By Philip Ball

Barbara De Angelis, a notable figure in pop psychology, famously stated, “Love is a force more formidable than any other.” This sentiment exemplifies how we often intertwine the principles of physics with social dynamics.

Expressions like “I was irresistibly attracted to him,” or “We recognize the force of public opinion” reflect a pervasive trend where we metaphorically employ the lexicon of physics to articulate social experiences. However, while we can quantify forces like gravity, we cannot measure such "social forces" in the same manner. The integration of physics into our understanding of social behavior is prevalent across various fields, including economics and psychology. The pertinent question, however, is whether this approach is beneficial or detrimental.

Portraying individuals as mere particles or magnets may seem demeaning. The real risk lies in utilizing the wrong physics to conceptualize society. Physicists recognize that classical equilibrium models, which suggest systems reach a stable state, do not always apply. Likewise, social theorists must avoid simplifying society into a deterministic framework akin to Newtonian mechanics, as human behavior is inherently unpredictable and often surprises us.

The allure and limitations of applying physics to social contexts are particularly evident in economics. Although Adam Smith did not coin the term “market forces,” he drew parallels between economic dynamics and gravity. He noted how market prices tend to gravitate toward a “natural” value, likening this to the gravitational pull described by Newton. Smith's metaphor of the “invisible hand” suggests an equilibrium within the economy.

During the 19th century, there was a widespread belief that economics operated under universal laws akin to those governing celestial bodies. Any attempts to interfere with market operations were seen as counterproductive. Ralph Waldo Emerson articulated this sentiment, stating that natural laws govern trade as surely as they govern the tides.

However, a key criticism of this analogy is that, unlike celestial bodies, economic actors are influenced by subjective motivations and unpredictable human behavior. Despite this, 18th and 19th-century scientists believed they could quantify human actions through statistical analysis. They discovered that even seemingly random events followed predictable statistical patterns, leading to the notion that societal laws exist similarly to physical laws. This idea further supported Auguste Comte's vision of a hierarchical science system modeled after Newtonian principles.

The question then arises: from where do these economic laws originate? They emerge from the myriad decisions of individual market participants. Mid-19th century scientists like James Clerk Maxwell and Ludwig Boltzmann used statistical reasoning to analyze matter, revealing that macroscopic properties could result from countless microscopic interactions.

This statistical approach found its way into economics, with Louis Bachelier developing a rudimentary theory of random walks as early as 1900, which he applied to stock market fluctuations. More impactful was Josiah Willard Gibbs, who laid the groundwork for statistical mechanics that remains relevant today. Gibbs’ student Edwin Bidwell Wilson mentored economist Paul Samuelson, who integrated Gibbs’ statistical insights into the foundation of microeconomics in his influential 1947 work, Foundations of Economic Analysis.

While it might seem advantageous to borrow concepts from physics, the issue arises when the physics employed is ill-suited for economic systems. Gibbs’ statistical mechanics was designed for systems at equilibrium, not for the volatile nature of markets. Traditional economic theories often depict markets as stable entities, yet real-world observations reveal significant fluctuations.

Economists generally attribute market volatility to random external shocks, but economic data consistently exhibit characteristics that contradict the idea of equilibrium, such as heavy-tailed distributions. Despite this, many economic models, including the Black-Scholes formula, neglect these features, which contributed to the 2008 financial crisis.

The failure to recognize that markets are non-equilibrium systems stems from a tendency to idealize economic models. W. Brian Arthur notes that while equilibrium models have provided a framework for understanding economic patterns, they overlook the chaotic and unpredictable nature of reality.

Modern economic research increasingly acknowledges that markets display signs of non-equilibrium behavior, where price fluctuations result from the dynamic interactions between market participants rather than isolated decisions. The phenomenon of herding behavior, where individuals mimic others, plays a significant role in market dynamics, reminiscent of Keynes’ concept of “animal spirits.” Non-equilibrium models that account for feedback mechanisms offer a more accurate representation of market behavior.

Despite the progress in understanding non-equilibrium systems, many economists remain hesitant to incorporate insights from contemporary statistical physics into economic theory. This reluctance is partly due to the entrenched nature of traditional models and the ideological implications of adopting non-equilibrium frameworks, which suggest a more complex view of market dynamics.

The consequences of clinging to equilibrium models are significant. The belief in stable markets led to misguided assertions before the 2008 crisis, yet there has been little introspection within economic circles since then.

Physicists have been exploring alternatives to equilibrium models for decades, seeking to understand systems that defy simple predictability. Lars Onsager’s work in the 1930s laid the foundation for understanding relationships between forces and processes in non-equilibrium systems, earning him a Nobel Prize in Chemistry. Similarly, Ilya Prigogine extended non-equilibrium thermodynamics, illustrating that systems can maintain order even while deviating from equilibrium.

The study of non-equilibrium phenomena has revealed that organized structures can emerge from chaotic systems, such as convection patterns in heated liquids, which are not in equilibrium yet exhibit remarkable order.

In social contexts, modeling crowd behavior as particles influenced by various forces has garnered interest. Early theories likened social interactions to charged particles, while contemporary models explore how crowd dynamics resemble statistical distributions of gas particles. However, many real-world social phenomena do not settle into stable patterns, reflecting the non-equilibrium nature of human interactions.

These insights have been applied to traffic modeling, which draws parallels between the behaviors of vehicles and phase transitions in physical states. Furthermore, voting behavior and opinion formation are analyzed through similar frameworks, highlighting how individual choices influence collective outcomes.

As researchers strive to apply physics-based models to complex social scenarios, collaboration across disciplines becomes essential. The aim is to develop predictive models that accommodate the intricacies of human behavior and societal structures.

Ultimately, a physics of society should aim to provide insights into possible outcomes rather than dictate moral choices. While it cannot prescribe solutions, it can help us anticipate the consequences of our actions, allowing us to design social systems that align more closely with human nature.

In a world marked by uncertainty, understanding the dynamics of social phenomena through the lens of physics may offer valuable perspectives on navigating future challenges.

Philip Ball is the author of Invisible: The Dangerous Allure of the Unseen and has written extensively on science and art.