Natural Science Forum / Physics / Relativity / November 2005

Dear Relativity geniuses such as Bilge and Old Man,

What do you think of the following sci-am discussion?

(The following article is reproduced for debunking & educational
purposes only)

http://www.pbase.com/image/52781937/original
(illustrations in the article)

"An Echo of Black Holes"

Sound waves in a fluid behave uncannily like light waves in
space. Black holes even have acoustic counterparts. Could
spacetime  literally be a kind of fluid, like the ether of
pre-Einsteinion physics?

By Theodore A. Jacobson and Renaud Parentani

When Albert Einstein proposed his special theory of relativity in
1905, he rejected the 19th-century idea that light arises from
vibrations of a hypothetical medium, the "ether." Instead, he
argued, light waves can travel in vacuo without being supported
by any material-unlike sound waves, which are vibrations of the
medium in which they propagate. This feature of special
relativity is untouched in the two other pillars of modern
physics, general relativity and quantum mechanics. Right up to
the present day , all experimental data, on scales ranging from
subnuclear to galactic, are successfully explained by these three
theories.

Nevertheless, physicists face a deep conceptual problem. As
currently understood, general relativity and quantum mechanics
are incompatible. Gravity, which general relativity attributes to
the curvature of the spacetime continuum, stubbornly resists
being incorporated into a quantum framework. Theorists have made
only incremental progress toward understanding the highly curved
structure of spacetime that quantum mechanics leads them to
expect at extremely short distances. Frustrated, some have turned
to an unexpected source for guidance: condensed-matter physics,
the study of common substances such as crystals and fluids.

Like spacetime, condensed matter looks like a continuum when
viewed at large scales, but unlike spacetime it has a well
understood microscopic structure governed by quantum mechanics.
Moreover, the propagation of sound in an uneven fluid flow is
closely analogous to the propagation of light in a curved
spacetime. By studying a model of a black hole using sound waves,
we and our colleagues are attempting to exploit this analogy to
gain insight into the possible microscopic workings of spacetime.
The work sug gests that spacetime may, like a material fluid, be
granular and possess a preferred frame of reference that
manifests itself on fine scalescontrary to Einstein's
assumptions.

Black Holes are a favorite testing ground for quantum gravity
because they are among the few places where quantum mechanics and
general relativity are both critically important. A major step
toward a merger of the two theories came in 1974, when Stephen W.
Hawking of the University of Cambridge applied quantum mechanics
to the horizon of black holes.

According to general relativity, the horizon is the surface that
separates the inside of a black hole (where gravity is so strong
that nothing can escape) from the outside. It is not a material
limit; unfortunate travelers falling into the hole would not
sense anything special on crossing the horizon. But once having
done so, they would no longer be able to send light signals to
people outside, let alone return there. An outside observer would
receive only the signals transmitted by the travelers before the
y crossed over. As light waves climb out of the gravitational
well around a black hole, they get stretched out, shifting down
in frequency and lengthening in duration. Consequently, to the
observer, the travelers would appear to move in slow motion and
to be redder than usual.

This effect, known as gravitational redshift, is not specific to
black holes. It also alters the frequency and timing of signals
between, say, orbiting satellites and ground stations. GPS
navigation systems must take it into account to work accurately.
What is specific to black holes, however, is that the redshift
becomes infinite as the travelers approach the horizon. From the
outside observer's point of view, the descent appears to take an
infinite amount of time, even though only a finite time passes
for the travelers themselves.

So far this description of black holes has treated light as a
classical electromagnetic wave. What Hawking did was to
reconsider the implications of the infinite redshift when the
quantum nature of light-is taken into account. According to
quantum theory, even a perfect vacuum is not truly empty; it is
filled with fluctuations as a result of the Heisenberg
uncertainty principle. The fluctuations take the form of pairs of
virtual photons. These photons are called virtual because, in an
uncurved spacetime, fa r from any gravitational influence, they
appear and disappear restlessly, remaining unobservable in the
absence of any disturbance.

But in the curved spacetime around a black hole, one member of
the pair can be trapped inside the horizon, while the other gets
stranded outside. The pair can then pass from virtual to real,
leading to an outward flux of observable light and a
corresponding decrease in the mass of the hole. The overall
pattern of radiation is thermal, like that from a hot coal, with
a temperature inversely proportional to the mass of the black
hole. This phenomenon is called the Hawking effect. Unless the
hole swallows matt er or energy to make up the loss, the Hawking
radiation will drain it of all its mass.

An important point-which will become critical later when
considering fluid analogies to black holes-is that the space very
near the black hole horizon remains a nearly perfect quantum
vacuum. In fact, this condition Is essential for Hawking's
argument. The virtual photons are a feature of the lowest-energy
quantum state, or "ground state." It is only in the process of
separating from their partners and climbing away from the horizon
that the virtual photons become real.

The Ultimate Microscope

HAWKING'S ANALYSIS has played a central role in the attempt to
build a full quantum theory of gravity. The ability to reproduce
and elucidate the effect is a crucial test for candidate quantum
gravity theories, such as string theory [see "The Illusion of
Gravity," by Juan Maldacenal. SCIENTIFIC AMERICAN, November]. Yet
although most physicists accept Hawking's argument, they have
never been able to confirm it experimentally. The predicted
emission from stellar and galactic black holes is far too feeble
to s ee. The only hope for observing Hawking radiation is to find
miniature holes left over from the early universe or created in
particle accelerators, which may well prove impossible [see
"Quantum Black Holes," by Bernard Carr and Steven Giddings;
SCIENTIFIC AMERICAN, May].

The lack of empirical confirmation of the Hawking effect is
particularly vexing in view of the disturbing fact that the
theory has potential flaws, stemming from the infinite redshift
that it predicts a photon will undergo. Consider what the
emission process looks like when viewed reversed in time. As the
Hawking photon gets nearer to the hole, it blueshifts to a higher
frequency and correspondingly shorter wavelength. The further
back in time it is followed, the closer it approaches the horizon
and the sho rter its wavelength becomes. Once the wavelength
becomes much smaller than the black hole, the particle joins its
partner and becomes the virtual pair discussed earlier.

The blueshifting continues without ,abatement, down to
arbitrarily short distances. Smaller than a distance of about
10-35 meter, known as the Planck length, neither relativity nor
standard quantum theory can predict what the particle will do. A
quantum theory of gravity is needed. A black hole horizon thus
acts as a fantastic microscope that brings the observer into
contact with unknown physics. For a theorist, this magnification
is worrisome. If Hawking's prediction relies on unknown physics,
should we no t be suspicious of its validity? Might the
properties, even the existence, of Hawking radiation depend on
the microscopic properties of spacetime - much as, for example,
the heat capacity or speed of sound of a substance depends on its
microscopic structure and dynamics? Or is the effect, as Hawking
originally argued, entirely determined just by the macroscopic
properties of the black hole, namely, its mass and spin?

Sound Bites

ONE EFFORT TO ANSWER these embarrassing questions began with the
work of William Unruh of the University of British Columbia. In
1981 he showed that there is a close analogy between the
propagation of sound in a moving fluid and that of light in a
curved spacetime. He suggested that this analogy might be useful
in assessing the impact of microscopic physics on the origin of
Hawking radiation. Moreover, it might even allow for experimentaI
observation of a Hawking-like phenomenon.

Like light waves, acoustic (sound) waves are characterized by a
frequency, wavelength and propagation speed. The very concept of
a sound wave is valid only when the wavelength is much longer
than the distance between molecules of the fluid; on smaller
scales, acoustic waves cease to exist. It is precisely this
limitation that makes the analogy so interesting, because it can allow
physicists to study the macroscopic consequences of microscopic
structure. To be truly useful, however, this analogy must extend
to the quantum level. Ordinarily, random thermal jigging of the
molecules prevents sound waves from behaving analogously to light
quanta. But when the temperature approaches absolute zero, sound
can behave like quantum particles, which physicists call
"phonons" to underline the analogy with the particles of light,
photons . Experimenters routinely observe phonons in crystals and
in substances that remain fluid at sufficiently low temperatures,
such as liquid helium.

The behavior of phonons in a fluid at rest or moving uniformly is
like that of photons in flat spacetime, where gravity is absent.
Such phonons propagate in straight lines with unchanging
wavelength, frequency and velocity. Sound in, say, a swimming
pool or a smoothly flowing river travels straight from its source
to the ear.

In a fluid moving nonuniformly, however, the phonons' velocity is
altered and their wavelength can become stretched, just like
photons in a curved spacetime. Sound in a river entering a narrow
canyon or water swirling down the drain becomes distorted and
follows a bent path, like light around a star. In fact, the
situation can be described using the geometrical tools of general
relativity.

A fluid flow can even act on sound as a black hole acts on light.
One way to create such an acoustic black hole is to use a device
that hydrodynamicists call a Laval nozzle. The nozzle is designed
so that the fluid reaches and exceeds the speed of sound at the
narrowest point without producing a shock wave (an abrupt change
in fluid properties). The effective acoustic geometry is very
similar to the spacetime geometry of a black hole. The supersonic
region corresponds

to the hole's interior: sound waves propagating against the
direction of the flow are swept downstream, like light pulled
toward the center of a hole. The subsonic region is the exterior
of the hole: Sound waves can propagate upstream but only at the
expense of being stretched, like light being redshifted. The
boundary between the two regions behaves exactly like a black
hole horizon.

Atomism

If the fluid is cold enough, the analogy extends to the quantum
level. Unruh argued that the sonic horizon emits thermal phonons
analogous to Hawking radiation. Quantum fluctuations near the
horizon cause pairs of phonons to appear; one partner gets swept
into the supersonic region, never to return, while the other
ripples upstream, getting stretched out by the fluid flow. A
microphone placed upstream picks up a faint hiss. The sound
energy of the hiss is drawn from the kinetic energy of the fluid
flow.

The dominant tone of the noise depends on the geometry; the
typical wavelength of the observed phonons is comparable to the
distance over which the flow velocity changes appreciably. This
distance is much larger than the distance between molecules, so
Unruh did his original analysis assuming that the fluid is smooth
and continuous. Yet the phonons originate near the horizon with
wavelengths so short that they should be sensitive to the
granularity of the fluid. Does that affect the end result? Does a
real f luid emit Hawking-like phonons, or is Unrub's prediction
an artifact of the idealization of a continuous fluid? If that
question can be answered for acoustic black holes, it may by
analogy guide physicists in the case of gravitational black
holes.

Physicists have proposed a number of black hole analogues besides
the transsonic fluid flow. One involves not sound waves but
ripples on the surface of a liquid or along the interface between
layers of superfluid helium, which is so cold that it has lost
all frictional resistance to motion. Recently Unruh and Ralf
SchiItzhold of the Technical University of Dresden in Germany
proposed to study electromagnetic waves passing through a tiny,
carefully engineered electronic pipe. By sweeping a laser along
the pi pe to change the local wave speed, physicists might be
able to create a horizon. Yet another idea is to model the
accelerating expansion of the universe, which generates a
Hawking-like radiation. A Bose-Einstein coridensate-a gas so cold
that the atoms have lost their individual identitycan act on
sound like an expanding universe does on light, either by
literally flying apart or by being manipulated using a magnetic
field to give the same effect.

As yet, experimenters have not created any of these devices in
the laboratory. The procedures are complicated, and experimenters
have plenty of other low-temperature phenomena to keep them busy.
So theorists have been working to see whether they can make
headway on the problem mathematically.

Understanding how the molecular structure of the fluid affects
phonons is extremely complicated. Fortunately, 10 years after
Unruh proposed his sonic analogy, one of us (jacobson) came up
with a very useful simplification. The essential details of the
molecular structure are encapsulated in the way that the
frequency of a sound wave depends on its wavelength. This
dependence, called the dispersion relation, determines the
velocity of propagation. For large wavelengths, the velocity is
constant. For short wa velengths, approaching the intermolecular
distance, the velocity can vary with wavelength.

Three different behaviors can arise. Type 1 is no dispersion-the
wave behaves the same at short wavelengths as it does at long
ones. For type 11, the velocity decreases as the wavelength
decreases, and for type Ill, velocity increases. Type 1 describes
photons in relativity. Type 11 describes phonons in, for example,
superfluid helium, and type II describes phonons in dilute
Bose-Einstein condensates. This division into three types
provides an organizing principle for figuring out how molecular
structure af fects sound on a macroscopic level. Beginning in
1995, Unriah and then other researchers have examined the Hawking
effect in the presence of type II and type II dispersion.

Consider how the Hawking-like phonons look when viewed backward
in time. Initially the dispersion type does not matter. The
phonons swim downstream toward the horizon, their wavelengths
decreasing all the while. Once the wavelength approaches the
intermolecular distance, the specific dispersion relation becomes
important. For type II, the phonons slow down, then reverse
direction and start heading upstream again. For type Ill, they
accelerate, break the long-wavelength speed of sound, then cross
the horizon .

Ether Redux

A TRUE ANALOGY to the Hawking effect must meet an important
condition: the virtual phonon pairs must begin life in their
ground state, as do the virtual photon pairs around the black
hole. In a real fluid, this condition would be easily met. As
long as the macroscopic fluid flow changes slowly in time and
space (compared with the pace of events at the molecular level),
the molecular state continuously adjusts to minimize the energy
of the system as a whole. It does not matter which molecules the
fluid is made of.

With this condition met, it turns out that the fluid emits
Hawking-like radiation no matter which of the three types of
dispersion relations applies. The microscopic details of the
fluid do not have any effect. They get washed out as the phonons
travel away from the horizon. In addition, the arbitrarily short
wavelengths invoked by original Hawking analysis do not arise
when either type II or II dispersion is included. Instead the
wavelengths bottom out at the intermolecular distance. The
infinite redshift is an avatar of the unphysical assumption of
infinitely small atoms.

Applied to real black holes, the fluid analogy lends confidence
that Hawking's result is correct despite the simplifications he
made. Moreover, it suggests to some researchers that the infinite
redshift at a gravitational black hole horizon may be similarly
avoided by dispersion of short wavelength light. But there is a
catch. Relativity theory flatly asserts that light does not
undergo dispersion in a vacuum. The wavelength of a photon
appears different to different observers; it is arbitrarily long
when v iewed from a reference frame that is moving sufficiently
close to the speed of light. Hence, the laws of physics cannot
mandate a fixed short-wavelength cutoff, at which the dispersion
relation changes from type 1 to type II or Ill. Each observer
would perceive a different cutoff. Physicists thus face a
dilemma. Either they retain Einstein's injunction against a
preferred frame and they swallow the infinite redshifting, or
they assume that photons do not undergo an infinite redshift and
they have to introdu ce a preferred reference frame. Would this
frame necessarily violate relativity? No one yet knows. Perhaps
the preferred frame is a local effect that arises only near black
hole horizons-in which case relativity continues to apply in
general. On the other hand, perhaps the preferred frame exists
everywhere, not just near black holes-in which case relativity is
merely an approximation to a deeper theory of nature.
Experimenters have yet to see such a frame, but the null result
may simply be for want of suffi cient precision.

Physicists have long suspected that reconciling general
relativity with quantum mechanics would involve a shortdistance
cutoff, probably related to the Planck scale. The acoustic
analogy bolsters this suspicion. Spacetime must be somehow
granular to tame the dubious infinite redshift.

If so, the analogy between sound and light propagation would be
even better than Unrub, originally thought. The unification of
general relativity and quantum mechanics may lead us to abandon
the idealization of continuous space and time and to discover the
"atoms" of spacetime. Einstein may have had similar thoughts when
he wrote to his close friend Michele Besso in 1954, the year
before his death: 9 consider it quite possible that physics
cannot be based on the field concept, that is, on continuous
structu res." But this would knock out the very foundation from
under physics, and at present scientists have no clear candidate
for a substitute. Indeed, Einstein went on to say in his next
sentence, ---Then nothing remains of my entire castle in the air,
including the theory of gravitation, but also nothing of the rest
of modern physics." Fifty years later the castle remains intact,
although its future is unclear. Black holes and their acoustic
analogues have perhaps begun to light the path and sound out the
way.

--

THEODOREA, JACOBSON and RENAUD PARENTANI study the puzzles of
quantum gravity and its possible observable consequences for
black holes and cosmology. Jacobson is a physics professor at the
University of Maryland. His recent research focuses on the
thermodgnamics of black holes, how spacetime might be
microscopically discrete and whether that fine structure could be
macroscopically detected. Parentani is a physics professor at the
University of Paris-Sud at Orsay who does research at the CNRS
Laboratory of T heoretical Physics. He investigates the role of
quantum fluctuations in black hole physics and cosmology. This
article is a translation and update of Parentani's article in the
May 2002 issue of Pouria Science, the French edition of
Scientific American.