Lawless Universe: Science and the Hunt for Reality

Explanation, Not Speculation

Theory

LAWS OF NATURE are worthwhile achievements. Besides their potentially useful predictive power, they offer a unifying description of natural phenomena. But we are not satisfied with that. We want to explain laws of nature, to know the reasons for them; we want to understand the reproducible and predictable aspects of nature, not just describe and predict their phenomena. And we want to do it in an objective way, in a manner valid for all. That is science in the big picture. Scientists’ term for an explanation of a law of nature is theory.

There are a number of criteria by which theories are judged for their acceptance or rejection in science. These criteria are not intrinsic to nature itself, are not imposed on us by nature in any way, but are imposed by us in our search for understanding. The criteria, however, are but rationalization. What determines a theory’s acceptability is its giving us the feeling that something is indeed being explained, so that it satisfies our curiosity about the reasons for whatever law we’re trying to understand. The detailed criteria are our attempt to rationalize that feeling. Yet it is difficult, if not impossible, to meaningfully communicate such feelings, and we have no choice but to discuss the criteria.

Yet in spite of that, the scientific mode of comprehension is still the most nearly objective mode of comprehension around, and we’ll have to make do with it. Actually, we make do very well, thank you. Nevertheless, an open-eyed realization of the irrational aspects of science as a human activity cannot fail to benefit our attempt to clarify the role of science in our understanding of the world around us.

Logical Implication and Objective Truth

Fundamentality is less simple than generality, since it depends on one’s scientific worldview and on the context of discourse. What you take to be fundamental might seem derivative to me, while what is underlying for me might appear superficial to you. Scientists working within the commonly accepted scientific worldview tend to agree on questions of fundamentality. Still, disagreements can arise. (Note the subjectivity, thus irrationality, here.)

As an example, a theory of genetics based on some macroscopic property of an organism, such as body weight, would not be acceptable to scientists, because heredity is generally considered to be more fundamental than, and to determine to a certain extent, the macroscopic and microscopic properties of organisms. But since biochemistry is commonly considered to underlie biological phenomena, a molecular theory of genetics, such as the currently successful one involving DNA, RNA, etc., could be acceptable.

Causation

Another advantageous property of an acceptable theory is that what is doing the explaining should be perceived, not merely as logically implying what is being explained, but as causing it. This means that some sort of causal linkage, some “mechanism,” should be perceived as joining what is doing the explaining (the cause) with what is being explained (the effect). It is the perception of such a causal linkage that enhances the acceptability of a theory. Whether there “actually exists” a causal mechanism or not can depend on one’s point of view, even on one’s scientific worldview, and so is not an objective property of nature. (Again note the subjectivity here.)

For example, a theory explaining Kepler’s laws might consist of a statement of general laws of motion valid for all bodies, not just for planets. Kepler’s laws, describing the motion of the solar system as a special case, would be derivable by mathematical means from those general laws. Thus, although the theory would have the property of logical (mathematical) implication, it would most likely not arouse the perception of causation, so that some might find such a theory not completely satisfying.

At the same time, a theory of Kepler’s laws might be stated, from a somewhat different point of view, as general laws of motion together with the existence of the Sun and the planets’ attraction to the Sun. Such a theory would most likely arouse the perception that the Sun causes the planets’ special motion through its pull on them. As a matter of fact, the standard theory of Kepler’s laws is just of this kind, as we will soon see.

Two other favorable properties of an acceptable theory are that what is doing the explaining should be simpler than what is being explained, and should also be more unifying than the latter. And the simpler and more unifying it is, the more acceptable the theory. Although some criteria for simplicity can be stated (nevertheless, we will not), a generally satisfactory objectification of the concept has not been achieved. Simplicity is largely a matter of subjective perception. (Yes, subjectivity again.) Simplicity depends very much on one’s taste and worldview, even on one’s education, although there does seem to exist a considerable degree of consensus about it among scientists working in the same field, perhaps not surprisingly. In any case, scientists prefer “simple” theories to “complicated” ones, however simplicity is judged.

For example, Albert Einstein’s (1879–1955) general theory of relativity is one of a number of theories of gravitation. (Let me remind you that gravitation is the universal force of attraction between all pairs of bodies in the universe, including the force holding us firmly down to Earth so that we don’t float off into space.) All these theories appear to be overwhelmingly complicated—even to most scientists. Still, theoretical physicists specializing in the field generally perceive Einstein’s theory as the simplest, and thus the preferred, one.

Unification is easier than simplicity to pin down. As a general rule, the more numerous the different concepts a theory involves, the more unifying it is. Thus a theory should tie together and interrelate more aspects of nature than are tied together and interrelated by what is being explained by the theory. For example, the concepts involved in Kepler’s laws are purely kinematic; they are solely concepts of motion: position, orbit, area, time, speed, and so on. Any explanation involving only these same concepts would not be more unifying than Kepler’s laws themselves. But a theory involving kinematic concepts along with additional ones, such as force and mass, would be more unifying. Unification can generally be expected to go hand in hand with generality.

We now come to a matter that might seem absolutely amazing, which is beauty in theories. To many, science has the image of a cold, rational endeavor, to which considerations such as aesthetics are perfect strangers. Yet, although rationality is indeed the major ingredient of science, aesthetic considerations are far from foreign to it. (I warned earlier in this chapter to expect irrationality in science!) Scientists are constantly heard referring to “beautiful ideas,” “beautiful experiments,” “beautiful laws,” and “beautiful theories.” And a scientist will always prefer a beautiful theory to an ugly one, other things being equal, and even often at the expense of some other desirable property of acceptable theories. Many scientists admit that the pleasure they derive from their profession has a large aesthetic component, and for some (including myself) the aesthetic consideration is predominant.

What is a beautiful theory? Well, here we go again. Just as an acceptable theory is one that gives the feeling that something is being explained, so a beautiful theory is one that arouses the feeling of beauty. Beauty is not an objective property of theories, but is wholly in the eyes of the beholder and completely subjective. So the most we can do is to rationalize again and try to point out those properties of theories that contribute to their perceived beauty. It appears to me that the main contribution to the beauty of a theory derives from its simplicity, its unification, and its generality. A theory deemed beautiful by scientists working in the relevant field is invariably simple, greatly unifying, and of broad generality.

Falsifiability amounts to testability, the property that a theory can be tested against as-yet-unknown natural phenomena to determine whether it is objectively true or false. This property, not directly related to a theory’s ability to give the feeling that something is being explained, is generally required of any acceptable theory. Karl Popper (1902–1994) introduced the idea in the 1930s as the criterion one should use to distinguish science from pseudoscience. To be falsifiable, a theory must predict something in addition to what it was originally intended to explain (and which it presumably does explain; otherwise it would not be a candidate for an acceptable theory). Its prediction is tested against experimental results that were not taken into account when the theory was devised (either because they had not yet been obtained or because they were not known to the deviser of the theory). To produce predictions, a theory must fulfill the criterion of generality, as we saw above. Then what is doing the explaining, being more general than what is being explained, can explain more than it was originally intended to explain and thus make testable predictions.

A falsifiable theory is in constant danger of being invalidated by even a single new experimental result. An un falsifiable theory, by contrast is, by its unfalsifiability, immune to invalidation. As an example of an unfalsifiable theory, imagine that a theory of the electron is found that explains all the known properties of the electron, but, unlike Dirac’s theory, predicts absolutely nothing in addition to that. Such a theory cannot be tested. Even if new properties of the electron are eventually discovered, the theory will not be invalidated thereby. It will still be valid, since it continues, correctly, to explain what has become only part of the electron’s properties, whereas it has nothing at all to say about the other properties, and, moreover, does not predict their nonexistence. As a putative theory of the electron, it is incomplete. A falsifiable theory is discussed in the following example.

An archetypal example of a theory is the explanation of Kepler’s laws of planetary motion by Newton’s laws of motion and gravitation. Newton pondered Kepler’s laws of planetary motion (presented in the section Law in the preceding chapter) and succeeded in formulating a number of laws of his own in order to explain them. Newton’s laws were based on observational data, as were Kepler’s, but were also based on Kepler’s laws themselves as input. Newton’s laws are somewhat counterintuitive, and their full experimental verification had to wait for future technological developments and refinements.

Newton proposed three universal laws of motion, whose modern formulation is more or less this:

1. In the absence of forces acting on it, or when such forces cancel each other, a body will remain at rest or continue to move uniformly in a straight line.

2. A force acting on a body will cause the body to undergo acceleration whose direction is that of the force and whose magnitude is proportional to that of the force divided by the body’s mass. Acceleration is change of velocity—that is, change of speed and/or direction of motion—per unit time. Mass measures the amount of matter in a body. (It is related to, though essentially different from, a body’s weight.)

3. For every force acting on it, a body will react upon the force’s source with a force of opposite direction and equal magnitude along the same line of action.

To these Newton added the universal law of gravitation: Every pair of bodies undergoes mutual attraction, with the force acting on each body proportional to the product of the bodies’ masses and inversely proportional to the square of their separation.

These four laws form Newton’s theory to explain Kepler’s laws of planetary motion (as well as a vast realm of other mechanical phenomena). How are they a theory? First of all, they do logically imply Kepler’s laws. With the appropriate mathematical tools, scientists and science students can show that the motions of bodies around a massive body will, under certain conditions, obey Kepler’s laws. These conditions are fulfilled by the planets in their motion around the Sun as well as by additional astronomical systems, such as the moons of the planet Jupiter in their motion around Jupiter.

Newton’s laws are certainly more general than Kepler’s, in the sense that they hold for all bodies (hence the qualifier “universal”) and not just for planetary systems. As a result, Newton’s laws explain far more than Kepler’s; they explain a wealth of mechanical phenomena, earthbound (such as falling apples) as well as astronomical. In addition, they are more unifying, since they show order among broader classes of phenomena than do Kepler’s laws. Whereas the latter involve solely concepts of motion, Newton’s laws involve also the concepts of force and mass. And they are also more unifying, in that, for example, the motions of comets are shown by Newton’s laws to be akin to the motions of the planets, whereas Kepler’s laws ignore cometary motion.

Whether Newton’s laws are more fundamental and simpler than Kepler’s is a matter of one’s worldview and taste concerning fundamentality and simplicity, but scientists generally consider them as such. We won’t go into details here, but let’s just note in connection with fundamentality that, whereas Kepler’s laws merely describe motion, Newton’s laws have to do with the causes of motion, that is, with forces (and their absence). The character of Newton’s laws is just as natural as that of Kepler’s, and so we have one aspect of nature being explained by another.

In the conduct of science, after finding laws of nature, we try to understand, that is, explain, objectively those laws by means of theories. For a theory to be acceptable, Whatever is doing the explaining must logically imply what is being explained. The former should form an aspect of nature just as much as the latter should. In addition, the former should be more general, more fundamental, more unifying, and simpler than the latter, and should be perceived as causing the latter. Beautiful theories are preferred. Theories should be falsifiable.

Bibliography

For the purpose of our discussions, it’s not necessary to understand Newton’s laws or even to be familiar with them. Still, if you are interested, I suggest you see any introductory college physics textbook.

Many of the bibliography entries of the preceding chapter are relevant to this chapter too. Independently of that, here are a few suggestions for specific subjects.

For a historical perspective on Newton’s laws, see

D. Park, The How and the Why (Princeton University Press, Princeton, N.J., 1988).

For theory, see

F. Rohrlich, From Paradox to Reality: Our New Concepts of the Physical World (Cambridge University Press, Cambridge, 1987).

R. G. Newton, What Makes Nature Tick? (Harvard University Press, Cambridge, Mass., 1993).

A. Zee, Fearful Symmetry: The Search for Beauty in Modern Physics (Macmillan, New York, 1986, and Princeton University Press, Princeton, N.J., 2007).

For introductory presentations of symmetry, see

G. Darvas, Symmetry (Birkhäuser, Basel, 2007).

J. Rosen, Symmetry Discovered: Concepts and Applications in Nature and Science (Cambridge University Press, Cambridge, 1975; reprinted with additions by Dover Publications, Mineola, N.Y., 1998).