Philip Phillips and Gabriele La Nave introduce fractional electromagnetism theory, could explain 'strange metals'

Sandhya Sivakumar, Staff Writer, Illinois Physics
5/29/2019

Illinois Physics Professor Philip Phillips presenting to his group at the Institute for Condensed Matter Physics in Urbana. Photo by L. Brian Stauffer, University of Illinois at Urbana-Champaign
Illinois Physics Professor Philip Phillips presenting to his group at the Institute for Condensed Matter Physics in Urbana. Photo by L. Brian Stauffer, University of Illinois at Urbana-Champaign
Illinois Physics Professor Philip Phillips and Math Professor Gabriele La Nave have theorized a new kind of electromagnetism far beyond anything conceivable in classical electromagnetism today, a conjecture that would upend our current understanding of the physical world, from the propagation of light to the quantization of charge. Their revolutionary new theory, which Phillips has dubbed “fractional electromagnetism,” would also solve an intriguing problem that has baffled physicists for decades, elucidating emergent behavior in the “strange metal” of the cuprate superconductors.

This research is published in an upcoming colloquium paper in Reviews of Modern Physics (arXiv:1904.01023v1).

The Phillips–La Nave theory builds on the well-known work of physicists Michael Faraday and Emmy Noether.

“Michael Faraday’s 1832 experiments proved unequivocally that electricity and magnetism are in fact two sides of the same coin—hence, any theory that treats them as separate is redundant. This redundancy is known as a gauge symmetry,” explains Phillips. “Emmy Noether, a prominent mathematician of the early 20th century, noticed a pattern in such redundancies. Her first theorem states that such redundancies imply that something is being conserved. Noether’s first theorem, underlies much of modern theoretical physics.

“However, Noether’s second theorem, considerably less well known, points to a potential problem with the first theorem. What she noticed is that the redundancies cannot be uniquely specified, and hence the form of the conserved quantity is inherently ambiguous.

“However, in showing how the redundancies cannot be uniquely formulated, Noether only considered ordinary derivatives,” notes Phillips. “No new information arises in this approach, and this is why the second theorem has been overlooked for a century. But the second theorem also allows redundancies formulated in terms of fractional derivatives. By such calculations, many nontrivial consequences arise for the conserved current and the basic equations of electromagnetism.”

A key consequence of Phillips and La Nave’s fractional electro-magnetism is that the dimensionality of the current isn’t just determined by the dimensionality of spacetime—it can acquire any value. Likewise, the charge is no longer quantized as in the standard Maxwell theory, turning classic physics on its head.

“One major consequence of fractional magnetism is that the current is free to take any value, which has a logical, yet surprising effect on charge,” Phillips asserts. “Because it can take any value, it’s no longer quantized. By exploiting this loophole, we have devised an entire class of new electromagnetisms, which also contains the standard Maxwell case.”

Phillips and La Nave’s new mathematical formulation of electromagnetism would solve the baffling strange metal problem of the cuprate superconductors. Strange metals exhibit emergent behaviors that deviate from the standard theory of metals and have defied explanation for the past 30 years.  

“Mathematically, a key component of the proof relies on extra dimensions,” Phillips explains, “and it is here that the mathematical insight of Professor Gabriele La Nave was crucial. Physicist Juan Maldacena showed that extra dimensions are useful in thinking about the relationship between gravity and quantum field theory. By exploiting this construct, we demonstrated that certain interactions in higher dimensional gravity theories reduce to fractional electromagnetism in a spacetime with one lower dimension.

“The implication here is that materials exhibiting non-standard redundancies in electromagnetism have hidden dimensions.”

Illinois Physics graduate student Kridsanaphong Limtragool contributed to the theoretical work pointing to charge no longer being quantized in this extra-dimensional formulation of fractional electromagnetism. According to Phillips, a smoking-gun proof of this higher dimensionality is the breakdown of charge quantization. Phillips says experiments designed to test this in the strange metal phase of cuprate superconductors could offer the first validation of extra dimensions in matter.

This work is funded by the National Science Foundation and the Center for Emergent Superconductivity, a Department of Energy Frontier Research Center. The conclusions presented are those of the researchers and not necessarily those of the funding agencies.

Recent News

  • Research
  • Condensed Matter Physics
  • Condensed Matter Experiment
  • Condensed Matter Theory

One of the greatest mysteries in condensed matter physics is the exact relationship between charge order and superconductivity in cuprate superconductors. In superconductors, electrons move freely through the material—there is zero resistance when it’s cooled below its critical temperature. However, the cuprates simultaneously exhibit superconductivity and charge order in patterns of alternating stripes. This is paradoxical in that charge order describes areas of confined electrons. How can superconductivity and charge order coexist?  

Now researchers at the University of Illinois at Urbana-Champaign, collaborating with scientists at the SLAC National Accelerator Laboratory, have shed new light on how these disparate states can exist adjacent to one another. Illinois Physics post-doctoral researcher Matteo Mitrano, Professor Peter Abbamonte, and their team applied a new x-ray scattering technique, time-resolved resonant soft x-ray scattering, taking advantage of the state-of-the-art equipment at SLAC. This method enabled the scientists to probe the striped charge order phase with an unprecedented energy resolution. This is the first time this has been done at an energy scale relevant to superconductivity.

  • Alumni News
  • In the Media

Will Hubin was one of those kids whose wallpaper and bed sheets were covered in airplanes and who loved building model airplanes. By the time he took his first flight in the late 1940s, he was hooked.

Now, he shares his passion for planes with children by taking them for their first flight, at no charge, in his four-seat 2008 Diamond DA-40 aircraft through the local Experimental Aircraft Association’s Young Eagles program.

“It’s a lot of fun and pretty rewarding. Anyone who loves flying likes to introduce others to it. It’s true of anything, any hobbyist. Some will talk constantly but they’re ecstatic,” said Hubin, a retired Kent State University physics professor.

Hubin learned to fly in 1962 when he was earning a doctorate in physics at the University of Illinois and has been flying ever since, adding commercial, instrument, instructor, multi-engine and seaplane ratings.

  • Research
  • Theoretical Biological Physics
  • Biological Physics
  • Biophysics

While watching the production of porous membranes used for DNA sorting and sequencing, University of Illinois researchers wondered how tiny steplike defects formed during fabrication could be used to improve molecule transport. They found that the defects – formed by overlapping layers of membrane – make a big difference in how molecules move along a membrane surface. Instead of trying to fix these flaws, the team set out to use them to help direct molecules into the membrane pores.

Their findings are published in the journal Nature Nanotechnology.

Nanopore membranes have generated interest in biomedical research because they help researchers investigate individual molecules – atom by atom – by pulling them through pores for physical and chemical characterization. This technology could ultimately lead to devices that can quickly sequence DNA, RNA or proteins for personalized medicine.

  • In Memoriam

We are saddened to report that John Robert Schrieffer, Nobel laureate and alumnus of the Department of Physics at the University of Illinois at Urbana-Champaign, passed away on July 27, 2019, in Tallahassee, Florida. He was 88 years old.

Schrieffer was the “S” in the famous BCS theory of superconductivity, one of the towering achievements of 20th century theoretical physics, which he co-developed with his Ph.D advisor Professor John Bardeen and postdoctoral colleague Dr. Leon N. Cooper. At the time that Schrieffer began working with Bardeen and Cooper, superconductivity was regarded as one of the major challenges in physics. Since the discovery of the hallmark feature of superconductivity in 1911—the zero resistance apparently experienced by a current in a metal at temperatures near absolute zero—a long list of famous theoretical physicists had attempted to understand the phenomenon, including Albert Einstein, Niels Bohr, Richard Feynman, Lev Landau, Felix Bloch, Werner Heisenberg and John Bardeen himself (who was awarded the Nobel Prize for his co-invention of the transistor at around the time that Schrieffer began working with him in 1956).