Quantum particle entangled with a stock chart

Quantum Leaps: Can Quantum Mechanics and Market Dynamics Reveal Universal Truths?

Mira Elwood in Science & Nature November 2025 • 4 min read.

"Unlocking the secrets of complex systems by merging quantum physics with financial models."

For decades, scientists have sought universal laws governing complex systems, from bustling financial markets to the intricate dance of quantum particles. These systems, characterized by numerous interacting components, uncertainty, and emergent patterns, challenge our understanding of how the world works. Complexity sciences, an interdisciplinary field, aims to decode these patterns, offering insights applicable across various natural and social science disciplines.

A new theory proposes a fascinating connection between quantum mechanics and financial markets, suggesting that principles governing the behavior of subatomic particles might also apply to the seemingly chaotic world of trading. This innovative approach seeks to uncover a universal law of complex adaptive learning, potentially revolutionizing our understanding of systems ranging from stock markets to quantum entanglement.

The theory delves into the mathematical underpinnings of both quantum mechanics and financial models, proposing a 'non-localized wave equation' that mirrors principles found in quantum physics. By bridging these seemingly disparate fields, researchers aim to address longstanding challenges, such as understanding non-Gaussian distributions in quantum entanglement and predicting market behavior.

Bridging the Quantum Realm and Financial Markets: A Bold New Theory

Quantum particle entangled with a stock chart

The core of this theory lies in the idea that complex adaptive systems, whether they involve atoms or stock traders, share fundamental characteristics. These systems adapt, learn from feedback, and generate hidden patterns as their components interact. The challenge, however, lies in finding a universal law that explains these behaviors across diverse domains.

To tackle this challenge, the researchers draw upon Schrödinger's wave equation from quantum mechanics and Shi's trading volume-price wave equation from finance. Schrödinger's equation describes the behavior of quantum particles, while Shi's equation models price fluctuations in financial markets. The theory suggests an inherent relationship between these equations, proposing a 'non-localized wave equation' in quantum mechanics that incorporates principles from financial modeling.

The proposed theory hinges on several key concepts:

Non-Localized Momentum: Redefining momentum in quantum mechanics to account for non-local interactions.
Skinner-Shi Coordinates: Introducing a coordinate system that combines reinforcement learning principles with quantum states.
Interaction Conservation: Suggesting that quantum entanglement is governed by interaction conservation rather than energy conservation.

This approach leads to a provocative conclusion: quantum entanglement, the phenomenon where particles become linked regardless of distance, is not merely a consequence of superposed coherent states but an 'interactively coherent state.' This means that entangled particles are constantly adapting to each other, driven by interaction conservation.

Implications and the Road Ahead

While this theory is still in its early stages, it offers a fresh perspective on complex systems and quantum entanglement. By suggesting a connection between quantum mechanics and financial markets, it opens new avenues for research and could lead to a deeper understanding of the fundamental laws governing the universe. Although further experimental validation is needed, the theory provides a compelling framework for exploring the intersection of seemingly disparate fields.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2306.15554,

Title: A Theory Of Complex Adaptive Learning And A Non-Localized Wave Equation In Quantum Mechanics

Subject: q-fin.gn nlin.ao quant-ph

Authors: Leilei Shi, Xinshuai Guo, Jiuchang Wei, Wei Zhang, Guocheng Wang, Bing-Hong Wang

Published: 27-06-2023

Everything You Need To Know

What is the core concept behind the theory that links quantum mechanics and financial markets?

The core idea is that complex adaptive systems, whether they involve atoms or stock traders, share fundamental characteristics. This theory suggests a universal framework for understanding these systems by bridging quantum mechanics and financial models. The theory proposes a 'non-localized wave equation' that mirrors principles found in quantum physics, aiming to uncover a universal law of complex adaptive learning.

How does the theory use Schrödinger's wave equation and Shi's trading volume-price wave equation?

The theory draws upon Schrödinger's wave equation from quantum mechanics, which describes the behavior of quantum particles, and Shi's trading volume-price wave equation from finance, which models price fluctuations in financial markets. It proposes an inherent relationship between these equations, suggesting a 'non-localized wave equation' in quantum mechanics that incorporates principles from financial modeling to better understand complex systems.

What are the key concepts introduced by this theory?

The theory introduces three key concepts: 'Non-Localized Momentum,' which redefines momentum in quantum mechanics to account for non-local interactions; 'Skinner-Shi Coordinates,' a coordinate system that combines reinforcement learning principles with quantum states; and 'Interaction Conservation,' suggesting that quantum entanglement is governed by interaction conservation rather than energy conservation.

How does the concept of 'Interaction Conservation' change our understanding of quantum entanglement?

The theory suggests that quantum entanglement is governed by 'Interaction Conservation' rather than energy conservation. This means that entangled particles, such as those described by the 'non-localized wave equation', are constantly adapting to each other. This perspective views entanglement as an 'interactively coherent state,' where particles are linked through continuous interaction and adaptation.

What are the potential implications of this theory, and what further steps are needed?

This theory offers a fresh perspective on complex systems and quantum entanglement by connecting quantum mechanics and financial markets. It opens new avenues for research and could lead to a deeper understanding of the fundamental laws governing the universe. Further experimental validation is needed to confirm the theory's claims, but it provides a compelling framework for exploring the intersection of seemingly disparate fields such as understanding non-Gaussian distributions in quantum entanglement and predicting market behavior using the 'non-localized wave equation'.