IN THIS column, we usually write about science and science fiction as if they are two different things. But actually the advancement of science requires science fiction—of a sort. In fact, Pat would go so far as to say that science fiction—that is, the fiction that scientists make up—is at the heart of science. To move science forward, scientists make stuff up.

To show you how this works, we're going to consider the history of atoms (a bit of science fiction that began with the Greeks). Then we'll compare the development of atomic theory to current work on string theory (a contemporary bit of science fiction sure to stretch anyone's imagination).

The atoms of atomic theory and the strings of string theory have one very important characteristic in common. Both are too small to see. Way too small. Back in 1900, when most scientists accepted that atomic theory provided a powerful way to understand chemical reactions, a lot of them also had a fundamental problem with the theory. Technology at the time had no way to make an image of these tiny, theoretical particles.

Today, that's true of the theoretical strings of string theory and its big brother superstring theory, which is sometimes known as the Theory of Everything. (And Pat would like to point out how incredibly excellent and over-the-top that name is.) The aim of string theory is to provide a framework for all known particles and forces. No sense setting the bar too low, is there?

As a scientist and a science fiction writer, Pat appreciates research scientists having strange ideas about things that people can't see. We writers of speculative fiction do it all the time, making stuff up about aliens and ghosts and the like. It's nice to have some (more or less) respectable company.
 

Feynman manages to pack a lot into his brief statement: Every thing is made of atoms. Atoms are always moving. And atoms push and pull on each other. It took scientists around 2500 years to come to those three, fundamental ideas.

An ancient Greek named Democritus first wrote down the notion that the world might be made of a small number of fundamental particles too tiny to see. Since Democritus's hypothetical particles were indivisible, he named them atomos, the Greek word for indivisible. Since the Greeks did not do quantitative experiments to test their atomic ideas, Democritus's atomic ideas remained just musings.

More than 2000 years after Democritus proposed atoms, scientists began taking baby steps to refine his idea. They proceeded in the usual way of scientists: they did experiments, and then made up stories about why those experiments had the results they did.
 

Boyle figured out that the harder you squeeze a volume of air, the smaller it gets and the more it pushes back. Or, to state that more precisely: at a given temperature, the volume of air was inversely proportional to pressure. (For the mathematically inclined, PV=K or pressure (P) multiplied by volume (V) equals a constant (K), an equation known as Boyle's Law.)

Paul often demonstrates this by taking an empty syringe without a needle attached, pulling back the plunger to fill the syringe with air, and then closing off the opening. When he pushes twice as hard on the plunger of the syringe, the volume of air is squashed to half of its initial value.

In Boyle's time, Isaac Newton came up with a model of gases to explain Boyle's law. Newton hypothesized that a gas was made up of compressible balls that touched each other. When squeezed, the stationary balls got smaller. (An aside here: Newton assumed that these fluffy balls obeyed Hooke's law of springs, which states that the change in length of a spring is proportional to the force pushing on the spring. In addition, Hooke was Boyle's assistant and actually did the measurements that Boyle used to formulate his law.) Newton's explanation advanced the notion of atoms, but it was just a start. More experiments had to be done.

More than one hundred years after Boyle, in 1802, French scientist Joseph Gay-Lussac published measurements showing that the volume of a gas was proportional to temperature. Gay-Lussac gave credit to unpublished work by Jacques Charles, and so this law became known as Charles's Law.

Paul demonstrates this law by cooling balloons full of air and watching them expand as they warm up. He particularly likes cooling helium balloons in liquid nitrogen. The balloons shrink to less than a third of their original volume and sink to the floor when removed from their chilling bath. As the balloons warm and expand they slowly rise. Paul has found that such demonstrations attract children and scientists alike.
 

The answer to that question came from the work of Amedeo Avogadro. In 1811, Avogadro published the idea that a given volume of gas at a specific temperature always contained the same number of molecules—no matter what gas it was. Being the astute reader that you are, we're sure you noticed that Avogadro talked about molecules, not atoms. The idea of clusters of atoms had been around for a hundred years or so, the notion being that atoms clustered because of chemical affinity. The word molecule had been around since the late 1700s, but it was used to talk about tiny particles, not specifically clusters of atoms.

Avogadro was the first to use the word molecule in the modern scientific sense and the first to suggest that atoms alone and molecules made of atoms bound together behave in similar ways. He was also the first to suggest that molecules could be made of two similar atoms: he thought hydrogen gas and oxygen gas were made up of molecules containing two identical atoms each.

Avogadro's amazing idea was that this law applied to all gases. It didn't matter whether you had hydrogen or uranium hexafluoride gas, the number of molecules in a given volume would be the same as long as the gas was at what we now call standard temperature and pressure.

Avogadro's story was initially ignored, for the most part. He was a modest guy, working alone. Dalton and Gay-Lussac were much bigger names in the world of natural philosophy. And the story that Avogadro was making up clashed with the story that Dalton was telling. Dalton was convinced that chemical reactions occurred only when two unlike elements came together—and he insisted that atoms of the same kind could not combine to make a molecule.

Finally, in 1860, Italian scientist Stanislao Cannizarro presented Avogadro's idea at the Karlsruhe Conference (the first-ever international scientific conference) and the implications for chemistry became clear. With the realization that equal volumes of gas contained equal numbers of particles (atoms or molecules), chemists could figure out equations for chemical reactions. If hydrogen and oxygen were diatomic gases (H₂ and O₂), they could react together and make water (H₂O). According to Avogadro's hypothesis, two volumes of hydrogen would completely combine with one volume of oxygen to create two volumes of water vapor. So the observation that 2 + 1 = 2 actually made sense.

Being unifying types, scientists put together all of these laws to create what they called the ideal gas law, which shows that the volume of a gas changes with the number of atoms or molecules as long as the temperature and pressure are constant. (For those of you who insist on seeing the math, the equation is PV=nkT where P is pressure, V is volume, T is temperature, and n is the number of atoms. The term k is Boltzman's constant.) It doesn't matter whether you have a gas composed of atoms or one composed of molecules. This law applies to all ideal gases. Paul says this equation is like the ring in Tolkien's Lord of the Rings—one equation to bind them all!
 

To get an idea of the size disparity, consider ocean waves with a wavelength of ten meters rolling past and hitting the side of a cylindrical lighthouse with a diameter of twenty meters. The waves will bounce off the lighthouse, making circular waves. Looking at these reflected waves, you could find the shape of the lighthouse. Now suppose those same ocean waves crashed into a stick just one centimeter in diameter. Any ripples bouncing off the stick are lost in the ocean wave, useless for revealing anything about the stick. Seeing an atom with light waves was hopeless.

So those scientists in 1900 were making up stories (logically consistent, reasonable stories, but stories nevertheless) about stuff no one had ever seen. As a science fiction writer, Pat notes that this sounds very familiar.
 

If you have a laser pointer, equipment not available back in Brown's day, you can also see Brownian motion by shining the laser light into a dilute solution of milk and looking at the scattered laser light on a white card after the light passes through the milk. The bright central dot of laser light will be surrounded by twinkling dots of light. These twinkling dots are produced by the interference pattern of all the light scattered by the fat globules in the milk. The pattern changes because the fat globules are in constant motion as they are bombarded with collisions with invisible particles. Those invisible particles are (according to the story of atomic theory) molecules of water in the milk.

For decades, scientists sought to analyze Brownian motion by trying to measure the changes in velocity of the particles as they jittered. But it's tough to measure the velocity of a particle jittering this way and that. In 1905, Albert Einstein made the critical mathematical breakthrough. Rather than measuring velocity, he looked at the position of the particles over time. Position was much easier to measure than velocity.

Einstein analyzed position versus time as a three-dimensional random walk. The random walk is sometimes called a drunkard's walk. In two dimensions, picture a staggering drunk who takes a step in one direction, then spins randomly about and takes another step in a new direction. Sometimes he retraces his steps. Particles in Brownian motion behave just this way.

Jean Perrin applied Einstein's ideas and did the experimental work to actually measure the random walk of particles in Brownian motion. By analyzing his experiments, the size of atoms could be calculated. (For this Perrin received the Nobel Prize.) Jean Perrin's work (based on Einstein's math) showed atoms to be about 10-to-the-negative-10th-power meters across or one ten billionth of a meter across. You would have to line up a million atoms to have them stretch across the diameter of a human hair.

Even though no one could "see" atoms, visible effects produced by their existence were enough to confirm that atoms truly existed. After 2400 years of experiments, the atomic theory was well established.
 

We don't have space to take you through the experiments that showed this (though Pat can't resist mentioning that the story involves the "plum pudding model" of the atom, her favorite theory name ever). But much more experimenting took us to where we are today, with a zoo of subatomic particles ranging from the familiar electrons, protons, and neutrons to the more exotic quarks (named from a quote in Finnegans Wake—"Three quarks for Muster Mark." It's an apt name since protons and neutrons are made from three quarks each.)

The current best model for all these particles and their interactions is called the Standard Model, quite a boring name.
 

Today, string theory is roughly where atomic theory was in 1900. Like atoms in 1900, strings are too small to see with current tools. And so far, no one has found the equivalent of Brownian motion for strings.

First, the question we know you are asking: what is string theory? We'll give you the Cliff's Notes answer and then get on to the topic Paul really wants to talk about: how big are those strings? Hang on—this will get weird pretty quick. But you're a science fiction reader so you're used to that.

When someone says "particle," most of us think of something more or less solid, like a marble or a crumb or a grain of sand. Put that image of a particle out of your mind. Try thinking of a particle as a musical tone, and while you are at it, think of a musical tone as a vibration (which it is).

In string theory, particles such as electrons and quarks are made of strings—very tiny loops that vibrate in patterns like the harmonic vibrations of a guitar string. In this case, the guitar string is wrapped into a circle and yet still somehow maintains a tension that lets it vibrate.

When the string vibrates in different patterns, you get different particles that are associated with physical forces: photons to carry the electromagnetic force, gluons for the strong nuclear force and even gravitons for the gravity force. In an extension of string theory called superstring theory, vibrating loops can model particles like electrons.

String theory has the potential to simplify our view of the subatomic particle zoo. To describe all the known particles and the forces between them in the Standard Model, a physicist needs to define twenty-five different values—such as the mass of each particle, plus terms for the strength of the strong and weak nuclear forces. Starting with a smaller number of variables (perhaps even just one), string theorists hope to produce descriptions of all the particles and forces we know. The optimists hope to predict the values for new yet undiscovered particles (such as the Higgs boson or the particles which make up dark matter, but that is grist for another couple of columns).

The Standard Model employs quantum mechanics to describe forces other than gravity, while gravity is described by general relativity. So we have two different theories that have never been found to be wrong in predicting the results of experiments: quantum mechanics, which describes the behavior of particles and objects at the smallest scales, and general relativity, which describes the behavior of the large scale universe as well as regions with high gravitational fields such as black holes. The two theories apply in regions of space and time with tremendously different scales. But they cannot be made to work together to create (for example) a theory of quantum gravity. String theory seeks to bring together our descriptions of the large and small under one theoretical roof. It seeks to join gravity into the mathematical framework that currently describes the other forces of nature: electromagnetism, plus weak and strong nuclear forces.
 

To find the size of a string, scientists need to find the scale at which both quantum mechanics and general relativity apply. To do this, they must consider the size of a quantum black hole. Normal black holes have the mass of a large star or of many thousands of stars, and form by gravitational collapse. They are larger across than a small city. The gravity of a black hole is so great that even light cannot escape across the surface of the black hole, a surface known as the event horizon. (By the way, Paul chuckles at the thought of a black hole of any kind being "normal.")

Quantum black holes are low-mass black holes. Such black holes have not yet been observed, but theoretically could have formed during the Big Bang. To make the gravity of the low-mass black hole strong enough to stop light, the black hole must be extremely tiny.

In quantum mechanics, every particle has a wavelike nature, and the wavelength of the particle depends on its momentum. (And by the way, everything can be considered as a particle—even you. The particle that is you has a wavelength.) A black hole has a wavelength. A quantum black hole would be one in which the radius (of its event horizon) is about the same size as its quantum mechanical wavelength. And that radius (which is equal to the wavelength) would be an estimate for the size of a string.

If you just want to know how small strings are, you can skip the next paragraph. If you want to know how scientists have figured out the answer and you are not afraid of equations, plunge ahead.

So here's the math. The radius of a black hole is proportional to its mass (R = 2GM/c2 where R is the radius, G is the universal gravitational constant, M is the mass, and c is the speed of light.) The wavelength is inversely proportional to its mass (L = h/Mc where L is the wavelength, M is the mass, h is Planck's constant, and c is the speed of light). These equations can be solved to find the mass of a black hole with a radius equal to its wavelength. (We'll do the calculation to within an order of magnitude so we can ignore factors of 2 or pi (π).) The quantum black hole is found to have a mass of 10^-8 Kg or 10 micrograms. If you were to take a strand of hair that's 0.1 mm in diameter and snip off a piece that was as long as one diameter, it would have a mass of about 10 micrograms. If this piece of hair were compressed to 10^-35 m in diameter, it would become a black hole with a wavelength of 10^-35 m. (If you actually want to do the math, Google can help. Just type in "what is G/c2" and "what is h/c," then use these values and plug in a mass of 10^-8 Kg. You'll be within an order of magnitude of the answer.)

These calculations show that the length scale at which both gravity and quantum mechanics are important is 10^-35 m. This is an estimate for the size of the loops of string in string theory, the string loops that encircle and bind quantum mechanics and general relativity. This length scale is called the Planck length. The Planck length is 1.6 * 10^-35 m.

To appreciate how small that is, consider taking a jump in size from a meter down 100,000 times smaller (10^-5m). This gets you to a size smaller than the diameter of a human hair. Jump down another 100,000 times (to 10^-10 m) and you get the diameter of an atom. Another 100,000 (to 10^-15 m) jump takes you to the diameter of a proton. Now, having taken just three jumps to go from a meter down to a proton, you have to take four more jumps this size to get down to the size of a loop of string (to 10^-35m). Thus our initial estimate for the size of a string is 1020 times or a hundred billion billion times smaller than the size of a proton, which is a whopping 10^-15 m in diameter. So now we are faced with the same problem as the scientists working on atomic theory back in 1900. A string is far too small to see with any tool we now have or can even foresee in the near future.

Like the proponents of atomic theory in the 1900s, we can hope to spot observable side effects of strings. The hunt is on for the string theory equivalent of Brownian motion. But physicists don't yet have all the tools they need to search for evidence of strings. To probe for the effects of strings would require a particle accelerator 1014 times more energetic than the largest current accelerator, the large hadron collider. Among the particles produced by the high energy collisions in such a collider, physicists would look for particles that are not predicted by the Standard Model—but do fit into string theory.

Today—some 2500 years since Democritus first made up a story about indivisible particles called atomos, we can make images of atoms using electron microscopes and scanning tunneling microscopes. These tools use the wavelengths of electrons and atoms, which can be made as small as atoms to create stunning images.

In the distant future (a place that you, as a science fiction reader, are no doubt comfortable), after scientists and science fiction writers have told many stories, a currently unimaginable technology may let us make an image of strings or superstrings or whatever story comes to take their place.

We hope it will take less than 2500 years.