starship-design: Quantum Gravity

["L. Parker" <lparker@cacaphony.net>]

I apologize if this is old news to anybody, but it sounds interesting since it relates (slightly) to this group's objective - 


Theory of Quantum Gravity Predicts Space Has a Discrete "Atomic" Structure 

The first experimentally testable prediction about the quantum structure of the geometry of space has been produced by physicists developing a theory of quantum gravity. 

Carlo Rovelli, professor of physics at the University of Pittsburgh, and Lee Smolin, professor of physics at Penn State and visiting member of the Institute for Advanced Study, describe their discovery in a paper published in a recent issue of the journal Nuclear Physics B. They discovered that the theory of quantum gravity requires that space, like ordinary matter, is not continuous but is made of a network of discrete elements. Rovelli and Smolin say the size of these elements is 10-33 centimeters-20 orders of magnitude smaller than the nucleus of an atom. 

The idea that space and time may not be continuous but are built, like matter, from very tiny "atomic building blocks" is not new-it was proposed previously by Roger Penrose, of Oxford University and Penn State, and other physicists and mathematicians. The work of Rovelli and Smolin is, however, the first to show that these discrete structures are required by the laws of quantum mechanics and relativity theory. 

"Just as an atom can have only a certain discrete set of energy levels, the results of geometrical measurements must come in discrete units," Smolin explains. In other words, measurements of the area or volume of any region in space cannot be just any number but must lie in certain sets of discrete numbers, which the calculations of Rovelli and Smolin are able to predict. "One way to describe these predictions is that the geometry of space itself is made out of discrete quanta analogous to the photons of light or the electron shells of the atom," Smolin explains. 

Although no instrument exists today that actually can measure small enough areas or volumes to see the discrete structures they predict, Smolin says "We are confident about these predictions and believe they could be tested sometime in the future." Rovelli adds, "That is what one wants in science-to make definite predictions that could lead to confirmation of whether a theory is right or wrong." 

Scientists have been looking for the right theory of quantum gravity to complete the revolutionary picture of nature begun early in this century with the invention of quantum mechanics, the modern theory of matter, and Einstein's theory of general relativity, the modern concept of space and time. "The unification of these two theories remains one of the key unsolved scientific problems," Rovelli explains. 

Rovelli and Smolin's discovery of the atomic structure of the geometry of space is the result of a seven-year collaboration, which they say is built on a breakthrough discovery in 1986 by Abhay Ashtekar, Holder of the Eberly Family Chair in Physics and Director of the Center for Gravitational Physics and Geometry at Penn State. Ashtekar discovered that the equations of Einstein's general theory of relativity could be translated into a much simpler form, making it easier to combine relativity with quantum mechanics. "Ashtekar's work was the breakthrough that has enabled us and others to finally make progress on this problem," Smolin says. The following year, Smolin and Ted Jacobson, professor of physics at the University of Maryland, discovered that Ashtekar's form of the theory could be used to solve the equations of quantum gravity for the first time. 

These solutions showed that the gravitational field could be seen in a new perspective. "Instead of thinking of the quantum unit of gravity as a particle or a wave, we describe the geometry of space as patterns of closed loops-the lines of force of the gravitational field," Smolin says. "The gravitational field has lines of force just like the lines of magnetic force around a bar magnet," Rovelli explains. 

These gravitational lines of force are the basis for the "loop representation" picture of quantum gravity that Rovelli and Smolin invented in 1988, which is the basis of their predictions about the atomic nature of space. "The way the lines of force form loops that knot and link and meet each other is the basis for the quantum description of the geometry of space we have discovered," Smolin explains. 

Rovelli and Smolin explain they use the word "loops" because the lines of gravitational force always form loops when there is no matter around. According to the physicists, Einstein's theory of relativity allows space to have a geometry even where there is no matter. "Where there is matter, the gravitational lines of force end on the matter," Rovelli explains, just as magnetic lines of force end on the poles of a magnet. He says lines of magnetic force in empty space form loops, as well. 

Rovelli and Smolin's calculations also reveal that these quantum loops of space must be linked together in networks called spin networks, which look like an electric-circuit diagram-a pattern of lines joined to each other at various points, or nodes. The lines and nodes in spin networks are labeled by geometric quantities, such as units of area and volume, rather than by voltages and resistances, as in circuit diagrams. "Spin networks are the quantum states of gravity just as electron shells are the quantum states of the atom," Rovelli explains. 

"Roger Penrose dreamed up spin networks 30 years ago as a beautiful picture of the quantum-mechanical geometry of space," Smolin says. He describes Penrose, the Francis R. Pentz and Helen M. Pentz Distinguished Visiting Professor of Physics and Mathematics at Penn State, as perhaps the most influential and creative relativity theorist living today. "Now our calculations have rediscovered these same wonderful structures mathematically, vindicating Roger's intuition that spin networks describe configurations of the basic building blocks of the geometry of space," Smolin says. 

Rovelli and Smolin suspect that, if the loop representation approach to quantum gravity turns out to be correct, it will have implications for other key unsolved problems. "In many theories in physics there are situations in which you try to make a physical prediction but you get an infinite quantity," Smolin explains. These infinite quantities are very troubling to scientists studying such things as the early universe, black holes, and other areas of physics. "If the loop representation is right about this prediction, then the infinities simply are not there because nothing can be infinitely small," Rovelli explains. "The networks of loops define space, they are not in it, so nothing can be smaller than them," says Smolin. 

The two theorists are investigating the relationship of their results to other approaches to quantum gravity-particularly string theory. "String theory is the only other approach to quantum gravity to have yielded definite physical predictions," Smolin says. "The loops in our theory are not strings, but there are deep connections between the two approaches that are most intriguing." 

This research was supported partially by the National Science Foundation and by Penn State. 

Barbara K. Kennedy

Note: This past May, an error was found in one of the calculations of Rovelli and Smolin that changed the values of some of the "units" of quantized volume, without changing the basic result that the volumes and areas are quantized. The error was detected by Renata Loll, a young German physicist who had been a postdoctoral fellow in the Penn State Center for Gravitational Physics and Geometry and is now a postdoctoral fellow in Florence, Italy. She did the calculation using a different method from the one used by Rovelli and Smolin. Looking back at their calculations, Rovelli and Smolin found they had made an error in the sign of a term in the expressions for the units of volume. 

In another recent development, the prediction that areas should be quantized has been used by another group of physicists as the basis of calculations in which they make new predictions about radiation emitted from black holes. 


Lee Parker

Long experience has taught me not to believe in the limitations indicated by purely theoretical considerations. These - as we well know - are based on insufficient knowledge of all the relevant factors." 

Guglielmo Marconi