Faith in The Simple

Science has yet to form a "theory of everything," a precise explanation that by itself explains all the forces of nature. However, many believe that science is getting close to forming such a Grand Unified Theory, and it is beginning to take shape what this theory will resemble, even though its specific components have not yet been found. Among its attributes is that it will be simple in concept and "beautiful"; that is, it will be mathematically pleasing, as if "that's the way it logically should be."

Stephen Hawking, Lucasian Professor of Mathematics at Cambridge University and considered by many to be the most brilliant theoretical physicist since Einstein, claims that, "if we do discover a complete theory it should in time be understandable in broad principles by everyone, not just a few scientists" (Hawking, 175). There is also a belief that it will be beautiful. Michio Kaku, Professor of Theoretical Physics at the City College of the City University of New York, sees the equations of physics as the poems of nature: "They are short and are organized according to some principle, and the most beautiful of them convey the hidden symmetries of nature." (Kaku, 130). Physicist Richard Feynman believes that "you can recognize truth by its beauty and simplicity. When you get it right, it is obvious that it is right...The truth always turns out to be simpler than you thought." (Kaku, 130).

But what is the basis of this belief of the scientific community that nature is easy to understand and symmetrically beautiful? There are many reasons. For starters, if it were not easy to understand, people could not understand it. This is perhaps circular reasoning, stating that the only reason we understand what we do is because it is understandable. (This is similar to the anthropic principle, which states that the reason the universe seems to have just the right conditions for life is that if it didn't, we wouldn't be here to ask about it.) Science wants the world to be understandable; if it were not, we wouldn't know it, precisely because it would then not be understandable. But perhaps the most obvious reason is that of experience: overall, history has slowly guided science through a process of reducing multiple theories into a smaller number of more concise theories that not only explain more, but that are easier to understand. As time goes by, new theories are formed that better explain the universe around us, are simpler, and explain what before were explained by multiple theories. Indeed, one of the goals (if not the ultimate goal) of physics is to find a so-called Grand Unified Theory that, by itself, will explain anything and everything in the universe.

One of the first major advances in physical theories, and one of the most important, was the formation of the Newtonian physical laws. With the foundations laid by Isaac Newton in the seventeenth century, these laws eventually would, with simplicity, explain all of the known universe up to the late nineteenth century. A portion of these laws, Newton's laws of motion and gravity, summed up what one would expect from gravity acting on bodies of matter:

• Every object moves uniformly in a straight line unless acted on by a force.
• When a force does act, the object's velocity changes at a rate proportional to the force and inversely proportional to its mass.
• Between any two objects in the Universe there acts a gravitational force that is proportional to the product of their masses and inversely proportional to the square of their separation. (Thorne, 61).

Scientists could use these simple principles to predict orbits of planets, tides, and even learn the weight of the Earth. This theory is simple to understand. It is mathematically elegant. As Professor Evans has noted, the gravitational force is simple products of masses and inverse proportions of squares, not something complicated, such as inversely proportional to the 5/3 root of the separation times 2e times pi.

However beautiful and precise these Newtonian principles are, they lie on certain principles that are fundamentally incorrect. (This does not however contradict the "beauty and simplicity of nature" assumption, as will be seen later). They assume that objects move through an absolute space in absolute time, which is not the way the world is. However, the differences between the predictions and what actually exists are so minute that they are not relevant in most normal processes, such as the orbit of the moon or someone driving a car down Memorial. The discrepancies are so small in normal life that it was only later that technology increased to the point that measurements could be accurate enough to measure them, at velocities closer to the speed of light. Indeed, as pointed out by Professor Duncan, "rocket scientists" still use these "flawed" simple principles for everyday activities, because they produce results close enough to the corret answers that discrepancies do not matter.

In 1864, James Clerk Maxwell formulated a set of elegant electromagnetic laws. Using these laws, it was possible for one to deduce all electromagnetic phenomena such as behaviors of magnets, electric sparks, electric circuits, radio waves and light (Thorne, 62). These laws, if calculated in terms of electric and magnetic fields for an object at rest in absolute space, were simple and beautiful. However, if one attempted to use these laws for a person in motion, they became complex and "ugly," involving a complex pattern of magnetic field lines getting cut, healing, getting recut, and so forth. Some beauty could be brought back by claiming that magnetic field lines never end, but this would require, through a certain process of logical reasoning, that all moving objects get contracted along their direction of motion, which was contrary to Newtonian precepts. If these logical musing were to be followed, other conclusions concerning time were inescapable, but these conclusions were ignored by most, and it would take the genius of others to take them to their fullest extent, and create a more perfect, beautiful theory (Thorne, 66).

A clerk in the Swiss patent office solved all of these problems. Albert Einstein showed that the solution to the "ugliness" of Maxwell's theory in motion, one had to abandon the Newtonian idea of absolute time (Hawking, 20). Time was then relative; each person has his/her own personal time that advances independently of all others. Time and space were no longer separate entities, under this idea, but are different aspects of "space-time." Another aspect of these ideas of relativity stated that matter can be changed into energy and vice-versa. This concept can be stated simply and precisely in the famous equation e=mc². This new idea, while radical, was a) simple, b) straightforward, c) self-consistent in its relevant range (more on this later), and d) explained many principles that before had taken separate theories to explain.

As already noted, this simple idea did not make it imperative that one abandon the Newtonian idea of motion and Maxwell's equations for electromagnetism. Both of these are used in the normal "real world" for most calculations pertaining to the environment one normally sees. Although Einstein's theories invalidated them for certain areas outside the range in which humans operate, it actually combined them with the idea of a combined space-time. This simple concept allows one to derive the same results (inside the relevant range) as the Newtonian and Maxwellian principles. It combines them, reducing them to a single, simple theory that is more accurate.

Each of the preceding theories have a relevant range that is, the range of inputs for which it gives valid answers. For the Newtonian theory, it is seen that its relevant range is that of the visible world, the everyday happenings that one deals with. When object move very quickly (close to the speed of light) or gravitation gets intensified enormously (such as near neutron stars), Newtonian physics break down. Einstein's theories of relativity extended the relevant range of Newtonian physics by accurately predicting what would happen to objects in the instances mentioned earlier. Yet, the theory was still simple, and beautiful. However, even Einstein's theories have their limitations. In the domain of the very small, even below the atomic level, scientists must use other theories to tell what will happen to the seemingly infinitely smaller particles that have been found. The ideas governing the ultra-small are termed quantum theory. To summarize, quantum theory says that:

• Forces are created by the exchange of discrete packets of energy called quanta.
• Different forces are caused by the exchange of different quanta.
• One can never know simultaneously the velocity and position of a subatomic particle. (Kaku, 112-113).

Kip Thorne, the Feynman Professor of Theoretical Physics at the California Institute of Technology, has this to say of quantum theory, and of scientific theories in general:

Why do I expect convergence in terms of predictions? Because all the evidence we have points to it. Each set of laws has a larger domain of validity than the sets that preceded it: Newton's laws work throughout the domain of everyday life, but not in physicists' particle accelerators and not in exotic parts of the distant Universe, such as pulsars, quasars, and black holes; Einstein's general relativity laws work everywhere in our laboratories, and everywhere in the distant Universe, except deep inside black holes and in the big bang where the Universe was born; the laws of quantum gravity (which we do not yet understand at all well) may turn out to work absolutely everywhere (Thorne, 86).

Quantum theory in many respects yields strange results that defy common sense, but have time and again been tested and verified in the laboratory. One problem with quantum theory, however, is that it seems to go against the reductive, simple, beautiful qualifications of theories of nature that science, through experience, have come to expect. The more energy that is added in particle accelerators, and the more scientists smash atoms into smaller pieces, the more smaller particles are found, which are in many cases strange and complicated. Quantum theory seems to be saying that, instead of one simple, inclusive reason for matter, matter is instead made up of many kinds of unlike particles. These particles may in time be broken down to the point where nothing is left! This would mean that what one perceives as matter is nothing more than the interaction of different forces.

The four known forces are the electromagnetic force, the strong nuclear force, the weak nuclear force, and the gravitational force (Kaku, 13-15). These forces are very diverse, and many have attempted to combine them (even Einstein himself!) into one collective theory. All unification attempts have failed. However, through recent developments, hope seems to be in sight. Recently, new theories have been developed that may in time be the single theory that encompasses and explains all observable phenomena. This would again reiterate what experience has shown: that nature can be explained by simple, beautiful, self-consistent ideas.

In the constant effort to combine the four forces, the ideas of relativity, and the uncertainty provided by quantum mechanics, a new theory became popular that is still very popular today. This theory has many variations and is in no wise close to being completely established (or even testable, to a large extent), but it has indications of combining all theories about the universe by literally adding other dimensions. This theory, called superstring theory, claims that all the particles are simply vibrations of "strings" in other dimensions of space-time (Kaku, 153). Like different frequencies of a guitar string, these superstrings have certain patterns in their existence and interaction with one another that they give the impression of particles.

Superstring theory is not new; it has been around since the 1960's (Hawking, 160), and multidimensional models have been around for much longer. As scientific knowledge increases and theorizing evolves, the ability to use this idea and to refine it increases. Currently, many scientists believe that superstring theory may hold the answer to the combining of everything known. These superstrings, according to current thought, only produce stable results in a certain number of dimensions: namely, 10 or 26 (Hawking, 162). This is certainly not the usual four (three spatial dimensions, plus time) that humans are used to seeing. The other dimensions are unseen because they are curled up into a very small space, much like rolling a two-dimensional sheet of paper into a long tube to the point that it seems to have only one dimension, length.

While superstring theory has many aspects that are just beginning to be developed (the ones mentioned only being a very small part of the overall developments), it is nonetheless giving indications that a theory can be formed that can derive the results of quantum theory and the diverse forces by a conceptually simple model. This model, in higher dimensions, may make understanding of the universe much easier than is possible today. What one sees now is very likely a theory in the making; a theory that is, if not the "ultimate theory," then possibly something close. It is giving indications that the "theory of everything" may continue the process that has been constantly occurring in science, giving it the faith in a nature that can be understood in a simple, self-consistent, and elegant way.

Works Cited

• Hawking, Stephen W. A Brief History of Time. New York, N.Y.: Bantam Books, 1988
• Kaku, Michio. Hyperspace. New York, N.Y.: Oxford University Press, 1994
• Thorne, Kip S. Black Holes And Time Warps. New York, N.Y.: W. W. Norton & Company, 1994