From This Angle, Geometry Rules the Universe
Mother Nature wears geometry on her sleeve. She spins the stars around in spirals, molds planets into perfect spheres, sends water undulating downstream in sine waves, pulls projectiles into neat parabolas and holds together the hydrogen and oxygen atoms in water molecules at precisely 105 degrees.
Geometry even grows on trees: Just look at any flower or leaf.
In fact, nature’s thing for geometry has gotten so out of hand, some scientists would say, that she has kissed fields such as physics goodbye for good. Forget forces, particles, fields, gravity, matter, motion--even space and time. Physics has become a chapter in a geometry book.
Today, many physicists believe that everything in the universe--forces, fields, particles, space, time--are merely manifestations of the twisted geometry of 11 dimensions: four make up the extended landscape of space and time; seven curl into origami-like structures too small to imagine, much less perceive.
This set of ideas goes under the name of “string theory.” But the name is misleading. These are not strings like pieces of twine. They are not made of anything. They are pure geometry.
String theory seems bizarre, but it is really just the latest in a long line of discoveries that have transformed physics into geometry, matter into shape.
In fact, the idea that geometry rules goes back--like everything else--to the ancient Greek philosophers. Plato’s academy in Athens did not admit those who did not know their geometry. “God is a geometer,” Plato pronounced.
Aristotle insisted that the planets moved in circles because circles were forms created by the gods. Atoms, to those who believed in them, conferred properties depending mainly on their shape. Fire atoms were jagged, so fire hurt. Water atoms were smooth, so water flowed. Earth atoms were cubical, so earth was solid.
Still, in the Greek universe, at least there was something--that is, matter--to take geometrical form. Geometry didn’t rule the universe in its own right.
The real corner turned when Michael Faraday introduced the notion of fields of force in the mid-19th century. Like political spheres of influence, electric and magnetic force fields pervade all space, directing the behavior of everything in their grasp. Iron filings line up around a magnet not because they are being pulled or pushed, but because of a geometrical distortion of space. They follow the curved paths of the magnetic field the way Dorothy followed the curling yellow brick road to Oz.
Before you knew it, physicists had turned everything into fields: Even so-called “particles” like electrons are merely kinks in the electromagnetic field.
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In the early years of this century, Albert Einstein added yet another geometrical dimension to our universe. A new dimension of time, he showed, wove together with the three familiar dimensions of space to create four-dimensional space-time. The curving and warping of space-time are behind the force we feel as gravity.
How can geometry be perceived as a force?
Imagine you’re a tiny ant living on a paved street covered with potholes. You walk in and out of the potholes unaware of their existence--just as people walk on the round earth without perceiving its curvature. The geometry of the landscape you live in is simply too huge, relative to little you, to be seen as anything but flat.
Even if you couldn’t perceive the pothole, however, you would notice that trucks and cars were coming to a grinding halt in the same spot of street. You might conclude that some mysterious kind of “force” was pulling them in--perhaps some exotic rubber-attracting magnet.
In the same way, the “force” we feel as gravity is really just the geometry of space.
“It almost appears that the physics has been absorbed into the geometry,” wrote Sir Arthur Eddington, the astronomer who provided many popular explanations of Einstein’s theories. “We did not consciously set out to construct a geometrical theory of the world; we were seeking physical reality by approved methods, and this is what happened.”
The idea of ascribing forces to the geometry of unseen extra dimensions caught on. In 1919, Polish mathematician Theodor Kaluza proposed that electromagnetism was due to the warping of an unseen fifth dimension, just as gravity is due to the unseen warping of a fourth. Then Swedish mathematician Oskar Klein suggested that this extra dimension might be coiled into tiny, subatomic-scale tubes.
String theory expanded Kaluza and Klein’s extra curled-up dimensions into wild new territory. Like Einstein’s space-time, the higher-dimensional landscapes of string theory circle into strange, convoluted shapes, forming holes, knots and handles. And just as the shape of a flute or violin determines the sounds it can make, the geometry of the extra dimensions determines how strings can interact to produce particles. In other words, the geometry determines the ingredients available to make our universe.
Not only do we live in a shapely universe; shape, it seems, is all there is.
“There is still a difference between something and nothing,” as longtime Scientific American columnist Martin Gardner sums it up. “But it is purely geometrical, and there is nothing behind the geometry.”
