Light was long considered to be a wave, exhibiting the phenomenon of interference in which ripples like those in water waves are generated under specific interactions. Light also bends around corners, resulting in fringing effects, which is termed diffraction. The energy of light is associated with its intensity and is proportional to the square of the amplitude of the electric field, but in the photoelectric effect, the energy of emitted electrons is found to be proportional to the frequency of radiation.
This observation was first made by Philipp Lenard, who did initial work on the photoelectric effect. In order to explain this, in 1905, Einstein suggested in Annalen der Physik that light comprises quantized packets of energy, which came to be called photons. It led to the theory of the dual nature of light, according to which light can behave like a wave or a particle depending on its interactions, paving the way for the birth of quantum mechanics.
Although Einstein’s work on photons found broader acceptance, eventually leading to his Nobel Prize in Physics, Einstein was not fully convinced. He wrote in a 1951 letter, “All the 50 years of conscious brooding have brought me no closer to the answer to the question: What are light quanta?”
A new focus on light
In a recent work published in the Annals of Physics, I have shown that light’s interpretation as quantized packets of energy or particles is an outcome of a more subtle kind of phenomenon, which is associated with the quantization of magnetic flux.
The work illustrates that the fundamental aspect of coupling between energy from light into electrons can be simply derived by using Faraday’s law of electromagnetic induction, where the energy of an electron of charge e in the field of time varying magnetic flux j of electromagnetic radiation, is edj/dt. I have further shown that its frequency or phasor domain representation is ejw, where w is the angular frequency of radiation..
Albert Einstein, in 1905, presented the revolutionary idea of light quanta of energy which equals ħw, where ħ is reduced Planck’s constant. There is plenty of experimental evidence on magnetic flux quantization from superconducting loops to two-dimensional electron gas, which is observed in the quantum Hall effect.
I have pursued an approach through classical electromagnetism to derive the expression of energy ejw, which is equal to Einstein’s concept of light quanta or photons. I have further argued that the energy of an electron can be discrete, and measurements of those discrete energy levels can give the appearance of the particle-like nature of light.
Quantum mechanics can explain and recover classical results under some specific approximations. However, deriving quantum mechanical results strictly from classical assumption is generally not possible due to fundamental differences in their frameworks. I feel that my work fills a major gap in our comprehension of the nature of light.
I have focused attention on the quantized nature of magnetic flux. I have also shown that the concept of photons emerges as a natural consequence of magnetic flux quantization against the framework of classical electromagnetism.
The work is partially derived from a prior study first published in Physical Review Letters in 2015, where we argued that radiation is an outcome of broken symmetry of the electromagnetic field.
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Historical gaps and the road ahead
Max Planck did not believe in electrons and he did not consider the work by Lorentz and Thomson (Nobel Lecture, 1922), but he knew about the electronic oscillator-based experiments by Hertz. He pushed forward the idea of quantized atomic oscillators with energy ħw in 1901, which was used by Einstein in his photon theory based on heuristics in 1905, which was published in Annalen Der Physik.
Bruce Wheaton, a noted science historian, writes in the journal Historical Studies in the Physical Sciences, “German thought of the1890s laid great emphasis on ethereal explanation of electric charge than on material interpretation… Millikan’s experiments did not bring about the acceptance of light quanta. In this period (1913–1923), there was simply no convincing explanation of the photoelectric effect. At its end, light quantum was reluctantly accepted to relieve what had become an intolerable state of affairs.”
The article holds special importance for research in the field of energy as we now understand that solar cells as well as electromagnetic generators work on the same physical law. A special focus of the article is on the fact that the fabric of Maxwell’s equations allows for quantization of charges. When Thomson discovered electrons, it was proved that electric flux is quantized. Magnetic flux quantization was discovered in the 1960s, but its study has remained confined to superconducting loops.
A number of leading academics with a background in quantum mechanics have offered feedback on the paper.
Lawrence Horowitz, emeritus professor of physics at the University of Tel Aviv says, “This article is indeed a valuable contribution to the theory of photons and electrons; an important complement to the book of Jauch and Rohrlich, particularly on classical aspects of the theory.”
Steven Verrall, who recently retired from the Department of Physics, University of Wisconsin La Crosse, says, “Dr. Sinha provides a new semiclassical approach to modeling quantum systems. I also think that Dhiraj Sinha’s unique approach may ultimately add valuable insights to the continued development of semiclassical effective field theories in low energy physics.”
In a personal note to the author, a leading physicist from the University of Bristol, UK, commented, “You want to use flux quantization to derive quantum mechanics, rather than deriving flux quantization from quantum mechanics. Probably you are correct, because with any physical theory there is freedom to define what is fundamental and what is derived.”
He further added, “We learned from Einstein that Maxwell’s equations were relativistic (i.e., invariant under Lorentz transformation) 40 years before relativity. Now we know that they were already quantum, 60 years before quantum mechanics! I find this amazing.”
This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.
More information:
Dhiraj Sinha, Electrodynamic excitation of electrons, Annals of Physics (2024). DOI: 10.1016/j.aop.2024.169893
Dhiraj Sinha holds a doctorate in electrical engineering from the University of Cambridge, U.K. and has spent the larger part of his research career working on the foundational aspect of electromagnetic radiation and associated symmetries. A part of the work was carried out at Massachusetts Institute of Technology, where he was a postdoctoral researcher, prior to his current appointment. He left Massachusetts Institute of Technology toward the end of 2019 and is currently teaching at Plaksha University, a newly established technology university in India led by a team of business leaders, educationists and philanthropists.
Citation:
Einstein’s light quanta through the lens of Maxwell’s equations (2025, March 3)
