杏吧原创

London

CATACLYSMIC events that release large amounts of energy are not only felt at
the point where they strike. Here on Earth, for example, an earthquake will send
seismic waves echoing around the world. These disturbances of the Earth鈥檚 crust
distort the rocks through which they pass, and can transfer some of the
earthquake鈥檚 energy to the far side of the world. Seismic waves illustrate three
characteristics common to all types of wave: they are created by an event that
releases energy; the disturbance is passed from one place to another at a finite
speed through a connecting medium; and they transfer energy from the original
disturbance to other bodies.

Physicists believe that gravitational waves should occur as a consequence of
events on an even larger scale than this. According to Einstein鈥檚 general theory
of relativity, they are radiated by accelerating masses, such as coalescing
black holes or exploding supernovae. They cause periodic variations in the
geometry of space-time (see 鈥淓instein鈥檚 theory鈥�) as they pass. They travel at the speed
of light. And they make distant masses vibrate, causing them to absorb some of
the energy carried by the waves.

Nobody has yet detected gravitational waves directly, though there is
compelling indirect evidence that they do exist. Physicists in several countries
are now setting up experiments that aim to observe gravitational waves. If they
are successful, these waves might open a new window for astronomical
observation, just as the first observations of radio waves and X-rays did in the
past. Indeed, the consequences could be even more profound because gravitational
waves are a completely different type of wave to light, radio and X-rays. If
detected, it would be like hearing the Universe for the first time whereas
previously we have only ever seen it.

The principle behind experiments to detect gravitational waves is simple. Any
object that has mass will vibrate in response to the waves as they pass, so all
that is needed is a test mass, plus a detector to pick up and measure its
vibrations.

In practice, however, there are huge problems. The vibrations that
gravitational waves produce are expected to be incredibly small. This is because
gravity is extremely weak compared to other fundamental forces such as
electromagnetism. The gravitational force between a proton and an electron in a
hydrogen atom, for example, is 10⁴⁰ times weaker than the electromagnetic force
between these particles. To pick up even the strongest gravitational waves
generated by the violent motion of massive bodies, a detector needs to be
sensitive enough to measure vibrations that change the shape of a test mass by
just 1 part in 10²². This is equivalent to measuring a change in height of a
human to about a hundred-millionth of the diameter of a single atomic nucleus.
Even gravitational waves from violent events in our Galaxy, such as a collapsing
star, would cause changes of less than 1 part in 10¹⁸, which would alter a
human鈥檚 height by much less than the diameter of an atomic nucleus.

Physicists have to look for vibrations such as these because there is no more
direct way to detect a gravitational wave. You can鈥檛 simply measure the change
in the weight of a test mass caused by a passing gravitational
wave鈥攅ssentially, a variation in gravity with time. This is because all
masses in a particular gravitational field free-fall at the same rate, so no
relative motion occurs. Gravity can only be observed through its tidal
effects鈥攖hat is, through distortions in a body that are caused by
differences in gravity at different points across the body.

To see the distinction, imagine a free-falling laboratory, first in a uniform
gravitational field and secondly in a nonuniform field. Imagine the laboratory
is full of dust which is initially spread evenly throughout the room. In the
first case, every dust particle falls with the same acceleration and retains its
relative position with respect to all the others. If the strength of the field
is uniformly cranked up everywhere, the acceleration of the laboratory and all
that it contains increases at the same rate, so the dust is not redistributed
and the change is undetectable.

Now think about the nonuniform field, perhaps in a laboratory free-falling
towards the Earth. Here, the field is stronger near its base. As the room falls,
dust particles near the bottom of the laboratory have a greater than average
free-fall acceleration so they collect on the floor. Those near the top collect
on the ceiling, as they have a less than average free-fall acceleration. There
is also a horizontal effect, since the direction of gravity converges towards
the centre of the Earth. This gives the falling dust particles a horizontal
component of acceleration, which makes them concentrate toward the centre of the
laboratory.

To an observer inside the laboratory, there is a tidal force that separates
the dust vertically and compresses it horizontally. This is exactly what happens
to the Earth as it free-falls in the gravitational field of the Moon: the oceans
are extended along the line joining the centres of the Earth and Moon and are
squeezed perpendicular to it, producing two high tides per day as the Earth
spins.

In the same way, gravitational waves appear as a periodic tidal force to a
stationary observer. This causes massive objects in the path of the wave to be
squeezed and stretched in the directions perpendicular to the incoming wave
(see Figure 1).

Catch the wave

Detection methods

Gravitational wave detectors are designed to respond to the tiny displacement
of particles caused by these tidal forces. These vibrations are expected to be
slighter than the random motion of atoms in the detector that is due to their
thermal energy. They are anticipated to be even smaller than the quantum
uncertainty in the position of atoms that stems from the inherent fuzziness of
nature at very small scales. And yet, physicists have been able to devise two
methods that they hope will detect gravitational waves as they pass.

The first of these is called a Weber bar, after the American physicist Joseph
Weber, who first pursued the idea at the University of Maryland in the early
1960s. He used a cylindrical aluminium bar about 2 metres long and 0.5 metres in
diameter. Waves travelling along the bar鈥檚 long axis cause it to stretch and
compress at right angles to this axis
(see Figure 2). The key to the bar鈥檚
sensitivity is that it has a natural frequency at which it prefers to vibrate.
If the incoming gravitational waves contain frequencies close to this frequency,
the bar will resonate and amplify the vibration. Piezoelectric sensors attached
to the middle of the bar convert the tiny displacements to electrical signals
that can be recorded and processed.

Weber guessed the likely frequency of incoming gravitational waves by
thinking about possible sources. For example, a very tightly bound binary star
system, in which two stars orbiting their common centre of mass were about to
coalesce, would be a strong source of gravitational waves. As the stars got
closer together, their orbital frequency would increase to about 1 kilohertz and
the system would generate gravitational waves which include this frequency. By
coincidence, some of the other sources of gravitational waves鈥攃olliding
black holes, coalescing neutron stars and exploding supernovae鈥攁re also
expected to produce gravitational waves which include similar frequencies.
Weber鈥檚 bars had a resonant frequency around 1 kilohertz and a sensitivity of
about 1 part in 10¹⁵.

Modern versions use bars cooled by super-cold liquids to minimise the thermal
motion of the atoms they contain. Reducing this thermal noise gives the bars a
sensitivity of about 1 part in 10¹⁸. They should be sensitive enough to detect
violent events in our own Galaxy. Work on such experiments is under way in the
US, Switzerland and Italy. Researchers are also working on similar experiments
using spherical detectors, which are equally sensitive to gravitational waves
from all directions. This work is being carried out in the US, Brazil and the
Netherlands.

Another way to detect small changes in position is to use a laser
interferometer. In this device light from a laser is split into two beams which
travel along paths at right angles to one another
(see Figure 3). The beams are
reflected back the way they came by mirrors placed at equal distances from the
beam splitter. The returning beams are recombined to produce an interference
pattern, similar to the bright and dark stripes seen when light passes through
two narrow parallel slits. If the length of either arm changes, one beam is
delayed with respect to the other and the pattern of bright and dark stripes
shifts. The path difference between the two beams鈥攚hich is twice the
difference in the lengths of the two arms鈥攃an then be calculated from the
changes in the interference pattern.

As a gravitational wave passes perpendicularly to the plane of an
interferometer, one arm is stretched while the other shrinks. A little later the
first one shrinks and the other stretches. Gravitational waves are likely to
contain a broad spectrum of vibration frequencies, and interferometers could be
used to detect and analyse this spectrum. As different sources are likely to
produce different gravitational wave spectra, this information could be used to
identify and measure the source.

Interferometers have two major advantages over Weber bars. First, they
respond to almost all frequencies of gravitational waves; in other words, they
have a very wide bandwidth. Secondly, by placing the mirrors a long way away
from each other, they can be made much more sensitive.

Several projects to detect gravitational waves are under way. The biggest of
these is in the US. The LIGO (laser interferometer gravitational-wave
observatory) project, run from Caltech in Pasadena, California, is building a
pair of interferometers in opposite corners of the country: one in Washington
state and one in Louisiana. Each interferometer consists of two freely suspended
test masses hanging at the ends of vacuum tubes 4 kilometres from the beam
splitter. Each test mass has a mirror attached, in order to reflect the laser
light. The two interferometers are about 3000 kilometres apart, and the idea is
to compare any signals they produce so that disturbances due to local effects or
seismic movements can be discounted.

Listening in

Monster experiments

In a smaller experiment, French and Italian researchers are collaborating on
the Virgo project, a 3-kilometre interferometer located at Pisa, Italy. A
similar project, GEO 600鈥攁 collaborative effort between British and German
scientists to build an interferometer with arms 600 metres long鈥攊s being
built near Hanover, Germany. And Japanese scientists are collaborating on a
project called TAMA鈥攁 300-metre interferometer at the National
Astronomical Observatory in Mitaka, near Tokyo.

The European Space Agency has proposed an even more spectacular project for
detecting gravitational waves. The LISA (laser interferometer space antenna)
proposal consists of six spacecraft orbiting the Sun about 20掳 behind the
Earth in its orbit
(see Figure 4), arranged in pairs at the corners of a giant
equilateral triangle. The sides of the triangle are 5 million kilometres long
and act as the arms of three giant interferometers.

LISA is also up against some tough technical problems. For example, a
gravitational wave that caused a disturbance of 1 part in 10²⁰ would change the
length of one of the arms by less than the width of an atom. Put another way,
the interferometer must be sensitive enough to detect a change of less than one
atomic diameter in a distance ten times that from the Earth to the Moon. For
LISA to operate effectively, all possible disturbances must be allowed for or
removed. The orbits of the spacecraft are chosen so that their configuration
remains stable. Even the pressure of light from the Sun, which measures about
10^-5 pascals, or one ten-billionth of normal atmospheric pressure, would
cause the spacecraft to drift out of position.

The interferometer鈥檚 mirrors will be small, highly polished solid cubes made
from an alloy of gold and platinum. Each cube will be totally enclosed, to
shield it from solar radiation, but it will not be attached to the craft that
surrounds it. Instead, it will float freely in space, and the spacecraft will
maintain its position with respect to the free-falling cube inside by means of
small thrusters. These will employ a technique called field effect electric
propulsion, which can apply a force as small as 0.1 micronewtons (see 鈥淭o catch
a space quake鈥�, New 杏吧原创, 10 August 1996, p 36).

LISA鈥檚 incredibly long arms will make it more sensitive to gravitational
waves than any ground-based interferometer. But there is another advantage to
building a gravitational wave detector in space. LISA will be able to detect
low-frequency gravitational waves from supermassive black holes merging in the
cores of active galaxies such as quasars. These low-frequency waves cannot be
picked up by ground-based detectors as they are drowned out on Earth by seismic
activity.

Using six spacecraft is an insurance policy, as it will be impossible to
service the craft once they are in position. LISA will continue to operate even
if two spacecraft fail, unless they happen to belong to the same pair

A source of light needs a source of energy to sustain it. A filament lamp in
a hand torch, for example, transforms electrical energy from the battery into
heat and light. As the battery runs down, the lamp becomes dimmer. Gravitational
waves transfer energy, so they must drain energy from their source just as the
light bulb drains the battery. In fact, the way in which certain astronomical
bodies are losing energy provides the most convincing evidence so far for the
existence of gravitational waves. Binary star systems, in which a pair of stars
orbit in partnership, should radiate gravitational waves because both masses are
accelerating as they orbit their mutual centre of mass. If gravitational waves
are transferring energy from a binary system, its orbital period will fall.

Convincing evidence

Pulsars slow down

In 1974 Russell Hulse and Joseph Taylor, two American physicists from
Princeton University in New Jersey, discovered a binary system called PSR
B1913+16 in which one star had collapsed to form a pulsar. Pulsars are rapidly
spinning, extremely dense stars emitting powerful beams of electromagnetic
radiation from certain points on their surface. As the pulsar spins on its axis,
this beam of radiation sweeps round like a lighthouse beam, so we see regular
pulses of radiation. The timing of the pulses is so regular鈥攖heir accuracy
is comparable to that of an atomic clock鈥攖hat when the first pulsar was
discovered 30 years ago, some people thought it might be a signal from an alien
intelligence.

But while the pulses from Hulse and Taylor鈥檚 pulsar are emitted at regular
intervals, they appear very slightly irregular when observed from Earth. This is
because they are affected by orbital motion in the binary system. Hulse and
Taylor used these observed variations to measure the orbital period of the
system and its mean radius, and to calculate the masses of the two stars to an
accuracy comparable to that with which we know the masses of planets in our own
Solar System. This information allowed them to calculate the expected rate of
energy loss from the system due gravitational waves, and to predict the rate at
which the orbital period should decline. By 1993, the period had fallen by about
1.4 milliseconds, a value that is in good agreement with the prediction, based
on Einstein鈥檚 theory, of about 75 microseconds per year. In recognition of this
work, Hulse and Taylor shared the Nobel Prize for Physics in 1993.

The expense and technical difficulties involved in trying to detect
gravitational waves are huge, so why bother? Of course, for theoretical
physicists the answer is obvious: a positive result will be a boost for
Einstein鈥檚 general theory of relativity, which predicted them. But there is
another spin-off from the successful detection of gravitational waves, which
could have much more significant consequences.

This is because the waves will tell the story of their source. Waves from a
supernova will look different to those leaving a binary star system. If the
incoming waves are recorded and analysed, perhaps by comparing results from
several sets of interferometers around the world, astronomers will be able to
identify their source, and link them to optical and X-ray sources detected by
other means. Gravitational waves also promise to provide definitive proof of the
existence of black holes. The boundary of a black hole has a characteristic
signature of vibration frequencies, like the ringing of a bell, and the
gravitational waves that black holes produce will be highly distinctive.

Large-scale disturbances of space-time are the strongest sources of
gravitational waves. So they could provide information about black holes,
collapsed stars and even the big bang itself that no other kind of observation
could reveal. A gravitational wave detector ought to be a particularly rich
source of information about huge masses and about the physics of regions of
intense gravity. The revolution in astronomy and cosmology that would come with
the detection of gravitational waves could be greater than that which followed
the birth of radio or X-ray astronomy.

* * *

Einstein鈥檚 theory

ISAAC NEWTON鈥檚 theory of gravitation, published in 1687, describes how masses
are attracted to each other as the result of an instantaneous action at a
distance. As Newton鈥檚 theory pictures it, the Earth orbits the Sun as a result
of a force of attraction between the two bodies, and if the Sun suddenly
vanished, the force would disappear at the same time and the Earth would fly off
at a tangent.

Albert Einstein鈥檚 general theory of relativity, published in 1915, is
different in principle, although many of the observable consequences are the
same. Whereas Newton assumed that space and time are the same for all observers,
Einstein鈥檚 theory built on his earlier work, the special theory of relativity,
which showed that different observers could have different views of space and
time. In this picture, the laws of physics take their simplest and most
universal form if space and time are combined into a four-dimensional continuum
known as space-time.

According to Einstein鈥檚 general theory, the presence of a massive body like
the Sun distorts the geometry of space and time, just as a massive ball placed
on a rubber sheet distorts the sheet. A body in free-fall follows the path of
least distance, known as the four-dimensional geodesic, through this distorted
space-time; there is no force of gravity. So, for example, as the Earth鈥檚 orbits
the Sun it is simply following the most direct route through this region of
space-time, just as a great circle is the most direct route over the spherical
surface of the Earth.

Einstein鈥檚 view can be summarised in two simple statements. Matter tells
space how to curve. Space tells matter how to move.

One consequence of this theory is that what we perceive as gravitational
attraction does not act instantly. If the Sun suddenly ceased to exist, the
distorted space-time around it would take time to change its curvature. The
flattening-out effect spreads out at the speed of light, so the Earth would
continue to move along its orbit for a full 8 minutes鈥攖he time it takes
for light to travel from the Sun to the Earth鈥攂efore it flew off at a
tangent.

The acceleration of masses through space-time generates ripples in space-time
geometry that travel at the speed of light. These are gravitational waves.