Infinite Extent

Brains Have 'Branes?

Life is a wave, which in no two consecutive moments of its existence is composed of the same particles.

- John Tyndall

Brane New Worlds

by Jerome Gauntlett

It is common sense that at everyday scales we live in a world with three large spatial dimensions. Lisa Randall and Raman Sundrum have recently made the bold suggestion in Physical Review Letters that an extra dimension of infinite extent may supplement the three spatial dimensions we observe. Not only do they claim that this can be entirely consistent with current observations, they also argue in a second paper that closely related scenarios could hold the key to some fundamental issues in attempts to unify particle physics with gravity.

The idea that the four space-time dimensions that we observe (three space and one time) could be supplemented by extra dimensions was first put forward by Theodor Kaluza and subsequently developed by Oskar Klein in the 1920s. The motivation then was to achieve a unification of Maxwell's theory of electromagnetism and general relativity, which is Einstein's theory of gravity. They considered an extra 5^th dimension curled up in a small circle that would be undetected at much longer length scales. Although Kaluza and Klein's model turns out to give wrong predictions and so cannot be a correct description of the real world, the beautiful idea of extra dimensions with finite extent ("compact dimensions") has become a central component of string theory - the leading candidate to unify all of the known forces of nature.

Some of the ingredients in the Randall-Sundrum papers were in fact suggested by developments in string theory. String theory was originally conceived of as a theory of oscillating objects with one spatial dimension, or strings. It is now known that in order for string theory to be mathematically consistent it must also include a rich spectrum of extended objects of higher dimension: "membranes" with two spatial dimensions, "three-branes" with three, and so on. Understanding the properties of these branes is very much an active area of research.

One of the key ideas in the papers by Randall and Sundrum is that the 4-dimensional space-time we observe at everyday scales is actually the evolution in time of a three-brane moving through an ambient space-time of higher dimension (Figure 1). In such "brane-world" scenarios, particle physics is confined to the brane but the particles can interact with the ambient space-time through gravitational interactions. When all the extra spatial dimensions of the ambient space-time are compact, these interactions can be so weak as to have escaped detection by experiments thus far.

Before the paper by Randall and Sundrum it seemed almost obvious that the ambient space-time in which the three-brane lives should not be of infinite extent. In the simplest example with a single, flat, infinite extra dimension, Newton's law of gravity would be modified: the force between two masses on the three-brane would be inversely proportional to the cube, not the square, of the distance between them. The surprising observation made by Randall and Sundrum is that if the extra dimension were infinite, and if the embedding space-time has a very particular curvature, then it is possible for the predicted corrections to Newton's law to be consistent with experimental results.

This remarkable insight has stimulated a flurry of subsequent papers developing the ideas and determining the implications for cosmology and particle physics. Directions being pursued include verifying in more detail how four-dimensional general relativity emerges on the three-brane, and studying ways in which the framework can be embedded in string theory.

The implications for particle physics are particularly exciting because other closely related ideas published by Randall and Sundrum may provide a resolution to the "hierarchy problem," one of the most important issues in going beyond the Standard Model of particle physics. The Standard Model is a fantastically successful theory of three of the forces of nature: electromagnetism, the weak nuclear force and the strong nuclear force. It unifies electromagnetism and the weak nuclear force into the electroweak force at characteristic length scales of around 10^-17 cm (roughly the limit of the scales probed by current accelerators). There are strong arguments that unifying particle physics with the fourth known force, gravity, into a theory of quantum gravity (string theory, say) will have a characteristic length scale of around 10^-33 cm. It is very difficult to account for such a vast gap between these two scales without fine tuning the theoretical parameters to an extraordinary extent. This is the hierarchy problem.

The conventional approach for dealing with this problem is to invoke a new symmetry between matter and forces called supersymmetry, which could be detected by the next generation of particle accelerators. An alternative approach (which might also include supersymmetry) is to assume that our world is a 3-brane. The first proposals along these lines considered a single 3-brane embedded in a space-time with at least 2 extra dimensions that are compact and flat. These dimensions could be as large as 1 mm without violating known experiments. In a string theory setting it is possible that the string length scale could be just below that probed by current accelerators, rather than about 10¹⁵ times smaller as previously supposed. These schemes are fascinating although they do introduce another hierarchy that needs explaining.

By contrast, Randall and Sundrum suggest that a curved ambient space-time with one extra dimension might provide a better setting. They consider a slab of this space-time bounded at each end by a three-brane. (Slabs of space-time bounded by branes were first introduced in string theory in reference 5.) One of these branes is our world and the other is a "hidden" world. Particles on our three-brane interact with the extra dimension and the hidden world through gravitational interactions. By assuming that the distance between the branes is very small, Randall and Sundrum showed that these interactions are weak enough to be consistent with experiment. They also showed how the hierarchy of scales on our 3-brane can be accounted for in a fascinating way by the curvature of space-time without introducing any extra hierarchy.

The Randall-Sundrum papers do not provide a detailed model of particle physics beyond the Standard Model. Indeed there are considerable difficulties to be overcome to achieve this goal. But they have provided exciting alternatives to conventional ways in which people thought the unification of particle physics and gravity might occur. Particle physicists, string theorists and cosmologists are currently devoting much effort to developing ideas and deriving predictions that could be tested by the next generation of particle accelerators and gravity experiments. If Randall and Sundrum are on the right track, there could be exciting experimental evidence in the near future.

Jerome Gauntlett is in the Department of Physics, Queen Mary and Westfield College, Mile End Road, London El 4NS, UK. e-mail: j.p.Kauntlett@qmw.ac.uk

1. Randall, L. & Sundrum, R. Phys. Rev. Lett. 83, 4690-4693 (1999).
2. Randall, L. & Sundrum, R. Phys. Rev. Lett. 83, 3370-3373 (1999).
3. Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. Phys. Lett. B 429, 263-272 (1998).
4. Antoniadis, I., Arkani-Hamed, N., Dimopoulos, S. & Dvali, G. Phys. Lett. B 436, 257-263 (1998).
5. Horava, P. & Witte D. E. Nucl Phys. B 475, 94-114 (1996).

Infinite Cycle of Big Bangs Make Universe

by Charles Choi

Princeton, New Jersey - A new, radical model of the cosmos proposed by scientists in the United States and Britain suggests there is no beginning or end of time, only an infinite cycle of Big Bangs that remake the universe endlessly.

"We may have misunderstood the nature of time," said co-researcher Paul Steinhardt, a cosmologist at Princeton University. "The Big Bang may not be the beginning of space and time, as conventionally assumed. Instead, time may exist forever."

The new theory also provides a role for the mysterious antigravity force known as "dark energy," which seems to be expanding the universe faster and faster over time. "This opens our eyes to a new and much more complete picture of the universe," said co-researcher Neil Turok, a theoretical physicist at the Center for Mathematical Sciences in Cambridge, England. Noted physicist Stephen Hawking of Cambridge University has already bet Turok that new cosmic microwave observations, to be made in 2007 by satellite, will prove standard ideas right. "I have accepted the bet," said Turok.

Although the idea of a cyclical universe is not a new one, it has been discounted for decades. If matter rushes out in a Big Bang and collapses in a Big Crunch, scientists argue, the universe must be finite in size. But images of cosmic background microwave radiation show the universe is "flat" or infinite. The standard model of the cosmos, which presumes a Big Bang and an eternal expansion into darkness, contains some cracks. For instance, there is no role for the recently discovered "dark energy," which appears to repel gravity and accelerate the universe's expansion. Dark energy plays a crucial role in Steinhardt and Turok's new model. Their notion is based on string theory, the branch of physics that seeks to unite all ideas about the forces of nature under a "theory of everything" by proposing the existence of extra dimensions of reality beside space and time.

The researchers believe dark energy is one of the many effects caused by the interplay of additional membranes of reality, or "branes," as they naturally contract and expand. Dark energy will spread apart all matter - such as black holes and other debris - and dissipate all energy over the course of trillions of years, ultimately emptying out the universe, leaving it in a state of virtual vacuum. If so, there would be nothing left to prevent one of the universe's extra dimensions from squeezing back in on itself - contracting in a Big Crunch.

Yet no matter in our universe would actually move.

In this distant future time, Steinhardt explained, "The space between you and me is not shrinking - it's not like we're coming back together again during this contraction phase. Our space remains infinite. Instead, it's the space between the extra dimensions is shrinking." As this extra space collapses, the researchers theorise the laws of physics would change. Gravity would strengthen, while the other fundamental forces - electromagnetism and the two nuclear forces - would grow weaker or stronger depending on which version of string theory you believe.

In the end, all these changes over uncounted years cause energy and matter to pop in and out of existence faster and faster, followed by a bang or crunch, which restores the fundamental forces of the universe to their original values and resets the cycle's clock. "Steinhardt and Turok have injected an imaginative new speculation," said Sir Martin Rees, Astronomer Royal of Britain and theoretical astrophysicist at Cambridge University. "Their work emphasises the extent to which we may need to jettison common sense concepts, and transcend normal ideas of space and time, in order to make real progress."

If correct, the new model requires different observations from the current picture of the universe. "The conventional picture predicts a yet-unseen spectrum of gravitational waves, and ours does not. Here we have to wait for improvements in experiments in the next few years to decades to decide the issue," Steinhardt told UPI.