Detecting Quantum Spacetime
By Marcus Chown
New Scientist, January 15, 2009
Edited by Andy Ross
The Anglo-German GEO600 experiment is looking for gravitational waves from
super-dense astronomical objects such as neutron stars and black holes.
GEO600 has not detected any gravitational waves so far, but it might
inadvertently have made the most important discovery in physics for half a
century.
According to Craig Hogan, a physicist at Fermilab, GEO600
has stumbled upon the fundamental limit of spacetime: "It looks like GEO600
is being buffeted by the microscopic quantum convulsions of spacetime. If the GEO600 result is what I suspect it is, then we are all
living in a giant cosmic hologram."
In the 1990s physicists Leonard
Susskind and Gerard 't Hooft suggested that the 3D world of our everyday
experience might be a holographic projection of physical processes that take
place on a distant, 2D surface.
This idea arose from work by Jacob
Bekenstein of the Hebrew University of Jerusalem and Stephen Hawking at the
University of Cambridge. Hawking had shown that black holes emit radiation.
When the black hole evaporates, all the information about the star that
collapsed to form it vanishes, which contradicts the principle that
information cannot be destroyed. This is known as the black hole information
paradox.
Bekenstein discovered that a black hole's entropy is
proportional to the surface area of its event horizon. Theorists have since
shown that microscopic quantum ripples at the event horizon can encode the
information inside the black hole, so there is no mysterious information
loss as the black hole evaporates.
Crucially, the 3D information
about a precursor star can be completely encoded in the 2D horizon of the
subsequent black hole. Susskind and 't Hooft extended the insight to the
universe on the basis that the cosmos has a horizon too. Juan Maldacena at
the Institute for Advanced Study, Princeton, has shown that the physics
inside a 5D hyperbolic universe is the same as the physics on its 4D
boundary.
Physicists have long believed that quantum effects will
cause spacetime to convulse wildly on the tiniest scales. At the Planck
scale, spacetime is made of units rather like pixels with a size of 10—35
m.
If spacetime is a grainy hologram, then you can think of the
universe as a sphere covered in Planck-sized tiles, each containing one bit
of information. The holographic principle says the number of Planck tiles
must match the number of bits in the universe.
But the volume of the
sphere is much bigger than its outer surface. Hogan realized that the world
inside must be made up of grains bigger than the Planck length. So while the Planck
length is too small for experiments to detect, the holographic projection
of that graininess could be much larger, at around 10—16 m.
Gravitational wave detectors measure length. If a
gravitational wave passes through GEO600, it will alternately stretch space
in one direction and squeeze it in another. To measure this, the GEO600 team
fires a laser through a beam splitter. The two beams pass down the
instrument's 600-m perpendicular arms and bounce back again. The returning
beams merge again at the beam splitter and create an interference pattern.
Any shift in the pattern shows that the relative lengths of the arms has
changed.
Hogan predicted that if the GEO600 beam splitter is buffeted by the quantum
jitters of spacetime, this will show up as noise in its measurements
(Physical Review D, v77, p104031).
In June 2008, Hogan sent his
prediction to the GEO600 team and discovered that the experiment was picking
up unexpected noise. GEO600 principal investigator Karsten Danzmann of the
Max Planck Institute for Gravitational Physics, Potsdam, and the University
of Hanover, says the excess noise, with frequencies of between 300 and 1500
Hz, had been bothering the team.
Gravitational-wave detectors are extremely sensitive.
"The daily business of improving the sensitivity of these experiments always
throws up some excess noise," says Danzmann. He says planned upgrades should
improve the sensitivity of GEO600 and eliminate some possible sources of
noise. "If the noise remains where it is now after these measures, then we
have to think again," he says.
It would be ironic if an instrument
built to detect astrophysical sources of gravitational waves inadvertently
detected the quantum graininess of spacetime. Danzmann: "It would be
one of the most remarkable discoveries in a long time."
AR Wonderful discovery! If
this really does turn out to be quantum jitters, the event is as momentous
as the discovery of the cosmic microwave background.
Toward Quantum Gravity
By Anil Ananthaswamy
New Scientist, August 12, 2009
Edited by Andy Ross
Physicists have been on the lookout for signposts to the right theory of
quantum gravity for the best part of a century.
"All approaches to
quantum gravity, in their own very different ways, agree that empty space is
not so empty after all," says theorist Giovanni Amelino-Camelia of Sapienza
University of Rome in Italy. Many models based on string theory suggest that
spacetime is a foamy froth of particles that appear out of nothing and
disappear again with equal abandon. The alternative approach, loop quantum
gravity, posits that spacetime comes in tiny chunks.
Last year, the
signature of quantum spacetime may have popped up in unexplained noise in a
gravity-wave detector in northern Germany. But most experts agree that a
more substantive sighting could only come from observing the possible
interactions of spacetime with particles passing through it.
According to many string theory models, particles of different energies
should speed up or slow down by different amounts as they interact with a
foamy spacetime. A minimum size for spacetime grains, as predicted by loop
quantum gravity, could violate Lorentz invariance, which states that the
maximum speed of all particles is the speed of light in a vacuum.
As
yet, we have only seen a handful of gamma-ray bursts of the energy and
intensity needed to see whether the delay effect is a consistent feature.
The uncertainties in the data make a definitive statement impossible.
In September 2008, the NASA Fermi Gamma-ray Space Telescope detected a
burst of gamma rays from a source nearly 12 billion light years away. At
CERN, John Ellis and colleagues used a theoretical model that assumes the
delay effect increases linearly with distance and photon energy to estimate
the delay that the highest-energy photon in the Fermi burst should have
experienced. They came up with 25 s, plus or minus 11 s,
compared with a measured 16.5 s.
The only way to find out
conclusively whether the delays are a consistent signature of quantum
spacetime is to get more data. Combining different data sets will provide a
wider spread of energies from which to tease out any energy-dependent
effect, and also overcome the fact that Earth's rotation makes observing a
highly directed beam of gamma rays from one direction tricky.
The new
gamma ray telescopes could well uncover quantum spacetime within the next
few years. Or the answer might come from a cubic kilometre of ice under the
South Pole, home to the IceCube Neutrino Observatory, whose strings of
detectors will watch for faint flashes of blue light emitted when neutrinos
from cosmic sources smash into the Antarctic ice.
Neutrinos are
thought to be produced in the same violent events that produce high-energy
gamma rays. As yet, we have seen hardly any neutrinos from outside our
galaxy. The neutrinos we see are lower-energy ones that come from nuclear
reactions in the sun and particle interactions in Earth's atmosphere.
IceCube aims to change that.
Because the wavelengths associated with
neutrinos of the very highest energies are even smaller than those of
high-energy photons, they could be more susceptible to disruption through
interactions with a spacetime that is grainy on very small scales. Francis
Halzen of the University of Wisconsin, Madison, who leads the IceCube
experiment, has calculated with his colleagues that in one model of quantum
spacetime such interactions could dramatically speed up higher-energy
neutrinos.
Neutrinos come in three distinct flavors: the electron,
the muon, and the tau. They tend to oscillate back and forth between these
flavors as they travel. If a distant source is emitting only electron
neutrinos, theory tells us how many should have changed flavor by the time
they reach us. If neutrinos were interacting with the quantum foam, they
would forget their original flavor along the way, leading to equal numbers
of all flavors by the time they arrive here.
Even if we find
indisputable signs that either neutrinos or gamma rays are being affected by
the structure of spacetime, it will be hard work to convert that evidence to
support for a viable theory of quantum gravity.
AR We have a way to go, sure,
but the picture looks good: spacetime is quantized somehow.
Breaking Lorentz Symmetry
By
Anil Ananthaswamy
New Scientist, August 9, 2010
Edited by Andy Ross
Petr Horava wants to rip time and space free from one another in a unified
theory that reconciles quantum mechanics and gravity.
For decades now, physicists have
tried to reconcile Einstein's general theory of relativity and quantum
mechanics. The stumbling block lies with their conflicting views of space
and time. As seen by quantum theory, space and time are a static backdrop
against which particles move. In Einstein's theories, by contrast, space and
time form a spacetime continuum that is curved by the bodies within it.
We need to marry relativity and quantum theory to understand what
happened just after the big bang or what's going on near black holes, where
the gravitational fields are immense. The problem comes to the fore in the
gravitational constant G. On large scales, the equations of general
relativity yield a value of G that tallies with observed behavior. But at
very small distances, quantum fluctuations of spacetime ruin any calculation
of G.
Looking for a way out, Horava found inspiration in the physics
of condensed matter. Graphene is a sheet of carbon atoms just one atom
thick. The motion of the electrons in the sheet can be described using
quantum mechanics, and because they are moving at only a small fraction of
the speed of light there is no need to take relativistic effects into
account.
But cool graphene down to near absolute zero and the
electrons speed up dramatically. Now relativistic theories are needed to
describe them correctly. In relativity, spacetime has Lorentz symmetry: to
keep the speed of light constant for all observers, time slows and distances
contract in exact proportion.
Lorentz symmetry isn't always apparent
in graphene. In our universe, space and time appear linked by Lorentz
symmetry. But the symmetry may have emerged as the universe cooled from the
big bang fireball, just as it emerges in graphene when it is cooled.
So Horava changed Einstein's equations in a way that removed Lorentz
symmetry. This led to equations that describe gravity in the same quantum
framework we use fo the other forces. He also made another change.
Einstein's theory does not have an arrow of time, but the universe as we
observe it does. Horava gave time a preferred direction and found that
quantum field theories could then describe gravity at microscopic scales
without producing nonsense (Physical Review D, v79, p084008).
An
approach to quantum gravity called causal dynamical triangulation stitches
spacetime together from smaller pieces.
Jan Ambjørn of the Niels Bohr
Institute in Copenhagen, Denmark, and his colleagues, used computer
simulations to analyze spacetime and found that space and time varied in a
strange way. Zoom out and space and time obey Lorentz symmetry. But zoom in
and time plays a far greater role than space. Ambjørn thinks Lorentz
symmetry may be broken as in Horava gravity (first abstract below).
Horava gravity has already been used to study black holes, dark matter, and
dark energy. In general relativity, black holes appear when the curvature of
spacetime increases without limit. By breaking the symmetry between space
and time, Horava's theory alters the physics of black holes in ways that are
still unknown.
Horava gravity might also help with the long-standing
puzzle of dark matter. Shinji Mukohyama at the University of Tokyo extracted
the equations of motion from Horava's theory and found that they allow
something like dark matter (second abstract below).
Dark energy is
more daunting. The theories of particle physics predict the strength of dark
energy to be about 120 orders of magnitude larger than what is observed.
Horava's theory contains a tunable parameter that can reduce the prediction
to a realistic value (third abstract below).
CDT meets Horava-Lifshitz gravity
J. Ambjørn, A.
Gorlich, S. Jordan, J. Jurkiewicz, R. Loll
The theory of causal
dynamical triangulations (CDT) attempts to define a nonperturbative theory
of quantum gravity as a sum over spacetime geometries. One of the
ingredients of the CDT framework is a global time foliation, which also
plays a central role in the quantum gravity theory recently formulated by
Horava. We show that the phase diagram of CDT bears a striking resemblance
with the generic Lifshitz phase diagram appealed to by Horava. We argue that
CDT might provide a unifying nonperturbative framework for anisotropic as
well as isotropic theories of quantum gravity.
Dark matter as integration constant in Horava-Lifshitz gravity
Shinji
Mukohyama
In the non-relativistic theory of gravitation recently
proposed by Horava, the Hamiltonian constraint is not a local equation
satisfied at each spatial point but an equation integrated over a whole
space. The global Hamiltonian constraint is less restrictive than its local
version, and allows a richer set of solutions than in general relativity. We
show that a component that behaves like pressureless dust emerges as an
integration constant of dynamical equations and momentum constraint
equations. So classical solutions to the infrared limit of Horava-Lifshitz
gravity can mimic general relativity plus cold dark matter.
The Cosmological Constant and Horava-Lifshitz Gravity
Corrado Appignani,
Roberto Casadio, S. Shankaranarayanan
Horava-Lifshitz theory of
gravity with detailed balance is plagued by the presence of a negative bare
(or geometrical) cosmological constant which makes its cosmology clash with
observations. We argue that adding the effects of the large vacuum energy of
quantum matter fields, this bare cosmological constant can be approximately
compensated to account for the small observed (total) cosmological constant.
We establish a relation between the cosmological constant and the length
scale of dimension 4 corrections to the Einstein gravity. We argue that
Lorentz invariance is broken only at very small scales.
AR I like it: the Lorentz
symmetry is philosophically procrustian in view of the arrow of time. See my
essay on time to reflect that the epistemologically anomalous nature of time
should dispose us to reserve judgment on full spacetime symmetry (chapter 13
in Mindworlds). Thus, too, we
avoid the ascent to sub specie aeternitatis fantasy of "Time Lords"
Einstein and Gödel (which I also gloss informally in my new book
G.O.D. Is Great).
Gravity Waves
By Robin McKie
The Observer, April 15, 2012
Edited by Andy Ross
Beside the village of Ruthe, near Hannover, Germany, scientists are hunting
for gravity waves. When big stars collapse into black holes or when pairs of
neutron stars spiral toward each other, they agitate the fabric of
spacetime, sending ripples of gravitational energy across the universe.
The Ruthe laboratory is part of the joint UK-German project Geo600 to
measure these waves, which were predicted a century ago by Albert Einstein
but have not yet been detected. Once they are found and detectors become
more sophisticated and sensitive, astronomers will use them to peer into the
hearts of stars in ways that are beyond current observatories.
The
detectors feature two long arms, set at right angles to each other,
extending from a lab fitted with sensitive measuring equipment. Glasgow
professor Jim Hough: "When a gravitational wave reaches a detector, it will
temporarily shrink one arm and slightly extend the other depending on its
angle of approach. It will be our task to measure that change."
Gravitational waves are generated by enormously energetic but incredibly
remote events. A wave's energy is dissipated so far that the change it makes
in a detector is less than the diameter of a proton.
This explains
why efforts to pinpoint gravitational waves have so far failed. But
scientists are confident that laser interferometry will measure them. A
laser beam passes through a beam splitter so that two identical beams shine
down each of the detector arms. At the end of each tunnel is a mirror. The
beams are reflected back to a detector and recombined. With careful tuning,
the beams can be superposed.
The gravitational waves alter the
relative positions of the mirrors. This changes the intensity of the light
observed. The light waves from the beams normally arrive in phase to give a
bright spot. But if the mirrors move even slightly the image is darkened.
That is the theory.
In reality, scientists have been frustrated by
all sorts of details. For example, if a person walks close to a mirror their
mass exerts a tiny gravitational influence on it, causing the mirror to
move. And thermal noise causes mirrors and mountings to vibrate slightly,
again creating spurious signals.
New detectors have arms several
kilometers long. And great care has been taken in their construction to
reduce vibrations. Their arms are suspended from rails that run the length
of the detectors' trenches; the tubes along which the laser light is
channelled inside an arm contain ultra-pure vacuums; while the lasers
themselves are high performance industrial devices.
The UK-German
team at Ruthe has developed delicate systems of silica mirrors and pendulums
use four platforms suspended from each other in layers, to isolate them from
vibrations, and used light squeezing to reduce quantum fluctuations in the
laser beam, thus easing measurement. Hough expects to see the waves by
around 2015.
Where Does Spacetime Come From?
By George Musser
Scientific American, April 12, 2012
Edited by Andy Ross
Two Russian physicists have proposed a new way of understanding space and
time. Mikhail Vasiliev and the late Efin Fradkin of the Lebedev Institute in
Moscow developed the theory in the late 1980s.
The basic idea of
modern physics is that the world consists of fields. VF theory posits an
infinite number of fields. They come in progressively more complicated
varieties described by the quantum property of spin.
Think of spin as
the degree of rotational symmetry. The electromagnetic field with its
particle, the photon, has spin 1. If you give it a full turn, it looks the
same as before. The gravitational field with its particle, the graviton, has
spin 2: you need to rotate it only half a turn. The known particles of
matter, such as the electron, have spin 1/2: they need 2 full turns to look
the same. The Higgs field has spin 0 and looks the same no matter how you
rotate it.
In VF theory, there are also spin 5/2, spin 3, and so on,
all the way up. Physicists used to assume that was impossible. These
higher-spin fields, being more symmetrical, would imply new laws of nature
analogous to the conservation of energy, and no two objects could ever
interact without breaking one of those laws. At first glance, string theory
runs afoul of this principle. An elementary quantum string has an infinity
of higher harmonics, which correspond to higher-spin fields. But those
harmonics come with an energy cost, which keeps them inert.
The above
reasoning applies only when gravity is insignificant and spacetime is not
curved. In curved spacetimes, higher-spin fields can exist after all.
Higher-spin fields promise to flesh out the holographic principle.
Suppose you have a hypothetical 3D spacetime (2 space + 1 time) filled with
particles that interact solely by a souped-up strong nuclear force, without
gravity. In such a setting, objects of a given size can interact only with
objects of comparable size, just as objects can interact only if they are
spatially adjacent. Size plays exactly the same role as spatial position;
you can think of size as a new dimension of space. The original 3D spacetime
becomes the boundary of a 4D spacetime, with the new dimension representing
the distance from this boundary. Not only does a spatial dimension emerge,
but so does gravity. In the jargon, the strong nuclear force in 3D spacetime
(the boundary) is dual to gravity in 4D spacetime (the bulk).
The
holographic principle describes a bulk where dark energy has negative
density, warping spacetime into an anti-de Sitter geometry. But dark energy
has positive density, to give something like a de Sitter geometry. The
boundary of 4D de Sitter spacetime is a 3D space lying in the infinite
future. The emergent dimension in this case is time. If physicists could
formulate a version of the holographic principle for a de Sitter geometry,
it would not only apply to the real universe but would also explain time.
VF theory works in either an anti-de Sitter or a de Sitter geometry. In
the de Sitter case, the 3D boundary is governed by a static field theory.
The structure of this theory gives rise to time in an asymmetric way, which
might account for the arrow of time.
In VF theory, the higher-spin
fields possess higher symmetry than the gravitational field, and hence less
structure. The general theory of relativity says spacetime is like silly
putty. Vasiliev theory says it is sillier putty, too silly for defining
consistent causal relations or keeping distant objects apart from each
other.
VF theory is even more nonlinear than general relativity.
Matter and spacetime geometry are so thoroughly entwined that it becomes
impossible to tease them apart. The primordial universe was an amorphous
blob. As the higher-spin symmetries broke, spacetime emerged.
The
Complete Idiot's Guide to String Theory
By George Musser
AR Duh. What's the next stage of dimmitude below
complete idiot?
Quantum Gravity and LIGO
Ashutosh Jogalekar and Freeman Dyson
Scientific American, May 3, 2013
Edited by Andy Ross
Physicists have long dreamed of a grand unified theory embracing all known
forces and laws. The pioneers of thermodynamics brought together mechanics
and heat. Faraday and Maxwell unified electricity, magnetism, and optics.
Einstein unified first space and time, then matter and energy, and finally
spacetime and gravity in relativity theory. Unification continued with
wave-particle duality and with quantum field theory uniting special
relativity and quantum mechanics. But the union of gravity with quantum
theory remains intractable.
A good way to probe quantum gravity is to
look for gravitons. Researchers have designed equipment so sensitive that it
should be able to detect a single graviton. The Laser Interferometer
Gravitational Wave Observatory (LIGO) uses an interferometer to detect
gravitational waves. A wave passing through the interferometer warps local
space-time and changes the effective length of one or both of the cavities.
This puts the light in the cavity out of phase with incoming light. The
cavity goes out of resonance, the beams detune, and a periodic signal will
emerge.
But LIGO may not work. Because of ambient noise, the actual
LIGO detectors can only detect waves far stronger than a single graviton.
But even in a quiet universe, an ideal LIGO detector cannot detect a single
graviton. In a quiet universe, the limit to the measurement of distance is
set by the quantum uncertainties in the positions of the mirrors. To make
them small, the mirrors must be massive. To detect a single graviton with
LIGO hardware, the mirrors must be so massive that they attract each other
irresistibly and collapse into a black hole. So LIGO no go.
Perhaps
theories of quantum gravity are untestable.
>> Freeman Dyson
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