In high-energy physics gravitational effects become important at the Planck scale, which is calculated by combining Planck’s constant, the velocity of light, and the Newtonian gravitational constant. At the Planck length scale of ~ 10-³⁵ m the particle mass scale is gigantic, at ~ 10¹⁶ TeV, 16 orders of magnitude beyond the reach of today’s particle accelerators. The enormity of the Planck mass scale leads to the hierarchy problem: why is the Planck mass scale separated by so many orders of magnitude from the weak mass scale, or, why is gravity so weak?

To solve these problems some physicists have turned to superstring theory, which uses 10 spatial dimensions, six of which are tightly crunched up or compacted at the Planck scale and therefore undetectable. The fundamental particles are not pointlike; they are closed strings in the compact space. Over the past five years Science Watch has tracked the rapid evolution of superstring theory, but nobody yet knows whether it has any relevance to the real world.

There are alternatives to many dimensional spaces with compactification, and this period Science Watch showcases four papers (#2, #3, #5, #7) which propose that the additional spatial dimensions are huge. Science Watch has already reported (see 11[1]:6, January/February 2000) on the proposals (#5,7) from Savas Dimopoulos, Stanford University, and collaborators, for new dimensions on the millimeter scale. New this time are #2 and #3 by Lisa Randall, Princeton University, and Raman Sundrum, Boston University, who propose to solve the hierarchy problem with one infinite extra dimension. They challenge the approach in #5 and #7 for large dimensions to solve the hierarchy problem. Instead, in paper #2, they present a higher dimensional scenario in which the usual four-dimensional metric has an additional "warp" factor for a fifth dimension. Their solution is quite distinct from that in #5 and #7, in that there is only one extra dimension, not two or more. But these models share the idea that standard model particles and their interactions are confined to a four-dimensional subspace referred to as a 3-brane which is attached to a higher dimensional space.

In paper #3 Randall and Sundrum show how an infinite fifth dimension in the presence of a 3-brane can generate a theory of gravity which mimics pure four-dimensional gravity. "The possibility of an infinite extra dimension is new," Lisa Randall tells Science Watch. "In fact, when the possibility of extra dimensions was first introduced by Kaluza in the 1920s, the outstanding question asked by the referee (Einstein) was, how big are they? They were always thought to have to be of finite size. Our proposal that gravity can be localized is very new. The second new idea is that the geometry we find in solving Einstein's equations is such that gravity is attracted to a brane, so that it is relatively weak everywhere the brane is not. This explains the weakness of gravity relative to other forces. This is truly a new idea and there are many new implications, for gravity, cosmology, particle physics, and possibly string theory."

The extra-dimension papers are receiving huge attention because they open up the possibility of rich and very distinctive phenomenology. Randall and Sundrum conclude paper #2 with the tantalizing suggestion that "should this solution prove correct, there is rich spectroscopy awaiting us at the Large Hadron Collider," which will go live in 2005.

John Bahcall, Institute for Advanced Study, Princeton, and collaborators have added a second solar neutrino paper (#6) to the Top Ten. Their starting point is that five experiments have now added significantly to our knowledge on the fluxes and energies of solar neutrinos. As is well known, divergences between the measurements and theory suggest there is new physics beyond the standard model. Their paper looks at uncertainties in the nuclear fusion reaction cross sections and comes to the conclusion that experimental errors from the nuclear physics are currently the largest source of error in neutrino predictions.