String theory and the quest for unification
David Cross
Why is string theory so interesting? Interest in it has exploded over the last couple of years thanks to Brian Greene, the string theorist who appeared on the PBS program The Elegant Universe, and who wrote a book of the same name. But why is it important to physicists?
Introduction Before I answer that, let's take a step back. What is the quest of science in general, and of physics in particular? In a word, unification: to be able to describe a number of different things with one overarching framework or model. Chemistry's basic unifying principle is that all matter is made up of protons, neutrons, and electrons. Everything we see manifests as it does because of the rules governing how these constituents of matter interact with each other - more specifically, how electrons on atoms interact with electrons on other atoms.
Biology has several unifying principles, but the one most commonly known is the theory of evolution, which expresses, in one framework, how the large diversity of life-forms we see on this planet came to exist as we see them today. Thus, evolution forms a coherent description of many different things that we've seen happen. Evolution's success in explaining organic life is based on natural selection, which operates on anything that must reproduce - from human beings all the way down to viruses. Those species that can survive better are more likely to reproduce, which leads to an adaptation of the species to their environment - hence, evolution. So the common cold you get every year is the result of successful adaptation by those strains which had some survival advantage over the strains that your body was able to combat last year. Exactly the same process can be used to show how we humans are related to the most unprepossessing seaweed (given a few hundred million years, mind you).
In physics, the quest for unification is perhaps most keen, partly because it must deal with phenomena more fundamental than those which chemistry and biology address. As a result, many names in physics are associated with what we call "unified theories." Isaac Newton is the first unifier, although the one who most commonly comes to mind for physicists is James Clerk Maxwell because his equations showed that electricity and magnetism are two facets of the same thing. We then have, in a rough chronological order: Albert Einstein (1905, 1915); Erwin Schroedinger and Paul Dirac (1920s); and Sheldon Glashow, Steven Weinberg, and Abdus Salam (1960s). Today there are the string theorists - people like Edward Witten, Brian Greene, Michael Green, John Schwarz, and others.
The unifiers Why are these names remembered? What did these people actually do?
Isaac Newton's theory of gravitation explained the behaviour of the heavens and the Earth, which put forth a single framework to explain everything from what happens when you drop your keys on the floor to the way the moon orbits the Earth.
James Clerk Maxwell's four equations showed that electricity and magnetism are two aspects of the same thing, and further proved that light is electromagnetic in nature and follows the same equations. Again, diverse phenomena - everything from why a compass needle deflects in a lightning storm to the light bulbs we flick off and on every day - explained in one framework.
Albert Einstein showed that your keys dropping to the floor and the light from your pocket laser flickering across the wall behave according to one set of rules, known as "transformation laws." This is another example of unification - a consistent mathematical description of many diverse things we see, with one set of rules. Before Einstein, it was thought that two separate sets of transformation laws applied, one for the dropping of keys, and another for the light coming out of your laser pointer. This was special relativity. General relativity explains the behaviour of gravity and its effect on both matter and energy. This supersedes Newton's equations, which only describe gravity's effect on matter.
Erwin Schroedinger and Paul Dirac are two founders (along with others, such as Niels Bohr) of what we know as quantum mechanics. Dirac's contribution was to apply the laws of special relativity to quantum mechanics. In doing so, he was able to show that tiny particles behave in the same manner as large spaceships when nearing the speed of light - time slows down and they get heavier. Again, a unified framework came into being, describing all the weirdness of the smallest things we know of, with one equation (the Dirac Equation). Chemistry uses both the Schroedinger Equation and the Dirac Equation routinely. Without them, we would not understand many aspects of the behaviour of atoms and molecules. Subatomic physics depends on the Dirac Equation as well; without it we would not be able to properly explain the behaviour of any particle at high speed.
Sheldon Glashow, Steven Weinberg, and Abdus Salam did something that blows my mind. They were able to prove that the electromagnetic force - which underlies all of chemistry, light, and your fridge magnets - can behave just like the weak force, which is a different force that governs radioactive decay. So, if you have the right conditions, which can be reached in particle accelerators, we can prove that the "electroweak interaction" is real and not just a mathematical accident that happens to show that the same set of equations describes two forces. Now if that doesn't blow your mind, you're Mr. Spock.
Taking the next step Currently we're 300 years into the ongoing quest to describe the world in terms of more fundamental, far-reaching frameworks than has previously existed. Each round of unification brings more of the universe under the purview of a common set of equations and laws to describe phenomena we see. You can follow it through the timeline in the preceding sections (although some names that should be included have been skipped).
Four forces into one? There are currently three theories that describe the whole of the universe: general relativity for gravity, quantum electrodynamics for the electroweak interaction, and quantum chromodynamics for the strong interaction. Until now, the biggest obstacle has been to show how to make gravity (general relativity) work with quantum mechanics (strong, weak, and electromagnetic forces). This problem has been bedeviling physicists for years, and it would be the single greatest triumph for physicists in our century to be able to conclusively show that a single set of equations describes the four known forces.
The milestone string theorists are hoping to reach is to describe four forces with the same set of equations: the strong (which binds protons and neutrons together in atomic nuclei), the gravitational (which keeps planets orbiting the sun), the electromagnetic (which keeps your fridge magnet attached to your fridge and current flowing through your light bulb), and the weak (radioactive decay). Some theorists however, refer to three forces, because the electromagnetic and weak forces are considered one force, called the electroweak.
Particle exchange and spacetime warps Quantum mechanics is based on the notion that all matter particles "sense" each other through the exchange of other particles. For example, the neutrino, a product of radioactive decay, senses protons by exchanging W particles with them, which may change a proton back into a neutron. This is the weak interaction. Protons and neutrons sense each other via exchange particles (called pi mesons, or pions) with each other in the nucleus. This is a strong interaction. Electrons sense and repel each other inside atoms and between molecules by exchanging photons. This is the electromagnetic interaction.
In theory, all matter also exchanges gravitons . . . but nobody has seen a graviton. General relativity makes no provision for gravitons, and expresses gravity as the warping of space. This is a very different conceptual framework, which treats matter and spacetime as mutually interacting, so that the movement of matter through space is a result of other matter nearby that is warping space. As a result, general relativity and quantum mechanics cannot be successfully merged, partly because they start with different assumptions about the behaviour of the universe. General relativity assumes that when someone observes something, the observer doesn't influence the observation. Quantum mechanics removes this assumption, but retains an assumption removed by general relativity - that space and time exist independently of matter and energy.
It seems to make sense to take general relativity and quantum mechanics, throw out the "wrong assumption" in each, and merge the two. But doing this is a bit like rebuilding SFU just to change the inside walls of the classrooms. A more sensible approach would be to knock out the drywall. Yet there are people who are going back to square one and trying to build a new theory of matter, energy, space, and time that will give us the same results that quantum mechanics and general relativity do, separately, but with the same set of equations.
There are good reasons for keeping the old theories, and modifying something else that's wrong instead (which is discussed below) - in a sense, changing just the drywall. In doing so, the assumptions to be changed are no less profound, but don't require throwing out all the mathematics that have been developed that successfully describe the universe as we know it. So, string theory does it, but how? String theory is one attempt to get around the problem of trying to unify general relativity and quantum mechanics by changing an assumption made in quantum mechanics - that certain particles are "pointlike," meaning they are the smallest particle (the electron and quark are assumed to be pointlike). String theory claims that all particles - everything from electrons to exotic particles like the top quark - are made up of something smaller, something which may possibly be the essence of everything. These "essence" particles would be "strings." The energy of the string (its frequency of vibration, or "note") is manifested in which particle we can detect. String theory's claim thus allows quantum mechanics to incorporate gravity and do so successfully. String theory is more appealing than loop quantum gravity because it arises out of the familiar "language" of quantum mechanics.
String theory and loop quantum gravity still have problems, because meshing two very conceptually different models, as outlined above, requires questioning old assumptions and ideas. It also requires a lot of mathematics, which is troublesome since the two theories often require computational power to come up with even approximate solutions because of their complexity.
Some people may point out that string theory may be mathematically beautiful but practically useless. In this respect, Sheldon Glashow may be the Albert Einstein of our time. Just as Einstein repeatedly questioned quantum mechanics ("God does not play dice with the universe"), forcing quantum theorists to justify and explain the model more rigorously, Glashow has pointed out defects in string theory's models, such as how there is not much experimental evidence, if at all, for the phenomena string theory suggests exist. For example, string theory proposes that there are new, heavy particles that current particle accelerators just don't have the energy to produce. It proposes 11 dimensions in our universe, seven of which we can't see. It even proposes that there are multiple universes.
In his objections and criticisms, Glashow finds good company with the basic principle of science: If you can't experimentally test something, it has no practical use. Also, the first time an experiment contradicts the theory, the theory has to be discarded or modified. Aristotle's theory that heavier things fall faster than light things was contradicted when Galileo rolled wooden and steel balls down inclines. The steel ball, being denser and heavier, should have rolled down the incline faster than the wooden one. It didn't. 2000-plus years and Aristotle's theory of gravitation went by the wayside as soon as that experiment was done.
Science, generally, is famous for theories that had to be junked after experiments contradicted their conclusions - the idea that heat was a real "fluid," for example, or the phlogiston theory of combustion, which suggested that things burned because of a mysterious liquid or gas inside them. Junked.
Conclusion So why string theory, then? Because there are things in the universe that exist or did exist that are very heavy, thus general relativity applies, but these things are also very compact and small, so quantum mechanics applies. The most famous example of one of these extremely heavy yet extremely small things is the black hole, which is so dense that once something enters the black hole itself, it cannot leave because the gravitational pull is so high. Both general relativity and quantum mechanics apply to the problem of asking what goes on inside a black hole, but you can't use two mutually incompatible theories to describe the same thing. But if string theory is wrong, then what it says happens inside a black hole may very well be nonsense.
Or take the Big Bang - the beginning of our universe. It was both very dense, and very heavy, yet very concentrated so that all the mass of our universe was in a very tiny space. Again, you need general relativity and quantum mechanics to get a complete picture of what went on, but you can't apply the two mutually incompatible theories here either. String theory is one way to try and get an answer - if it turns out to be useful.
String theory may be a dead end that's wasted a lot of time. But personally, I am tantalised by the possibility that two mutually incompatible theories - general relativity and quantum mechanics - can be made to work together with the same set of equations. And so I hope that the string theorists do prove right, after all, and the quest for unification will have taken another step forward.