TOWARDS A UNIFIED COSMOLOGY

by     Reginald O. Kapp

PART IV - GRAVITATION

Chapter 22 - Unsolved Problems of Gravitation


22.1: Gravitation Appears to be an Isolated Phenomenon
One of the major problems presented by gravitation has been discussed in the preceding Chapter 21. But there are others and these will now be examined.

One of them is how to bring gravitation into association with other natural phenomena. At present it appears curiously isolated from them. In this it is unique. Mention has already been made in Chapter 1 of the unification of the various branches of physical science that has been achieved during the past few centuries. Heat, light and sound, electricity and magnetism, mechanics, chemistry are now all under one common roof. Quite a lot is known about the relation between them. One can often express observations made in one of these branches in terms appropriate to another one. Chemical processes are explained with reference to electrical forces. Light is interpreted as an electromagnetic phenomenon. The effect of a magnetic flux on the polarization of light is a subject for study. The temperature of a gas is attributed to the momentum of the constituent molecules, a mechanical effect. Wherever one turns in physical science one meets this same close interlocking between its various branches. More and more generalizations in physics are, let me repeat here, found to be logical inferences from other, more basic, ones.

Gravitation is one of the few phenomena in physical science that have entirely escaped this process of unification. It does not interlock with any branch. It stands outside the roof that covers all the others. The few generalizations that can be made about gravitation have not been found to be logical inferences from any more basic generalizations. Gravitation is, in a word, still one of the phenomena that cannot be explained.

I propose to show in this Part Four that it need not continue to be so. Gravitation, like so many other natural phenomena, will be shown to be a logical inference from the Principle of Minimum Assumption.

22.2: The Principle by which a Process Tends to Reduce its Cause
A third puzzling fact about gravitation is that it seems to violate one of the most basic principles known to physics. This is that in a self-contained system every process tends to be such as to reduce its cause. Something has already been said about this principle in Chapter 3, when the reasons for rejecting hypothesis (Al) were presented. It will be convenient to repeat a little of this here.

The movement of electric charges in an electrostatic field provides an example of a process that reduces its cause. At the origin of the field is an accumulation of electrons. As like charges repel each other, any of those that are free to move are propelled out of the field, thus weakening it. Any unlike charges, on the other hand, that come into the field are attracted. They neutralize the charge at the origin, again with the consequence that the field is weakened. In this example the process is the movement of electric charges; the cause is an electrostatic field; and the process reduces the intensity of this field.

Another example is the transfer of heat between surfaces. The cause is the difference in the temperature of the surfaces. As the process of transfer continues, the temperature difference decreases and the rate of heat transfer becomes slower.

The principle can be further illustrated. Most chemical substances are reactionable, which means that they enter into combination more or less vigorously with other substances. But when they do so the resultant products are always less reactionable; the process of chemical reaction tends to reduce the capacity for reaction. Oxygen and iron, for instance, combine with some vigour at certain temperatures, but rust, the product of their combination, is comparatively inert.

Causes of physical change can be expressed in terms of gradients. When an electric charge moves, it follows an electrical potential gradient. When heat flows from one place to another it follows a temperature gradient. In chemical reactions there are strong potential gradients between atoms and molecules. According to the principle being discussed here, we live in a world in which gradients are flattened out as time goes on.

If the opposite principle prevailed all causes would become more and more pronounced in the course of time, gradients would become ever steeper and steeper; the world would become a place of ever-increasing contrasts. Every electrostatic field that had begun as a weak one would have been becoming stronger and stronger in the course of timewithout limit. Every hot surface would be getting hotter as it radiated heat and every cold surface would be getting colder as it received it. We should be living in a universe in which chemical processes were becoming ever more violent. Such a universe would be unstable and so the principle by which processes reduce their causes can be called the Principle of Stabilization. As there will be occasion to refer to it again, this name will be useful.

This principle is, of course, only observable so long as the system is self-contained. If, for instance, an electric generator supplies fresh electrons as fast the old ones are removed or neutralized, there is no reduction in the intensity of the electrostatic field.

The Principle of Stabilization is generally regarded as even more basic than the first and second laws of thermodynamics, for it embodies both. If starting a process sufficed to increase its cause, perpetual motion would be possible and the first law would be refuted. If the transfer of heat caused temperature differences to augment, every thermal change would be accompanied by a decrease in the entropy of the system and the second law would be refuted. To deny the Principle of Stabilization would be heresy indeed.

And yet! Gravitation has the appearance of violating it. When bodies are free to move in a gravitational field they fall on to the attracting mass; but they do not thereby reduce the intensity of the field, as electric charges do when they fall in an electrostatic field. The bodies that fall in a gravitational field add to the mass at its centre and thereby increase its intensity. We live in a world in which all gradients tend to become flatter in the course of time with the exception of gravitational ones. These seem to tend to become steeper.

The implications of this strange characteristic of gravitation cannot be dismissed lightly. Every accumulation of matter must be attracting neighbouring bodies towards it and, in doing so, becoming increasingly powerful. It will be shown in Appendix B that, as a consequence, the cosmological model that is based on Asymmetrical Impermanence does not resemble actuality. In this model the whole of the matter in the universe would eventually fall together into one single unit. The reason is that any two neighbouring accumulations of matter may be regarded as in competition for the substance that occurs between them. The larger accumulation will always acquire a greater proportion of it and thereby become able to compete still more successfully with its smaller neighbour. In the absence of anything to counteract this tendency for the larger concentration always to grow at the expense of the smaller ones, the largest of all must eventually swallow the others one by one.

It would be easy to show that the models based on either hypothesis (Al) or hypothesis (A2), as listed at the beginning of Chapter 3, would be similar in this respect. Only the model based on the combination of (A3) with (B3), on Symmetrical Impermanence, will, if the reasoning in Appendix B is confirmed, continue to contain discrete concentrations at all times. But the reason is, it will be found, that every large concentration, every galaxy, finds itself at intervals of about three-and-a-half thousand million years in a position where the loss rate from extinctions within its domain exceeds the gain rate from new origins. The galaxy can, in consequence, capture less new matter than it loses and so must dwindle for a while.

If one rejects Symmetrical Impermanence, one can only arrive at a model that resembles actuality by inventing sundry ad hoc hypotheses. Perhaps, one has to speculate, the expansion of space is effectively opposing gravitational forces, a surmise that cannot easily be justified quantitatively.

Or perhaps some other, as yet unknown, force operates in extragalactic space to keep the galaxies apart. Or perhaps such a force operated once-upon-a-time only in the remote past and caused all celestial bodies to acquire a momentum away from each other. If quantitative reasoning leads to an unwelcome conclusion one can always, as I have said repeatedly in these pages, save the favoured view with the help of sufficient hypotheses.

But those who adopt these, as also those who prefer to base their cosmological model on the Principle of Minimum Assumption, must all feel some uneasiness at the apparent failure of gravitation to conform to so basic a principle as that of stabilization. A single exception to a principle that is otherwise absolutely universal calls for inquiry.

22.3. Gravitational Fields are Unidirectional
Gravitational fields always have the same sign. In this they differ from other known fields. In electrostatics like charges repel and unlike ones attract each other. Hence in some fields a given particle moves towards the centre of the field and in others the same particle moves away from the centre. This is expressed by saying that electric fields may be either positive or negative. It is the same for magnetic fields. A north-seeking pole moves in one direction in one kind of field and in the opposite direction in another kind. But it is not the same with gravitation. Like gravitational masses do not repel but attract each other, and unlike masses are not known. In other words, electrostatic and magnetic fields are described sometimes as positive and sometimes as negative, but one has no reason to describe gravitational fields in similar terms. These are observed to be unidirectional; bodies move always towards, and never away from, their centres.

This does not appear to be the logical consequence of any other known fact. It cannot be deduced from the definition of gravitation; it is not, so far as can be ascertained, a tautology. No reason has been found why inert masses should not do what electric charges do, sometimes attract and sometimes repel others. Such explanations as have from time to time been offered are far-fetched and by no means convincing. The uni- directional nature of gravitational fields is just one of those stubborn facts that have persistently defied explanation.

22.4: The Relative Intensities of Electrostatic and Gravitational Fields
Nearly all inert masses consist of protons, electrons and neutrons. All protons have identical masses and identical positive charges. All electrons also have identical masses and identical negative charges. All neutrons also have identical masses and zero charge. Thus there are con- stant ratios between charge and inert mass. As these ratios are not directly concerned with gravitation they need not concern us here.

But it is generally assumed, rightly or wrongly, that each proton and each electron has attracting as well as inert mass. On this assumption a proton, for instance, is the centre of two fields of which one is electrostatic and the other gravitational. If it is so, one has to conclude that there is a law according to which a motionless electrostatic field cannot occur unless it is accompanied by a gravitational one. (The word 'motionless' is necessary because the field that moves with the velocity of light and is coupled with a magnetic one is not coupled with an attracting one.) One has further to conclude that the ratio between the intensities of the electro- static and gravitational fields around an elementary particle must be one of a few constant values.

As already mentioned electrostatic fields, like gravitational ones, may be regions in which the geometry of space-time is non-Euclidean. It is indeed difficult to imagine what else they could be. But if they are, their geometry must be of a fundamentally different kind from that of the gravitational field; for it does not affect the movement of inert masses; the path of a neutron is the same whether it passes through an electrostatic field or not. Correspondingly the path of a proton or an electron is not influenced by a gravitational field except by virtue of its inert mass. And yet, according to the generally accepted view, gravitational and electrostatic fields invariably occur in association around every charged particle. By what principle, one is led to ask, should two quite different (and non-interacting) kinds of field be coupled in this way? By what principle is the ratio of the intensities of the two fields limited to certain constant values? Existing knowledge offers no hint of an answer to these questions.

These are the questions that are being asked by those who are seeking a unified field theory. They will not be further discussed in these pages. But there is a further question about the ratio of the charge and attracting mass that is, by traditional theory, attributed to elementary particles and this question does have a place in the present inquiry.

Why, it may also be asked, are the two field intensities of such widely different orders of magnitude? The electrostatic field around a proton is large enough to be readily measurable. But its attracting field, if it has one, is so weak that vast numbers of elementary particles, the numbers that make up a sizeable leaden sphere, are needed to form a field of measurable strength.

It has been suggested that gravitation may be a differential effect; and if a gravitational force were indeed simply the difference between a push and a pull, the pull preponderating very slightly, one would, of course, expect the force to be very weak. But that suggestion is pure speculation and is not supported by any evidence. That the two fields associated with the same particle should have such enormously different intensities has yet to be accounted for.

22.5: Gravitation is Uncontrollable
A further puzzling feature of gravitation is that it is, in an absolute sense, uncontrollable. This cannot be said about other natural phenomena. Even radio-activity can be influenced by nuclear bombardment.

One can direct a beam of light in any desired direction. One can vary its intensity and colour, reflect and refract it, break it down into the component wave-lengths of its spectrum, polarize it. One can so control temperature that a given substance may be nearly as cold as the absolute zero or hotter than the sun. One can insulate a charged conductor and thus prevent the charge from having an influence on bodies in its vicinity. One can shield a magnetic pole and thus exclude magnetism from places where it would interfere with an experiment. One can conduct electricity along any desired path, vary at will its magnitude, vary its rate of change, switch it on and off. One can arrange and rearrange the chemical elements into a virtually unlimited number of different compounds, accelerate or retard the speed with which they react, influence the physical properties of substances. One can, in short, obtain in any given place any desired amount and quality of light, heat, sound, electricity, magnetism, chemical property.

None of these things can be done with gravitation. One cannot direct, reflect or refract it. One cannot vary its intensity. One cannot conduct it. One cannot insulate or shield it. One cannot switch it on or off. Why not?

We have become so used to the uncontrollability of gravitation that we tend to take it for granted and do not often ask questions about it. When a writer of science fiction introduces into his story the notion of a substance that intercepts gravitation or of a machine that controls it, we may smile at the ignorance of those gullible readers who accept such an impossible notion uncritically. But we should rather reflect on our own ignorance; for there is not a scientist who can say why such an insulating substance and such a controlling machine are but figments of an exuberant imagination, never to be implemented in the world of reality.

It is true enough that one cannot control the weather either. But its uncontrollability is of a different kind from that of gravitation. The reason is that the circumstances by which it is influenced are on a scale beyond man's mastery. Changes in the weather are brought about by the movement of vast quantities of air, changes in the ionization of hundreds of cubic miles of the upper atmosphere, changes in atmospheric pressure, sunspots, in fact by all kinds of occurrence that, though uncontrollable in practice, are not so in theory. If we disposed of unlimited resources, we could control the weather. Even though meteorology is not a subject on which much research can be done in the laboratories of our scientific institutions, it is a suitable subject for study in what is sometimes rather fantastically called nature's laboratory.

Many things happen in this laboratory to light, heat, sound, electricity, magnetism, chemical compounds, the nuclei of elements. Circumstances, great or small, may cause the same thing to become brighter or darker, hotter or colder, to move faster or slower. The sun, like other objects, undergoes many changes. A part of its surface sometimes experiences a magnetic storm. Its surface is a region of turmoil.

Gravitation, on the other hand, is no more influenced by cosmic than by man-made events. No circumstances ever cause the same body sometimes to exert an observably greater and sometimes a smaller gravitational pull. The inert mass at the centre of a gravitational field may be hot or cold, diffuse or concentrated, at rest or violently agitated, electrically charged or neutral, it matters not. The steady field persists. There are magnetic storms on the sun but the sun is always quite free from gravitational storms. The most shattering cosmic catastrophe does not send as much as a faint tremor through any gravitational field. Gravitation is not observed intermittently, but continuously, so that we never for a moment lack evidence that there is such a phenomenon. We feel its steady influence when we walk and when we lie down to sleep, when we raise an arm and when we swallow our food. Gravitation is literally the only natural phenomenon to assail our senses insistently and without interruption.

True, it is just possible to argue that the above statement may not be quite strictly correct. If it could be proved that the attracting mass, Mg, of a body increases with its velocity according to the law by which the inert mass, M does so, one could control gravitation, be it to a limited extent, by changing the velocity of the source of the field. If the leaden sphere used to measure G were spun, a different value of this constant would be obtained than if the sphere were at rest. If the sphere were heated, moreover, the component molecules would have a greater velocity. It is known that they would also have a greater inert mass. If they had a greater attracting mass as well, a neighbouring sphere would be attracted with a greater force.

But I have shown in Chapter 21 why such a conclusion is not implicit in relativity theory. Those inclined to disagree with me about this should remember that the relativity equations seem peculiarly difficult to interpret in physical terms, which explains why experts sometimes differ about their correct interpretation. In such interpretations as I have found there has been no attempt to discuss the relation between attracting mass and the other two kinds. The problem of understanding this relation has not been solved by relativists; it has not even been tackled, it has ignored.

22.6: The Gravitational Field of a Body is Changeless
To say that gravitation is uncontrollable, even in nature's laboratory, is to say that the gravitational field of a given body is changeless. In this it is different from most other natural phenomena. These do change with circumstances. Even the electrical field of a proton or an electron does so. For it may be converted into a photon .This difference between the electro- static and the gravitational field may, incidentally, explain why all attempts at finding a unified field theory have failed.

But there is one other class of phenomena that are as changeless as gravitation. The emission from a radio-active isotope is also a constant quantity, no matter what is done to the emitting body. A given lump of radium produces a known, constant amount of radiation and has a known, constant gravitational field. But every other property that one may assign to it varies with circumstances.

However, there is one significant difference between the changeless radio-activity per unit mass and the changeless gravitational force per unit mass. The former is attributed to a change in the material, namely to the disintegration of atoms; but according to the traditional view the latter is not attributed to any change at all.

The changelessness of the gravitational field is, incidentally, the reason why there was no god of gravitation in the mythology of the ancient Greeks. They believed that all natural phenomena that they could recognize as such were controlled by some mythical being. All events depended, in their mythology, on someone's conscious will just as events in our laboratories do. The notion of nature's laboratory would not have been remote from the Greek attitude. The Greeks saw the sea sometimes tranquil and sometimes in violent turmoil and attributed the changes that it underwent to the work of the sea-god Poseidon. They were alarmed by a raging storm with flashes of lightning and peals of terrifying thunder and explained it as a consequence of the anger of the god Zeus. They saw the fruits of the field grow and ripen ready for the harvest and said that the process was guided by the goddess Demeter. When a tree that began as a sapling grew into a thing of grace and splendour, they concluded that a charming dryad was the cause of the miraculous transformation.

But it was only changes, not steady states, that they attributed to their gods. If the weight of things were to change from time to time, so that, according to circumstances, a stone or a spear was sometimes heavier and sometimes lighter, the ancient Greeks would, no doubt, have included a god of gravitation in their pantheon. But the weight of a thing is the only property that never changes. So there was no such god. Had there been he would have had an idle time.

The remark is not as far off the point as one might think, for the reason why there was no god of gravitation in the Greek pantheon is fundamentally the same as the reason why there are no chairs of gravitation in our universities. A phenomenon on which one cannot conduct experiments, on which experiments are not even conducted in nature's laboratory, does not lend itself to much scientific study. Like a god of gravitation, a professor of that subject would have an idle time, and a dull one.

22.7: Gravitational Effects do not seem to be Associated with Expenditure of Energy
It has already been pointed out that the sun expends vast quantities of energy in sending its rays into space, but that, according to the traditional view of gravitation, it does not expend any energy in keeping the planets to their orbits. This important difference between gravitation and other phenomena deserves some discussion.

One can speak of the energy in an electrostatic field. This is produced when electrical charges are separated and the energy consists in the work done to separate the charges. When the charges are allowed to fall together again, the energy is released and appears in some other form.

The gravitational field is not analogous. While energy is expended in creating the electrostatic field, none is expended, according to the traditional view, in creating the gravitational one. It is claimed instead that this field just is. When, again, an object falls under the influence of the electrostatic field, when, for instance, a charged particle falls down the potential gradient, the field is weakened. This is the reason why one says that the energy is stored in the field. But it seems to be meaningless to say that energy is stored in the gravitational field. One can speak of the energy stored in the water of a mountain lake, for this, when released, flows over stones and pebbles and the friction converts this energy into heat. But the field that causes the water to flow down the valley is not in the least reduced in the process; the earth's hold on the moon is as strong after, as before, the water has flown out of the lake.

22.8: Action at a Distance
The earth is in one place and the meteor that is accelerated by it is in another. Yet we attribute the acceleration to the earth. So the earth exercises an influence in a place where it is not. How? This is yet another of the facts about gravitation that have to be explained.

The problem is known as that of action at a distance. That it presents itself in Newtonian mechanics is obvious, but strangely enough it has sometimes been denied that it also presents itself in relativity theory. However, the only difference is in the thing on which the earth is assumed to act.

According to Newtonian mechanics the earth acts directly on the stone, though it be from afar. But according to relativity theory the action of the earth is indirect. The earth is claimed to act, not on the stone, but on space; it causes this to be curved. It is the space that, in turn, acts on the stone. So action at a distance is presumed in both theories; in the one it is between the earth and the stone, and in the other between the earth and the part of space where the stone is.

The expression 'action at a distance' is ambiguous. It could mean a kind of action that does not puzzle us at all. When a person sends a letter to someone in another town and asks him to do something he can be said to be exercising an influence in a place where he is not. When a shell is fired out of a gun and explodes some miles away one can say that the gun is exercising an influence at a place where it is not. One can say the same of a lamp in a photographer's studio. The lamp is in one place and the photographic plate on which the light falls in another, and yet the lamp exercises an influence on the plate.

In these examples the action at a distance is effected by means of a transfer of energy; something moves from the one place to the other. Action is between the writer and the letter that he is writing in one town and between the letter and the recipient in the other. It is similarly between the gun and the shell in one place and between the shell and the building destroyed by it in the other place. It is between the lamp and the light rays in one part of the photographer's studio and between the light rays and the photographic plate in another part. In all these cases nothing separates the cause and its immediate effect and the distance to the final effects is spanned by something that moves from the one place to the other, be it a letter, a shell, or light waves. Such movement involves the transfer of energy from the one place to the other and so one can speak of the kind of action at a distance that is effected by a transfer of energy.

This is not usually understood by the expression 'action at a distance'. What is meant is action without an accompanying transfer of energy. It is so understood in the generally accepted view of gravitation, both in Newtonian mechanics and in relativity theory. At the moment when a stone falls it is not assumed that something leaves the earth and travels towards the stone. It is assumed in Newtonian mechanics that the falling occurs without the simultaneous transfer of anything from the earth to the place where the stone is.

The same assumption is usually made in relativity theory. It is assumed that the mere presence of the earth causes space in remote places to be curved. It is not assumed that to maintain this curvature anything leaves the earth and produces its effect at the remote place. The earth is not said to be depleted of anything by creating this curvature around itself. Once again the analogy to radiation and other phenomena fails. When there is action at a distance by the transmission of energy the action is the result of something that happens. This is easy to accept. But it is not so easy to accept the notion of action at a distance as the result of something that merely is. A radiating body loses energy when it acts at a distance; but the traditional view is that the earth acts gravitationally at a distance without losing anything, be it repeated.

Here the mathematician is in an enviable position. He can write down an expression for action at a distance and is not called upon to give it a physical interpretation. But the physicist is in a quandary. His task is to give meanings to the symbols with which the mathematician has provided him. If the symbols say that there is action between distant places without transfer of energy from one place to the other he is puzzled.

22.9: Summary
The questions discussed above remain to remind us that we do not yet know as much about gravitation as we should like to know. For the sake of convenience let them be repeated here. They are:
(1) Can gravitation be brought into association with the main body of physical science?
(2) Why do inert and attracting mass always occur in association? The question can take the alternative form: Why does an accumulation of inert mass cause the surrounding space to be curved?
(3) Why does gravitation seem to contradict the Principle of Stabilization according to which every process in a self-contained system tends to reduce its cause?
(4) Why do gravitational fields always have the same sign?
(5) Why is there a limited number of constant ratios between unit electric charge and the inert mass of the elementary particles? Why, moreover, are the gravitational fields attributed to such particles vastly weaker than the electrostatic ones?
(6) Why is gravitation uncontrollable?
(7) Why is gravitation the only phenomenon that does not seem to require a transfer of energy?
(8) How can one reconcile what is known about gravitation with action at a distance?

These are, I venture to claim, the kinds of question about natural phenomena that scientists find it profitable to ask. Answers to this kind of question usually lead to new insight into the nature of the physical world. At least some of these questions have not been ignored in the past, perhaps. But they have certainly not been asked with the insistence that they require. It may be that the prospect of finding answers has seemed to be too remote to justify the effort. But I hope to make it clear in the following chapters that such defeatism is not warranted. There is an excellent prospect that satisfactory answers to very nearly all the above questions can be found by the same procedure that has served for answers to questions about the spiral nebulae. No further hypothesis will be needed than that of Minimum Assumption.

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