Braneworlds

Particle physics and cosmology are mysterious subjects, embracing such strange concepts as ‘dark energy’, ‘braneworlds’ and ‘wormholes’ – terms people may have heard of or perhaps read about, but still don’t really understand. Brian Greene, a leading expert in string theory, has now followed up his earlier, very successful book, The Elegant Universe, to give lucid and accessible explanations of a wider range of cosmological abstractions. In particular, he demonstrates the intimate relationship between the physics of the infinitely small and of the infinitely large, worlds that one might have supposed to be completely unconnected.

Greene starts by examining Newton’s notion of space as an immutable medium, the background against which all motion is measured. ‘Space’ is a slippery concept, and the search for its definition, from 17th-century Newtonian mechanics to the present-day notion of a space-time knitted out of vibrating strings, underpins the whole book. Even in Newton’s day, opinions differed as to whether space should be regarded as something absolute or something relative. While Newton asserted that space would exist as a frame of reference even in a completely empty Universe, Leibniz portrayed it as a mathematical concept, useful only for describing the relationship between objects and their motion, an abstraction that would be meaningless without its constituent objects. Later, Mach suggested that motion is relative not to absolute space, but to the average distribution of matter in the Universe.

The success both of Maxwell’s equations in the mid-19th century, which described the motion of light as an electromagnetic wave, and of Michelson and Morley’s demonstration of the constancy of the speed of light, paved the way for Einstein’s theory of special relativity. Einstein’s innovation was to show that two observers moving relative to each other will perceive different outcomes when conducting the same experiment – even in something as basic as measuring distances or durations. The crux of the theory is that all motion should be considered as occurring not only through space, but also partly through time. We are unaware of relativity in everyday life, since its consequences become apparent only when a sufficient proportion of motion through time is diverted into motion through space – as in the familiar example of an astronaut who has spent a short time moving close to the speed of light only to return to Earth and find that many millennia have passed. A decade later, Einstein extended these ideas by proposing an equivalence between gravity and accelerated motion: space was now no longer Newton’s fixed framework, but a flexible medium that warps and bends in response to large masses and large energies. The question of whether it should be regarded as a physical entity or a theoretical abstraction remained unanswered.

Einstein’s equations accurately describe the behaviour of objects that are very massive or travelling at very high speeds. Analysis of microscopic extremes, however, requires the physics of quantum mechanics. Quantum mechanics is concerned with the behaviour of single particles, especially with such simple attributes as their location and velocity. At this level, it asserts, there can be no certainty as to the result of any experiment; all possible outcomes are valid, though with varying degrees of probability.

So far so good, but if these two highly successful theories are combined in an attempt to address the physics of something that is both extremely small and extremely massive – a black hole, say, or the very early Universe – the results are nonsensical. This isn’t a major hurdle to most physicists, who confidently use these theories to predict the behaviour of most objects, but it is still a cause for concern, since the inability of either theory to extend across all possible physical circumstances shows that the underlying physics is not completely understood.

Only by accessing the very earliest state of the Universe can we hope to find an explanation for the asymmetry, fundamental to our experience, according to which we only ever perceive time as moving forwards. Physical laws have an inherent symmetry that permits them to operate either forwards or backwards through time; yet we observe all physical processes progressing relentlessly towards an increase in entropy, the gradual degeneration of order. Time’s so-called ‘arrow’ is not a consequence of either the relativistic or the quantum laws of physics; rather, it is thought to have been programmed into the Universe from its inception as a low-entropy (i.e. simple, highly ordered) entity. To progress any further we need to be able to investigate these early conditions, but we can only do this once we have a mathematical framework that either combines or supersedes the two branches of 20th-century physics in a unified theory.

The earliest manifestation of our Universe that we are able to detect directly is what is known as the ‘cosmic microwave background’, a relic from the time, around 300,000 years after the Big Bang, when the cosmos had cooled sufficiently for its hot, charged particles to begin combining into neutral atoms, so freeing the photons that eventually reach us as background radiation. Beyond this barrier, the Universe is inaccessible to astronomical observation.

Any attempt to access its earliest state therefore relies on mathematical theorising. For example, it’s thought that the cosmos as we know it is suffused with something called a ‘Higgs field’. We are barely aware of its effects, and it still awaits observational confirmation, but it is thought to play a vital role in concealing from us the underlying unity of physical laws. Matter responds to an increase in temperature by changing from a solid to a liquid to a gas, each shift accompanied by an increase in the level of symmetry. Fields can undergo similar transitions in phase and symmetry. In the post-Big Bang Universe, the Higgs field is thought to have existed in a more symmetrical phase than the one we infer for the cosmos today. At that higher level of symmetry, the unity of two of the four fundamental physical forces – the electromagnetic and weak nuclear forces – is revealed. It can then be supposed that at an even earlier, hotter stage of the Big Bang, the Higgs field might have existed in a still higher state of symmetry that would divulge the fundamental unity of these two forces with the remaining two, the gravitational and strong nuclear forces, so unifying the relativistic and quantum physical models.

As it is, the cosmic microwave background provides a number of important clues about the Universe. The CMB is surprisingly uniform, with only tiny variations in temperature. The present-day Universe appears to have preserved this homogeneity in all directions, despite all the intervening evolution and expansion, which means that it can have one of only three possible shapes: a sphere, an infinite plane or a saddleback.

Astronomers bridge the awkward gap between the properties of the point-like Universe that existed just after the Big Bang and its current scale by hypothesising a period of ‘inflation’. Were the Higgs field immediately after the Big Bang to have jumped momentarily to a higher-energy configuration, one of the consequences would have been that gravity acted as a repulsive force. For the tiniest fraction of a second, the entire Universe would then have expanded in a sharp burst. This inflation of space-time would help to explain the uniformity of the cosmic background radiation, because very similar neighbouring regions would have been dispersed very widely. Inflation also provides a direct link between the astronomical and microscopic scales. The idea is that quantum ‘jitters’ caused turbulence and minute fluctuations in the properties (such as temperature) of matter in the very early Universe; these were then amplified during inflation, eventually leading to the formation of stars and galaxies. Finally, inflation offers an explanation as to why the average density of matter is so close to the critical value differentiating between an open Universe (which expands for ever) and a closed one (which eventually collapses in on itself).

When estimating the density of mass in the Universe, astronomers are faced with the problem that only about five per cent of it is visible; a further 25 per cent comprises unseen ‘dark matter’, the presence of which is detectable only through its gravitational effects. The remaining 70 per cent of the density predicted by inflationary cosmology is thought to be contributed by ‘dark energy’, a modern version of the ‘cosmological constant’ Einstein invoked in his theory of general relativity to prevent the stars and galaxies from coming together under the influence of gravity. It was soon discovered, however, contra Einstein, that the Universe is not static, but continues to expand, with the galaxies receding from each other, so that there is no need for any cosmological constant. Even this interpretation has recently been refined, thanks to one of the major discoveries in astronomy over the last decade. Observations of the light coming from objects at the furthest reaches of the Universe have shown that the expansion is accelerating, owing to the repulsive force of the mysterious – and still hypothetical – dark energy, which pushes against gravitational attraction.

But though inflation is extraordinarily successful in accounting for many observed features of the present cosmos, understanding what set the inflation off still requires a unified theory. The most successful approach so far has been provided by string theory, which postulates that all particles are differently vibrating representations of even more elementary components, small filaments called ‘strings’. The varying patterns of oscillation in these strings yield particles of differing mass, spin and electric charge. The particles include gravitons, the ‘messenger particles’ inferred to account for the transfer of ‘information’ about gravitational fields across space. String theory has thus given us the first quantum interpretation of gravity. It also provides a finite size for the smallest discrete building block of the Universe – a single string – which is just large enough to avoid any contradiction between relativity and quantum mechanics. Below this limit, the concepts of space and time cease to have any meaning.

String theory is currently beyond experimental confirmation. Not only is a single string a billion billion times too small to be seen using current instruments, but most of the predicted particle masses correspond to energies too large to be produced even in such accelerators as the Large Hadron Collider currently being built at CERN. There is a further catch: string theory can provide a mathematical consistency between the gravitational and quantum forces only if the Universe has at least ten dimensions of space and time: the extra six dimensions are concealed at every point in ordinary space-time by being furled tightly into a complicated structure known as a Calabi-Yau shape. Strings are able to access all nine dimensions of space, and the form of the Calabi-Yau shape dictates the possible oscillations – and thus the particle properties – expected from the string vibrations.

There are in all five mathematical interpretations of string theory, which can be reconciled as different manifestations of an underlying theory known as ‘M-theory’ (as long as we now accept a further increase in the total number of space-time dimensions to 11). M-theory allows other building blocks to be inferred beyond the one-dimensional string, such as a two-dimensional (or higher) ‘brane’. Unlike strings, branes are not necessarily only microscopic, and so could spread throughout our familiar three dimensions. A further ramification is that some strings (and hence some of the messenger particles that are key to our observations) may vibrate only between and within a subset of these 11 dimensions. Indeed, gravity may be the only one of the four forces free to sample the dimensions outside our own Universe; it appears to us as the weakest force only because its effects have been diluted throughout space-time. The fundamental fabric of space-time would then be stitched together from strings. It is also possible that strings themselves comprise an even more elementary particle, a ‘zero-brane’ with no spatial extent.

The potential of M-theory is attractive, but how does it match up to experimental confirmation? Greene is honest about the limitations, but doesn’t let them dim his enthusiasm. Only a few specific combinations of longer strings that exist within the larger extra dimensions are expected to yield observable consequences. The presence of extra dimensions could be revealed by the precision measurement of discrepancies occurring in only three dimensions; and if the energy carried by gravity leaks into the other dimensions, it is possible that the Large Hadron Collider may produce reactions that appear to contradict notions of the conservation of energy. But such experiments remain a long way off, and M-theory may be sufficiently flexible and elusive to end up being refined rather than contradicted by any negative observations. The extra dimensions are probably curled up on a scale too small to be experimentally investigated. It is hoped, however, that in the near future accelerator experiments may detect the fundamental messenger particles of the Higgs field, thus providing evidence for its existence. The experiments may also be successful in filling in the blanks in the particle ‘families’, particularly the lighter particles that have been predicted by string theory but not as yet detected.

So will M-theory provide a better understanding of the pre-inflationary universe? Standard inflationary cosmology has not yet been successfully incorporated within string theory, but M-theory does yield an alternative framework in which our space-time is thought of as a three-brane moving through time. On this interpretation, the initial inflationary expansion was set going by a collision between two such braneworlds. Although a whole succession of Universes – each beginning with an increasing amount of entropy – might be triggered by consecutive clashes of this kind, this alternative theory is no better than the standard inflation model at accounting for the singular, low-entropy start to the whole process.

How, anyway, could we ever distinguish between an inflationary burst caused by colliding braneworlds and one caused by conditions immediately after a Big Bang? To do this, we have to appeal to the idea of ‘gravitational waves’. According to the theory of general relativity, not only do massive objects warp the surrounding fabric of spacetime, but fast-moving or rotating objects cause other geometrical distortions of space-time that travel away from their point of origin: gravitational waves. The Big Bang model predicts that such disturbances would be formed from the quantum restlessness of the primordial particle chaos, and would in turn leave their signature on the cosmic microwave background. Gravitational waves are not predicted by the braneworld models, however, so were their imprint to be detected, it would be a way of making a choice between the two cosmologies. Such an observation is now well within our reach thanks to the new satellites studying the background radiation.

In his final chapter, Greene proceeds from studies of the entropy of black holes to suggest that all the physical processes that we perceive could be occurring only on a distant surface, and that the Universe as we know it is merely a three-dimensional projection of them. In so doing, he ends this vivid, exciting book by raising the possibility that the space-time physicists have spent so long trying to understand might, in the end, turn out to be an illusion.