A fractal universe?

A fractal universe?

The theories of particle physics and cosmology seem to be uniting lately to tell us that the universe must have more dimensions than we perceive. To do what they want to do, the people who make these theories have to work in more than the three spacelike and one timelike dimensions that we have up to now thought defined the universe. The most popular theories (SN: 7/7/84, p.12) require a dozen dimensions, give or take one or two, but numbers into the hundreds have been suggested from time to time.

Although some physicists believe that these extra dimensions are nothing but mathematical conveniences, others regard them as real. If they are real, they must exist in a way in which we don't perceive them directly. Most theorists "arrange" this by "compacting" them, or curving them tightly into ultramicroscopic balls around every point in space, so that an object that tried to move in one of those directions would almost immediately return to its starting point. We are much too big to perceive anything so fine-grained.

However, if the extra dimensions are real, even submicroscopically, their presence could affect the dimensionality we perceive. Instead of a precise integral three dimensions, the perceived spacelike dimensionality might be a fractal, three-point-something. While working at the University of Tokyo, Berndt Muller and Andreas Schafer of the Johann Wolfgang Goethe University in Frankfurt, West Germany, did some calculations to find out if this might be so. They report their conclusions in a paper in the March 24 PHYSICAL REVIEW LETTERS.

Fractals, figures with fractional dimensions, have become an important topic in mathematics and science only in the last few years, but they have found so many applications in all branches of science that scientists are becoming accustomed to thinking in fractional dimensions. The notion of a fractal universe, which would have been a joke 10 years ago, is now a serious question.

To investigate the question Muller and Schafer chose two physical effects at extreme ends of the range of our perception, the Lamb shift in atomic hydrogen and the precession of planetary orbits. The Lamb shift is a subatomic effect; it happens to the electron inside a hydrogen atom. Planetary precession has the whole solar system for its range. So, from the atom to the solar system, are there any fractal effects?

The Lamb shift depends on electromagnetic forces; planetary precession depends on gravitation. Both kinds of force have similar mathematical descriptions. Particularly they both depend in the same way on the distance between bodies. Because the forces depend on the distance, any fractal quality in the three spacelike dimensions of the universe is going to affect them slightly. Both effects have been well researched experimentally; very precise numbers are known for both. Calculating what fractality might do and comparing that to the measured quantities, Muller and Schafer find that if they take the planetary precession as a criterion, the fractality of the universe has to be less than 1 part in 1 billion; using the Lamb shift, the fractality has to be less than 3.6 parts in 100 billion. They note also that in a work not yet published, C. Jarlskog and F.J. Yndurain of the CERN laboratory in Geneva, Switzerland, using the precession of orbits in binary stars, also find a limit of 1 part in 1 billion. Thus, if there is any fractality to the three spacelike dimensions, it has to be extremely small, almost imperceptible.

"[We] have shown that the dynamical symmetry associated with motion in [the relevant kind of force field] provides extremely stringent limits on any possible deviation of the number of dimensions from the integer value of 3, on both atomic and astronomical length scales," they conclude.