As you read this millions of photons of light are hitting your eyes, their energy changes the configuration of protein within the eye that then creates an electrical signal to the visual cortex allowing you to see. What does this have to do with quantum computing I hear you ask and the answer is – everything. Photons are fundamental to not only our understanding of quantum mechanics and therefore quantum computing our knowledge on photons or simply light illustrates how far we have come and, perhaps, how far we still have to go.

Part One – The Basics Understanding

Aristotle and the Element of Light (340BCE)

Light is one the most important attributes of the visible universe. The old joke goes ‘On the first day God created light but before that He created mathematics’. As human beings we are very sensitive to light using it for hunting during the day when the day was warmer allowing us to hide at night time from the cold and predators. Light is the foundation of many myths and legends with Zeus ruling over mythical Greece with a lightening rod which came with a free scary rumble. Light is also one of those things that clearly demonstrates the world we live in: we can see that light creates shade, that it moves in straight lines, can bounce of things, heat things up. No fancy equations needed.

The story of light can be broken into three main parts: elements, optics, waves. Across all historical cultures light is seen as a fundamental part of the environment. Ancient Greece is where we’ll start as this is where a lot of the Western thinking started and where scientific reasoning was founded consisting of reason and logic with what can be tested and tested. Philosopher, student of Plato and overall smart chap Aristotle (384BCE – 322BCE: 61 years old) stated the light was one of the five fundamental elements (earth, water, air, fire [light], and aether). The first four correspond directly to the energy states of solid, liquid, gas, electromagnetic radiation and, at a stretch, dark matter/energy (the stuff we can’t see because light doesn’t interact with it – much).

Whilst Aristotle can been as one of the first scientists with his thoughts on the physical world of stuff and motion, chemistry of interaction, and the biology of animals and plants he wasn’t known for one crucial skill – mathematics. Mathematics is crucial because it changes an idea into a proved theory or law. When it comes to mathematics and the start of any scientific journey then you must start with another ancient Greek that you may not be so aware of compared to Aristotle is Euclid (325 BCE – 265 BCE) or, to give him his full title Euclid of Alexandra.

Euclid – Proven Lines, Shapes and Angles (300 BCE)

Euclid – Elements

Euclid was the father of geometry and many other areas of mathematics which he published in his book Elements. Elements would be the fundamental book of mathematics that you were taught geometry at school from the area of rectangle to the angles in a triangle. Mathematics was a tool to better understand and build the world with topics on flat and solid shapes, angles, lines, and numbers (the elements). This logical progression, agreement and proofs allowed a language of mathematics to be agreed without any godly or human interference (compare Pythagoras and his pursuit of mathematical purity that would tie him and his followers in knots). The ancient Greeks and others from other parts of the world created a space of free thought that in certain circumstances could be tested and proved the very foundations of science and within in physics.

Elements was not the only book Euclid published. He also published a book on the study of light – optics. Light was a great thing to apply many of the mathematical work into something practical as light could produce perfect parts of geometry namely straight lines, angles, and both plane (flat), solid shapes and often forgotten when studying geometry as it seems pointless is the point which has no dimensions (little geometry joke there). Euclid postulated 7 things about how we see light with respect to geometry. One of the most fundamental to the geometry is that light travels in a straight line – light didn’t travel around corners like sound – it hit things and bounced of or went straight through (we’ll ignore rainbows – we’ll get there in a couple of paragraphs).

With the Euclid’s elements of geometry and a universal way of testing and proving things through mathematics the study of light (optics) has a fundamental path to progress starting with how light interacts with objects. Hero (or Heron) of Alexandria (CE 10 -70) looked at how light does and does not reflects (catoptrics) of objects leading to the idea polished surfaces reflect (easily observed through visualisation) and that rough on porous surfaces can absorb light. This observation is another fundamental piece of thinking – not pointing out what does happen but what does not happen. The absorption of light is another key finding we have to leave but will pick up nearly 2000 years later when we look at emission theory and some clever Germans.

The final part of this ancient look at the final and odd property of light – refraction where light ‘bends’ when it enters a different medium like water. For this we bring in a huge influence Ptolemy (100 CE – 170 CE) who published on many subjects including astrology where he created the geocentric (Earth) view of the universe where the heavens rotate around the Earth – this would be a key driver in setting up the scientific revolution as the maths didn’t add up that well when you have a key optics tools – the telescope. Ptolemy’s work in optics brought in refraction where light changes it’s direction when it changes from one medium density to a different one (anyone that spear fished would know that you need to know the spear ahead of fish to offset the bending of the light).

In summary by around 200 CE humans know that light travels in straight lines, reflects off certain surfaces, is absorbed by others, and can pass through denser mediums where the straight line path deviates (refracts) from the original path.

Alhazen – the light we see (990 CE)

The fundamentals of light property were now in place. These fundamentals were confirmed and improved from the Islamic world that learnt from the Greeks, Romans and, other civilisations. Of remarkable note was the work of Alhazen (965 -1040 CE) from Basra modern Iraq (his full name was Ibn al-Haytham which becomes Alhacen or Alhazen when translated to Latin and the Latin alphabet). Alhazen moved the understanding of light forward in many ways through bringing the minds and experiments of European scholars with those of the Islamic world in effect doubling the field of knowledge. Alhazen advanced this understanding through a black box.

Camera Obscura – upside pictures

Light was being used for all sorts of practical things all the time for those not as interested in the pure physical properties of light. One these practical and curious ways was through a thing called the camera obscura coming from the Latin – room dark -> Dark Room – Black Box (the black box reference will return later when things start to heat up). The results of a camera obscura were known before one was built as all that is needed for the effect is a small hole that lets a beam of light fall onto a flat surface in a dark chamber. Due to the nature of the setup the effects were often seen at night time with a full moon as the moon light falls through a small hole into a dark room. A more practical use was found where a camera obscura could be built to help paint a landscape in effect tracing the outline as it was projected onto a canvas. This allowed the right dimensions and ratios to be captured with accuracy before any painting. The only slight problem and curiosity was the image was upside down and blurry if the hole was too big.

Alhazen study of light and lenses resulted in our understanding of how we “see” through an explanation of what was going on in the camera obscura. To summarise Alhazen proven a few fundamental properties of light. The first one will seem odd but Alhazen proved that we don’t see through light coming out of eyes. This may indeed seem odd but within the scientific thinkers the idea is that we see through looking – when we open our eyes we send out light which then detect somehow (bounces back into the eye causing sight). Alhazen showed that light comes from outside goes through a whole in the eye (pupil) with the image presented upside down on the back of the eye (it’s not clear if the function of the lens was understood in focussing light to the back of eye). The other property of light that Alhazen proved was how light travelled in straight lines which explained how the image in the camera obscura was upside down and mirrored. This knowledge was crucial in moving the next stage of our understanding of light – lenses and enlightening.

[camera obscura]

PART TWO – The Enlightenment and Science

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We pick up our light story in the late 17th century as the study of light reaches upwards, outwards and maybe sideways depending on a point of view.

The first place to start is the art world more specifically the renaissance art world and Leonardo da Vinci famous for this paintings, sculptures amongst other skills.

From the From the 1600 – 1700 a lot happens in the world of science discovery was later to be called the era of enlightenment as common doctrine was begin challenged and understanding updated based on experiment rather than what people where told, believed, experienced. Things come thick and fast so I’ll switch to a chronological order to help explained what happened.

< 1600 – Glass to focus light. Capturing Light.

Camera Obscuras – Latin: chamber/room dark – dark room. A closed room with a small hole in one side that projects light from the outside onto a wall showing the outside image upside down.

1600 – William Gilbert primary scientific work—much inspired by earlier works of Robert Norman (inclination of the Earth’s magnetic field – magnetic dip) — was De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth) published in 1600)

1646 – The English word “electricity” was first used in 1646 by Sir Thomas Browne, derived from Gilbert’s 1600 New Latin electricus, meaning “like amber“.

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Early in the century it was proposed that the Earth is spinning on it’s axis (William Gilbert of magnetic and electricity fame), and the Earth and other planets are rotating around the Sun instead of the planets and Sun revolving around the Earth (Copernicus – circular orbits, Galileo – confirmed the presence of other heavenly bodies like the moons of Jupiter and, confirmed planetary orbits, Kepler – improved orbits from circular to elliptical which fitted the maths to name just three with one I’ll talk about later for his work in light (you might have guessed who this is already).

With the improvements in optics through better lenses better and better telescopes were invented allow a clearer picture of the night sky. This turned the heavens from being one for the Gods to a laboratory to test big things such as planetary movement and the properties of light that had been limited to small experiments with prisms. Again, as before we see observation, measurement and mathematics come together to move the understanding forward. In the area of light we see two ideas come together – what actually is light? Watch the timings on this as things come thick and fast.

The Light Travels Breakthrough (Rømer – 1679)

1679 – Rømer – Light travels

First in 1679 Ole Christensen Rømer who measured the speed of light somewhat by accident. Rømer was studying the moons of Jupiter that Galileo saw for the first time in 1610 proving the heavens were not fixed – that a supernova appearing out of nowhere. Skipping over the genius of how the speed of light was worked out we now have a critical piece of knowledge not confirmed before this that are very important for the world of quantum – light travels.

The fact that light travels means a few things. 1 – it’s not ever present which means it is a physical thing that can be measured, changed etc – it can be studied and understood. 2 – the properties will change when it’s travelling e.g. when it moves from one medium (air) to another (glass or water). 3 – light is created by something and then absorb by something.

The discovery that light travels (not infinite) in 1679 with the three parts that follow from it opened the question – how does it travel? Light is a form of energy and energy can move in two different ways. It can retain all it’s energy in a single block and move through the universe in the same way any physic body does from a star to atoms. The particle view. Or the energy can propagate through physical things moving the energy from one thing to the next thing. The wave view. These views can not both be correct. Either the energy stays within a body or it transfers it’s energy to something else. This problem was addressed by two brilliant physicist who didn’t agree. Both would define our fundamental understanding of the universe.

Light as a wave – Christiaan Huygens (1690)

The Basics of Waves

Before we get stuck into the wave theory of light I we need to understand a little bit about waves. This will explain why describing light as a wave is, frankly, really hard. The basics of a wave is movement through a medium in an oscillating, up and down pattern like a pendulum of a clock swinging from side-to-side. The maximum movement from the middle is the amplitude and it contains all the energy either as potential energy when the amplitude is at its greatest distance away from the middle or kinetic energy (speed) in the middle. The time it takes to complete one cycle – to set off and return to the same position is the wavelength as you can measure the distance travelled over time. The final thing for a wave is the speed of the wave as it moves. The time it takes for a wave to complete a cycle is called a period e.g the time it takes for a large pendulum to swing from one side to the other could be five seconds. To allow waves of different speeds to be compared the frequency can be taken which is the number or waves in a standard time normally a second. For example you could have one pendulum complete 2 full cycles in a second to high a frequency of 2 hertz (hz) compared to a slower pendulum which completes one half a cycle per second giving a frequency of 0.5Hz. Amplitude, Wavelength, and Frequency are the fundamental properties and measurements of a wave

[picture of wave with properties]

Types of Waves

So far an example of a clock’s pendulum has been used to describe the properties of a wave. For a more practical view we need to describe the two types of wave: uppy-downy, inny-outy.

Transverse (Uppy-Downy) wave

Transverse waves more energy through the passing the energy in a direction at an angle from the direction of the travelling wave (up – down, or side-to-side). Waves on a pond when you through a stone in or waves in the sea are transverse as they move up and down and make you feel a bit sea sick. For these transverse waves in a liquid there is tension or viscosity in the liquid that defines how the energy is absorbed by the liquid or dissipated through stretching and contracting bonds creating a wave away from the source of energy. Transverse waves are also in musical instruments with strings or drums as the are plucked or struck. For instruments it is the elasticity of the material or tension that it is held in that defines how the transverse is shaped. Whilst transverse waves in the sea or from vibrating strings are the both transverse only the sea wave is travelling whilst the string is static as is if held at both ends. The string is the same as a weight on a spring oscillating same wave one is moving through space and the other is fixed.

Longitudinal (inny-outy)

The other option for the energy moving through a wave oscillating up and down (transverse) the energy can move in the same direction or through the wave. In contrast to a transverse wave the medium is compressed then stretched (rarefraction) as the energy moves through. A weight on a spring bouncing up and down is a good visualisation of a longitudinal wave as the energy can be seen moving through the spring as it stretches at the far end (rarefraction) and then compression as it recoils upwards. Sound waves are longitudinal waves as air is compressed and stretched in pressure waves recognised by a microphone or an ear.

Both the transverse and the longitudinal have amplitude that defines the packet or weight of energy moving and speed of delivery in the frequency through the number of packets (wave lengths) are delivered in a period of time.

Polarisation – filtering waves

Despite transverse and longitudinal waves being similar there are some key differences and one of the fundamental ones is polarisation. Only transverse waves can be polarised as they can be travelling at different angles from the direction of the wave (you can’t polarise a sound wave. The movement from the direction of travel can be done in three ways. To help with this you need to see the wave as if it was coming straight at you

1. 90^o

Traditionally this is shown by a vertical and horizontal movement but it can be at any angle. Due to the differing angles transverse waves can be polarised – to be given a pole or single orientation. Waves polarisation happens not only when going through a filter but also when a wave reflects (bounces off) and refracts (pass through a medium of different densities). When light is absorbed to allow a certain wavelength or direction (polarisation) through that is called dichroism – splitting of light in two colours.

Now that you have an understanding of waves let’s return to the problem of light

In one corner is the brilliant Dutch mathematician, physicist, astronomy, and inventor Christiaan Huygens. Huygens first stated then published that the energy of light is passed as a wave through experiments especially on experiments of refracted light in glass. Reflected light can be easily explained as bouncing off a surface. Refracted light is trickier as the path of light changes. Huygens looked at double refracting in a special material – Iceland spar or calcite which produces two rays of light from one entering. This behaviour could be explained if a wave is passing from a lesser dense to a move dense material. Experiments and drawings are all well and good but Huygens was a genius with mathematics as well taking on a mathematical description of how light would behave if it were a wave and the results were compelling. The model and the mathematics proved that light was a wave.

Light as a particle – Issac Newton (with help from René Descartes) – 1704

1666 – Newton observed that white light is refracted into different colours with different colours refracted at different angles (red > blue).

1672 – Newton showed that recombining refracted white light into a spectrum (all colours) could be reconstituted back to white light proving all colours make up white light (Newton’s Theory of Colour).

1704 –

In the other corner was was the brilliant mathematician, physicist, astronomy and inventor Sir Issac Newton. Newton, when he’d defined a new form of physics of motion and force, turned his attention and curiosity to optics and light through the neat use of prisms. Before Newton’s studies the idea that light was a particle came from philosopher René Descartes. Descartes today is better known as a philosopher famous for the reflecting saying “Cogito ergo sum. (I think, therefore I am.)”.

But Descartes plays a part in the story of light. As well as his thoughts on philosophy and bringing forward the idea that everything including the soul and therefore gods themselves Descartes also brought forward the idea a system of investigation that allowed thinking to be better seen as it was Descartes who created cartesian algebra (mapping algebra) that presented algebraic formula and values on a graph (map – cartography) to show the shape or geometry of equations. Newton used this form of mathematics to further develop a form or mathematics called calculus that was crucial in proving how accelerating and decelerating bodies would behave. From this came Newtonian understanding of gravity and the reason the planets moved around the Sun. This created Newtonian physics which would be used by physicist and engineers to power the industrial revolution. That and thermodynamics which will also play a part in the story of light and quantum mechanics.

Prisms, triangular blocks of glass do cool things depending on the angles of the triangle. One of the cool things is to refract or ‘split’ the white light into different colours. To cut another long story short Newton proposed the idea in 1692 (but held off publishing for 12 years later in Optiks – 1704) that light was made of different colours of different size particles that changed course when travelling through different densities of materials. When all the particles are added back together they create white light again. This Newton called the corpuscular theory of light where light is a body (corpuscular) or particle like a tiny ball bearing who’s energy moves with it rather than a wave where the energy moves through the medium.

Newton’s Simple Solution – Light was a particle

The advantage of Newton’s theory of light was three fold:

1) it was simple and intuitive. Light travelled in straight lines like bullets from a gun hitting solid things where the light either bounced off (reflected), absorbed as heat – objects get hotter when light is shined on them never colder (this idea would be tested in the 19th century leading to another important discovery), and could also explain refraction if the light particles were to have different weights with “heavier” colours refracting more when the density of the medium changed.

2) Newton published the work Opticks in 1704 at the age of 62 in English with pictures – people could actually read and, unusual for a science publication, enjoy it. The writing was easy to take on and talk about light, rainbows, and other things that normal people would be curious about. This allowed for the ideas to become popular and in science sometimes the common view is the accepted view.

3) He was Issac Newton and he had friends. Newton was part of the established group of scientists and philosophers who could be seen as the wise men of the age. Descartes who helped with the mathematics of gravity also thought light was best described as a particle along with others where the fashion at the time was focussed on the mechanics of the solar system – things bumping into things with force and momentum through Newton’s publication commonly known as Principia containing the laws of motion and universal gravitation in 1687.

The logical presentation of Newton’s work and his position in science meant that Newton’s work was the accepted view that light was a particle the corpuscular theory was “accepted”, Huygens was asked to try harder and the world moved on with Newton’s particle theory accepted at the time and for the next 100 odd years.

Waiting out controversy

There is another, more gossipy view on this that I’ll add for interest. Newton through his studies and publications made lots of friends. However, he also made a few enemies that he either annoyed or were not happy with the progress and fame that Newton made. Whatever the reason the timings of Newton’s publication puts an interesting view on why he published Optiks when he did.

The first was the advocate of the light as a wave theory – Christiaan Huygens. Huygens met Isaac Newton in 1689 where Huygens was 60 and Newton 47 where they talked the physics of motion about light and its double diffraction (birefringence) through Iceland spar where two light beams can emerge. There is no record that Huygens and Newton did not get on but it is clear that Newton didn’t publish his thoughts on light as a particle until after 1695 when Huygens died. However, it is worth remembering that Newton was working on a lot of stuff so may have prioritised other work.

1686 – Newton Publishes Principia setting the foundations of Newtonian Physics (force, momentum, gravity)

1690 – Huygens – Light is a wave

The other work was the laws of motion and gravity in Principia. Newton had been asked by Robert Hooke a more established scientist at the time for recognition on the force of gravity in the first volume of Principia published in 1686. Newton did not included any reference to Hooke. Hooke and Newton didn’t agree on the corpuscular theory of light either resulting in Newton not publishing until Opticks until after Hooke died in 1703 where Newton became the President of the Royal Society so published Opticks in 1704 with more gravitas.

1703 – Newton publishes Opticks and becomes President of the Royal Society – Light Particle of Light

What ever the reason was by 1704 and for the next 100 years Newtonian physics would be the general accepted view on how light worked. The lack of interest was really a practical one – what could you do with this knowledge?

Diffraction and Interference – Grimaldi

“Accepted” was the position as Newton’s work explained many aspect of how light worked. However, there was a problem – big problem and Newton probably knew it: diffraction. Diffraction was a property of waves where a wave can make its way through a gap or around an object producing a different wave pattern afterwards it effect going around and behind an object. Through a stone into a pond and the ripples will spread out and around objects and through gaps. This allows for water and sound waves to “bend” around corners”. If light was a wave then it would show signs of diffraction.

Francesco Grimaldi (1618 – 1663) – free falling objects, diffraction of light measurements

1666 – Grimaldi formulated a geometrical basis for a wave theory of light in his Physico-mathesis de lumine (Newton used inflection but diffraction stuck).

Although the phenomena of waves interacting with themselves and other waves is physical trying to understand diffraction is difficult as, by their very nature, waves move. At around the same time that Newton was studying gravity an Italian Jesuit priest called Francesco Grimaldi was assisting Giovanni Battista Riccioli. The pair of them would go on to prove that objects fall at the same speed regardless of the objects weight – a stone falls as fast as a boulder proving that gravitational force on Earth was constant something Newton proved in his laws of motion.

As with all the people studying the sky and gravity Grimaldi also studied optics having built lenses for his astrology work. As part of this work Grimaldi argued against the idea that light was a particle (corpus) with the introduction of light bending around an object like a wave. He did through the simple demonstration of creating a box with a small hole in it to let a beam of light through. This created a circle of light on the back of the box as you would expect. He then tilted the box so the circle became an oval and then placed a rod between the incoming light cone and noticed two strange things.

The first one was the shadow was bigger than would be expected if the light was coming straight through the hole in tiny packets. The shadow would be very sharp not blurry increasing the size of the shadow. The second one was at the edges of the shadow Grimaldi saw a rainbow with the red light on the outside, white light, then a violet colour before the shadow. How was happening if the light was in particles? Grimaldi did further experiments that broke the incoming light from where the word comes from Latin diffringere ‘to break into pieces’. His work was published after is death in 1665. James Gregory, a friend of Issac Newton produced the first diffraction grating by shining light through a bird’s feather. The effects of diffraction grating was to separate out a white light beam into a rainbow or spectrum of colour in the same way that a glass prism can.

Newton used prisms to split white light proving that white was made of several colours combined as Newton demonstrated by splitting and then reforming the light. He termed this the inflexion of light

The idea that

Augustin-Jean Fresnel: 10 May 1788 – 14 July 1827 (39)

Huygens-Fresnel principle

Thomas Young (1773 – 1829)

1807 – Double hole experiment – single light source, 2 holes, interference pattern on a screen due to diffraction of light through the holes – light behaves like a wave

James Clerk Maxwell (1831 – 1879)

1864 – Maxwell’s Equation – predicted the existence of electromagnetic waves. Travel at speed of light – horizontal waves (also did Maxwell-Boltzmann distribution Kinetic theory of gases)

Albert Einstein (1879 – 1955)

1905 – 3 papers – 1) photoelectric effect theory – light is made of photons, 2) theory of Brownian motion utilizing kinetic theory of molecules (heat) and, 3) Special Relativity. Special relativity – principle of electromagnetism

Thomas Young Double Slit Experiment

Thermodynamics – invisible light

Electricity and Magnetism

Max Plank – Black Box Radiation

Eistein and his special and general relativity