by     Reginald O. Kapp


Chapter 1 - The Concept of Unification in Physics

1.1: The Meaning of Unification
This study is the search for a unified cosmology. Before it is begun clarity must be reached as to the meaning attached to the word 'unification'.

As understood here it constitutes the replacement of many specific laws, principles and hypotheses by a smaller number of more general ones. An example of the process, which is frequently quoted and which stands out as pre-eminent, is the unification achieved by Newton.

Before his day there were no general laws of mechanics; there was only a variety of specific laws, each applicable to a specific mechanical system. It was believed that a specific law, applicable only to planets, required these to move in elliptical orbits; that a quite distinct specific law, applicable only to pendulums, required their period of swing to bear a specific relation to the length of the pendulum; that yet another specific law, applicable only to vacuous spaces, required these to be filled. If there were such a thing as a Cosmic Statute Book, this would have had to contain, according to the pre-Newtonian view, separate entries under the respective headings Planets, Pendulums, Vacuum. The book would have been a bulky one.

But Newton showed that many such specific laws were implicit in other more general ones. A large number of observed facts could be inferred from his laws of motion and gravitation. If the Cosmic Statute Book contained these all-embracing laws, there would be no need for further entries to say that planets shall move in elliptical orbits, that the period of swing of a simple pendulum shall be proportional to the square root of its length, that a projectile shall have a parabolic path, that a vacuous space shall be filled: Newton, it might be said, did much to whittle down the Cosmic Statute Book.

Another way of describing the same achievement is to say that Newton 'explained' a large number of facts. For in physics a fact is explained by showing how it can be inferred from something more general. All explanations there are steps in the direction of greater unification.

Since Newton's day the unifying process has extended into more and more branches of physical science. The first and second laws of thermo- dynamics have had great unifying power. From them much can now be inferred that would otherwise have to be attributed to specific, ad hoc, laws. The relation between the once quite distinct subjects of electricity and magnetism is found to be so close that they are now considered as one subject. A study of the relation between chemical reactions and thermodynamics, as also of that between chemical reactions and atomic structure, has led to the new branch of science called physical chemistry. This has taught us that chemical processes and properties are implicit in atomic structure. At one time it must have appeared that an entry in the Cosmic Statute Book would be necessary to say that hydrogen shall combine with oxygen and form a substance with the properties of water. But we now know that such a clause would be redundant. Physical chemists can tell us that, provided there be atomic nuclei with, respectively, one and eight positive unit charges, the rest is assured. One can infer with the help of certain general laws that atoms having such nuclei must combine and that the resultant compound must have the properties of water. This unification is making it possible to explain more and more chemical facts in terms of atomic structure.

1.2: Unification leads to Predictions
A most valuable feature of unification is that it enables one to replace observation and experiment by inference and calculation. Galileo could discover the law of the pendulum only by observing pendulums; but after Newton anyone who had never seen a pendulum could have discovered the law. He would have done so by the reasoning that is now taught in schools, where the formula is deduced from first principles. Similarly the elliptical orbits of planets could have been discovered before Newton's day only by making careful observations of successive positions of planets. But now a person who had lived all his life under a blanket of impenetrable cloud and learnt for the first time that there was a massive sun surrounded by less massive bodies could predict that, when the cloud lifted, one would observe the less massive bodies to move in elliptical orbits. There was a time, again, when the chemical properties of substances seemed to be discoverable only by observing those substances. But this is not necessary today. Long before the element hafnium had been found chemists did not only say that there was such an element; they also predicted its properties. The properties are implicit in the general laws that chemists have discovered and can be inferred from these laws.

It is this kind of unification that has made the rapid progress of technology possible. If every chemical substance had to have a clause in the Cosmic Statute Book definining its properties, chemists would have to make the substance and submit it to a laborious series of tests before they knew what the properties were. But the properties are implicit in general laws. If these are known, the properties follow automatically. Hence it is a commonplace of chemical research to predict the properties of a new compound before making it.

It is the same in all other branches of technology. Without a unified physics one would have to make a gun and fire it before one could know what path the projectile would take. One would have to make and test a bridge in order to discover its strength. One would have to make and test every new kind of engine before one could determine its thermal efficiency or the critical speed of its shaft. But the technologist's aim is to substitute inference for observation. Doing this, he can predict the performance of guns, the strength of bridges, the efficiency of steam engines while they are still in the blue-print stage. In technology, tests, observations, experiments, do not only serve the purpose of facilitating predictions but, often instead, of verifying them and of correcting errors and oversights. This can be done because what is predicted is implicit in general and known laws and principles.

1.3: The Search for Greater Unification Continues
By the process of unification the whole of physical science is gradually being fashioned into one complete and consistent structure of thought in which the various parts bear a logical relation to one another. Mechanics, electricity, magnetism, thermo-dynamics, chemistry, heat, light, sound, to mention only some branches, have been brought under one common roof.

During the present century we have seen two conservation principles, those respectively of energy and mass, united. Einstein has established in the general theory of relativity a connection between gravitation and space and has thereby brought space under the common roof with the rest of physics. There has, further, been the formulation of the very basic and comprehensive law according to which physical changes cannot be by indefinitely small amounts. This law forms the foundation of the quantum theory and has brought under the common roof a large number of observa- tions that previously seemed to be isolated and each to require its own clause in the Cosmic Statute Book. Predictions of all sorts are being based every day on the principle that all physical changes are quantized.

The search for greater and ever greater unification continues, but with varying success. One of the failures is worth mentioning because it illustrates the nature of the problem. Three different types of field of force have been observed: magnetic, electrostatic, and gravitational. Something is known about how the first two are related to each other, and one commonly speaks of them jointly as the electromagnetic field. But yet they remain distinct from each other and quite distinct from the gravitational field, which has been shown by Einstein to be a region where the geometry of space-time differs in a specific way from the geometry of Euclidean space. The difference can be expressed in a mathematical formula.

The hypothesis is near at hand that the magnetic field is also a region where the geometry of space-time differs from Euclidean geometry, though in a different way, and that the electrostatic field represents a third departure. If so, one might expect to be able to generalize Einstein's relativity equations in such a way that they would represent any kind of field. If that could be done, one specific value of a term in the equation would define the gravitational field only, another the magnetic field only and a third the electrostatic field only. Each field would then appear as a special case of something common to them all; its properties could be predicted from the great sweeping law that was applicable to all fields; magnetic, electrostatic and gravitational fields would be brought under a common roof. The attempt to achieve this has been called the search for a unified field theory.

Assiduously though it has been conducted by a number of scientists, of whom Einstein was one, the search has so far led only to disappointment, It is impossible to say yet whether the failure is due to the inherent difficulty of the subject or because the search has taken a false hypothesis as its starting point, i.e. that all fields of force have enough in common for them to be represented in terms of the geometry of space-time. Yet, in spite of the apparent reasonableness of this assumption, it may not be true. Electrostatic and magnetic fields may be so different from gravitational ones in their nature, their effect, their cause, that they cannot be represented in any comparable terms at all. Some other hypothesis, one that has not yet been formulated or even thought of, might prove a better starting point for bringing electromagnetism and gravitation under a common roof.

Be that as it may, no attempt will be made here to succeed where Einstein and others have failed. The present study is in no way concerned with the search for a unified field theory, desirable though it is that the search should continue. But the example will help to define the scheme according to which unification in physics is achieved.

1.4: How Unification is Achieved
In the process of unification in physics a general principle is first found. Examples are Newton's laws of motion, the great conservation laws, the principle of least action, the principle according to which all observable physical changes are quantized, the principle of the equivalence of mass and energy, the principle by which the chemical properties of substances are related to the number of electrons that surround the nuclei of the constituent elements.

At the next step towards unification various phenomena are shown to be implicit in one or other of these principles. They can therefore be inferred from them and so could be struck off the Cosmic Statute Book as redundant.

Sometimes the phenomena are observed first and the principles are found later. The principles are then said to explain the phenomena. Thus the observed behaviour of planets was explained by the laws of motion and gravitation. Similarly, attempts to make a perpetual motion machine failed for unexplained reasons until the principle of conservation of energy provided the explanation.

At other times the principle is found first and some phenomenon that is implicit in it is described before it has ever been observed. In such instances it may, or may not, be observed later. One then says that the phenomenon is predicted by the principle. Engineers, as mentioned already, follow this course as a matter of routine. They invent and design new kinds of machines on the basis of the great sweeping principles of physics and they predict their performance. Observation and experiment come laterand not to test the principles but to test the soundness of the designer's reasoning. In physics, too, it sometimes happens that a phenomenon is predicted as an inference from a general principle before it has been observed. The properties of hafnium have already been quoted as an example. The discovery of Neptune by Adams and Leverrier and of Pluto by Lowell are other examples. But physicists work most often with things that they are observing at the time. Their concern, unlike that of the machine designer and the industrial chemist, is more often to explain observed effects than to predict those that will only later become observable.

The striving to bring ever more phenomena under the common roof, to unify the whole of physics, is, of course, not the whole of the physicist's work. Indeed most research workers are concerned only with the discovery of the detailed facts, qualitative and quantitative, of the physical world; and necessarily so, for we still have much to learn about the laws of mechanics, heat, light, sound, electricity and magnetism; about the physical and chemical properties of solids, liquids and gases; about the macrostructure and the microstructure of the material universe, about the positions and movements of the heavenly bodies. But, nevertheless, it is worth stressing that much of the thinking done by most physicists is directed towards the discovery of generalizations and that it is on these as much as on collections of observed facts that physical science is based.

The distinction between the search for isolated facts and the search for unifying generalizations is well illustrated by the elliptical orbits of planets. We can now understand why these orbits could not be explained before Newton's day. It was because of a wrong outlook. During and for some time after the Middle Ages the notion was prevalent that every phenomenon was the result of what might be called a distinct act of legislation, that it was ensured by what I have metaphorically called a separate clause in a Cosmic Statute Book. Those who held this view were bound to think that it was idle to ask why the planets moved in the observed orbits. The acceptable answer was that such orbits were a legislative requirement, about which no further questions could or should be asked.

But we can now realize that, if the planetary orbits could not be explained before Newton, it was not that they were inexplicable. Nor was it that not enough was known about planets. It was that not enough was known about mechanics. No further astronomical research, no careful observation of the orbits, no precise measurement could have provided the explanation. But Newton's laws of motion and gravitation did so. In other words, scientists found the answers to some specific questions about planets only when they had found statements that were general enough to apply to all ponderable objects. In medical metaphor, ignorance about planets proved to be, not the disease itself, but a symptom of the disease. Newton followed the course of a doctor who seeks to treat the disease rather than the symptom.

Similarly our inability until a short while past to explain why given chemical substances react in the observed ways proved to be, not due to our ignorance of the substances, but to our ignorance of the more general subject of atomic structure. The great generalizations on which modern chemistry is based could not have been discovered by work conducted only in the field of chemistry.

These considerations are relevant to the present study because I propose to demonstrate here the great explanatory power of the generalization that is reached when one pursues the search for a unifying principle in physics with uncompromising persistence. It will be shown in the next chapter that one then reaches a very comprehensive principle, one that is applied by physicists on occasion but which has not been given the status it deserves. It will be called the Principle of Minimum Assumption and will be described fully in the next chapter. It will be shown in the remainder of this book that one can infer from this principle, and without the need for any further hypotheses, a number of cosmic phenomena that have hitherto eluded explanation. The selected examples will be the expansion of space, the occurrence and detailed structure of nebulae, and the familiar observation that every large accumulation of inertial mass is the source of a gravitational field.

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