More than a century ago, Albert Einstein searched for a single theory that could describe two or more known interactions—electromagnetism, gravity, and the weak and strong forces—previously described in separate theories. The search for this “unified field theory” has ultimately been left unfinished.
Now, a team of researchers says they have produced a purely geometric theory that can unite gravity and electromagnetism—two of nature’s fundamental forces—by borrowing from advanced geometric frameworks and building on ideas of 20th-century pioneers like Hermann Weyl, Arthur Eddington, and Erwin Schrödinger.
The team’s new theory is detailed in a paper published in the Journal of Physics.
While concepts that include string theory have left researchers hanging on promises of a unified theory, the new approach proposed by researchers Jussi Lindgren, Andras Kovacs, and Jukka Liukkonen sees a return to Einstein’s original vison: one where electromagnetism could emerge from the fabric of spacetime itself, very similar to the late physicist’s ideas on gravity.
Employing generalizations of differential geometry and calculus variations, the team successfully derived nonlinear field equations from optimized variations on the spacetime metric, which gave them the basis for a new geometric foundation for Maxwell’s classical equations.
“String theory is hardly testable (at least in Popperian terms) with its 11 dimensions,” said study co-author Jussi Lindgren in an email to The Debrief. Citing recent work by physicists like Stanford University Professor Leonard Susskind that suggests approaches taken in string theory are not correct, Lindgren and his colleagues offer an intriguing alternative: that electromagnetic forces, electric charges, and currents are not independent entities but are instead intrinsic features of spacetime geometry.
In the research team’s new model, electric charge is interpreted as a local compression—or covariant divergence—of spacetime, with charged particles following geodesics, just as in Einstein’s general relativity.
“In our approach, the local geometry of spacetime creates electric and magnetic fields as well as electric charge,” Lindgren told The Debrief. “Electric and magnetic fields are kinds of twists of spacetime, and charge is a local compression of spacetime.”
“At Planck scales I would expect random electric and magnetic fields and random creation and annihilation of charge, kind of quantum foam as described by John Wheeler,” Lindgren said, adding that similar concepts may apply to cosmic phenomena like black holes. For now though, he says, “it is too early to tell.”
Additionally, a once-dismissed theory, Weyl’s original scale geometry of 1918, plays a key role in this framework. The researchers combined it with modern geometric algebra, finding that their combination allows for a natural and consistent description of how electromagnetic fields emerge from localized spacetime distortions.
“I personally prefer Weyl geometry, as this geometry is truly relativistic, it is aesthetically appealing,” Lindgren told The Debrief. “Lengths are local phenomena, as well as directions. It also fits better in the framework of general relativity.”
Notably, Lindgren and his colleagues say this model also accounts for quantum phenomena like the Aharonov-Bohm effect, predicting forces even in regions where no classical electromagnetic field is present.
“The electromagnetic potential turns out to be a building block of the metric tensor itself,” Lindgren and his paper’s co-authors wrote in a recent essay describing their work. “Light, in this theory, is not just a wave or a particle—it is a ripple in spacetime, a view that echoes Einstein’s own later musings about the aether being nothing more than spacetime itself.”
The team’s findings also suggest that electromagnetic vacuum fluctuations at the Planck scale could lead to spontaneous charge creation and annihilation—a potential bridge to quantum field theory.
Lindgren told The Debrief that he and his colleagues believe their new approach has the potential to help resolve several lingering questions in modern physics, such as why an electromagnetic force is present when electric and magnetic fields are absent.
“The framework of General Relativity has been tested successfully, and our approach can explain many questions, such as, ‘In which medium do electromagnetic waves oscillate?’” Lindgren told The Debrief.
“Our paper provides testable and quantifiable predictions on Lorentz force and the effect of strong electromagnetic fields on spacetime geometry.”
While much work remains, the authors believe a sufficiently complete geometric theory of electromagnetism now exists for deeper exploration. If independently validated and accepted into the broader framework of modern physics, Lindgren and his colleagues’ new work may not only help complete Einstein’s unfinished dream of a unified field theory but also mark a turning point in how we understand the universe’s most fundamental forces.
The team’s paper, “Electromagnetism as a purely geometric theory,” was published in the Journal of Physics: Conference Series.
Micah Hanks is the Editor-in-Chief and Co-Founder of The Debrief. He can be reached by email at micah@thedebrief.org. Follow his work at micahhanks.com and on X: @MicahHanks.