Einstein’s Photons Hidden in the Fabric of Maxwell’s Fields

Light behaves like a wave in free space. In fact, the waves of light interfere with each other, the way water waves interact and generate ripples.

This viewpoint is scientifically described using Maxwell’s fields. The energy of a wave is confined in its amplitude i.e. higher the height of a wave, more energetic it is. However this perspective was shattered at the onset of the 20th century as it was observed that while interacting with matter, the energy transferred to charged particles like electrons by light is dependent on its frequency i.e. the number of times the wave oscillates in a second. This observation was first recorded by Philipp Lenard in experiments on photoelectric effect, where current is generated when light falls on a metal plate.

The observations motivated Einstein in 1905, to suggest that light comprises of packets of energy, which he called light quanta, with energy proportional to the frequency of light. Hence, electron’s energy is proportional to the frequency rather than amplitude of input radiation as light behaves like particles while interacting with matter. Einstein got the 1921 Nobel Prize in physics for this explanation, which appeared to mark a shift in our understanding of light. It led to the theory of the dual nature of light according to which, light can behave like wave or particles depending on its interactions. The idea is closest to empirical observations and forms the basis of our broader understanding of the nature of light.

Thus, for more than 100 years, we have been led to believe that Maxwell’s mathematical fabric widely terms classical electromagnetism cannot explain how light energises electrons. In a recent work, published in Annals of Physics, Dr. Dhiraj Sinha, a faculty member at Plaksha University, has used some basic equations of Maxwell’s electromagnetism, while offering a novel perspective on light matter interaction. While focusing attention on the magnetic field of light, he has argued that its variation in time generates an electric voltage, the way a vibrating magnet induces an electric voltage in a coil. From a mathematical perspective, the magnetic flux of light, j generates a voltage defined by dj/dt over a differentially small variation in time  t . The energy transfer to an electron of charge e is, W= edj/dt . Its frequency or phasor domain representation is ejw, where w is the angular frequency of radiation. This expression is similar to the Einstein’s expression on the energy of a photon, ħw, where ħ is the reduced Planck’s constant. In other words, the magnetic flux of radiation field energises the electrons in accordance with the Faraday law of induction.

The theoretical framework offers the missing link between classical electromagnetism and quantum mechanical concept of a photon as currently, the energy of a photon is considered to be an experimental fact which does not have any formal mathematical derivation. The fact that magnetic flux is quantised has been observed in two dimensional electron systems as well as superconducting loops supports this viewpoint. Maxwell’s equation is about fields, although it is silent on quantisation, it does not oppose it. Thus, by using flux and charge quantisation, Maxwell’s equations can be used to explain light matter interaction.

Currently, there are two approaches on understanding the interaction between electromagnetic fields and electrons. The first one is governed by Maxwell’s equations, which is extensively used in energy conversion devices like generators and motors, besides their applications in telephony and wireless communication. The second approach is based on the concept of light quanta, which is used in solar cells, light emitting diodes and lasers. These two theoretical approaches drive two different technological tracks, which influence our life, business and society and the associated challenges. For example, the current efficiency of solar cells and light emitting diodes are defined by the nature of interaction between photons and electrons in semiconductor devices. The current work integrates these two approaches.

A number of leading physicists have expressed support to the idea including, Jorge Hirsch, Professor Emeritus at University of California, Steven Verrall, former faculty member at University of Wisconsin La Crosse and Lawrence Horwitz, Professor Emeritus at the University of Tel Aviv. A leading physicist after reviewing the work wrote to the author, “We learned from Einstein that Maxwell’s equations were relativistic forty years before relativity. Now we know that they were already quantum, sixty years before quantum mechanics! I find this amazing.”

To conclude, the current work on quantised energy transfer to an electron from electromagnetic radiation while incorporating the role of quantised variations of magnetic flux leads to the derivation of the expression energy of a photon. It highlights the fact that frequency dependence of photoemission can be formally derived if we consider the frequency domain representation of the interaction energy between radiation field and the electron while using Maxwell’s equations.

Additional Information

Sinha, D. (2025). Electrodynamic excitation of electrons. Annals of Physics, 473, 169893.(https://www.sciencedirect.com/science/article/abs/pii/S0003491624003002)