String Theory for My Friends

I’m always delighted when friends make requests for specific PVBlogs. This morning at Starbucks Mark asked for a white paper on string theory. Now, I have the greatest respect for Mark for that magical day in 1955 when he went head-to-head against Jim Brown in a lacrosse match. Some don’t know that Brown was an All-American in lacrosse at Syracuse as well as football. He outweighed Mark by 40-50 pounds of muscle, but Mark made up for it by being … ummm…. slower. Mark is one brave guy. Anyway, in honor of that RPI versus Syracuse lacrosse match, here is a bit of string theory for Mark and the rest of the Starbuckers.

String was invented by the Egyptians back around 4000 B.C. as a thin, flexible version of rope which may be used to tie, bind, or hang other objects. String can be made from a variety of fibres including date palms, flax, grass, papyrus, leather, water reeds or animal hair. The use of the rope version pulled by thousands of workers allowed the Egyptians to move the heavy stones required to build their monuments. (ref. Wikipedia)

Ropes and strings can also be used as flogging device with widely different impact depending on length, weight, number of strands and the presence or absensce of knots. Thus aboard ships, a rope's end or starter was frequently used to administer the lightest discipline to sailors, while the fearsome cat o' nine tails was used for more severe punishment. Mark may have some experience with cats from his days in the navy.

The mathematics of strings began with Euclid who noticed that strings may form a variety of geometrical shapes. Here is a question for the reader: Given a length of string, how many squares may be constructed? How many rectangles?

A few centuries later, Georg Riemann, a student of Carl Gauss, noticed that a string laid on the surface of a sphere can no longer be formed into a perfect square. This seminal discovery led immediately to the invention of non-Euclidian differential geometry and the theory of complex manifolds utilizing the Riemann curvature tensor.

This was a very good thing because, when Einstein derived his theory of General Relativity, in 1915, he needed a mathematical formulation of curved spaces. Einstein rejected the Newtonian theory of gravitational forces believing instead that the Earth sucks. (Sorry…. just a little joke.) No, Einsten believed that matter and energy bend space into a spherical shape and that matter and energy in turn move along the surface of the sphere, like following the piece of string. John Wheeler described it by saying that “matter tells space-time how to curve, and space-time tells matter how to move.” So-long to straight line motion unless there is no mass around.

Once the field equations of General Relativity were in place, Einstein became aware of some disturbing features. He first realized that the presence of matter in the universe meant that a static universe is impossible; it would ultimately collapse. (That sucked!) This was a real philosophical problem for any scientist, even a radical like Einstein, who was raised with Aristotle’s model of an unchanging universe. Einstein was so disturbed by his collapsing universe solution that he concluded the equations needed another term to counteract the attractive force of gravity. He invented the “cosmological constant” term that acted like anti-gravity and allowed the universe to be permanently static.

Not long after, in 1922, the Russian Alexander Friedmann showed that Einstein’s equations also admitted a solution corresponding to an expanding universe and by 1927 Georges Lemaitre had worked out the details. Einstein rejected the solution as un-physical although mathematically correct. But only two years later Edwin Hubble published data showing that stars and galaxies are all receeding, leading to the obvious conclusion that sometime in the past the universe must have burst on the scene from a miniscule point. Lemaitre called it a cosmic egg; Fred Hoyle called it, dismissively, the “Big Bang.” Einstein figuratively kicked himself in the butt for insisting on the cosmological constant and a static universe.

Now what about that Big Bang? Physicists have concluded that at the instant after the bang, the universe must have been so dense and filled with energy to such a degree that gravity had quantum properties. Unfortunately a quantum theory of gravity does not exist. Enter string theory. Underlying the fundamental particles (quarks, etc), string theory assumes there are more fundamental entities having some properties of strings.

The basic strings are mighty small, with a length equal to the “Planck length” (about 10 to the negative 33-power centimeters). Like a violin string under tension, the quantum strings support standing waves, and the fundamental particles of matter are thought to correspond to different vibration frequencies. This is not such an unusual idea as it is related to the wave-particle duality of quantum physics. We do not “see” the stringiness in experiments because its dimension is so very small.

The mass-frequency relationship is easily derived. The Planck-Einstein photo-electric effect showed that energy is related to frequency by the simple relation E = hf, where h is Planck’s constant and f is the frequency. Add to this Einstein’s mass-energy relationship, E = mcc, and we obtain an equation that defines particle mass from the string frequency: m = hf/cc. For the electron, the wave frequency is about 10 to the 21-power cycles/sec, and the proton frequency is about 1840 times higher.

The basic idea is pretty simple, but the theory quickly becomes muy complex. Some of the fundamentals are unsettling (eg 10 dimensions of space) and some are contradictory (eg faster than light particles). But the major problem for string theory is that it has yet to make a testable prediction, and the current thinking is that the theory allows an astronomically large number of physical possibilities so it seems impossible to ever test it. Peter Woit has called the theory “Not Even Wrong,” the title of his recent book. Normally this situation would cause physicists to run for the exits, but string theorists seem to be a hardier lot, not easily frightened.

I’m skeptical.