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