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The picture on the left is a
"corral" of iron atoms, arranged in a circle by hand (actually using
a scanning tunnelling electron microscope. The corral is around one billionth
of a meter across. The circular ripples inside the corral are electron waves,
which show that at the microscopic levels, particles such as electrons are not
localised. This picture, in addition to being a technological marvel, is
striking verification of the bizarre predictions of quantum mechanics, the
theory known to accurately describe the world of atoms and electrons. The
picture on the right was taken by the Hubble space telescope. It shows the
accretion disk of a monstrous back hole at the core of a galaxy many light
years away. This picture too is a technological marvel, taken by a telescope
in orbit around the Earth, and provides beautiful support for the existence of
black holes, which are among the more bizarre predictions of Einstein's theory
of gravity, or general relativity as it is known by scientists. General
relativiy is known to accurately describe the dynamics of very massive, large
gravitating objects. It is an amazing circumstance that the two physical
theories graphically represented on this slide are in fact not compatible with
each other. If one applies the rules of quantum mechanics to Einstein's
theory, one gets puzzling contradictions, an indication that one or both
theories must be substantially revised before they can co-exist. The search
for a consistent theory of "quantum gravity" unifying the laws of
the very small with those of the very large, is currently one of the most
important tasks confronting modern physics. The purpose of this talk is to
give an overview of Einstein's gravity and black holes, and then to show how
black holes are playing such a vital role in this quest for a unified theory
of quantum mechanics and gravity. The outline of the talk is given on the next
slide.
First I will describe the problems
associated with Newton's theory of gravity and then briefly outline the key
features of Einstein's theory of general relativity. The remainder of the talk
will focus on black holes: their definition, properties, and most importantly
how they are observed in nature. Finally I will try to describe why black
holes are so important to theoretical physicists, and in what sense they are
posing riddles whose resolution will point the way to a viable theory of
quantum gravity.
Newton's laws of mechanics and universal
gravitation worked wonderfully well in describing virtually all terrestial
phenomena as well as the motions of the moon and the planets. In this sense
Newton provided a beautiful synthesis of two previously distinct sets of
phenomena: the terrestrial and the celestial. However, as with all theories
and combination of experimental results and conceptual reasoning ultimately
forced Newton's gravitation theory to be modified and replaced by Einsein's
theory of general relativity. There were essentially three problems with
Newton's theory. First of all, there was a conceptual problem. In Newtonian
gravity, the strength of the gravitational force bewteen two bodies was
proportional to the product of the inertial masses of the bodies. Inertial
mass was therefore doing double duty: by definition, it was a measure of the
resistence of an object to a change in velocity. In addition, inertial mass
seem to also play a role as the "gravitational charge". In much the
same way that electric charge determines the strength of electrostatic forces
between two charged objects, the inertial mass (a.k.a. the gravitational
charge) determines the strength of the corresponding gravitational force. This
is the reason that, as found by Galileo, all objects fall to Earth at
precisely the same rate. The reason for this double duty is a complete mystery
in the context of Newtonian mechanics, but is essentially a trivial
consequence of Einsteinian gravity. The second problem with Newton's theory
was that it described gravity as an instantaneous force of attraction between
two massive objects. Consequently, if you move one of them, the other knows
about the move immediately due to the change in gravitation, irrespective of
the distance between them. FInally, and most importantly, there was a
discrepancy, albeit very tiny, between the predictions of Newton's theory, and
experimental observation for the precession of Mercury's orbit.
As stated above, Newton explained why
objects fall towards the earth by postulating an instantaneous force of
attraction between all objects. This works really well to a point, but it
leaves at least unexplained one startling fact: all objects fall towards the
earth at the same rate. This is a complete mystery in Newton's gravity theory.
In order to explain this simple fact, Einstein had to completely overturn the
Newtonian view of the Universe. In particular, Einstein taught us that that
gravity (as an instantaneous force of attraction between two objects) is a
myth. Morever, space is not merely an inert stage on which physical phenomena
occur. Space is a dynamical entity: it has a shape and structure that is
determined by the matter it contains. Objects fall towards the earth at the
same rate because they are all trying to follow the (same) straightest
possible trajectory in the curved space surrounding the Earth. (Actually, I
should be talking not just about space, but space and time together, but it is
easier to visualize the geometry of space, rather than spacetime .) A simple
sheet, or membrane, like a stretched piece of spandex, can provide a very
accurate two dimensional representation of how gravity works, as shown on the
next transparency.
Think of space as a stretched rubber
sheet. When something heavy is placed on the sheet, it causes it to dip. The
heavier the object, the deeper the resulting gravitational well. In the words
of John Wheeler "matter tells space how to curve". Once one accepts
the curvature of space, it is rather easy to see that smaller objects will
move along the straightest possible line that they can in that curved space.
However, this straightest possible line has different properties than in flat
space. In fact, the line itself looks curved, as shown above. Again in the
words of Wheeler, the curved space tells the matter how to move. In curved
space the rules of Euclidean geometry are no longer valid. For example, it is
possible for parallel, straight lines to meet: think of the lines of longitude
on a the curved surface of a spherical globe: they are parallel at the equator,
straight and meet at the poles. Also, the sum of angles in a triangle does not
have to equal 180 degrees: think of the triangle made by two lines of longitude
that meet at the north pole, and the segment of the equator joining them. This
triangle has two right angles at its base (the equator), and a non-zero angle
at the apex (the north pole). Hence the sum is greater than 180. Once space
itself is curved, everything moving in it is affected. Thus not only particles,
but light too must feel the effects of gravity.
In the context of the membrane paradigm
in the earlier slide, clearly the more matter that is put in the center of the
sheet, the deeper the well that is created, and consequently the harder it is
for matter to "climb out" . According to Einstein's theory, if
enough matter is packed into a small enough volume, the well will get so deep
that the matter inside can never escape. A circle of no return forms. Any
matter that passes the point of no return can no longer escape to the outside
world. It necessarily keeps collapsing, moving towards the center. The well
gets deeper and deeper until finally a hole is literally torn in the fabric of
spacetime: the density of matter at the center becomes essentially inifinite,
at least to the extent that Einstein's theory of gravity is still valid. Thus,
what I mean by " a hole in the fabric of spacetime" is: a tiny region
of space where the known laws of physics break down. A black hole is then a
region of space so tightly packed with matter, that nothing, not even light
can escape. Hidden at its (crunchy?) center is a tear in the fabric of spacetime.
Anything that falls into this region of space is irrevocably lost to the rest
of the universe. No light can emerge or pass through this region, so it appears
totally black. In some sense therefore, a black hole marks a boundary to
spacetime: a horizon beyond which no one can see without travelling through
it. This radius of no return is called the event horizon of the black hole.
This is a two dimensional representation
of what the space containing a black hole would like like. Far from the black
hole, the space is curved, just like around our Earth, or an ordinary star.
Somewhere in the space there is a circle (actually sphere) which marks the
point of no return. Anyone who travels inside that circle can never emerge,
and is doomed to travel inevitably towards the "tear" in the center.
Anything that can be cut can also be
sewn. It is mathematically possible to take two black hole geometries, and sew
them together along their "tears". This gives rise to wormhole
solutions to Einstein's equations, in which two otherwise separate
"universes" are connected by a throat, or tunnel, as shown in the
top figure above. Such wormholes could also connect different regions of the
same universe, as in the bottom picture. In principle this would enable us to
take shortcuts to distant parts of the Universe just like they do in Star Trek.
The problem is that within Einstein's theory such wormholes are very unstable.
The throats tend to collapse in a much shorter time than it would take to get
through to the other side, so that traversing such wormholes is in practice
impossible.
The space far from a black hole is kind
of boring. It has no distinguishing features besides the degree to which it is
bent, and this bending, is no different than that of an ordinary star of the
same mass. In fact there is a "no hair" theorem that guarantees
black holes to be virtually featureless when viewed from far away. All the
bumps and wriggles of the matter from which they were formed are smoothed out
as the matter contracts, so that the final shape of the horizon is always
perfectly smooth and round. Near the event horizon, things are more
interesting. To a distant observer, events near the horizon appear to slow
down. If you drop a clock into a black hole it appears to tick more and more
slowly as it approaches the event horizon. Time actually appears to stop right
at the horizon. The clock's motion towards the black hole also slows down and
to a distant observer it takes literally forever to fall through. If you are
unfortunate enough to be falling with the clock, time appears to progress normally.
You fall through the horizon in a relatively short time, and once you are past
it, you get sucked to the singularity at the center in a millionth of a second
(for a solar mass black hole). Time and space interchange roles, and you can
no more avoid falling to the center than you can avoid moving from the present
into the future. The only 100% reliable way to detect the presence of a black
hole is to fall through the horizon and verify that it is literally impossible
to stop moving towards the center. Of course your discovery won't do your
career much good: there would be no way to publish your results.
It is unlikely that we will be able to
manufacture black holes in the laboratory. The density of matter required is
too great. In order to make a black hole the size of a baseball, you would
have to pack all the matter in and on the Earth into a volume the size of my
fist. This is much greater than the density of nuclear matter, for example.
There have however been suggestions recently that certain types of microscopic
black holes can be made by smashing heavy ions together in particle
accelerators. Such suggestions depend critically on some as yet speculative
assumptions about the nature of gravity at the microscopic level. It will be
interesting to see whether these conjectures can be realized. Nature, on the
other hand, seems to have not difficulty making black holes. Gravity is always
attractive. Matter naturally collapses unless there is some other force to
hold it up. The objects in this room are kept from collapsing by
electromagnetic forces. The gas in an active star is held up by thermal
pressure. However, once a star uses up its thermonuclear fuel, it starts to
collapse, and if there is enough mass to overcome other, microscopic forces, it
invariably collapses into a black hole. Stars in galaxies also collapse, and there
is considerable evidence for the existence of black holes at the center of most
galaxies, including our own.
According to what I have been saying,
from the outside black holes are simply that: black holes in space. They would
therefore be very difficult to spot from very far away. This cartoon suggests
the difficulties faced by astronomers in their search for black hole
candidates. Luckily the situation is not as bad as it seems.
One possible way to spot them in
principle is to use the fact that they act as powerful lenses. Any light
passing near the black hole gets bent and any stars that we see behind the
black hole get distorted. This is a computer generated image of the effect a
black hole would have if it passed in front of a field of stars.
Unfortunately, this is only useful if the black hole is moving relative to the
distant star field, so that we can detect the change. The black hole has to be
passing by fairly close to the Earth, and we have to be looking at the right place
at the right time.
The gravitational lensing effect can be
used to spot black holes in another way. If a black hole passes between us and
a single distant star, the black hole would focus the light from the star into
our telescope and, instead of causing it to blink out by passing in front of
it, it would instead cause the star to appear temporarily brighter. Thus
another way of looking for black holes is to observe distant stars, perhaps by
computer, and look for this characteristic temporary brightening. This slide
shows a candidate event of such a "micro-lensing effect". The star
in the box in the lower left picture appears brighter in November, 1996 than
it did in April, 1996 because there is an invisible, dark very heavy object
directly between the star and us, focussing the light into our telescope.
Unfortunatly, this particular event seems to be due to a compact burnt out
star, rather than a black hole, but the search continues...
Luckily, black holes are rarely formed in
complete isolation. There is almost always other matter around. For example,
binary star systems, which contain two stars in close orbit, are very common.
This slide is an artist's rendition of what it would look like of one of the
stars in a binary system collapsed into a black hole The intense gravitational
field of the black hole sucks matter off of the companion star. The matter
does not fall directly into the black hole. It swirls around and spirals in,
much like water down a bathtub drain. As this matter fell towards the black
hole it gains energy, and heats up to the point where it emits a great deal of
radiation (x-rays in fact). This radiation is emitted while the matter is
still relatively far from the black hole, so it can escape and this is what we
detect. The evidence is somewhat circumstantial, since the same sorts of
x-rays would be emitted even if the collapsed star was some other compact
object such as a neutron star or white dwarf. However, if we can measure the
masses of the two stars, and the collapsed star is heavy enough, theoretical
arguments force us conclude that the x-rays are being emitted by matter
falling in to a black hole.
This slide shows the x-rays (in red)
being emitted by a black hole candidate. We can see the bright companion star
in the center, but the black hole does not emit visible light, only x-rays.
This is the slide I started with. It is a
spectacular picture taken by the Hubble space telescope of the matter (stars)
swirling around a smaller black hole (only 500 million suns) in a distant
galaxy. Note that it looks very much like the artist's rendition I showed you
earlier. The two jets of matter that you see on the left are basically thrown
out by the intense swirling motion near the center.
Illustration of how the night sky might
look to a dweller in the core of galaxy NGC 4261, which harbors an
800-light-year-wide disk of dust and 1.2 billion-solar-mass black hole:
This is a picture of the stars near the
center of our own galaxy, the Milky Way. It is now virtually certain that a
black hole with a total mass of 2 million times that of our sun is located at
the center of the Milky Way. Astronomers have come to this conclusion by
closely following over a long time period the orbits of the stars closest to
the galactic center. In one particular case,
using one of the
Paranal
Observatory's very large telescopes and a sophisticated infrared camera,
astronomers patiently followed the orbit of a particular star, designated S2,
as it came within about
17 light-hours of the center of the Milky Way
(17 light-hours is only about 3 times the radius of Pluto's orbit). This
star’s
motion suggested that it was
moving in the gravitational field of a supermassive black hole.
Hopefully I have indicated what black
holes are, some of their properties and why we believe they exist. Why are
they important, apart from providing material for Star Trek episodes, and in
particular, why I am spending a great deal of time studying them
theoretically? Stephen Hawking showed in the mid-seventies that black holes
aren't black. They glow in the dark like very faint light bulbs. They emit
radiation via microscopic processes that occur just outside the horizon. The
net effect is to remove energy from the black hole, although at a very, very
slow rate. Thus black holes ultimately evaporate. In reality, a solar mass
black hole will take many many times the lifetime of the Universe to
evaporate, so who cares? This process gives rise to two related fundamental
theoretical problem: the problem of information loss and the mysterious source
of black hole entropy. The first is a bit easier to visualize, so I will
describe that.
Suppose I throw a computer into a black
hole. This computer's hard disc contains a great deal of usefull (and useless)
information. Once the computer falls below the "point of no return",
the information on this hard disc is lost for ever to the outside world. This
is not a problem since in principle, if I wanted it badly enough, I can fall
down the black hole after it, and retrieve it. But now we know that black
holes are not stable: they evaporate. Moreover, this evaporation occurs due to
microscopic processes just outside the "horizon", and it cannot know
about anything what has already fallen through the horizon. Thus it cannot
contain any information about what is inside: the radiation that it emits
carries no information. We call it pure heat, or thermal radiation. The second
picture indicates the black hole after it has evaporated a little: the
surrounding universe is a bit hotter, and the black hole, which has lost
energy, is correspondingly smaller. If we follow this process to its logical conclusion,
what we have at the end is no black hole, only thermal radiation filling the
universe. The information on the hard disc has irrevocably disappeared along
with the black hole, and there is no way to retrieve it, even in principle. In
physics, such information loss is unacceptable: it means among other things
that the future cannot be predicted by knowing the past. There is no apparent
correlation between the thermal radiation that fills the Universe, and the
state of the Universe (i.e. the hard disc) before it was thrown into the black
hole.
So clearly our laws of physics are
breaking down. I already said this happens at the center of a black hole, so
why is this more of a problem? As long as the "tear in the fabric of
spacetime" was hidden below the event horizon of a black hole, it did not
ruin the predictability of things that went on outside. However, now we have a
breakdown of predictibility, a loss of information, that essentially affects
the rest of the universe. Moreover, the problem is not occurring at absurdly
high temperatures and pressures that exist at the center of the black hole.
Its source is just outside the horizon, and has to do with the interplay
between macroscopic physics, and the microscopic processes that cause the
evaporation. Thus the laws of physics are breaking down a lot sooner than we
had any right to expect. To resolve this problem we have to understand this
evaporation process, and ultimately, we need to understand how gravity and
quantum mechanics are to be unified into a single theory. The strange
behaviour of black holes is providing us with value clues that will ultimately
lead us to the Holy Grail of theoretical physics: a correct and consistent
unification of gravity with the other interactions. The currently popular
candidates for such a theory are string theory and loop quantum gravity. Both
theories are based on similar fundamental geometrical objects, namely one
dimensional loops or strings, but the technical details are quite different.