When Albert Einstein first debated the strange logic of quantum mechanics, he probably didn’t imagine his ideas might one day help predict stock market meltdowns. However, according to a new study, that’s exactly what could be happening.
In a paper to be published in the December 2025 edition of The Journal of Finance and Data Science, researchers from Germany, the United Kingdom, and Poland propose that mathematical tools originally developed to test whether subatomic particles are “entangled” could also serve as early warning indicators of financial crises.
The team, led by Arefeh Zarifian of the Technische Hochschule Mittelhessen and the Justus Liebig University in Gießen, tested a concept called Bell inequalities—a foundational principle in quantum physics—on real-world market data.
Their findings suggest that these so-called “Bell violations,” long used to probe the boundaries of reality, may also signal when global markets are on the brink of collapse.
“Traditional approaches to crisis analysis do not, in general, adequately represent event-based dependencies and the distribution of tail risks inherent in complex financial systems,” the researchers write. “The proposed approach is underwritten by a generic causal framework, which we think is suitable for financial analysis: we offer an index for financial stress and we explore its value in detecting extreme market co-movements, which may serve as an early crisis warning signal.”
Bell’s inequalities, first introduced by physicist John Bell in 1964, were designed to determine whether the behavior of quantum particles could be explained by classical physics—or whether something deeper, stranger, and more interconnected was at work.
In essence, the equations test whether two seemingly separate systems are correlated beyond what normal cause-and-effect could predict.
In this latest study, researchers have taken that logic out of the lab and into the markets. They built a mathematical model that treats pairs of stocks like quantum particles—“Alice and Bob,” in the language of physics—whose movements can appear mysteriously correlated.
When those correlations exceed a certain mathematical limit, known as a Bell violation, it suggests that something beyond ordinary market randomness is at play.
In the financial context, those violations may signal the buildup of systemic stress that often precedes crises. The researcher’s framework translates the physics concept into an index they call the S1-violation proportion, a measure of how often pairs of stocks move in unexpectedly synchronized ways.
When that synchronization spikes, they argue, it’s a red flag.
To test their theory, the researchers applied the Bell-based index to historical data from the S&P 500 and STOXX Europe 600, covering three of the most turbulent financial crises of the past two decades: the 2008 global financial meltdown, the 2010 European debt crisis, and the 2020 COVID-19 crash.
Across all three cases, the quantum-inspired signal showed remarkable consistency. Before and during each crisis, the S1-violation index surged—tracking, and sometimes even anticipating, the spikes seen in traditional volatility measures like the VIX, known as the “fear gauge.”
“The findings demonstrate the framework’s ability to align the number of observed Bell inequalities violations with observed peaks in market stress,” the researchers write.
For instance, during the 2008 collapse, researchers found that the Bell-violation index remained stable through early fluctuations but began to rise sharply just as the crisis reached its tipping point—coinciding with the September 2008 bankruptcy of Lehman Brothers. Unlike the VIX, which bounced erratically throughout the panic, the Bell-based index stayed high and steady, reflecting a prolonged period of systemic stress.
A similar pattern emerged in Europe’s sovereign debt crisis of 2010, when concerns over Greece’s default spread through the Eurozone. The new index rose in parallel with European volatility measures and continued to climb even after the initial panic subsided, capturing the lingering effects of economic uncertainty that followed.
And when the COVID-19 pandemic sent shockwaves through global markets in early 2020, the same signal reappeared, rising sharply as stock prices plummeted worldwide.
Financial analysts have long relied on a handful of standard measures to gauge risk, including credit default swap (CDS) spreads, which reflect the cost of insuring against corporate or sovereign defaults, and implied volatility indices such as the VIX and its European counterpart, VSTOXX.
However, those traditional tools have blind spots. CDS spreads often react after a crisis is already underway, and volatility indices only exist for markets with highly liquid options. The Bell-based approach, by contrast, can be applied to any market with price data, making it potentially applicable to a universal market.
“It can provide a stable and persistent signal of financial risk that remains elevated even as implied volatility indices exhibit a temporary jump during the crisis period,” the researchers explain.
In other words, this “quantum” indicator doesn’t just spike in moments of panic—it lingers, reflecting deep interconnections that remain stressed even after markets appear to calm down.
The paper’s results also showed that this new measure was less erratic than conventional correlation-based methods. While Pearson correlation coefficients can swing wildly even during normal trading conditions, the Bell-violation index proved far more stable, suggesting it could help analysts separate noise from genuine warning signs.
Researchers are careful to note that their use of Bell inequalities isn’t about quantum mechanics invading economics. The stock market isn’t literally a quantum system.
However, the mathematical logic behind quantum entanglement, researchers argue, provides a more accurate model for understanding nonlinear relationships and event-based dependencies that classical financial equations often overlook.
That’s because real-world crises rarely follow neat, linear patterns. They emerge from cascading, often invisible interconnections. These are precisely the kind of complex dependencies Bell’s framework was designed to detect.
While the research is still experimental, its implications could be profound. If refined, this quantum-inspired method might help central banks, regulators, or financial institutions detect instability earlier. Consequently, this could provide policymakers with an opportunity to act before the next contagion spreads.
Future work, the team suggests, could extend the approach beyond stocks to include macroeconomic data such as GDP, unemployment, or global trade flows. In time, that might offer a way to build a “Bell barometer” for entire economies—an algorithmic early-warning system rooted in one of physics’ most profound insights about cause and effect.
For now, the study offers a tantalizing reminder that the strange mathematics used to probe the nature of reality could also illuminate the delicate, interconnected machinery of human markets.
By adapting Bell’s theorem into what they call a causal model for financial systems, the researchers hope to build more realistic tools for crisis prediction. As they describe it, financial markets, like quantum particles, are entangled networks—where small shocks can propagate unpredictably through the system.
“By identifying warning signals in the form of changes in a causal relationship, as indicated by measures such as the S1-violation proportion, stakeholders can implement preventive measures, for instance, more effective macroprudential regulations,” the researchers write. “Ultimately, such foresight could limit the socio-economic fallout of crises, preserving employment, maintaining financial stability, and minimizing long-term structural damage to economies.”
Tim McMillan is a retired law enforcement executive, investigative reporter and co-founder of The Debrief. His writing typically focuses on defense, national security, the Intelligence Community and topics related to psychology. You can follow Tim on Twitter: @LtTimMcMillan. Tim can be reached by email: tim@thedebrief.org or through encrypted email: LtTimMcMillan@protonmail.com