We Are All Waves

Light is something that we tend to take for granted in everyday life. It’s not light itself that we are usually interested in, but the things that light illuminates: the shapes of objects, colors, faces, and cherry blossoms that seemingly spring out of nowhere and inspire us with their beauty.

Light is also something I have been dealing with in the lab for several years now. Low levels of light that carry information, quantum information, that one day, I hope, may find an application in low-energy, high-speed optical communications. But certain things about light have always puzzled me. Like the way it just appears, or is emitted, when electrons relax to lower energy levels. Where does it come from? Where does it go when it gets absorbed, like in solar cells? Does it just disappear? After travelling approximately 100 million miles from the sun to the earth, it just up and disappears? We know it travels at a very high speed, but how? With all the advances in modern physics, the true nature of light is still a mystery. So what is light, exactly?

Philosophers and scientists alike have grappled with this question for centuries, and their views seem to generally place the nature of light into two vastly different categories: 1- Light is composed of tiny particles traveling in straight lines and bouncing off objects, or 2- Light consists of oscillating fields propagating through the fabric of the universe as waves. Quantum mechanics makes things even more confusing, stating that light behaves sometimes like a particle and sometimes like a wave.

This duality has fueled numerous debates over the years. Some of the earliest Greek philosophers, including Empedocles (5th century BCE) and Plato (4th century BCE), held that light originates from our own eyes, and bounces off objects and returns to our eyes, allowing us to see them. Empedocles believed that Aphrodite, the Greek goddess of love, lit a fire in our eyes, fire being one of the four elements, serving as a source of light. To address the problem of not being able to see at night, he postulated a necessary reaction between the rays from the eyes and the rays from a source, such as the sun. Aristotle’s view was radical at the time, in thinking of light as a disturbance in the element air created by a source such as the sun and only detected, not created, by the eye. Meanwhile, Democritus, the father of atomistic thinking, considered light to be no different from matter in the sense that it is ultimately composed of indivisible, unbreakable units, which places him in the particle camp and makes him an early visionary of the modern concept of the photon.

Much later, Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel were able to explain many properties of light, such as reflection, refraction, and later diffraction and interference, by treating light as a wave where each point on the wave front can itself be considered to be a point source of a secondary spherical wave. Meanwhile, Newton was convinced of the particle, or ‘corpuscule’ nature of light, due to the power of Euclidean ray optics in describing how reflection occurs in mirrors and how prisms produce rainbows from sunlight.

Art work for Pink Floyd's Dark Side of the Moon, arguably one of the most recognizable album covers of all time.

Art work for Pink Floyd’s Dark Side of the Moon, arguably one of the most recognizable album covers of all time.

James Clerk Maxwell seemed to settle the matter once and for all with his laws of electromagnetism. His laws did away with the particle theory and considered light to be composed of intertwined electric and magnetic fields that oscillated perpendicularly to each other and to the direction of propagation at a constant speed, where this constant popped out naturally from the equations. This framework was not only intellectually satisfying and elegant, but was very useful in developing early long-distance communication and broadcasting technologies such as radar, radio and television. This view went unchallenged until the early twentieth century, and even Maxwell himself famously declared that all the major problems in physics had been solved.

However, a major problem presented itself in the form of radiation emitted from a heated body, like our sun. The frequencies of light emitted from a heated body, known as blackbody radiation, were measured in experiments to shift to higher frequencies as the body was further heated. This is much like a metal object, which may glow red when heated and then glow orange and eventually white when heated further (just like an incandescent light bulb). The problem was that the frequencies of light emitted from the heated object could not be explained by the existing theories of electromagnetic radiation. Max Planck solved the problem by making the ‘monstrous assumption’ that the black body only emitted energies that were integer multiples of hf, where h is known as Planck’s constant and f is the frequency of emitted light. He was very troubled by his breaking down of electromagnetic radiation into chunks, or ‘quanta’, and asserted that his was only an approximate theory to reality. Apologetically, Planck was ushering in the era of quantum physics.

A few years later, Einstein revisited this problem when studying the interaction of light with metals. His discovery, which became known as the photoelectric effect and serves as the basis for solar cells, was that the energy of the electrons emitted from a metal upon irradiation with light depended on the frequency of the light according to Planck’s constant, while the number of electrons emitted depended on the intensity of the light, or the integer number of ‘energy packets’ with energy hf. Basically, every incoming ‘quantum’ of light released an electron with energy hf. It was a one-to-one relationship: light particle in, electron particle out. Einstein made the bold conclusion that light is composed of ‘quanta’, later known as photons, with energy hf. He was quite alone in his conviction at the time, but when his theory was later proven experimentally by American physicist Robert Millikan in 1916 (who was himself originally largely skeptical of the photon theory), it became widely accepted and eventually won Einstein his Nobel prize in Physics in 1921 (followed by a Nobel Prize for Millikan in 1923).

Around this time, a young French aristocrat named Louis de Broglie took Einstein’s idea of light quanta to a whole new level. In his Ph.D. dissertation he claimed that it was not only light that comes in discrete packets of energy while being endowed with wavelike properties such as a frequency, but all particles, including electrons and heavier particles, were wavelike in nature and had frequencies that were related to their energies by the Planck constant. This was all too much for de Broglie’s thesis committee, who found themselves unable to judge the scientific merit of the theory. They sent the dissertation to Einstein, who returned it with a whole-hearted stamp of approval. In de Broglie’s own words:

“The fundamental idea of [my 1924 thesis] was the following: The fact that, following Einstein’s introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated… My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons.”

Louis de Broglie postulated the wave nature of particles

Louis de Broglie postulated the wave nature of particles

It is well-known today that such a wave-particle duality applies to electrons, which seem to behave as charged indivisible particles in electronics and as waves in electron microscopes. The fact that we can see sub-micrometer features in electron microscopes is precisely because the wavelengths of the electrons accelerated in these microscopes are on this order, which is much smaller that the wavelengths of visible light. Recent experiments have found wave-like properties in neutrons, and in fact neutron diffraction is a rare technique that allows for measuring antiferromagnetism in solids.

Remarkably, experiments carried out at the University of Vienna show that large organic molecules, such as the fullerene C60 molecule, show quantum interference in high-precision interferometers. This indicates that organic molecules have wave properties, namely they diffract and interfere with themselves just like waves. It is not a long stretch of the imagination to envision living organisms such as bacteria and viruses to be endowed with wavelike properties as well. The extrapolation of wave-particle duality to large living organisms like plants, animals, and humans may exceed some currently unknown physical boundary to the wave-particle duality, and requires a level of experimental sensitivity that does not exist today. But it is certainly a tantalizing thought, that we may exhibit wave-like properties that interact with our environment and each other in ways that we cannot even fathom.

Note: For an introductory overview of the treatment of photons and photon-matter interaction from the perspective of quantum electrodynamics, I recommend Richard Feynman’s lectures in New Zealand, which can be found here.


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