Light is a fundamental feature of our life’s, but when the nature of light is questioned every rational person thinks they know the answer. Even the great mind of Albert Einstein did not know the full answer. He wrote “all fifty years of conscious brooding have brought me no closer to the answer to the question: what is a light quanta? Today, people are in the same ignorant state of mind. This essay hopes to shed some light onto the real nature of light.


The Ancient Egyptians


The quest to uncover the nature of light dates back several thousands of years.  The ancient Egyptians view light as if it came from their sun gods eyes. When Ra’s eyes were open it was day, and when they were closed it was night.  The Greece also connected light to the sense of vision. They were under the impression that light was from within the eyes of human beings instead of a god. The Greeks and many of their predecessors thought the human eye held a “pure ocular fire” that would radiate out onto the world as to illuminate their surroundings.  Some may question how they explained the darkness of night. It was only when an Ibn al-Haytham who alter the views of light by using his camera obscure to show that light streamed from a source in straight lines to the eye.


Early Europeans


Then in the 1600’s Europeans believed light to be a stream of particles that travelled through the ether.  Pierre de Fermat proposed the idea of Principles of least time to account for refraction phenomenon. It states that the path light takes between two points is the one that can be transverse in the least time. This leads to the common conception of a light ray. The Principles of least time can describe reflection, refraction and total internal reflection. This became the foundation for geometric optics today.


It was only in the scientific revolution that the well known debate about wave-particle duality first appeared.  Scientists and philosophers were divided into two groups believing either that light was a particle or that light was a wave. Some believe the age old debate about  light being a particle or a wave started with Christiaan Huygens, a Dutch physicist, and Sir Isaac Newton.  Huygens was an advocate for the wave theory of light while Newton was holding the particle theory of light. Huygens theory proposed that any point where light was disturbed becomes a source of a spherical wave. The addition of all these spherical waves determined the form of the subsequent wave. While Newton’s applied his laws of mechanics onto light and founded his corpuscular theory of light. It states that light is made up of small discrete particles called corpuscles which travel in straight lines. With his scientific prestige, his hypothesis dominated for over a century.   Several other wave theories were proposed for the photon by Rene Descartes and Robert Hooke.


Newton’s theory hit complications in the early nineteenth century when Thomas Young and August Fresnel demonstrated interference and diffraction of light, this lead to substantial support for the wave theory of light over Newton’s theory. By 1850 the wave theory of light was more generally accepted in the scientific community.


In the 1860’s, James Clerk Maxwell published his famous Maxwell Equations. He then predicted that the photon was an electromagnetic wave. This was later proven by Heinrich Hertz with his experiments with radio waves. He showed that radio waves reflected and refracted the same way that light would. He also showed that radio waves travelled at the same speed of light, therefore establishing that light and subsequently photons were a type of electromagnetic radiation. This was the first blow to Newton’s Corpuscular hypothesis.


Photoelectric Effect


In 1905, Albert Einstein explained the photoelectric effect. This effect could not be explained by the wave theory of light. He did this by postulating the existence of photons, quanta of light energy that had particle properties. The term photon was first used to describe a model for chemical bonding by Gilbert N. Lewis in 1926, a chemist at Stanford University.  His model did not catch on; however the term photon became the term to describe a discrete bundle or quanta of electromagnetic energy.


This quantised energy, that Einstein proposed, was related to the frequency of light by  .  This came to be known as the photon theory of light.  From this, the ether was no longer essential as a means of propagation, but the theory did not explain all the behaviour that was observed.  According to the photon theory of light, photons move at a constant velocity i.e. the speed of light in free space. They have zero rest mass and rest energy.  They carry energy and momentum which is related to their frequency and wavelength. They can be destroyed and created while being absorbed and emitted. And they also can have particle like interactions with electrons and other particles, i.e. the Compton Effect.


As more experiments were conducted and evidence accumulated it became clear that light functioned as both a particle and a wave, depending on the observation and experiment.


Then in 1924; Louis-Victor de Broglie claimed that all matted has a wave like nature. He then generalise Einstein’s formula for matter. De Broglie’s claim was confirmed later with the observation of diffraction by electrons in two independent studies. It is interesting to note that the electron was discovered to be a particle and then the wave behaviour was observed. While a photon was discovered as a wave and then the particle behaviour was observed.


Quantization of Energy


The quantisation of energy is the basis for Niels Bohrs proposed quantum theory of the atom.  This is where the electron is said to orbit with discrete energies which is analogies with standing waves in a box.  From this, Erwin Schrödinger introduces the famous wave equation for matter. This leads to another perspective on the wave-particle debate through quantum mechanics.  That is that all behaviour of light and matter can be explained through differential equations representing waves this is the so called wave-particle duality.


The wave-particle duality is a principle of quantum mechanics.  It states that all matter and light exhibit both the behavior of waves and particles depending on the circumstance that the experiment or observing technique.  On the other hand the physical meaning of wave-particle duality is much more elusive.


From these developments quantum field theory was born. Quantum field theory of radiation is an important tool to describe the many interesting characteristics of light. In the middle of this theory is the idea of quantisation of the field. Field quantisation can be compared to the quantisation of the quantum harmonic oscillator in quantum mechanics.


In quantum mechanics the electric field and magnetic field of light, which is polarized mode and has a given vector, satisfies the commutation relation . This is similar to the particle oscillating which satisfies the same computation relation for its momentum and position.


Uncertainty Principle


Each of the quantization of the field corresponds to a given mode of light in the field. This leads to a Heisenberg uncertainty principle associated with the magnetic and electric components of light satisfying . A Fourier decomposition of these light modes in the cavity can be done resulting in  where  corresponds to the amplitude of oscillation in each  mode travelling in space. The exponential terms are related to negative and positive frequency.  The term  is analogues to the creation operator in quantum mechanics and the term is analogues to the annihilation operator in quantum mechanics. The creation operator produces a field state with one more quanta of energy while the annihilation operator creates a field state with one less quanta of energy.


This leads to discrete energies of in the radiation field associated with each mode in the field.


This model incorporates both particle and wave properties of light. The annihilation and creation operators relate to the photon acting as a particle. While the equation relates to a wave description of the photon. The photon can then be thought of as a discrete excitation of a set of modes, k, of an electromagnetic field in a cavity.  The normal modes and cavity to be used all depend on the set up in the laboratory.


So what is a photon


So what is a photon? When first introduced, the photon was perceived as having particular properties with discrete light energy  from concepts of radiation interacting with matter.  With quantized theory, the question of spatial discreteness arises.  The debate consists with whether or not the photon has a wave equation similar to the wave equation of a neutron or electron. If the photon was to have a wave equation, then we can interpret  as the probability of finding the photon in some infinitesimal volume of interest only constrained by the uncertainty principle. This would allow us to the mechanics of a massive particle, like electrons, on the photon.  This question is how does a particle that can be localised in space only constrained by the uncertainty principle travel through both slits in young’s-type experiment. Richard Feynman stated “nobody knows, and it’s best if you try not to think about it.”


So the photon ideology has come a long way from the time of gods to the quantum revolution. But despite all the progress made in understanding the nature of light it still remains an open question.  After reading a short literature review on the nature of light, published in Optics and Photonics News, to try and understand the nature of a photon it has come clear that there are more questions than answers.  The photon may be hiding new aspects that are yet to be discovered.


What does this have to do with Radiotherapy


So this was a research article I wrote during my physics undergraduate classes about the nature of the photon. What does this have to do with radiotherapy you ask- well radiotherapy uses photons to treat cancer- specifically it uses x-rays, which are high energy photons.


It is interesting that in the pure physics there is still a debate going on whether or not a photon is a particle or a wave, or possibly some combination of both- while in healthcare photons are being used to treat and diagnose people every day. And in healthcare, we generally think x-rays as being wave like, rather than particle like.


Understanding the photon has come a long way from the Ancient Egyptians, and all the great physicists have had a crack at explaining it. Christiaan Huygens, Sir Isaac Newton, Rene Descartes, Robert Hooke, James Clerk Maxwell, Louis-Victor de Broglie, Niels Bohrs, Werner Heisenberg, and Richard Feynman have all had an influence into the modern physics explanation of a photon. Thankfully for use, we don’t have to understand it as well as them to use it to treat patients and save people’s lives.