THE
MIRACLE OF LIGHT
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There
may be more to celebrate in the International Year
of Physics than meets the eye. Indeed, the Year marks
not only the centenary of Einstein's miraculous year
but also the millennium of the founding of modern
optics by physicist Ibn Haitham (Iraq, 965-1040).
Among a number of major contributions, Ibn Haitham
put experimental science on the map by decisively
settling the heated debate over the basics of vision,
through a remarkable series of experiments.
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| Having
pioneered the pinhole camera, he successfully explained
sight in terms of light travelling into the eye rather
than the other way round. This finally discredited the
now absurd emission theory of Plato and Ptolemy1,
effectively rewriting centuries of scientific thought….
Here, we voyage through one thousand years of the physics
of light, with a special focus on optics. |
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The
upper-cone is called the future light-cone, showing
how a pulse of light spreads out in space (represented
horizontally) as time passes (represented vertically).
The lower-cone is called the past light-cone and is
simply an extension of the future light-cone into the
past. There are two basic properties of light underpinning
a lightcone diagram. The first is that light travels
in straight lines, which was experimentally proven by
Ibn Haitham using the pinhole camera 1000 years ago.
The second, also proposed by Ibn Haitham, is that light
has a finite speed |
The
organizers of the International Year of Physics 2005 (originally
labelled the World Year of Physics) could hardly have chosen
a more elegant logo than a colourful sketch of a light-cone
diagram, reminiscent of Einstein's seminal work of 1905.
Light-cones, as the famous Oxford physicist Roger Penrose
put it, 'represent the most important structures in space-time.'
What a light-cone shows is simply how a pulse of light spreads
out in space as time passes, just like ripples spread out
on the surface of a pond.
The reason why light lends itself to such elegant geometry
in the first place is because of two basic properties. The
first is that light travels in straight lines (ignoring
the curvature of space-time), the second that light has
a finite speed. These two properties lead us to the 11th
century Arab physicist Alhasan Ibn Haitham, more commonly
known to the West by his Latinized first name Alhazen, the
founding father of modern optics.
•
Ibn
Haitham's light beam
In order to settle the long-standing debate over how vision
worked, Ibn Haitham pioneered an experimental set-up of
surprising simplicity: the pinhole camera, or camera
obscura2,
the principle behind all photography from the earliest cameras
to modern-day digital ones. His pinhole camera consisted
simply of a tiny hole that led to a dark room. He placed
several lamps outside the room and observed that an identical
number of light spots appeared inside the room on the opposite
wall. Upon placing an obstacle between one of the lamps
and the hole, he observed that one of the light spots disappeared
and, when he removed the obstacle, that the light spot reappeared.
Crucially, he observed that each lamp and its corresponding
light spot were always aligned perfectly in a straight line
passing through the hole.
Thus, using the pinhole camera, Ibn Haitham proved that
light travels in straight lines. Further, by observing that
light from different lamps did not get mixed up in going
through the hole, he drew a parallel, concluding that vision
occurred by means of light travelling into the eye and forming
an ordered point-for-point image of the visual scene. The
pinhole camera was in fact the climax of a series of observations
and experiments, which meant that the eye could be studied
as an optical instrument. Indeed, Ibn Haitham studied the
anatomy and physiology of the eye in great detail, giving
many eye parts their present-day names, for instance: the
cornea, the lens and the retina.
By defining a beam of light, he was able to describe the
propagation of light in a way which perfectly fitted the
laws of geometry, highlighting a unique relationship between
physics and mathematics. But for him, unlike his predecessors,
theory had to be supported by experiment. Therefore, in
order to prove his theories, he invented devices of varied
complexity which were designed not merely to test qualitative
assertions but also to obtain quantitative results. Regarding
the phenomenon of diffuse reflection, essential for understanding
vision, he showed by experiment that reflected light from
each point on the surface of an illuminated object radiates
in all directions in straight lines. In particular, reflected
light from a visible object forms a cone of rays with its
base at the object and its tip at the eye. This is the principle
behind linear perspective, the foundation of Renaissance
art. Artists like the Italian Leonardo da Vinci (1452-1519)
used linear perspective masterfully to achieve a realistic
three-dimensional sense in their paintings. Yet Ibn Haitham's
influence on the development of science in Europe was still
more profound. Following the revival of logic by Spanish
polymath Ibn Rushd (1126-1198), the transmission into Europe
of Ibn Haitham's theory of light and vision played a singular
role in illuminating the European Dark Ages.
•
Science
through the pinhole camera
Before we turn to the second property of light underpinning
a light-cone diagram, let's take a closer look at the impact
of the pinhole camera, an invention which has powered centuries
of scientific thought. The pinhole camera became a standard
method for generations of physicists after Ibn Haitham.
Isaac Newton, for example, used it to conduct his famous
prism experiment in which he analysed white light into basic
colours, 'The Sun shining into a dark chamber through a
little round hole in the window-shut and his light being
there refracted by a prism to cast his coloured image upon
the opposite wall...,' Newton explained in Opticks (1704).
Referring to his discoveries in optics, Newton wrote in
a letter to his arch-rival Robert Hooke, 'If I have seen
further, it is by standing on the shoulders of giants.'
Two and a half centuries later, photographs of stars taken
from the island of Principe, off the west coast of Africa,
provided the proof needed to convince the international
scien-tific community once and for all of the soundness
of Einstein's general theory of relativity. Einstein had
predicted that light passing near a massive object like
the Sun would be deflected by an amount given by his new
theory of gravity. The 1919 solar eclipse provided an opportunity
for a British expedition led by Arthur Edington to test
Einstein's prediction. Edington compared photographs of
stars from the Hyades star cluster, seen in the vicinity
of the eclipsed Sun, with photographs of the same stars
when the Sun was off the visual field. The photographs confirmed
the predicted shift in the stars' apparent position, turning
Einstein into a celebrity.
•
Speed
of light infinite or finite?
Two of the most fundamental phenomena in optics are reflection
and refraction, both of which Ibn Haitham investigated through
countless experiments. In explaining refraction (the bending
of light as it enters or leaves a denser medium), he went
against the accepted wisdom by arguing that light has a
finite speed, which is the second property of light underpinning
the light-cone diagram of the Year of Physics' logo. In
a flash of insight, he realized that refraction was caused
by the slowing down of light as it enters a denser medium.
He characteristically based his proposition on an experimental
model.
Quantum Electro-Dynamics (QED), the climax of the quantum
revolution which Einstein kick-started in 1905, tells us
that light always takes the path of least time in travelling
between two points. Within the same medium, this path is
simply a straight line. But because the speed of light is
slower in a denser medium, the path of least time for light
crossing between two mediums is no longer a straight line,
causing light to bend. The theory of QED developed by Paul
Dirac, Richard Feynman and others fantastically explains
a wealth of optical phenomena.
Why does it not suddenly get dark when the Sun sets? The
phenomenon of the twilight is so common that one hardly
stops to ponder. In his book, the Balance of Wisdom, Ibn
Haitham calculated on the basis of the duration of the twilight
that the Sun is actually 19 degrees below the horizon when
the twilight ends, due to the reflection of sunlight by
the Earth's atmosphere. In a spectacular feat, he ingeniously
used the onset of the twilight to calculate geometrically
the approximate height of the atmosphere from the Earth's
radius, opening a new chapter in the quest to unravel the
mysteries of the universe.
•
Optics
masterpiece
An in-depth analysis of reflection and refraction appears
in the second half of Ibn Haitham's masterpiece Kitab Al-Manazir,
or Book of Optics, translated into Latin as Opticae Thesaurus
- a revolutionary work firmly based on geometry and experiment,
reforming the established optical tradition of Ptolemy.
Here, Ibn Haitham decisively distinguished the study of
optics (both physical and geometric) from that of visual
perception, experimentally establishing optics and more
generally physics as an independent science. It was in optics,
rather than mechanics, that the concept of experimentation
as systematic and ordered proof was first born. Ibn Haitham's
Book of Optics must rank alongside Newton's Principia Mathematica
as one of the most influential books ever written in physics.
'He was the greatest Muslim physicist and student of optics
of all times. Whether it be in England or faraway Persia,
all drank from the same fountain. He exerted a great influence
on European thought from Bacon to Kepler,' wrote George
Sarton in his History of Science (1927). There is a unique
copy of Opticae Thesaurus in the archives of the Institute
of Electrical Engineers in London, which once belonged to
the celebrated French physicist André Ampère
(1775-1836).
•
Designing
the perfect lens
According
to legend, Archimedes (Greece, 287-212 BC) set invading
Roman ships afire by focusing sunrays onto them using huge
mirrors. Whether or not the story is true, the quest to
construct a perfectly focusing mirror has inspired much
research
in optics since antiquity. Ibn
Haitham's predecessor, 10th century
Baghdadi mathematician Ibn Sahl, redefined the goal of this
research more generally as constructing a perfectly focusing
optical device. He pioneered the study of the lens, formulating
the first geometric theory for lenses. Unfortunately, Ibn
Sahl's work was lost for centuries.
However, recently discovered manuscripts of his work, analysed
by French historian of science Roshdi Rashed, leave no doubt
that Ibn Sahl was the first to discover the elusive sine
law of refraction. This makes the law of refraction, together
with the law of reflection - first given in full by Ibn
Haitham - probably the oldest dynamic laws formulated for
nature. Armed with this discovery, Ibn Sahl achieved a centuries-old
goal by deriving the geometric shape of a perfectly focusing
lens, otherwise known as an 'anaclastic'. What's more, he
designed elaborate mechanisms for drawing his lenses and
mirrors.
Yet, the basic understanding of lenses took on a whole new
dimension after Ibn Haitham launched the study of their
visual and magnifying properties with his Book of Optics.
It was undoubtedly this new understanding of the lens, based
on geometry and experiment, which underpinned the craft
of the Dutch spectacle-makers (makers of eye-glasses) who,
by holding one lens in front of another, invented the first
microscope and telescope, two instruments crucial to the
subsequent development of science.
•
Light's
dual nature: simply miraculous
Three centuries after Ibn Haitham, the Persian physicist
K. Al-Farisi (1267-1319) wrote an important commentary on
the Book of Optics, in which he set out to explain many
natural phenomena. For example, by modelling a water drop
using Ibn Haitham's study of double refraction in a sphere,
he gave the first correct explanation of the rainbow. Al-Farisi
also proposed the wave-nature of light. By contrast, Ibn
Haitham had modelled light using solid balls in his experiments
on reflection and refraction. Now the question presented
itself: is light wave-like or particle-like?
Despite the wave theory of light becoming very dominant
by the start of the 20th century, it could not account for
certain experimental observations, most notably the phenomenon
of the photo-electric effect, the subject of Einstein's
first paper of his Miraculous Year. Einstein reintroduced
the idea of light particles, now called photons, successfully
explaining the photo-electric effect and thus initiating
the quantum revolution. We now have to think of light as
being wave-like and particle-like at the same time: light's
paradoxical wave--particle duality.
In fact, duality was a key concept in Einstein's thinking
at the beginning of the last century. In what is considered
to be his most important work of 1905, the special theory
of relativity, he showed that mass and energy are two aspects
of the same thing. Indeed, stars including the Sun shine
by converting mass into energy in gigantic nuclear-fusion
explosions. Einstein expressed the mass-energy duality elegantly
in the famous equation E = mc2, where E is energy, m is
mass, and c is the speed of light - a universal physical
constant.
•
Alhazen's
Billiard Problem
The recent proof of Fermat's Last Theorem3, hailed as one
of the biggest mathematical triumphs of the 20th century,
left perhaps the last of the great problems in classical
geometry half-solved: Alhazen's Problem. This mathematical
puzzle named after Ibn Haitham has a colourful history dating
back to the time of the Greek geometricians. In his Book
of Optics, Ibn Haitham tackled the problem in terms of optical
reflection in spherical, cylindrical and conical mirrors.
It is also known as Alhazen's Billiard Problem, since it
can be formulated as 'finding the point on the boundary
of a circular billiards table at which the cue ball must
be aimed, if it is to hit the black ball after one bounce
off the cushion.' Ibn Haitham was the first to find a solution
for this geometric riddle, solving it using conic sections.
Indeed, mathematics was his passion, with half of all his
surviving works on pure mathematics. But Ibn Haitham's mathematical
genius is a story for another occasion.
The brilliant mathematician Al-Khwarizmi (Iraq, 780-850)
is said to have invented algebra while writing a book on
how to divide inheritance based on the Quran. Al-Khwarizmi's
mission as a mathematician was simple: he set out to make
mathematics more systematic. Indeed, the very word 'algorithm'
is derived from his name. Successive generations applied
algebra to the existing branches of mathematics, giving
rise to new mathematical branches. This is why algebra is
considered by many as the foundation of modern mathematics.
While it became possible to ex-press geometric problems
in terms of algebra, Alhazen's Problem defied an algebraic
solution for many centuries. Finally, an Oxford pro-fessor
of mathematics solved it algebraically one thousand years
after Ibn Haitham penned his geometric solution, drawing
the curtain over a rich chapter of mathematics in time for
the new millennium.
•
Science's
oldest puzzle;
Have
you ever wondered why the Moon looks much bigger when it
is near the horizon? This intriguing phenomenon, known as
the 'Moon illusion', is arguably the oldest unsolved scientific
puzzle today. A similar effect is observed for the setting
and rising Sun. The ancients wrongly attri-buted the illusion
to the magnifying properties of the atmosphere. But is this
a physical phenomenon anyway?
Surprisingly, the answer is no. The Moon illusion was correctly
redefined by Ibn Haitham as being to do with visual psychology
rather than physics. As has been mentioned, this clarity
of thinking was key to establishing physics as an independent
science. On a slightly different note, there is a famous
quote in which Einstein expressed his discontent with the
haziness of quantum mechanics by asking a friend: do you
really believe that the Moon exists only when you look at
it? The Moon illusion gives Einstein's rhetorical question
a touch of irony.
One can easily test the Moon illusion by taking pictures
of the Moon near the horizon and comparing them with pictures
of the Moon near the zenith. Most people are astonished
to find that the size of the Moon in the photographs remains
almost exactly the same!
A mind-bending explanation for the Moon illusion was given
by Ibn Haitham in his Book of Optics. First, he proposed
what is now called the Size-Distance Invariance Hypothesis
(SDIH), basically explaining why an object would appear
to be larger if it is perceived to be further away, an effect
purely to do with visual processing in the brain. Indeed,
most present-day explanations of the Moon illusion are based
on some version of Ibn Haitham's SDIH. Second, he explained
why the dome of the sky appears flattened; in other words,
why the stars near the horizon seem to be further away than
the stars directly above. Paradoxically however, most people
say that the large horizon Moon actually seems closer; that's
why little children are sometimes seen to jump in an attempt
to catch it! It is precisely this paradox which many present-day
researchers are trying to resolve.
•
The
search for quantum gravity
One of the intended goals of the International Year of Physics
is perhaps to inspire another paradigm shift, which might
well be needed in order to solve the central problem in
physics today: finding a theory for quantum gravity. That
theory needs to unify quantum mechanics with general relativity
(the theory of the very small and the theory of the very
large). If we reflect on the last 1000 years of science,
comparing Einstein's paradigm shift at the beginning of
the 20th century, which established modern physics, with
Ibn Haitham's paradigm shift at the beginning of the last
millennium, which established physics on experimental grounds,
one thing strikes us: the central theme for both was light,
not gravity.
Interestingly, many physicists today seem to give special
prominence to the laws which govern gravity, since, as famous
Cambridge physicist Stephen Hawking explains, 'it is gravity
which determines the large-scale structure of the universe.'
We can still ask however: does the curious similarity between
the paradigm shifts in physics of 100 years ago and 1000
years ago give away any clues about the nature of the paradigm
shift which might solve today's central puzzle of quantum
gravity?
•
Over
the Moon!
Today,
in celebration of Ibn Haitham, who correctly explained the
nature of the Moon's surface, a lunar crater has been named
after him. Alhazen crater lies near the eastern rim of the
Moon's near side (Latitude: 15.9° N, Longitude: 71.8°
E). Another lunar crater celebrates Einstein: Einstein crater
lies along the western limb of the Moon (Latitude: 16.3°
N, Longitude: 88.7° W). It is a fitting coincidence
that, on the Moon, Alhazen crater lies in the east whereas
Einstein crater lies in the west, beautifully reflecting
their birth places back on Earth - Basra in Iraq and Ulm
in Germany.
Einstein once said, 'It has always pained me that Galileo
did not acknowledge the work of Kepler.' But has the work
of Ibn Haitham, which established experiments as the norm
of proof in physics, been properly acknowledged? Let's make
the centenary of the miraculous year a celebration of one
thousand years of physics - from Ibn Haitham to Einstein
- and a celebration of light, the universal metaphor for
knowledge.
H. Salih, M. Al-Amri and M. El Gomati4
The
historical content of this article is based primarily on
original writings of Ibn Haitham, as well as on the analysis
of Roshdi Rashed, recipient of UNESCO's Avicenna Gold Medal.
For
details, contact: M. El Gomati: mmg@ohm.york.ac.uk
