December 13, 2019 | David F. Coppedge

Maxwell’s Equations Touch Quantum Mechanics

MIT physicists are cheering a breakthrough that celebrates the applicability of Maxwell’s theory to the nano scale.

James Clerk Maxwell, a devout Christian who revolutionized physics with his theory of electromagnetism in 1865, has been vindicated again and again. One scale of phenomena, however, has been difficult to reconcile with the famous Maxwell’s Equations: the nanometer scale, where electromagnetic forces clash with quantum mechanics. Now, Massachusetts Institute of Technology (MIT) is saying, “Cheers! Maxwell’s electromagnetism extended to smaller scales.

Maxwell's EquationsMore than one hundred and fifty years have passed since the publication of James Clerk Maxwell’s “A Dynamical Theory of the Electromagnetic Field” (1865). What would our lives be without this publication? It is difficult to imagine, as this treatise revolutionized our fundamental understanding of electric fields, magnetic fields, and light. The twenty original equations (nowadays elegantly reduced into four), their boundary conditions at interfaces, and the bulk electronic response functions … are at the root of our ability to manipulate electromagnetic fields and light….

Therefore, wondering what our life would be without Maxwell’s equations means to try to envision our life without most of current science, communications and technology.

Indeed, it would be difficult to overstate the impact of Maxwell’s work, which built on the experimental work of Michael Faraday (another devout Christian). It gave engineers both a theoretical understanding and practical equations to use. Those equations cover an enormous range of phenomena from atoms to galaxies. Formulated within the classical physics era, Maxwell’s theory nevertheless was ready for Einsteinian relativity without needing revision. Newton, Maxwell and Einstein are often portrayed as a triumvirate of the greated physicists in history.

On large (macro) scales, bulk response functions and the classical boundary conditions are sufficient for describing the electromagnetic response of materials, but as we consider phenomena on smaller scales, nonclassical effects become important…. Why does this powerful framework break down towards nanoscales? The problem is that electronic length scales are at the heart of nonclassical phenomena, and they are not part of the classical model. Electronic length scales can be thought of as the Bohr radius or the lattice spacing in solids: small scales that are relevant for the quantum effects at hand.

Now, Yang et al. found a way to connect Maxwell’s Equations to the scale of subatomic particles, where quantum phenomena tend to overwhelm the behavior of phenomena – and the equations still hold. The physicists are clearly excited about what this means.

On the experimental side, the authors investigate film-coupled nanoresonators, a quintessential multiscale architecture. The experimental setup was chosen because of its nonclassical nature. Even so, recently graduated postdoc and lead author Yi Yang comments: “When we built our experiment, we were lucky enough to run into the right geometry that enabled us to observe the pronounced nonclassical features, which were actually unexpected and excited everyone. These features eventually enabled us to measure the d-parameters, which are hard to compute for some important plasmonic materials like gold (as in our case).”

The new model and experiments are momentous both for fundamental science and for diverse applications. It makes a hitherto unexplored connection between electromagnetism, material science, and condensed matter physics—one that could lead to further theoretical and experimental discoveries in all related fields, including chemistry and biology.

The world is poised to get better with Maxwell’s Equations still intact after 155 years, now extended to the realm of the very small. What might we see? Notice the enthusiasm:

Application-wise, this work points to the possibility of engineering the optical response beyond the classical regime – an example would be to explore how to extract more power from emitters using antennas.

MIT Professor Marin Soljačić is enthusiastic: “We expect this work to have substantial impact. The framework we present opens a new chapter for cutting-edge nanoplasmonics—the study of optical phenomena in the nanoscale vicinity of metal surfaces—and nanophotonics—the behavior of light on the nanometer scale—and for controlling the interaction of nanometer-scale objects with light.”

It appears God gave his humble servant a peek behind the veil into the fundamental workings of nature, but a view even more magnificent than Maxwell was able to comprehend at the time.

Related reading: “Has physics ever been deterministic?” – a philosophical discussion from the University of Vienna on

Be sure to read our biographies of Maxwell and Faraday and Newton, and all the other godly scientists who believed the Bible, trusted God as Creator, and helped make our modern world.

Artwork by J. Beverly Greene commissioned for this biography. All rights reserved.

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