraction:
- High-frequency traders (HFT) exploit the temporal ambiguity between the "true" local order and the SIP's consolidated order.
- Citing Aquilina, Budish, and O'Neill, the paper estimates that $5 billion per year is extracted globally via latency arbitrage "races" caused by this ambiguity.
- HFTs win 96–99% of races involving stale quotes.
Refutation of Counterarguments: The paper refutes the argument that the NBBO is "97% accurate" (Bartlett and McCrary). It argues that accuracy is irrelevant if the underlying concept is incoherent; the 3% failure rate is where the $5 billion is extracted, representing a fundamental conceptual error, not statistical noise.

5. Significance

Regulatory Implications: The paper argues that U.S. financial regulation (Regulation NMS) is built on a pre-relativistic assumption of absolute time. Recognizing that the NBBO is a "convention" rather than an "objective measurement" is a prerequisite for principled system design.
System Design: It highlights that treating timestamps as physical measurements of ordering in distributed systems is a category mistake. Systems must either acknowledge uncertainty intervals (like Spanner) or accept that their "consolidated" view is inherently subjective to the observer's location.
Economic Efficiency: The current structure creates a socially wasteful extraction of wealth ($5B/year) based on temporal ambiguity rather than value creation (liquidity provision or price discovery).
Theoretical Bridge: The work successfully bridges the gap between high-energy physics (Special Relativity) and computer science (Distributed Consensus), showing that the "impossibility of distributed ordering" is a physical law, not just a computational challenge.

In conclusion, the paper asserts that the U.S. equity market's core regulatory mechanism is physically impossible to define objectively. The "NBBO" is a useful engineering convention, but presenting it as an objective reality allows for significant, physics-based arbitrage that undermines market fairness.