Postdocs unify physics theories

For decades, physicists have accepted that the universe has two sizes: small and large. So-called classical equations govern big objects like baseballs and galaxies, while quantum mechanics describes the strange world of subatomic particles. But researchers led by chemistry postdoc Denys Bondar have developed a systematic approach, known as operational dynamic modeling, to fuse those equations.

To accomplish this daunting task, which has been traditionally thought impossible, the team’s framework inverts a standard vantage point of theoretical physics. Rather than validating existing mathematical models with experimental data, Bondar uses the data to derive the equations.

“In physics, we are constantly presented with data, and we’re tasked with explaining it,” Bondar said. “Traditionally, scientists would go off and try to develop elegant theories to fit the data by trial and error. Our goal is to systematize this process, to make it more efficient.”

Bondar co-developed the process with chemistry postdoc Renan Cabrera.

In a recent paper published in the journal Physical Review Letters, the team attempts to reconcile the equations of classical and quantum mechanics through a single question, which, in simplest terms, is “to commute or not to commute?”

An equation is said to “commute” if the order in which the data appears does not affect the outcome. Commutative equations characterize classical mechanics, while non-commutative laws arise in quantum mechanics.

By classifying data in this manner, operational dynamic modeling can produce equations that work equally well at the quantum and classical levels. Previously, physicists were forced to choose between different sets of equations to describe systems with which they were working.

This framework, according to Bondar, is reflective of a broader trend in the scientific community toward large-scale information processing.

“It represents what’s going on nowadays. If you look beyond the sciences, with the rise of information technology, we have vast amounts of data that need to be understood,” Bondar said. “Our hope is to evolve operational dynamic modeling into a kind of data mining technique.”

To this end, Bondar’s team, working in the research group of chemistry professor Herschel Rabitz, hopes to apply the process to validate other fundamental physical theories, and perhaps to generate some new ones.

On a philosophical level, their research challenges a central tenet of early modern physics.

The believed impossibility of reconciling quantum and classical mechanics dates from 1900, when the German mathematician David Hilbert published a list of 23 unsolved problems that he believed to be fundamental to the progress of modern knowledge. The sixth of these was to generate a list of central axioms for physics from which almost all future equations in the discipline would follow.

Get the best of the ‘Prince’ delivered straight to your inbox. Subscribe now »

Bondar’s research proposes a unique solution to Hilbert’s sixth problem.

“The answer is kind of a trivial answer: The question is wrong,” he joked. “Let’s not search for the one law or the one unifying theory. Physics is the result of data, and data, along with the tools to process it, is the unifying element.”

The perceived disconnect between classical and quantum theory traces its earliest origins to Austrian physicist Paul Ehrenfest, who first noted similarities between classical and quantum theory in the early 20th century. Ehrenfest’s work has been long overshadowed by the work of more famous contemporaries — like fellow Austrian Erwin Schrodinger, whose equation has long been considered a cornerstone of modern quantum mechanics. However, the Princeton team has demonstrated that Ehrenfest’s ideas might be the more powerful in a data-driven world. Traditionally, Schrodinger’s equation was used to derive Ehrenfest’s. But “in the spirit of ODM,” according to the paper, Bondar’s team flipped that relationship, generating Schrodinger’s equation from Ehrenfest’s.

Although the system is currently being used to study small systems like single electrons, Bondar hopes its novel approach will prove able to verify all the fundamental equations of modern physics, and perhaps beyond.

“It’s like we’re looking at the world through a new lens. Our ultimate aim is to systematize science, to use ODM to generate new theories of unknown phenomena,” Bondar explained. “And if we can develop this into a computational rather than a conceptual model, there’s nothing to say we can’t apply the same ideas to other areas of research.”

The paper appeared in the journal Physical Review Letters on Nov. 8, 2012. Along with Cabrera and Rabitz, Bondar co-authored the report with Robert Lompay of the Uzhgorod National University in Ukraine and Misha Ivanov of Imperial College, London.