A Preliminary Contemplation
on the True Nature of "Theory"
by Tony Rothman and George Sudarshan
from their 1998 book
Doubt and Certainty

It is said that on witnessing Academy disagreements, the Theban Sphinx became so despondent that nothing seemed to be known with certainty that she hurled herself off a cliff and perished. In other versions of the story, she became so incensed at having been subjected to technical disputes that she found the nearest physicist at the Academy café and ate him.

That would be a sensible reaction. The topics debated at the Academy are far removed from daily life. They are ... academic. One might reasonably put aside such luxuries and devote oneself to caring for the sick and the homeless. However, in encountering an Academy physicist today, people do not tell him to join the Peace Corps; they demand his views on UFOs and alien abductions. These interrogations take place with alarming frequency, alarming enough that you have almost certainly carried out such an ambush yourself. The ensuing arguments, while not profound, are predictable.

In fact, your first Academy dispute undoubtedly began when, baffled by the squabble before you, you innocently remarked, "I have a theory that the government is hiding aliens in Area 51," and were met with incomprehension.

The jaw of the cornered academician dropped, not only at the idea of UFOs in Area 51, but at the ill-considered use of the word "theory." On the streets, people speak loosely; when you proclaimed, "I have a theory that the government is hiding aliens in Area 51," you almost certainly meant no more than you had an idea or, being conspiracy minded, you held a deep suspicion. Once aliens were discovered in Area 51 most people would shrug, "There are aliens in Area 51" and no longer refer to it as a theory. Trial lawyers, on television, declare, "That is a very nice theory, but what does it have to do with the facts?" The everyday usage of "theory" is for an idea whose outcome is as yet undetermined, a conjecture, or for an idea contrary to evidence.

But scientists use the word in exactly the opposite sense. On Academy grounds stands a sacred temple consecrated to theories. Inscribed on the altarpiece is a description of "theory": it refers only to a collection of hypotheses and predictions that is amenable to experimental test, preferably one that has been successfully tested. It has everything to do with the facts. Any physicist will tell you that Einstein's theory of relativity does not refer to some arbitrary conjectures Einstein dreamed up while smoking his pipe, which you are at liberty to reject as it pleases you. It refers to a complete mathematical construct that says some things happen in nature and other things don't. The most famous prediction of Einstein's theory is that no material object may attain the speed of light. This is not an assumption of the theory but an outcome of the theory; it has been tested perhaps millions of times and has never been found to be violated. Neither has any other prediction of relativity.

For these reasons your interlocutor, once having recovered, merely shrugged off your claim that "the government is harboring aliens in Area 51"; it does not amount to a substantial theory. If you could prove it, you would have succeeded in establishing only a single fact (an interesting fact, one that might result in presidential action, but one with little predictive power; and one of the hallmarks of a theory is its power to predict the outcome of experiments or further observations). If you could not prove it, you would undoubtedly find an excuse to explain your failure, such as declaring that the government is holding the aliens in another dimension. Of course, there is no way to test such an assertion, and so to a traditional scientist it does not rate as a theory.

Scientists are highly discriminatory in this area. The creationist contention that the Earth was created in 4004 B.C. -- or thirty seconds ago -- with all fossil records and memories intact is also not susceptible to any experimental test. If all dating methods indicate that fossils are billions of years old, then as far as science is concerned, they are billions of years old. Science deals only with appearances.

These points are basic ones, but lack of their appreciation results in a deep misunderstanding between scientists and nonscientists. Your academic interlocutor may have suggested you commit to memory the Aphorism: "Zapomnyat" means to remember in Russian, but "zapomniec" means to forget in Polish.

The Transient Nature of All Things; the Preliminary Contemplation Continued

In many fairy tales the hero reaches a fork in the road at which stands a stone bearing the inscription "If you go to the right you will die by one means, if you go to the left you will die by another means, and if you go straight ahead you will die all the same." Such fairy tales are usually not read to small children at bedtime. However, a similar situation arose in the above argument. While being berated by the physicist for your views on theories, several objections to his line of thought came to mind. Depending on which of these objections you raised, the debate probably went along one of two paths and you died all the same.

You might have protested that scientists have merely defined "theory" to their own terms. Other types of theories exist that may not yield to experimental test, such as mystical experiences, ESP or occult phenomena. One is at liberty, of course, to define "theory" any way one likes. However, if one is going to try to prove ESP by experiment, it is unfair to term it a science, then resort to nontestable explanations when the experiment fails ("The subject was experiencing bad vibrations today and was unreceptive"). By the same token, if one is going to term creationism a "science" it behooves the practitioners to accept the scientific definition of theory. Otherwise, they are merely talking about something else. Mystical experiences, depending on what one means, offer some room for debate, which the authors are agitating to begin below.

A more interesting question along the same path is whether science itself has abandoned the traditional experimental basis for theories. Many scientists hold the opinion that the newest theories (in particular the highly publicized "string theories") lack any possibility of experimental verification and have effectively become metaphysics or religion. We find a genuine issue here, which the academicians will take up in detail [later in the book].

Along the same path lies the question whether history (or even economics) can be considered a science. When a scientist requires that a theory be experimentally testable, he or she implicitly demands that a result be reproducible, which requires many experiments. History, by definition, deals with events that have occurred only once. Politicians frequently argue that "massive nuclear deterrence prevented a third world war." The statement certainly has a peculiar ring to it. The event (the absence of WWIII) is unique. The experiment cannot be reproduced. It is therefore unclear whether one can assign definite causes to the event, in particular to an event that never took place.

Conceptual difficulties arising from unique events are rampant in cosmology, the branch of physics that deals with the origin of the entire universe. If "universe" truly means "everything" this is an event that can have taken place only once. Yet cosmologists frequently make such statements as, "the odds of the universe being created in a completely uniform manner are infinitely remote." If the universe was created only once, can any meaning be attached to such a statement?

The two directors of the Academy Division of Sports and Recreations schedule the question, If history is not a science, is cosmology a science? for the Ninth Debates.

Short Graphic Rule

At the fatal fork in the path, you may have resolved to experience death in a more traditional fashion and remarked, "All scientific theories are overturned sooner or later." Raising this objection during a scientific debate is obligatory. During an "Aliens in Area 51" debate, the moment generally comes when one or more physicist-academicians vetoes the idea of UFOs on the grounds that, according to Einstein, nothing can travel faster than the speed of light. The time required for a UFO to reach Earth from the nearest star would be prohibitively long (over 100,000 years from Alpha Centauri at the velocity of the space shuttle) for UFOs to zip back and forth, transporting abductees to home base for analysis.

During the debate, such a remark may well have elicited your reply that Newtonian physics which describes the motion of objects -- was thought to be correct for three hundred years until it was supplanted by relativity and by quantum mechanics. Why should anyone believe relativity to be correct? At this juncture Academy visitors cite Star Trek and warp drives, at which the physicist pulls his hair, if he has any.

Recovering his composure, he will, with a 97 percent probability, answer that the prohibition of faster-than-light travel is a law of nature, and it cannot be violated. Here, another essential term has been introduced and the discussion of theory becomes intertwined with an argument over laws and principles. But suddenly the carillon in the Academy tower begins to play. Like most visitors, you glance at your watch, struck by how many hours have already trickled away since you passed through the Academy's portals. You also realize you are coming down with a headache and request directions to the nearest analgesic vending machine. They are located on every column, and after taking two aspirin, you return to the debate, fortified.

The Metaphysics of Laws and Principles Is Briefly Described

The opening deliberations have reminded all concerned that the terms "laws" and "principles" are impossible to avoid in any scientific discussion. This was not always true. The concept that the universe should operate lawfully is a comparatively recent development, having originated at the time of Kepler, Galileo and Newton. As we have mentioned, in China the concept does not seem to have taken root at all before modern times, the Chinese words for law, li and fa, having been applied exclusively to human affairs.

The world of contemporary Western scientists could not be farther from the world of the ancient Chinese. The scientists' world is rigidly lawful. A handful of laws and principles provides the very foundation for a scientist's outlook and, according to textbooks, on the same laws and principles scientists build their theories. The crucial assumption of special relativity, for example, is that the speed of light is constant to all observers, 300,000 kilometers per second. On the basis of this postulate, Einstein showed that the mass of any object increases with speed until it actually becomes infinite at the speed of light; and the closer the speed gets to light-speed, the more energy it takes to accelerate the object. For this reason, no material object can reach light-speed, much less travel faster; to push it above the speed limit would require an infinite amount of energy.

Each time particle physicists perform an experiment in their accelerators, they verify the correctness of Einstein's predictions. If Newtonian physics were true and Einsteinian physics false, the Superconducting Supercollider, the enormous accelerator of 85 kilometers' circumference that was never built in Texas, could have been built inside a basement and for several thousand dollars instead of ten billion.

If you are in an intransigent mood, you might insist, "Einstein will yet be proven wrong, just as Newton was." Warp drives do not accelerate starships faster than the speed of light; they somehow bypass it altogether, perhaps by creating wormholes through spacetime. It is true that one cannot prove a law of nature in the same way that one proves a mathematical theorem. Traditionally, one can do only one of two things: perform experiments until you are convinced that there are no exceptions to the rule (or until all the opponents of the theory have died off). This is the experimentalist approach. The other is to show that one theory is logically connected to another theory that you already believe. This is the reductionist approach.

It is true that all theories have holes in them. Newtonian mechanics is applicable only to objects traveling at velocities small compared to the speed of light. Special relativity does not take into account the effects of gravitation. Nevertheless, within their applicable domains, it does appear that these theories describe how nature operates, if only in the restricted meaning of predicting the outcome of experiments to arbitrary accuracy. Relativity, as we have said, has been subject to millions of experimental tests and each one has confirmed the theory. The same can be said for quantum mechanics. This is about as certain as things get in science.

The physicist's debating quiver is full of laws. As Apollo's chariot passed high in the sky above the First Debates, at least one physicist-academician vetoed the idea of UFOs on the grounds of the law of conservation of energy, which says that energy can be neither created nor destroyed. More precisely, she remarked that the amount of energy a UFO would need to travel from the nearest star to Earth was more than our civilization has used since the dawn of time, making the entire enterprise doubtful. Apart from the laws there are also famous principles: Mach's principle, the Heisenberg uncertainty principle, the principle of equivalence, et cetera.

Indeed, when you bolstered your argument that nothing is certain by referring to Star Trek and the new developments sure to come in physics, for instance the transporter, one physicist objected: "Transporters are impossible because they violate the Heisenberg uncertainty principle" Heisenberg's uncertainty principle states that it is impossible to measure precisely both an object's position and velocity at the same time and hence it would be impossible to reassemble the atoms of Captain Picard or Data with the required precision to ensure they were reconstituted in some manner resembling their previous selves.

However, at this point you may have noticed that the uncertainty principle sounds suspiciously like a law of nature and have rightly questioned your opponents on the precise difference between a law and a principle. Traditionally, a natural law is a statement about the way the universe operates that can be experimentally tested, for instance conservation of energy. A principle is a more general statement, one that does not necessarily yield to experimental test, but that one hopes is nevertheless true and that guides the seeker to a precise statement about laws.

But, as you observed, scientists carelessly use the terms "principle" and "law" interchangeably. The Heisenberg uncertainty principle is misnamed; it is really a law of nature, which can be subjected to experimental test. The principle of equivalence, which states that all objects fall at the same rate in a gravitational field, is also a law of nature. To test it one merely measures, as accurately as possible, the acceleration of falling objects.

Yet, there are principles of another category. Reductionism is one of these, and some visitors claim to have overheard the term during the previous conversation. The belief that all phenomena can be reduced to a few laws and principles is traditionally said to have begun with the presocratic Thales, whom Plato wished to exclude from the Academy, and who believed that water was the primary substance. Since then reductionism has had undoubted success in guiding physicists in their search for new theories, but it is the theories that are experimentally tested, not reductionism.

At this, New Age tourists surround the authors, taking exception to the remark about reductionism's success, and the authors reply that they suspect reductionism will be a featured contention throughout, in particular in the Sixth Debates, which deal in part with complexity and emergence.

There are other guiding principles in science, such as the principle of mechanism, which will figure prominently in the Fourth Debates, on causality, but in the twentieth century, another principle has gradually dominated the search for fundamental theories. This is sometimes referred to as the principle of beauty, which states that the most mathematically beautiful theories are the correct ones. In the famous words of academician Keats,

For particle physicists, the principle of beauty has come to mean the principle of symmetry, which states that correct theories shall display certain mathematical symmetries not unlike those found in regular geometric designs. (Symmetry is scheduled for the Third Debates.)

The principles of reductionism and beauty are clearly of a different nature than conservation of energy, and so your confusion, that scientists use the terms "principle" and "laws" interchangeably, is fully justified. If you encountered Steven Weinberg at the Academy, he would almost certainly argue that the success of reductionist theories validates the principle.

A Practical Exercise: Are Principles More Sacred Than Laws?

It seems indisputable that scientists hold principles to be more fundamental than laws. A decisive experiment would cause most physicists to abandon relativity, or perhaps conservation of energy. But even if this were to happen, many physicists would continue to believe that nature is inherently symmetrical. As theorist Michio Kaku puts it, "...nature, at the fundamental level, does not just prefer symmetry in a physical theory, nature demands it." Nevertheless, such principles are verified only indirectly, through the success of the theories based on them and, as an experimentalist will argue in the Third Debates, there must be a certain amount of faith involved in adhering to them despite the scientist's frequent abhorrence of metaphysical statements, an abhorrence evidenced by Steven Weinberg's remark, "I know of no one who has participated actively in the advance of physics in the postwar period whose research has been significantly helped by the work of philosophers."

There is buried in such statements the conviction that we have honed the methods of science over the millennium and are now closer to the Truth, not only in terms of facts, but in terms of principles. For example, tourists at the Academy are often surprised at the disdain physicists bear for the Academy's early director, Plato, and his most famous pupil, Aristotle, whom physicists accuse of setting back the course of science one thousand years, if not two. The general reason for the contempt is explained by F. M. Cornford, who has dropped by for a few minutes: "Knowledge, Plato thought, was to be found not by starting from 'facts' observed by the senses, framing generalizations, and then returning to the facts for confirmation, but by turning away and escaping as fast as possible from all sensible appearances." In other words, the universe can be understood by pure logic, without recourse to experimentation, a notion exactly contrary to the whole concept of modern science.

The specific reason for the contempt is Plato's contention that the planets move in circular orbits around the Earth, a contention that Aristotle enshrined and that went unchallenged by philosophers for over fifteen hundred years. Modern physics was born only when Copernicus in the sixteenth century proposed that the Earth was not the center of the solar system, when Kepler discovered that the orbits of the planets were ellipses and when Newton explained that elliptical orbits resulted from his law of gravitation.

Late in the afternoon of your day at the Academy, on your search for the coffee machine, you encounter a modern physicist and Aristotle crossing paths. You are surprised that the physicist begins an argument before introducing himself or saying hello, but he launches right in and loses no time in challenging Aristotle, the great proponent of circular motion: "By what right do you decree that the orbits of the planets should be circles?"

Aristotle responds by declaring that "circles are the most perfect shape and circular motion is the most perfect motion."

The physicist will have nothing of this and properly objects, "But the planets don't move in circles; they move in ellipses."

Aristotle, taken by surprise at this intelligence, scratches his chin. "But are they really moving precisely in ellipses?"

"Well" admits the modern physicist, "there are slight deviations from ellipses due to the gravitational pull of the other planets. But to a high approximation, the orbits are ellipses, not circles. Furthermore, each planet moves faster or slower depending on whether it is nearer or farther from the sun. Nevertheless, the area swept out by a line joining the planet to the sun will always be the same for equal time periods."

Aristotle has a difficult time understanding this, so the modern physicist draws a picture. Nevertheless, the Greek has difficulty swallowing Kepler's second law and asks, "But why does the planet behave this way? This seems far from perfect."

The modern physicist replies, "There is a quantity in physics called angular momentum, which in this case is the product of a planet's mass, velocity and distance from the sun. Physicists have discovered that angular momentum is conserved; in an isolated system it cannot change. The conservation of angular momentum results in the equal-area law, which we call Kepler's second law in honor of the astronomer who discovered it."

This news really bothers academician Aristotle, who after fierce cogitation exclaims, "Why should angular momentum be conserved?"

"Ah," replies the modern physicist. "This is a consequence of an underlying symmetry of nature: that space is the same in all directions."

"What do you mean by that?" asks the Greek.

"That space has the same properties north, south, east or west. To put it another way, that in an ideal universe you cannot tell which direction you are facing. One can show that a lack of preferred direction results in the conservation of angular momentum."

Aristotle scowls. "Philistine! This is no different from declaring that circles are the most perfect shapes."

After a pause, the modern physicists replies with some temperance. "Well, we do have experimental evidence that orbits are ellipses, not circles."

"Yet, you have already claimed that the orbits are not quite ellipses. Does this mean that space is not quite perfect?"

"Well yes, but that is merely because the other planets have gotten in the way."

"But you have never observed the solar system empty of planets. What grounds do you have for assuming that in a vacuum space has no preferred direction?"

"This is the simplest, most natural assumption."

"But nature abhors a vacuum. You can never observe the solar system without planets."

And so on, until you depart for coffee.

Short Graphic Rule

Aristotle was mistaken about the planetary orbits. However, he might have said, "The most perfect motion is rest" but given that the planets were moving, he picked the most perfect -- the most symmetric -- orbit he could think of: a circle. The declaration that space is the same in all directions -- isotropic, to use the technical term -- is no different in this regard; it is not based on any observations that can actually confirm it. Thus the modern approach may be more successful empirically, but is no different in character from the ancient approach. To claim that momentum is conserved because space is uniform is a teleological statement -- a statement that says nature behaves as it does to achieve certain goals -- no different from Aristotle's statement about vacuums. Modern academicians who claim that physics is devoid of philosophical considerations are not being entirely forthright.