In 1965 Arno Penzias and Robert Woodrow Wilson (who had been my apartment-mate when we were undergraduate physics majors at Rice University) accidentally discovered the cosmic microwave background radiation as “noise” in a large Bell Labs antenna that they were rehabilitating as a radio-telescope. Their discovery won them the Nobel Prize in Physics and proved to be the key to our current understanding of the universe. Now, the unexpected background noise measured in a new gravity-wave detector may offer the possibility of a breakthrough of similar importance in the area of quantum gravity. Let me explain.
Planck’s constant divided by 2π, which physicists denote by the symbol ħ (or h-bar), sets the action scale at which quantum phenomena become important. This measure of quantum importance can be converted to a distance scale, called the Planck length, which is defined as Lp = (Għc)½/c2, where G is Newton’s gravitational constant and c is the speed of light. The Planck length Lp is an extremely small distance, 1.616 x 10-35 m, about 10-20 times smaller than the diameter of a proton. Since the 1950s, there has been a general agreement among the physicist practitioners of general relativity that quantum effects on space-time itself should become significant only at distance scales on the order of the Planck length, and that the quantum mechanics of space-time can be comfortably ignored elsewhere. Since the probing of Planck length distance scales is not possible with present and planned high energy accelerators, any experimental tests that might reveal the quantum behavior of space-time appear to be a far off dream, according to this mainstream outlook.
However, there are those with other views. In 1976 Stephen Hawking proposed what has come to be called the Black Hole Information Paradox, the problem that information, a form of entropy subject to the 2nd Law of Thermodynamics, appears to vanish for objects that fall into a black hole that subsequently evaporates thermally by Hawking radiation. (See my AV Column “Hawking’s Retreat” in the June – 2004 issue of Anlog). Nobel Laureate Gerald t’Hooft analyzed this information loss problem and pointed out that infalling particles must modify the event horizon of a black, creating tent-pole shaped bumps in the event horizon. Thus, in a sense the two-dimensional event surface of the black hole is a map of the contents of its interior volume.
Prof. Leonard Susskind of Stanford University, using the techniques of string theory, took these ideas farther by showing mathematically that the oscillations of the event horizon of a black hole provide a complete description of both the infalling and outgoing matter of the system. In effect, the outer surface is a two-dimensional hologram that maps all of the three-dimensional space-time contents of the interior volume.
While these ideas were originated to deal with problems associated with black holes, they have been generalized to apply to the universe itself. In a sense, our entire universe is a black hole with us inside, containing mass that is in delicate balance with expansion (Ω=1. In a sense, light is trapped in our universe as it would be in a black hole, because light attempting to escape from our vicinity is Doppler-shifted to zero frequency and energy at the visible horizon of the universe (the surface outside which stars and galaxies recede from us at greater than the speed of light). This generalization leads to the holographic principle of space-time, the assertion that all of the space-time points in a given volume of 3+1 dimensional space can be holographically mapped onto the 2+1 dimensional surface that surrounds this volume.
My former University of Washington colleague Craig Hogan, who has just left us to become the new Director of the Center for Particle Astrophysics at Fermilab in Illinois has recently discovered a remarkable way of exploiting this holographic principle to make experimentally testable predictions. He argues that if one takes the holographic 3D to 2D mapping seriously, the map’s-cell dimensions must be determined by the Planck length, i.e., the 3D points in space mapped on the 2D surface can be specified no more accurately that a square of dimensions Lp on a side.
The “degrees of freedom” of a physical system are the enumerated ways in which one physical system can be different from another similar system. For example, an electron’s spin direction is a degree of freedom because it may point either up or down, and spin-up electrons can be distinguished from spin-down electrons. Hogan argues that number of degrees of freedom in all of 3+1 dimensional space-time will be severely restricted by the holographic mapping, making the space in which we live “grainy”, like the low-resolution image of a continuous object.
This “graininess” inevitably leads to a new spatial uncertainty principle. In particular, Hogan predicts that Planck-length hologram cells lead to an irreducible quantum noise associated with high precision measurements of position in three dimensional space, i.e., length or location measurements. For example, if a length L0 is measured, the uncertainty in the measurement will always be larger than 2(L0Lp)½ where Lp is the Planck length. To be specific, suppose a high precision measurement of a 1.0 km distance is measured, for example using optical interferometry. The uncertainty “noise” in the measurement is predicted to be about 2.56 x 10-16 m. This is an extremely small distance uncertainty, a fraction of the diameter of a proton, but it happens to fall within the range of measurements that are presently being accomplished in the field of gravity-wave detection (see my AV Column “Gravity Waves and LIGO” in the April – 1998 issue of Anlog). Hogan suggests that existing gravity-wave detectors may be able to detect the quantum noise of space-time itself.
Of particular interest in this context is the German-English Gravity Wave Detector GEO600, which was developed by the Max Planck Institutes of Quantum Optics (Garching) and for Gravitational Physics (Potsdam), the Institute for Gravitational Physics (University of Glasgow), and the Institut für Gravitationsphysik (University of Hannover). It is located at a site 20 kilometers south of Hannover, Germany. GEO600 was constructed between 1995 and 2001 and is one of five large scale interferometric gravitational-wave detector projects operating at various sites around the world. In the past two years the GEO600 project reached a sensitivity that is sufficient to detect some of the stronger gravity-wave signals that may originate in our galaxy, and it is now in continuous operation, taking data and looking for indications of gravitational waves.
There is an important difference between GEO600 and the other operating gravity detectors, for example the NSF-sponsored LIGO gravitational-wave detector systems in Washington State and Louisiana. The other detectors measure the lengths of two laser-beam flight paths independently using Fabry-Perot interferometry techniques and then compare the two independent measurements. GEO600 is unique in that it splits a single laser beam into two components, sends them in double round trips over a pair of 600 m flight paths, and compares the distances thereby measured using optical interference. This difference in detection strategy means that GEO600 turns out to be much more sensitive than the other gravitational-wave detectors to the predicted holographic noise arising from the graininess of space-time. Craig Hogan predicts that at frequencies above 550 Hz, the frequency at which the light beams in GEO600 reach optical resonance in the “cavity” formed by the mirrors of the detector, the holographic noise should be observable in the GEO600 detector.
In what may or may not be a coincidence, the GEO600 detector has observed what the experimenters call “mystery noise” in the region between 550 Hz and 5.0 kHz. Their modeling of the noise that should be present in the detector predicts a noise minimum at 1.0 kHz and a rise by a factor of 20 between 1.0 and 5.0 kHz. In their data, however, no noise minimum is visible in the 1.0 kHz region. Instead, the measured noise rises smoothly from 550 Hz on, and in the 1.0 kHz region where the minimum is predicted, the observed noise is about 40 times higher than the model prediction.
Does this mean that holographic noise has in fact been observed? Not yet. The GEO600 group is still working to improve the sensitivity of their detector, and they have not made any claims, published or otherwise, about the sources of noise in their detector system above 550 Hz. It is possible that they will find a noise source that was not included in their model or find a subtle flaw in their detector system that the modeling did not take into account. Still, the correspondence between Hogan’s predictions and the GEO600 mystery noise is suggestive that we may be on the verge of a major breakthrough, the observation of the quantum noise of space-time itself. Very soon, we should know whether or not space-time is holographic.
What would be the implications of such a discovery? It is very difficult to say. The discovery of that other noise, the cosmic background radiation, had the immediate effect of legitimizing Big Bang cosmology, but its implications for nailing down the detailed structure and properties of the universe required several decades to be realized. Similarly, discovery of the quantum noise of holographic space-time would have the immediate of legitimizing certain approaches to quantum gravity, but its long-range implications are certainly beyond my ability to predict. The sensitivity of GEO600 to the quantum noise of holographic space-time is a lucky accident, but if it is observed there will certainly be dedicated detectors designed to study the holographic effect with much richer detail and accuracy, and it is difficult to predict what might emerge from such observations.
From the point of view of science fiction, one interesting implication of holographic space-time is that points in 3D space are much farther apart than they would be on the holographic surface on which they were mapped. One could imagine a method of space travel, a Holo-Drive, in which the universe in navigated by moving from point to point on the 2D map rather than in the 3D space that it encloses. The speed of light limit on the hologram might correspond to a much higher speed in 3D space.
G. 't Hooft, in Conference on Particle and Condensed Matter Physics (Salamfest), edited by A. Ali, J. Ellis, and S.Randjbar-Daemi (World Scientic, Singapore, 1993),
L. Susskind, J. Math. Phys. 36, 6377 (1995).
“Indeterminacy of Quantum Geometry”, Craig J. Hogan, arXiv:gr-qc/0806.0665v2.
“Measurement of Quantum Fluctuations in Geometry”, Craig J. Hogan, arXiv:gr-qc/0712.3419.
The GEO600 Project:
“GEO600, The German-British Gravitational Wave Detector”, Web Site: http://geo600.aei.mpg.de
SF Novels by John Cramer: my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks by Book View Cafe and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .
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