The Speed of Light

In the time it takes you to read this sentence light could travel to the Moon and back. Light moves so rapidly
that for much of human history it was assumed to travel instantaneously. We now know that it doesn't, of course,
and we have learned how to control its speed. We can slow light down, even stop it, and then get it moving again
with the flick of a switch. We can watch light beat itself in a race, and we can use the speed of light to
measure the age of the Universe. It even determines your height.

The Danish astronomer Ole Rømer made the first successful calculation of the speed of light in the 17th century.
He used the regular orbit of one of Jupiter's moons like a clock, and each time the moon was eclipsed by the
giant planet he recorded a "tick". But his careful observations showed that these ticks did not arrive as
regularly as expected when observed from Earth. They were several minutes slow or fast during the course of the
year.

Rømer worked out that these delays were due to variations in the distance between Jupiter and Earth as they
orbited the Sun. By calculating the relative positions of the Earth, Jupiter and this moon in their orbits at
different times of year, he was then able to calculate the speed of light as it travelled through space. Rømer
presented his results, which were within 30 per cent of the present accepted value, to the French Academy of
Sciences in 1676.

Theoretical work on the nature of light has also provided insights into its speed. By the mid 1860s the Scottish
physicist James Clerk Maxwell had worked out a set of equations that describe how electromagnetic fields must
behave in space. One solution to these equations described electromagnetic waves that had to be travelling at
about 300,000 kilometres per second in a vacuum, remarkably close to the speed of light measured by Rømer and
others after him.

Michael Faraday, at the Royal Institution, London, used the idea of electric and magnetic fields to explain
electrostatic and magnetic forces and show that light could be affected by magnetic fields. This confirmed that
visible light is indeed part of a spectrum of electromagnetic waves. Direct measurements of the speeds of other
components of the electromagnetic spectrum—microwaves, infrared, ultra-violet, X-rays and gamma-rays—showed that
they all have the same velocity in a vacuum.

Experiments to measure the speed of light continued to become more accurate. By the 1950s, electronic timing
devices had replaced the old mechanical equipment, and by the 1980s the speed of light (c) was calculated by
measuring the frequency (f) and wavelength (l ) of laser light and applying the equation c = fl . These
calculations were based on the standard definitions of the second and the metre. The metre was defined as
1,650,763.73 wavelengths of light from a krypton-86 source, while the second was 9,192,631,770 periods of the
radiation emitted from a hyperfine transition in caesium-133, just as it is today. This gave an impressively
precise result for c, accurate to a few parts in a billion.

In 1983 the speed of light was chosen to be the defined quantity, rather than the metre. It was fixed as
299,792,458 metres per second, which was chosen to be consistent with the length of the metre at that time. The
defined values for the second and the speed of light mean that the metre is therefore defined as the distance
travelled by light in a vacuum in 1/299,792,458 of a second. So from 1983 onwards, any refinements in our
measurements of the speed of light do not affect its value, but they do affect the length of the metre. The
speed of light actually defines how tall you are.

But the speed of light defines something much more fundamental than just a length. The work of Albert Einstein
demonstrated the real significance of the speed of light, and thanks to him we know that it is not just the
speed of photons in a vacuum. It is also the fundamental constant linking space and time.

As a young man Einstein had asked himself what light would look like if one moved fast enough to keep up with
it. In principle it should appear as a stationary peak alongside you, but Einstein knew that Maxwell's equations
don't allow such a result. He concluded that either that Maxwell's theory does not apply to a moving observer or
that the mechanics of relative motion had to change.

Einstein solved this problem in his special theory of relativity, which was published in 1905. It was based on
the universal principle that both the laws of physics and the speed of light are the same for all observers who
are moving with a constant velocity, regardless of what that velocity is. Einstein's special relativity has
revolutionised our view of space and time and emphasised the fundamental role of the speed of light in physics.

Imagine you are in a rocket, racing a laser pulse into space. Observers on the Earth will see the pulse moving
away at the speed of light. No matter how fast you're moving away from the Earth, say 99 per cent of the speed
of light, the light beam still overtakes you at the speed of light. It might seem absurd, but it's true. And
the only way that this can be true is if time and space are measured differently by the occupants of your rocket
and the observers on the surface of the Earth.

Time and space certainly look different depending whether you're on Earth or in space. Einstein's general theory
of relativity describes gravity as a distortion of space-time geometry. One consequence of this is that light
rays, which follow the shortest possible path through space-time, appear to bend around massive bodies. This was
observed to be the case in 1919 when measurements made during an eclipse showed that starlight passing near the
Sun was bent by the Sun's mass. This observation led to the final acceptance of Einstein's theory and made him
famous around the world.

But if light is deflected, then basic mechanics says it must be accelerating. Surely this makes the speed of
light variable and undermines the original principle of relativity? In one sense this is correct: the speed of
light, as seen by us here on Earth, does appear to vary as it passes close to the Sun. But relativity and the
constancy of the speed of light need not be abandoned.

Gravity Tricks

Seeing is not believing

Einstein realised that gravitational forces are a kind of illusion experienced by observers who are not moving
freely. Imagine jumping off a wall. While in free fall you do not experience the local effects of gravity, but
anyone on the ground watching you fall would explain your motion in terms of a gravitational force. The same
argument applies to astronauts inside a space station: as far as they are concerned they are in a "zero-g"
environment, but looking up from the Earth's surface we use gravitational attraction to explain their orbital
motion. So when we watch from the Earth, light passing the Sun appears to bend and accelerate, but if we were
falling freely toward the Sun the light passing us would appear to move in a straight line at constant velocity.
The speed of light is constant to any freely falling observer as it passes him. However, it will appear to bend
and accelerate when it passes distant massive objects that distort the space and time that surrounds them.
Another strange consequence of relativity is that nothing can accelerate to the speed of light. However powerful
we make our rocket ships, they will never get to the speed of light. That's because the faster an object moves,
the more kinetic energy it has. And Einstein showed that energy itself has mass or inertia, summed up in his
famous equation, E = mc2. So as an object's kinetic energy increases, so does its inertia, which makes it harder
and harder to accelerate further. It's a law of diminishing returns: the more work you do on the object, the
more massive it becomes and the smaller the effect of the accelerating force.

It would take an infinite amount of energy to accelerate a single electron to the speed of light, and particle
physicists are well aware of this restriction. When protons enter the Tevatron accelerator at Fermilab, Batavia,
Illinois, they are already travelling at 99 per cent of the speed of light. The final stages of the accelerator
increase their energy by a factor of 100, but their speed only creeps up to 99.99995 per cent of the speed of
light—less than 1 per cent greater than when they entered the machine.

Quantum theory, however—which has always been in conflict with relativity—does seem to allow things to travel at
speeds greater than the speed of light. In the 1920s quantum theorists worked out that distant parts of a system
can be connected instantaneously. For example, when a high energy photon decays into two lower energy photons,
their states (whether they are spinning clockwise or anticlockwise, for example) are not fixed until an
observation is made on either one of them. The other particle appears to sense that an observation has been made
on its partner, and the result is that any subsequent measurement made on the second particle will always yield
a result consistent with that obtained on the first particle. An instantaneous connection at a distance such as
this is rather like a message that passes between the particles at infinite speed. This "spooky action at a
distance", as Einstein called it, seems implausible but has been shown to be a real phenomenon.

In 1993, Raymond Chiao at the University of California at Berkeley showed that quantum theory also allows another
kind of faster-than-light travel: quantum tunnelling. Imagine kicking a football against a solid wall. Newton's
laws predict that it will bounce off, but quantum theory says there is a small probability of it appearing on the
other side of the wall. One way of thinking about this is to imagine that it can "borrow" the extra energy it
needs to pass through the wall as long as it pays it back pretty rapidly once it reaches the other side. This
doesn't break the laws of physics, since energy, momentum and other properties are all conserved in the long run.
The German physicist Werner Heisenberg's uncertainty principle states that there are always properties of a
system—in this case the energy—whose values cannot be pinned down, so the rules of quantum physics allow the
system to exploit this uncertainty and take some extra energy for a short time. In the case of tunnelling, the
time between the particle disappearing on one side of the barrier and reappearing on the other can be almost
negligible, and the barrier can be as wide as you like—though as its length increases, the probability of a
particle tunnelling through it drops rapidly towards zero.

Chiao demonstrated "faster-than-light" tunnelling by measuring the tunnelling times of photons of visible light
moving through a special filter. To do this he raced them against photons that travelled over a similar course
through a vacuum. The tunnelling photons reached the detector first, and Chiao showed that they must have
travelled at 1.7 times the speed of light while inside the filter.

In 1994 Ferenc Kraus at the Technical University in Vienna showed that the tunnelling time reaches an upper
limit independent of the barrier thickness, implying that there is no limit to the speed at which photons can
tunnel through the barrier. Günter Nimtz at the University of Cologne has also demonstrated such "superluminal"
travel using micro-waves. He even modulated his signal with Mozart's 40th symphony and transmitted it through a
12-centimetre barrier at 4.7 times the speed of light.

Full Speed Ahead

A limit for information transfer.

Both of these ideas seem to violate the principle of relativity, which forbids faster-than-light travel. But
all is well, because what relativity actually forbids is the transfer of information faster than light.
Experiments have shown that the "instantaneous connection" between two quantum objects cannot be used to
transmit information. The tunnelling effect is similarly limited. That's because quantum theory is intrinsically
statistical, which means it relies on the properties of large groups of particles. So the appearance of a few
photons ahead of time is not enough to transmit information. Tunnelling distorts the incoming waveform so that
a given peak may well be received earlier than expected. However, the information is carried not by a single
peak, but by the entire wave packet, and this does not travel faster than light. Careful analysis of tunnelling
experiments does seem to support the idea that the information content of the signals is still restricted to the
speed of light, although this remains a controversial topic.

This limit on the speed of information transfer protects causality, the notion that an event's cause must happen
before the event itself. If this weren't the case, observers who were moving at different speeds could never
agree on a unique order of connected events. Someone could drop a cup and watch it shatter, while another
observer would see the broken pieces before they saw the cup dropped. Without this speed limit on information
transfer, the Universe would seem a very strange place indeed.

Although it is impossible to make a massive particle travel faster than light in a vacuum, this is not the case
inside other materials that have a "refractive index" greater than 1. In water, for example, light travels at
about 60 per cent of its speed in a vacuum. The fact that light slows down in different transparent materials
has been known for more than three hundred years. It explains why light refracts and disperses, and is the
principle behind all kinds of optical instruments. Refraction occurs because photons—the individual units of
energy that make up light—interact with electrons inside atoms. The photons do travel at full speed between
atoms, but are continually absorbed and re-emitted as light moves through the material, so the information they
carry is transmitted at a reduced speed. As a result it is perfectly possible for high-energy electrons, say,
to travel through a medium such as water at speeds faster than light in that medium. When they do so they
radiate electromagnetic waves, which cannot travel as fast as the moving particle and so bunch together to
form an intense shock wave in the direction of travel. This is much the same mechanism that produces the sonic
boom from a supersonic aircraft. The radiation emitted in this way by faster-than-light particles in a material
medium is called Cerenkov radiation. It is often used to detect otherwise invisible particles travelling faster
than light—such as neutrinos in huge water-filled detectors at the Kamio-kande Institute for Cosmic Ray Research,
Tokio.

Most materials don't slow light down significantly, and its speed cannot be reduced by much more than about 50
per cent in ordinary matter. However, in 1998 Lene Vestergaard Hau at Harvard University announced that she had
slowed light to a mere 17 metres per second, and in 2001 she brought it to a complete stop. Of course, her team
was not working with ordinary matter. They used what has been called the fifth state of matter (after solid,
liquid, gas and plasma): the Bose-Einstein condensate.

This remarkable state of matter consists of a cloud of atoms cooled to within about a millionth of a degree
above absolute zero and suspended in a magnetic field. The cloud then forms a Bose-Einstein condensate,
effectively a single quantum object, something like a huge atom. All its constituent atoms are in a single
quantum state and behave in a coordinated way, as if they were just one object.

The trick to slowing light down is to shine two perpendicular beams into the condensate. One beam, the probe,
carries information, and the other is called a coupling beam. While this coupling beam is switched on it makes
the material perfectly transparent, so that the probe beam can pass through it.

The sodium atoms have one electron in their outermost orbital, and interaction between the light from the probe
beam and this electron is crucial to the process. When an atom absorbs a photon from the probe beam, the outer
electron jumps to a higher energy state. A short time later it drops back to the ground state and emits a
photon. Unfortunately this emission process is completely random, so any information contained in the original
beam is lost.

The various frequency components of the probe pulse all travel at different speeds through the condensate. The
result of this is that an incoming pulse bunches up inside the sodium cloud and travels slowly through it. As
it does so the spins of the atoms change in response to the pulse. If the coupling beam is switched off at this
stage, the pulse (or at least the information it contains) becomes trapped in the pattern of atomic spins.
Effectively, the light stops. When the coupling beam is switched back on, the condensate re-emits the light pulse.

Slowing and stopping light could have applications for computing. Physicists have long wanted to create optical
computers that use beams of light instead of electrons to transmit information and carry out computations. They
also want to create quantum computers, which will use the quantum states of atoms and the strange rules of
quantum theory in order to create hugely powerful processors. Hau's tricks with light may also help scientists
model the behaviour of light in the vicinity of a black hole. In fact, playing with the speed of light could be
the best way to uncover the deepest mysteries of the Universe—the very things that the speed of light helps to
determine.

Tricks of the light and illusions in space

There are many examples in which objects might appear to move faster than the speed of light. But they don't
actually violate the principle of relativity. For example, the line drawn by an electron beam sweeping across
a TV screen can, in principle, go faster than the speed of light. The reason for this is that the fluorescent
pixels at successive points on the screen are excited by different electrons. So nothing actually moves from one
point to the next faster than light, it just looks like it because they light up in a regular sequence.

Astronomers have seen faster-than-light illusions in space: quasars sometimes emit jets that appear to be moving
much faster than light. In order to measure the speed of the jet, astronomers need to make two observations of
its position. Using the time between these observations, they can deduce the jet's speed. But if this works out
to be greater than the speed of light, there's a good reason: it's because the jets are emitted directly towards
the observer. In that case, successive observations have to allow for the fact that the jet is getting ever
closer, and the time taken for the light to reach Earth is reducing. This makes it appear that, during the 
nterval between observations, the jet has moved farther than it really has.

Two American astronomers, Edwin Hubble and Vesto Slipher, discovered another illusion in the 1920s. They found
that the Universe is expanding, and the galaxies in it are flying apart like debris from an explosion. But in
this case, the farther apart the galaxies are, the faster they are receding. If the galaxies are far enough
apart, their speed of recession is faster than the speed of light. So if this apparent expansion were due to the
galaxies racing outwards through space, it would violate the principle of relativity that says nothing can go
faster than light. But it is in fact an illusion. The superluminal motion of the galaxies is actually the result
of the space between the galaxies expanding. Despite what anyone might think they see, the speed of light
remains unsurpassed.


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