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The topology of the Internet

There are already over 300 million documents on the Internet, and only 34% of them have been catalogued by the most popular search engines such as Hotbot. This has made the topology of the Internet extremely difficult to describe or measure. However, Reka Albert, Hawoong Jeong and Albert-László Barabási of the University of Notre Dame in the US have developed a measuring technique based on power-law distributions from statistical physics. According to their technique, any two randomly selected Web pages are, on average, 18 hyperlinks or clicks apart. This figure, they claim, represents the “diameter” of the Web.

Albert and co-workers built a robot that adds all the Web links found on a document to a database, and then follows these links to other Web pages and so on. This allowed them to calculate the probability distribution for the number of outgoing and incoming links to a given Web page, and then to construct a simple equation which can calculate the shortest route between any two random selected pages.

Their technique also predicts that if the number of pages on the Web grows by 1000%, its diameter will only grow from 18 to 20 clicks. Their results have implications for finding information on the Web. If an intelligent robot agent could interpret and follow the relevant Web links, it could find information much faster than the current generation of search engines.

UK university launches science fiction degree

“Most people in the UK receive their science education through science fiction so it makes sense to study the link between science fiction and science fact,” says Brake. The three year degree course will be split into thirty modules, over half of which will be based on astronomy and space science. There will be seven modules on science fiction, with the remaining modules covering the media, society and culture. According to Brake the students will study science topics such as quantum physics and then look at the science fiction works associated with them. They will also study the interaction between science/science fiction and the space race, the cold war and so on.

The students will be expected to read popular science books such as The Making of the Atomic Bomb by Richard Rhodes and Black Holes and Time Warps: Einstein’s Outrageous Legacy by Kip Thorne, as well as books by H G Wells, George Orwell and Philip K Dick. They will also study computer games, merchandising and movies such as Blade Runner and The Terminator.

Glamorgan already runs a course on life in the universe, which includes material on the search for extra-terrestrial life, and a course on popular science and culture, which looks at various aspects of Einstein’s theories of relativity, including their cultural impact. “It is important that we retain high academic standards which develop new and innovative ways of teaching science-related courses,” says Brake. He hopes that graduates from the course will go on to careers in publishing, education and social research.

Vortex look for lasers

Scheuer and Orenstein used so-called vertical cavity surface-emitting lasers. In these devices the light is emitted from the top of the active region of the laser, rather than from the edge as in conventional semiconductor lasers. This gives a two-dimensional output in which the patterns can form, rather than the one-dimensional output from conventional devices. The Israeli team used microcavity lasers in which the active region contained three 8 nanometre thick layers of indium gallium arsenide. The laser output had a diameter of 20 microns.

Vortex structures occur widely in science and nature – in gases, fluids, plasmas and DNA, for example. The optical vortices produced by Scheuer and Orenstein are the smallest and most complex spontaneously-produced vortices ever seen. In an optical vortex the phase of the electric field experiences a singularity at the centre of the beam, where the amplitude also goes to zero. The vortex has an order or a charge, which is the number of times the phase changes by a factor of 2p on the path around the vortex. When the current through the laser was increased above 16 milliamps, a complex figure-of-eight pattern consisting of two vortices with the same charge was created, followed by a four-vortex pattern at 17.2 mA. As the current was increased further, a radial symmetric pattern was formed, followed by arrays of three, five and seven vortices.

Physicist lined up for top EU research post

New director for DESY

Wagner, who is 58, studied physics at the Technical University of Munich and the universities of Göttingen and Heidelberg. After spells as a research associate at Heidelberg and the Lawrence Berkeley Laboratory in California, Wagner became a full professor of experimental physics at Heidelberg in 1984. He accepted a chair at the University of Hamburg in 1991 and, in the same year, became director of research at DESY.

Wagner’s research has centred on electron-positron collisions at DESY and at CERN. He was also closely involved in the preparation of the 1100-page conceptual-design report for TESLA, a superconducting 500 GeV electron-positron linear collider that he and Wiik hoped to build at DESY. The Hamburg laboratory is one of three particle physics centres hoping to host the next-generation linear collider. Wagner has sat on many scientific advisory committees in Germany and further afield, including Italy, Japan, Russia and the United States.

New generation of neutrino experiments begins

Neutrinos come in three flavours – electron, muon and tau neutrinos. According to the Standard Model of particle physics they have zero mass and only interact weakly with matter, which makes them very difficult to detect. However, muon neutrinos can change or “oscillate” into electron or tau neutrinos, and so on. Last year the Super-Kamiokande team announced that they had strong evidence to show that atmospheric muon neutrinos – which are created when cosmic rays collide with nuclei in the atmosphere – can oscillate into tau neutrinos as they pass trough the Earth (see Super-Kamiokande finds neutrino mass).

The advantage of accelerator-based experiments, such as K2K, is that the initial flux of neutrinos can be measured at the accelerator and then much further away. This is not possible in experiments with atmospheric neutrinos. The neutrino source at KEK produces muon neutrinos. If the flux detected at Super-Kamiokande is lower than that at KEK, that is evidence for neutrino oscillations.

The Super-Kamiokande experiment consists of 50000 tons of water surrounded by hundreds of photon detectors. It is placed 1000 metres below ground in a lead and zinc mine. A tiny fraction of electron and muon neutrinos give off faint flashes of light known as Cerenkov radiation when they interact with electrons in the water molecules. This allows them to be distinguished from tau neutrinos.

There are also plans to send neutrino beams from the CERN particle physics lab in Geneva to the Gran Sasso underground lab some 730 km away in Italy, and from Fermilab near Chicago to the Soudan experiment, 710 km away in Minnesota.

New hope for the travelling salesman

Kirkpatrick and co-workers found that the computer algorithms used to solve NP-complete problems can undergo sudden phase transitions as the various criteria used to search for a solution are varied. The solutions get harder to find at the onset of the phase transition – as the search ‘freezes’ – and then easier again once the system has passed through the phase transition. The team noticed that if the phase transition is abrupt, like the freezing phase transition, the problem is exponentially hard. However, if the transition is continuous, like the demagnetization of iron when heated, then the problem is only polynomially hard.

String theory: simple yet elegant

String theory dates back some 30 years, but it was the “first string revolution” of 1984 that intensified interest in this, the most promising candidate for a “theory of everything”. In this book Brian Greene declares that his central concern is “to explain the workings of the universe according to string theory, with a primary emphasis on the implications these results have for our understanding of space and time”. As readers of Physics World may already be aware, Greene’s response to the challenge has put his book on the best-seller lists on both sides of the Atlantic (see String theory tops the best-seller list).

To place his central concern in context, Greene gives an excellent account of the key ideas behind first special, and then general, relativity. It is hard to be original in writing about these well popularized topics, but Greene has a clear and lively style, with some fresh analogies to lead the reader to accept the reasons for the radical overhaul of classical Newtonian “common-sense” concepts of space and time. He also introduces “warps and ripples” of space-time, black holes and cosmic expansion with a minimum of fuss, disguising the mathematics with both visual and verbal illustrations.

The “microscopic weirdness” of quantum mechanics is, however, treated rather more swiftly than some might wish. Perhaps Greene was anxious to get to the need for a new theory to reconcile the conflict between general relativity and quantum mechanics. As he explains, this reconciliation becomes acute when trying to understand the properties of space-time at the scale set by the Planck length (10^-35 m). At these short distances, the inevitable quantum fluctuations in energy lead to a curvature of space-time that may become so disruptive that it produces what John Wheeler has so vividly described as “space-time foam” – the smooth fabric of space-time undergoing ever more violent fluctuations as the scale is decreased.

And so to string theory, which is widely accepted as the only game in town when it comes to providing a quantum theory of gravity. More accurately, I should say that it is not just string theory that is the current focus of attention and expectation, but rather the enlargement of string theory into what is called “M-theory” (where “M” may stand for mystery). And this is where Greene really excels. What he has achieved is to drain all of the mathematical complications from an up-to-date survey of M-theory – without destroying its most significant content – and to then present this distillation of the theory in a way that is both compelling and informative.

String theory replaces the point-like quanta of “conventional” theories (particles like the quarks and gluons, the leptons and the vector bosons of the Standard Model of high-energy particle theory) by strings. The scale of the strings is so small – of the order of the Planck length – that a string will look like a point even at the scales to be probed by the Large Hadron Collider at CERN, which will be the world’s highest-energy particle accelerator. And in this limit string theory yields an effective quantum field theory rich enough to include the fields of the Standard Model.

But that is not all. The mathematical consistency imposed in constructing a quantum string theory has a remarkable consequence. Strings can vibrate, and the different modes of vibration in the quantum theory correspond to different species of particle. And among them there is one with precisely the properties of the graviton, the quantum of the gravitational field. As Ed Witten, one of the world’s leading string theorists, puts it: “String theory has the remarkable property of predicting gravity.” (Greene observes that it is more precisely a postdiction, but it is no less remarkable for that.)

But what also follows from the quantum theory of strings is that space-time has more than four dimensions. This is required to keep the theory both consistent and finite. And in order that strings can describe both fermions (like quarks and leptons) and bosons (like photons and the W and Z particles), the theory has to have an additional kind of symmetry over and above that associated with special relativity; this is supersymmetry. Supersymmetric string theory in turn requires space-time to have ten dimensions. The six extra dimensions at every point in our familiar space-time are “curled up” into structures on the scale of the Planck length.

The properties of the effective field theory that emerges from the ten-dimensional superstring theory depend sensitively on the geometry of the curled-up structures. These are called Calabi-Yau spaces, and Greene has himself made important advances in understanding their properties. The account of his work on mirror symmetry, “space-tearing flop transitions” and conifold transitions conveys the intensity and excitement of the research. It also gives the reader something to hang onto when the conceptual going gets tough.

String theory went through a period of some stagnation after the wave of enthusiasm following the first revolution had subsided. It had emerged during the early period that there were in fact five consistent string theories and several thousand ways to “compactify” the six extra dimensions, which seemed to destroy the hope that a unique consistent theory was within reach. However, the second superstring revolution of 1995 re-ignited the flagging hopes that this goal might yet be achieved. The breakthrough came in being able to go beyond the perturbative approximate approach, which was all that had thus far been possible, enabling the non-perturbative structure of superstring theories to be explored.

The pay-off was spectacular. We now know that strings are not the only objects in the theory, but there are also soliton-like structures, called “p-branes”. There are also symmetries that relate the five superstring theories to one another. And they in turn are related to a sixth theory, supergravity in 11 dimensions. We now believe that there is an 11-D theory, as yet imperfectly understood, which in different approximations yields the previously discovered superstring theories. This over-arching theory is called “M-theory”, and Greene tells us how it has already yielded many profound insights – with the promise of more to come.

Albert Einstein said that elegance is for tailors. Maybe so. But M-theory is more than elegant; it might describe our universe.

Century old mystery solved

Invar has a face-centred cubic structure and is composed of about 65% iron and 35% nickel. In addition to its anomalously low thermal expansion, the alloy also has unusual elastic, thermal and magnetic properties. Most metals expand when they are heated because the amplitudes of the atomic vibrations inside the metal increase with temperature. It has long been known that the unusual magnetic properties of Invar somehow compensated for this expansion — Invar’s unusual properties disappear when its magnetization disappears at the Curie temperature. However, the exact mechanism was not clear.

Van Schilfgaarde and co-workers modelled a supercell of Invar containing 21 iron atoms and 11 nickel atoms. The electron spin at each atomic site was free to point in any direction. They found that at low temperatures the spins all pointed in the same direction: in other words the alloy was ferromagnetic. As the temperature was increased, however, the spins started to point in random directions and the volume of the supercell decreased. This reduction in volume compensates for the expansion caused by increased thermal vibrations.

Light feels the heat and slows down

The researchers also showed that the rubidium gas, which they say is a “relatively easily created medium”, exhibits extremely efficient nonlinear interactions. Materials with such properties could be used for fundamental research, such as high-precision spectroscopy, or for applications such as the compression of optical information.

In electromagnetically induced transparency a “pump” laser is used to drive transitions between various electron energy levels in the atom. If the conditions are correct, quantum interference effects can cause the probability of transitions between two of the levels to fall to zero. This means that a second “probe” laser with a frequency that is resonant with this transition can travel through the media without absorption. The quantum interference can also increase the refractive index of the material at this frequency by many orders of magnitude, thereby greatly reducing the speed of light in the material.

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