Paul R. Heyl
GRAVITATION: AN ENIGMA
(Title of article by Robert H. Dicke, American Scientist, March, 1959)
Here is an unintentional but graphic commentary on the progress that has been and is being made toward an understanding of one of the most Conspicuous and most fundamental of all physical phenomena. At the time Heyl wrote his article, almost three hundred years after Newton first grasped the significance of the falling apple and formulated the mathematical expression which represents the gravitational force and enables us to calculate its magnitude with extreme precision, the nature and origin of the phenomenon could still be described as a “mystery.” Five more years of effort by scientists of the highest caliber sufficed only to raise this mystery to the status of an “enigma”: a rather imperceptible advance, to say the least. “It (gravitation) may well be the most fundamental and least understood of the interactions,”1 Dicke tells us.
Of course, some scientists disagree with this evaluation, and Dicke concedes in his article that many of his colleagues would take exception to the use of the term “enigma” in this connection. However, the record clearly corroborates the opinions of these two specialists in gravitational research. Some progress has been made in the experimental field since Newton’s day, but aside from the accurate measurement of the gravitational constant, the experimental gains have been largely of a negative character; that is, they consist of increasingly precise measurements which demonstrate the absence of certain effects that might be expected, or at least suspected. Progress toward a theoretical understanding has been meager; indeed the growing disillusionment with Einstein’s General Relativity Theory indicates that progress along this line is practically non-existent.
This General Theory is the only major theoretical step taken since Newton, which can even claim to have any factual backing, and while it achieved widespread acceptance initially, doubt as to whether the claims made on its behalf are justified has been increasing as time goes on. As Dicke appraises the situation, “In addition to dissatisfaction with the scanty observational evidence supporting Einstein’s theory of gravitation, there are certain conceptual difficulties which are a source of doubt concerning the complete correctness of the theory in its present form.”2 Similar expressions of skepticism are currently being voiced by many other observers. H. Bondi tells us, for example, “The very few and minor points of discrepancy (between Newton’s gravitational theory and Einstein’s) are observationally not too firmly established.”3 Louis de Broglie elaborates this same thought: “The new phenomena predicted by it (the General Theory) are indeed very small and, even when they are actually observed, it can always be asked if they really have their origin in the cause which the theory of Einstein attributes to them, or rather in some other very small perturbation which was neglected in the analysis.”4 Werner Heisenberg adds, “For the theory of general relativity the experimental evidence is much less convincing… this whole theory is more hypothetical than the first one (the Special Theory).”5 G. J. Whitrow concurs in this appraisal of the observational evidence: “…the General Theory has a far less impressive list of crucial empirical tests to its credit,” and he comments further, “…there is an ambiguity latent in this method (of reducing gravitation to geometry)… Indeed, in developing the theory this ambiguity continually arises.”6 Martin Johnson tells us that Einstein followed up his 1905 success with a “less certifiable sequel in 1915 which has in some of its implications led science astray.7 Even Henry Margenau, one of the strong supporters of the Relativity doctrine, admits that General Relativity has “suffered a certain loss of glory.”8
E. A. Milne may be regarded as somewhat prejudiced on this score, as he is the author of a competing theory, but the mere fact that competent investigators such as Milne see a necessity for some other approach is itself a serious reflection on the adequacy of the General Theory, and Milne’s comments are therefore of interest in this connection. General Relativity, he says, “in the writer’s opinion, is of a nature alien to the main tradition in mathematical physics.”9 Bondi sums up the situation: “It (the General Theory) is considered to be correct by a majority of theoretical physicists, but there is a substantial minority that considers it to be wrong or, at least, not established.”10 The existence of this “substantial minority” is all the more significant when we note the kind of individuals who are included in the group: specialists in gravitational research such as Dicke and Heyl, world-renowned leaders in the field of physics such as Bridgman, de Broglie and Heisenberg, active investigators in the areas where General Relativity should be most applicable, such as Bondi, Whitrow, Johnson and Milne, and so on.
A factor that has contributed heavily to this increasing skepticism as to the validity of the General Theory is that it seems to have arrived at a dead end. One of the criteria by which we are able to recognize a sound physical theory is the manner in which it fits in with existing knowledge in related fields and sheds new light on phenomena other than that for which it was originally constructed. The failure of Einstein’s gravitational theory to accomplish anything of this nature or to show the normal amount of improvement of its own internal structure during the half century that has elapsed since its inception therefore weighs heavily against it. Freeman J. Dyson describes the situation in this manner: “…the view of the world (given by General Relativity)… has remained since 1929 almost totally sterile”.11
But in any event, whether or not these increasing doubts are justified, this theory does not carry gravitational knowledge very far beyond the point where Newton left it. The contributions of the General Theory to an understanding of gravitational processes are greatly overestimated in current scientific thinking. Even if the assertions of the theory were correct, which the succeeding pages will demonstrate that they are not, they do not furnish actual explanations for the things which they purport the explain; they merely push the need for explanation farther into the background where it is less obvious and can more conveniently be disregarded.
Such a statement may seem rank heresy today, at a time when, in spite of the doubts expressed by the more critical observers, Relativity Theory has been elevated to the status of an article of faith on a par with or even superior to the established facts. The textbooks tell us that Newton’s gravitational theory is grossly deficient in that it merely assumes the existence of a gravitational force without giving us any explanation of how such a force originates, and Einstein’s work is hailed as a great theoretical advance that provides us with the explanation which Newton was unable to supply. Typical of the positive and explicit statements to this effect that can be found throughout present-day scientific literature is the following: “Strange as Einstein’s idea (General Relativity) seemed, it was able to explain something which the Newtonian law of gravity had not been able to explain.”12But neither Einstein nor his fellow relativists make any such claim. What they say they have done is to furnish us some good reasons why we should not ask for an explanation.
Willem de Sitter is very explicit about this situation in his book Kosmos. He points out that no one, Einstein or anyone else, has actually explained gravitation, in spite of all the effort that has been devoted to the task: “In the course of history a great number of hypotheses have been proposed in order to ‘explain’ gravitation, but not one of these has ever had the least chance, they have all been failures.”13 De Sitter then goes on to say that Einstein’s actual accomplishment is to make gravitation identical with inertia, which eliminates the need for an explanation, as “Inertia has from the beginning been admitted as one of the fundamental facts of nature, which have to be accepted without explanation, like the axioms of geometry.”
Einstein himself admits that he cannot give any explanation for the properties with which he is endowing the “space” in which the physical processes represented by his theories take place. “Our only way out,” he says, “seems to be to take for granted the fact that space has the physical property of transmitting electromagnetic waves, and not to bother too much about the meaning of this statement.”14 In the light of this half-apologetic admission by the originator, some of the present-day encomiums of the theory are nothing short of ridiculous. “…the (general) theory of relativity is a step of almost conclusive power,” says one modern author, “It banishes from physics that occult force of gravity which Newton would not defend, reaching instantaneously across the equally occult idea of void.”15 How much “conclusive power” can we legitimately attribute to anything that we are asked to “take for granted” without inquiring too closely into its meaning? Is this any less “occult” than the unexplained aspects of Newton’s theories?
At the same time, the inability of existing gravitational concepts, whether connected with General Relativity or not, to account for some of the observed characteristics of gravitation has had the very curious effect of convincing the physicists that the observations give us the wrong picture of the gravitational phenomenon. No one has been able to conceive of a mechanism whereby one mass can exert an influence on another distant mass instantaneously, and hence it is generally assumed by the physicists that there must be some kind of propagation of the gravitational effect at a finite velocity, even though there is not the slightest evidence that this is true. Similarly, there is a general tendency to accept the existence of some sort of a gravitational unit—a graviton, or some such thing—as a fact, without any experimental or observational evidence to back up the assumption, merely because this facilitates setting up certain kinds of gravitational theories.
In all practical applications the picture of the situation inferred from the results of observation is accepted as correct. All astronomical calculations and other computations involving gravitation are made on the assumption that the effect is instantaneous, and so far as we are aware, no inconsistencies result from this procedure. But the theorists then turn around and repudiate all of this, simply because they have been unable to discover any satisfactory theory that fits the observed facts. Max van Laue, explains, on their behalf, “Nowadays we are also convinced that gravitation progresses with the speed of light. This conviction, however, does not stem from a new experiment or a new observation, it is a result solely of the theory of relativity.”16
When taken in conjunction with the grave doubts now being entertained as to the validity of General Relativity by some of today’s foremost physicists, this necessity for adjusting the facts to the theory rather than the theory to the facts, has some very definite implications that deserve serious consideration, irrespective of whether or not a satisfactory alternative theory is available. The presentation of a new theory of gravitation in this work merely emphasizes a serious weakness in the structure of current scientific thought that should have been evident in any event.
The objective of this present work is to show that gravitation can be explained and therefore we do not need to try to convince ourselves that we must accept it as an “unanalyzable.” It will be demonstrated in the subsequent pages that a simple and logical theory of gravitation can be constructed without the necessity of explaining away any of the known characteristics of this phenomenon: a theory which accounts for each of these characteristics in the exact form in which it is revealed by observation, and which goes on from there to provide a great deal of information in collateral fields, as a valid gravitational theory should do. This presentation will show that gravitation can act instantaneously, without an intervening medium, and in such a manner that its effects cannot be screened off or modified in any way, and can do all of this in a perfectly natural and logical way, without the necessity of utilizing any philosophically unacceptable assumptions such as that of action at a distance.
As a background against which to set up the new gravitational theory, it will be desirable to outline briefly just what is known about the gravitational phenomenon at the present time. In this respect we are, of course, limited by the accuracy of existing methods of measurement. For instance, if the available instruments allow us to measure a certain effect to within one part in 1010, and we find no indication of such an effect with these instruments, this creates a strong presumption that there is no effect of this kind. It must be conceded, however, that a theory which predicts an effect amounting to less than one part in 1010 is not inconsistent with the experimental results and therefore could be correct, but any theory which depends primarily on assumed effects that are beyond the reach of the extremely accurate instruments now available is certainly highly speculative, to say the least.
The following paragraphs summarize what is now known to the degree of precision of the measurements. In order to be satisfactory, a theory must either agree with these conclusions derived from experiment, or at least must not predict any deviations large enough to be detected by existing methods.
General. There is no question but that a gravitational effect actually exists. Newton attributed this effect to the existence of a gravitational force, but this interpretation has been challenged by some of the more recent investigators, notably Einstein, whose contention is that the gravitational effect is produced by a distortion of the space-time structure in the vicinity of a mass, and that there actually is no such thing as a gravitational force. However, if we analyze this conflict from a critical standpoint, it becomes apparent that what we have here is not a physical question but a question of semantics. The word “force” normally suggests some kind of a pull or a push and Einstein’s contention, in essence, is that his explanation attributes the gravitational effect to something that is not in the pull-push category. But Newton did not limit his concept of gravitational force in this manner; in fact, he specifically refused to express any opinion as to the nature of the force. So far as Newton’s theory is concerned, force is simply a quantity which relates mass to acceleration, and if we set up our definition of force on this basis (that is, define it by means of the equation F = ma) the consequences of the postulated space-distortion constitute a gravitational force, and can be treated as such. Einstein does this himself in his mathematical treatment of gravitation.
Relation to distance. The gravitational force between two masses is inversely proportional to the square of the distance between the centers of the masses.
Gravitational constant. The numerical constant in the gravitational equation based on the mass and distance relationships just stated is 6.67×10-8 when expressed as dynes × cm2 × g-2
Relation to chemical composition. The gravitational force is independent of the chemical composition of the masses involved.
Relation to crystal orientation. The gravitational force is independent of the direction of the crystallographic axes.
Relation to temperature. The gravitational force is independent of temperature.
Relation to physical state. The gravitational force is independent of the physical state of the masses involved.
Velocity of propagation. So far as is known at this time, the effect of gravitation is instantaneous, and in all practical applications of the gravitational equation the calculations are made on this basis, even at galactic distances. Many theories of gravitation, including the Einstein theory, assume a finite velocity of propagation of the gravitational effect, but there is no experimental or observational evidence to support this assumption.
Screening. The gravitational force cannot be screened off or modified in any way by any means now known.
In addition to listing the things that we know about gravitation, as a preliminary to a critical study of the phenomenon, it will be helpful to list some of the things that we do not know, because there is a general tendency to confuse fact with fancy when the consideration of a problem extends over such a long time and involves so much speculation. The speculative hypotheses of a century or half-century ago are likely to have acquired the standing of axioms by this time where they have remained unchallenged in the interim.
Curved space. There is no evidence that space is, or can be, curved or deformed in any way. It is true that Einstein has set up a system wherein some of the characteristics of gravitation are explained on the assumption that space is deformed by the presence of matter, but the phenomena which an assumption was specifically designed to fit cannot be used as proof of the validity of that assumption, and there is no other evidence of an independent character to verify the existence of a deformation of space.
Gravitational fields. There is no evidence that a gravitational field exists in any physical sense. All that we know is that a test particle placed in a particular location experiences a gravitational force due to the proximity of a mass. So far as we have any actual knowledge, the only participants in this phenomenon are the two masses; any theory that calls for an intermediate effect on or by a field, a medium or space itself, is purely speculative.
Mediums. There is no evidence of the existence of a medium of any kind through which gravitational effects could be propagated. Furthermore, there is no evidence that space has the properties of such a medium.
Gravitational units. There is no evidence of the existence of “gravitons” or any such gravitational unit.
Variability with time. There is no evidence that the strength of the gravitational effect has varied or is varying with time.
On the basis of the foregoing, a satisfactory theory of gravitation must produce an explanation of how two masses can exert a force on each other instantaneously, without an intervening medium, and in such a manner that the effects cannot be screened off or modified in any way, or alternatively, if one or more of these requirements is not met, the theory must provide an acceptable explanation of the observed facts which now appear to lead to these requirements.
Before undertaking to present all explanation of gravitation, it is first necessary to define what we mean by the term “explanation.” This is one of those words whose significance seems perfectly obvious in ordinary usage, yet proves rather difficult to down when we attempt to be more specific, and current literature is full of discussion and controversy over the various philosophic aspects of the explanation process. A recent book by R. B. Braithwaite, for example, devotes its entire 376 pages to this one subject of Scientific Explanation.
As is so often true under similar circumstances, much of this debate is actually meaningless, since it is essentially a discussion of the question as to what significance ought to be assigned to the word “explanation.” This question assumes that the word has an inherent meaning and that the identification of this true meaning is a task for the philosopher or the scientist with philosophical interests. The truth is, however, that no word has an inherent meaning; it has only the meaning that we choose to assign to it. Of course, the object of language is communication, and in order to accomplish that objective it is necessary to have some sort of a general agreement as to the significance that is to be attached to the words that are utilized in that language, and we have compiled dictionaries to keep a record of the meanings that are agreed upon. It does not follow, however, that a particular word must necessarily be used in exactly the same way by everyone, nor even that it always be used in the identical manner by the same individual. Eddington, for example, makes it very clear that he has no intention of restricting himself to a single meaning for every word. He remarks, “A correspondent has pointed out to me that in various places in The Nature of the Physical World the word “space” occurs with four different meanings. I think he expected me to feel penitent. But the word has these meanings…”17
In order to be intelligible, the word “explain” must be used in the same general sense specified in the dictionary; that is, to make clear. But clarification can be accomplished in more than one way, and there is no compelling reason why one way should be any more official than another is. Each individual therefore has the option of selecting the type of explanation which he wishes to offer, and the proper criterion that should be applied in evaluating the explanation is not whether it conforms to some particular philosophical idea of what constitutes an explanation, but whether it actually does clarify the situation in one way or another. The first aim of the present discussion will therefore be to describe the kind of explanation, which will be offered in this work.
All explanations must necessarily be based on certain specified premises and if the phenomena to be explained are of a basic nature, these premises cannot be other than assumptions. Braithwaite regards the explanation of a law or principle as a process of deducing it from some more general law or principle (the validity of which must, of course, be assumed) and since this process can conceivably continue endlessly, he concludes, “…there is no ultimate end to the hierarchy of scientific explanation, and thus no completely final explanation.”18
R. E. Peierls expresses the same point of view: “All explanations of natural phenomena therefore consist in reducing them to some basic laws. To ask for an explanation of these laws would merely mean reducing them to some other laws.”19 This is orthodox positivist doctrine—it can be found almost word for word in the writings of Comte but, with all due respect to the positivist philosophers, unless we define the term “law” in an unusually broad manner, this assumption that a law can only be explained by reducing it to some other law is not correct. If we pursue our quest for an explanation long enough we should ultimately be able to account for the law in terms of some basic property or properties of the universe. This is something quite different from what Peierls and Braithwaite envision. Braithwaite admits that in some other fields of activity we can have “a complete explanation in the sense that no further question can be asked of the same sort.”20 When we reach the point in scientific research where the next question must ask why the universe has a certain specific property, no “further question of the same sort” is possible in the physical field either.
Let us consider, for example, the relation of the intensity of illumination to the distance from the source of light. We start from the premises that such a light source exists, and that it emits photons, which are distributed uniformly in all directions and move linearly outward at a constant velocity. We then want an explanation of the fact that under such circumstances the intensity of the illumination at any distance d from the light source is inversely proportional to d2. Here we can see that a complete explanation is provided by geometry alone, since the surface area of a sphere of radius d is proportional to d2, and under the conditions specified in the initial assumptions the total illumination striking such a spherical surface must necessarily be constant irrespective of the radius. If we then assume! that the universe is three-dimensional and Euclidean, both of which assumptions are supported by observational evidence independent of the behavior of light, these assumptions explain the observed relationship.
From a purely physical standpoint, this is as far as we can go. So far as we know, a four-dimensional universe or a five-dimensional universe may be possible, but the question as to why our particular universe is restricted to three dimensions is a “question of a different sort”: one that cannot be answered by means of any information that we can obtain within our three-dimensional universe. In order to consider such a question at all, we must leave physics and enter the domain of metaphysics. When we have carried our explanation to the boundaries of the physical realm in this manner we therefore do have a “completely final explanation” in the sense that Braithwaite is using the term. (Of course, it is possible that the explanation might be wrong, and hence not “completely final” in this sense.) Such an explanation which relates the phenomenon in question directly to some simple inherent property or properties of the universe, the existence of which can be independently confirmed, constitutes what we may call an explanation of the first order.
Newton’s Law of Gravitation falls considerably short of this status; in fact, on this same basis, we will have to classify it as an explanation of the third order, since it leaves two physical issues unresolved, in addition to the metaphysical question that we cannot avoid. The essence of Newton’s theory is the assumption that a force of attraction exists between each mass and every other mass. But merely assuming the existence of such a force leaves us with two unanswered questions: (1) How does the force originate? and (2) How does it work?
Einstein’s gravitational theory still leaves us in essentially the same position. This theory rests on the assumption that the existence of mass causes a deformation of the space-time structure which, in turn, accounts for the gravitational attraction. Here again we have the same two unanswered questions: (1) How does the deformation originate; that is, what is there about the property of mass that deforms space or space-time? and (2) What is the mechanism of the deformation; that is, how does it operate? Thus, whether or not Einstein’s theory is superior to that of Newton from other standpoints, it is not an explanation of a higher order, it is still a third order explanation.
At this point it is necessary to call attention to the fact that the classification of scientific explanations outlined and discussed in the foregoing paragraphs does not indicate how satisfactory the explanations may be, as this involves some additional factors. It is quite possible that an explanation of the third order might be quite satisfactory as far as it goes, whereas some first order explanation might be wholly unsatisfactory. The optimum, of course, is a fully satisfactory first order explanation.
The most important requirement of a satisfactory explanation, irrespective of the class to which it belongs, is that it should satisfy the tests that any physical theory must meet in order to be considered valid; that is, it must be internally consistent, and in agreement with all of the pertinent facts as revealed by observation or measurement, or at least not inconsistent with any of these facts. Next the explanation must be complete. It must not only account for the existence of the phenomenon itself, but must also account for the known characteristics of that phenomenon, both qualitatively and quantitatively. Finally a truly satisfactory explanation must contribute toward fittings the phenomenon into the general fabric of physical theory by enlarging its field of application or by relating it to other physical phenomena.
In relatively recent years a new twist has been introduced into the question of what constitutes a satisfactory explanation of a physical phenomenon. The entities with which modern science has had to deal—phenomena of the very small, the very large, and the high velocity regions—have been extremely difficult to describe and explain in the terms of reference provided by knowledge of physical relations in the more familiar regions, but a reasonable degree of success has been attained in the construction of mathematical expressions to represent these phenomena. Under such conditions, the normal conclusion would be that formulation of the mathematical expression simply represents the first step on the way to a complete explanation. This is, in fact, a very common sequence of events in scientific research. For example, Planck’s results on the distribution of frequencies in black-body radiation first took the form of a mathematical equation which achieved the agreement with experimental results that the previous expressions of Wien and Rayleigh failed to attain. After the mathematical relationship was discovered and verified, Planck turned his attention to finding an explanation of this radiation equation and, as he tells us in his account of his discoveries, a great deal of hard work was required before the quantum idea emerged.
We would naturally expect that any other mathematical expression which correctly represents some physical relationship could likewise be translated into physical terms if sufficient study is applied to the problem, but many of the basic mathematical relations of modern physical science have thus far resisted explanation, even though these matters have been given long and intensive study. If our assumption as to the existence of a physical explanation for any correct mathematical relation of this kind is valid, we are forced to conclude either (1) that these mathematical expressions are not correct representations of the physical relations to which they are supposed to apply, or (2) that the amount of effort applied to the task of finding the explanations has been insufficient, or (3) that the abilities of those who have attacked these problems are not equal to the task. All of these alternatives are definitely distasteful, and to avoid facing them the scientist of the present day has resorted to one of the ingenious techniques which modern science has devised to cope with this kind of a situation: a principle of impotence. The theorist who fails to solve such a problem simply meets the issue by postulating that the problem is inherently incapable of solution.
In order to soften the impact of this dictum to some degree, it is now customary to accompany this postulate that a physical explanation is impossible with an argument to the effect that such an explanation is unnecessary anyway, since a purely mathematical explanation is entirely adequate for those who accustom themselves to thinking in mathematical terms. “To him (the modern scientist) the algebraic law of gravitation, for example, is the satisfying explanation for a host of phenomena, whereas to many nonscientists the very same law would be regarded as an additional unexplained mystery.”21
There is a bit of Chinese philosophy which asserts that if one cannot get what he wants, he can arrive at exactly the same result by persuading himself to want only what he can get. Whether those who are attempting to persuade us to accept the mathematical equations as ultimate explanations of physical phenomena are deliberately employing this ancient philosophy, or are doing so unconsciously, this is certainly the direction that the arguments take. When Eddington tells us, “We do not ask how mass gets a grip on space-time and causes the curvature which our theory postulates. That would be… superfluous,”22 he is enunciating exactly this point of view. Philipp Frank gives us the same thing in the form of a general proposition: “The task of physics is only to find symbols among which there exist rigorously valid relations, and which can be assigned uniquely to our experiences.”23
But regardless of any validity that this renunciatory idea may have in application to purely personal desires, it does not hold water when applied to scientific research. In the case of gravitation, we want to know how the gravitational force, or gravitational effect, originates and how it operates, not only because we have an innate desire for knowledge, but also because we are confident on the basis of past experience that this additional knowledge of the gravitational phenomenon will open the door to further advances in related fields. The mathematical expression of gravitation, the “algebraic law” which Holton and Roller, the authors of the statement quoted in the preceding paragraph, are asking us to accept as a “satisfying explanation” gives us no help of this kind. In the words of Paul F. Schmidt, “mathematical propositions tell us nothing about the character of nature; they are uninterpreted formalisms.”24
We can get an idea of where this currently popular “Be satisfied with a mathematical explanation” philosophy leaves us if we consider what would have happened to Planck’s discoveries if he had stopped with his mathematical expression for black-body radiation, and had not gone on to formulate his explanation of this equation in terms of quanta. In this event progress would have ceased with black-body radiation; it would not even have been possible to take the next step, Einstein’s extension of the theory to the photoelectric effect, to say nothing of all the subsequent development that has taken place in this area. Planck recognized this situation clearly. He explains, “But even if the absolutely precise validity of the radiation formula is taken for granted, so long as it had merely the standing of a law disclosed by a lucky intuition, it could not be expected to possess more than a formal significance. For this reason, on the very day when I formulated this law, I began to devote myself to the task of investing it with a true physical meaning.”25
If we accept the Confucian viewpoint of the “modern scientist” who wants us to be content with the mathematical expression of the gravitational law, we are deliberately restricting ourselves to the limited field in which we now know this law to be applicable, and we are closing the door to any increase in scientific knowledge that might be possible through a more complete understanding of the gravitational phenomenon. Of course, the physicist who champions the mathematical equation as the ultimate explanation of gravitation can justify this stand only on the basis of the contention that this equation expresses the full range of the phenomenon, and that there are no other pertinent facts which could be revealed by a physical explanation. No attempt will be made to refute this contention at this point, as the entire work from here on constitutes such a refutation. The subsequent pages will show that a complete and satisfactory explanation of a higher order can be found, and that with the benefit of this more adequate and comprehensive explanation, the gravitational relations can be extended to a much wider field. Part Two of this volume will raise Newton’s theory to the status of a second order explanation by deriving his assumption of the existence of a gravitational force from a more general set of basic assumptions which will have the effect of reducing force to motion. This still leaves us with a question as to the origin of the motion, but it eliminates one of the two questions that are unanswered in both Newton’s and Einstein’s treatment of the subject, since we do not have to ask how motion works. Part Three will extend this to a first older explanation by showing that the gravitational assumptions utilized in Part Two can be deduced from certain independently confirmed postulates as to the general nature of the physical universe.
The great dilemma that has faced gravitational theory ever since its inception is the fact that in order to account for the gravitational attraction it seems to be necessary either to postulate the existence of a medium capable of transmitting the gravitational effect from one mass to another or else to concede the possibility of action at a distance. There is no evidence of any medium, and the properties which such a medium would have to possess in order to account for the observed effects are fantastic. On the other hand, the idea that one mass can exert an influence on another mass at a distance without the benefit of any connecting medium is philosophically unacceptable to most scientists. Newton himself called it “absurd.”
It is commonly contended that Einstein resolved this dilemma by devising an explanation of gravitation based on geometry rather than on force, but if we examine his gravitational theory carefully, it is apparent that he has merely moved the dilemma to a new location; he has not eliminated it. Newton’s problem in this connection was to account for the existence of the gravitational force. Einstein accounts for the force (or the equivalent of such a force) by a distortion of the space-time structure, but if we subject this explanation to a critical examination instead of just following the currently fashionable practice and accepting it on trust, it is obvious that Einstein faces exactly the same problem in accounting for the space-time distortion that Newton does in accounting for the gravitational force. In order to explain how mass A is able to influence the structure of space-time at the location occupied by mass B. we either have to postulate the existence of a medium connecting location A with location B (postulating that space-time has the properties of a medium is, of course, equivalent to postulating a medium) or else we have to postulate action at a distance: some mechanism whereby mass A can exert an influence on the space-time structure at a remote location B without any connection between the two.
The general attitude of the scientific profession toward these problems is a very strange phenomenon: one that might well serve as the basis for an interesting study in psychology. Bridgman suggests that it “may some day become one of the puzzles of history.”26 In spite of the fact that Newton refused to commit himself to any specific explanation of the gravitational force which he postulated, and took the eminently sound position that the existence of this force should be accepted as an empirical fact pending the discovery of some satisfactory explanation at some future date, the scientific profession in general has refused to concede that any possibilities can exist beyond its current range of vision and has taken the stand that Newton’s system necessarily involves the assumption of action at a distance. “Newton’s mechanics assumed action at a distance between the different bodies,” says Max Von Laue, “His law of gravitational attraction shows this very distinctly.”27 At the same time, the attitude toward action at a distance has been one of strong distaste. Pascual Jordan expresses the general sentiment in these words:
But even in Newton’s day there were physicists who looked with misgivings on this idea. That two bodies in the cosmos should exert a reciprocal force which leaps, as it were, over the vast empty space between them—that each of these bodies should exert a force where it is not, on a body far removed from it—struck these critics as incredible. They desired an explanation of how the energy emanating from one body spreads or propagates itself through space, until it finally reaches the other, remote body28
In such an atmosphere, where the great majority of physicists were firmly convinced that Newton’s theories were solidly tied to this thoroughly unpalatable concept of action at a distance, Einstein’s General Theory came as a welcome relief from an intolerable situation, and under the circumstances most scientists were quite content to accept Einstein’s conclusions at face value without any very serious attempt to inquire into their validity. As Eddington admonishes us in the statement previously quoted, “we do not ask” about such matters, and Einstein’s theory has therefore been incorporated into the current dogma of the scientific profession substantially on the terms which he laid down; that is, on the basis that we should “take for granted” the properties which he assigns to space, and not “bother too much” about their meaning.
There are, it is true, a few prominent members of the scientific community who have refused to accept on trust these explanations that do not explain. G. C. McVittie is outspoken: “To say instead that gravitation is a manifestation of the curvature of four-dimensional geometrical manifolds is to account for a mystery by means of an enigma”29 Bridgman says essentially the same thing: “I believe, however, that an analysis of the operations that are used in specifying what the field is will show that the conceptual dilemma (connected with the difficulty of imagining any ’mechanism’ by which action at a distance occurs) has by no means been successfully met, but has merely been smothered in a mass of neglected operational detail.”30 As these observers indicate, what Einstein has actually accomplished, so far as the great dilemma of gravitation is concerned, is not to resolve it, but to push it farther into the background where its existence is less obvious.
The salient fact here is that the substitution of a hypothetical finite velocity of propagation for action at a distance is purely a matter of wishful thinking; there is no experimental evidence of such propagation—“…it certainly cannot be measured at the present time, even if it does exist,”31 reports Bryce S. De Witt in a review of the present gravitational situation—and there is no evidence of any kind which conflicts with the hypothesis that the effect is instantaneous. All practical gravitational calculations are carried out on this instantaneous basis by means of Newton’s equation. Einstein himself admits, “Newton’s law (of gravitation) still remains the basis of all astronomical calculations.”32 Most scientists accept the General Theory of Relativity but no one uses it except as a mental and mathematical exercise; indeed it is doubtful if anyone knows how to use it in anything other than an artificially simplified situation.
The impetus for the acceptance of this purely hypothetical finite velocity of propagation comes almost entirely from a pronounced distaste for what appears to be the only alternative. It is, of course, easy to understand why the scientific community is reluctant to accept the concept of action at a distance. There would be little reason for making any attempt to comprehend nature unless we have some underlying philosophical convictions as to the rational character of the relationships with which we are dealing, and action at a distance does not come within our usual definition of rationality. What is not so easy to understand is why this particular concept should be singled out as so overwhelmingly objectionable that it must be avoided at all costs. What have we gained if we dispense with action at a distance only by admitting such a concept as that of distortion of space? We object to action at a distance mainly because we cannot conceive of any mechanism whereby this can take place, but can anyone explain the mechanism whereby space can be distorted? The relativists have no explanation to offer. Eddington says “we do not ask.” Einstein tells us that we should “take it for granted.” Margenau gives us the same answer: “At the present stage of science we cannot ask why the law of the metric is true.”33
After all, what is wrong with Newton’s attitude toward this question: a frank admission that he did not know how the gravitational force originates? Of course, we cannot be satisfied with this situation; we must continue to search for an explanation. But as long as we have no explanation, the best thing that we can do is to say so. Here is one of the most serious faults of present-day scientific practice: an almost psychopathic unwillingness to admit ignorance. Where the truth is unknown, present-day scientists seem unable, in most instances, to resist the temptation to present their opinions, or those of the “authorities” in their respective fields, in the guise of established facts.
There is no lack of warning as to the dubious character of this kind of “knowledge”; clear-sighted observers are continually sounding the alarm. For example: from Louis de Broglie, “…many research workers take a number of contemporary theories as fully proven simply because they do not realize on what shaky foundations these theories rest”;34 from Paul Freedman, “…existing scientific knowledge is not nearly so complete, certain and unalterable as many textbooks seem to imply”;35 from Sir Edmund Whittaker, a caution aimed particularly at General Relativity, “It is unwise to accept a theory hastily on the ground of agreement between its predictions and the results of observation in a limited number of instances: a remark which perhaps is specially appropriate to the investigations of the present chapter (title: Gravitation)”;36 from P. W. Bridgman, “But it seems to me that our present theories, even the successful ones, are not yet constructed so completely in accord with sound principles but that in this day and generation criticism is a most necessary and useful enterprise for the physicist.”37 But this wise counsel is for the most part unheeded.
A collateral factor that has had some influence toward encouraging the assumption that the gravitational effect is propagated at a finite velocity is an analogy with electromagnetic radiation. The line of reasoning in this case is as follows:
Even a minimum of consideration of this reasoning is sufficient to make it clear that there is only a very tenuous connection between the initial premise (1) and the final conclusion (4). The need for a very careful and thorough evaluation of the evidence is therefore definitely indicated, but here we find that the conclusion that has been reached is so highly satisfactory to a scientific world desperately anxious to have something—anything—which can replace the unwelcome concept of action at a distance that the usual processes of critical scrutiny and verification have been waived.
For present purposes, however, it is essential to have a realistic appraisal of the merits of this analogy. Let us therefore review the characteristics of electromagnetic radiation. It has been found that this radiation consists of discrete units of an oscillating character—photons—which originate from matter at specific locations and travel outward from these points at a constant velocity, which we recognize as the velocity of light. In empty space these photons travel in straight lines, but when they encounter matter their direction is subject to various modifications such as reflection, refraction, etc.
Each photon has a definite frequency of vibration and a corresponding energy content, hence these photons are essentially traveling units of energy. The emitting agency loses a specific amount of energy whenever a photon leaves. This energy travels through the intervening space until the photon encounters a unit of matter with which it is able to react, whereupon the energy is transferred, wholly or in part, to this unit of matter. At either end of the path the energy is recognizable as such, and at either location it is readily interchangeable with any other type of energy. The radiant energy of the impinging photon may, for instance, be converted into kinetic energy (heat), or into electrical energy (the photo-electric effect), or into chemical energy (photochemical action). Similarly, any of these other types of energy which may exist at the point of emission of the radiation may be converted into radiation by appropriate processes.
Now let us ask, are these the characteristics of gravitation? The answer must be an unequivocal No! They have no resemblance at all to the characteristics of the gravitational phenomenon. Gravitational energy is not interchangeable with other forms of energy. At any specific location with respect to other masses, a mass unit possesses a definite amount of gravitational (potential) energy, and it is impossible to increase or decrease this energy content by conversion from or to other forms of energy. It is true that a change of location results in a release or absorption of energy, but the gravitational energy which the mass possesses at point A cannot be converted to any other type of energy at point A, nor can the gravitational energy at A be transferred unchanged to any other point B (except along equipotential lines). The only energy that makes its appearance in any other form at point B is that portion of the gravitational energy which the mass possessed at point A that it can no longer have at point B: a fixed amount determined entirely by the difference in location.
This behavior is totally different from that of the electromagnetic photon. The photon carries its total complement of radiant energy undiminished up to the point of action, and at that point there is complete freedom as to the disposition of the energy. The photon may he reflected or refracted, retaining the full energy with which it originated, or it may transfer part or all of its energy to the matter with which it reacts. If the radiant energy at point A is x at time t1, this does not in any way determine the energy which will exist at time t2. The same is true of the energy at point B. Both of these values depend on the relation of the amount of radiant energy produced to the amount radiated in the interim. But if a quantity y of energy is radiated from point A and travels through free space to point B. it is still y when it reaches point B. Radiant energy thus remains constant in magnitude while traveling in free space, but it can vary almost without limit at any specific location.
The behavior of gravitation is exactly opposite. The gravitational effect remains constant at any specific location but varies if the mass moves from one location to another, unless the movement is along an equipotential line. If the gravitational energy at point A is x at t1, it remains x indefinitely (providing that no changes take place in the masses responsible for the gravitational effect). If the mass is allowed to fall to point B it arrives there with a gravitational energy z, which is determined solely by the conditions existing at point B and is completely independent of the magnitude of the original gravitational energy x and also independent of the nature of the events that have taken place along the route.
Energy is defined as the capability of doing work. Kinetic energy, for example, qualifies under this definition, and hence any kind of energy that can be converted to kinetic energy also qualifies. But gravitational energy is not capable of “doing work” as a general proposition. It will do one thing and one thing only: it will move masses inward toward each other. If this motion is permitted to take place, the resulting decrease in gravitational energy makes its appearance as kinetic energy and the latter can then be utilized in the normal manner, but unless gravitation is allowed to do this one thing which it is capable of doing, the gravitational energy is completely unavailable; it cannot do anything itself, nor can it be converted to any form of energy that can do something.
Gravitational energy, or potential energy, is purely energy of position; that is, for any two specific masses, the mutual gravitational energy is determined solely by their spatial separation. But energy of position in space cannot be propagated in space; the concept of transmitting this energy from one spatial location to another is totally incompatible with the fact that the magnitude of the energy is determined by the spatial location. Propagation of gravitation is therefore inherently impossible. The gravitational action is necessarily instantaneous as Newton’s Law indicates, and as has always been assumed for purposes of calculation.
Although these energy considerations are sufficient in themselves to demonstrate that there can be no such thing as a propagation of the gravitational effect analogous to the propagation of electromagnetic radiation, there are many other points of difference between these two phenomena which show that they are entities of a totally different character. For example, the emission and the absorption of light, or any other electromagnetic radiation, are two separate and distinct events. Although matter usually absorbs the emitted photons sooner or later, the absorption is not a necessary consequence of the emission and it is theoretically possible that some photon might never be absorbed. Gravitation, on the other hand, is a cooperative phenomenon. The gravitational attraction exerted by mass A upon mass B is never independent of the attraction exerted by mass B upon mass A; the gravitational effect is a mutual attraction of the two masses toward each other (or more properly, as we will see in Part Two, the equivalent of a mutual attraction).
Likewise, the behavior of gravitation in its action upon matter is altogether different from the behavior of electromagnetic radiation. The property of transparency, for instance, is entirely unknown so far as gravitation is concerned. Many substances are transparent to light, many more to x-rays; that is, the radiation passes through these substances more or less readily and to the extent of the transparency the behavior of these substances toward radiation is that of empty space. But so far as we have been able to determine, no material substance is in any degree transparent to the gravitational force. Then again, if a body is not transparent the electromagnetic radiation that falls upon it is absorbed or reflected and the space beyond the opaque body is shielded from this radiation, but there is no known way of screening off gravitation or of modifying it in any respect. When the earth comes between the sun and the moon, for instance, the solar radiation is intercepted by the earth and there is an eclipse of the moon, but observations of the moon’s orbit show that the gravitational effect of the sun upon the moon is not altered in the least by the presence of the earth in the intervening space. All of the available information indicates that the gravitational force between mass A and mass B is completely independent of the environments in which the two masses are located and unaffected by anything that may be present in the intervening space.
All in all, gravitation and electromagnetic radiation are about as dissimilar as any two physical phenomena can be, and the attempts that have been made to draw conclusions from an assumed analogy between the two are simply meaningless. There is no support anywhere for the idea that gravitation is propagated at a finite velocity and, however painful it may be, the scientific profession would be better off if it faced this issue squarely. Burying the head in the sand and refusing to recognize the facts accomplishes nothing. If no acceptable explanation of these facts is currently available, the only logical course of action is to take a stand alongside Newton and look upon the gravitational laws simply as empirical findings until such time as we are able to discover a satisfactory theoretical explanation.
Of course, the present-day contention is that three hundred years of intensive effort by scientists of the highest caliber have failed to produce any alternatives other than the two possibilities—action at a distance or propagation through a medium—which have been recognized from the start, and that this experience is sufficient to demonstrate that there is no other alternative. From a logical standpoint this contention is completely untenable, since it can be valid only if the scientists who have attacked the problem are, or were, infallible, but it has a strong appeal nevertheless, particularly to the baffled investigators and their colleagues, and it is a difficult argument to combat. However, it is a very vulnerable argument, since it is Immediately and utterly demolished when the allegedly non-existent alternative is actually produced, as will be done in the pages that follow.
In undertaking to present a complete and satisfactory explanation of gravitation it is not only necessary to show how and why the gravitational force acts as it does, but also why it does not do some things that would naturally be expected to result from whatever causes produce the observed effects. If we accept Newton’s concept of gravitation, either with or without Einstein’s modification, we would expect to find all particles of matter everywhere in the universe moving inward toward each other and Continuing in this motion until they eventually join, either by actual consolidation or by the establishment of stable orbital motion. Observation shows, however, that the behavior of matter in certain regions of the universe deviates very decidedly from this pattern which should theoretically be produced, and since there is no independent evidence, in any of these regions, of any counter force that could cause the abnormal behavior, a complete gravitational theory must necessarily explain why the individual particles do not move toward each other in these particular regions, as well as why they do exhibit a mutual attraction in what is generally considered the normal situation.
Looking first at the far distant regions of the universe that have been brought within observational reach in relatively recent years by the giant new reflecting telescopes, particularly the 200-inch Hale telescope on Mount Palomar, we find that the distant galaxies not only show no evidence of any gravitational motion toward our own location but, according to the testimony of their spectra, are reversing the gravitational direction and are receding from us at enormous speeds which increase proportionately with the distance. Of course, it is easy to assume a force of “cosmic repulsion” to account for this galactic recession, but no independent evidence of the existence of any such force has been produced by those who advance this hypothesis, and a purely ad hoc assumption can hardly be regarded as a satisfactory explanation. Gravitational theory therefore faces the problem of accounting for the recession of the distant galaxies in one way or another.
There is a possibility, to be sure, that the spectral red-shift, which is generally interpreted as a Doppler effect and hence as evidence of motion, is actually due to some other cause, but no other explanation that is anything more than an unsupported speculation has thus far been offered and the prevailing opinion at the moment is that the red-shift indicates a real recession. As matters now stand, therefore, this is a part of the general gravitational problem.
Moving inward toward the regions of shorter distances, the next discrepancy that we encounter is in the inter-stellar relationships. Here again, both the Newton and Einstein theories require the stars to move continually inward toward each other and eventually to join either by consolidation or by the establishment of stable orbital systems. We do find many relatively large stars, which conceivably could have resulted from consolidation of smaller masses, and we do find some small orbital systems, binary stars and a small proportion of more complex systems, the largest now known having six or eight components. We would expect to find more and larger stellar aggregates in a universe in which Newtonian gravitation had been operative for a long period of time, but the existing situation could be plausibly explained on the assumption that we are still in the early stages of gravitational agglomeration. On this basis the existing star systems are not inconsistent with existing gravitational theories.
If we accept this explanation, however, there should be a distribution of stars throughout the entire distance range from the radius of the largest orbital system to the radius of the galaxy: stars which are on their way to the eventual consolidation that must be the end result of the postulated gravitational attraction. But the observed distribution is totally different from this expectation. Beyond the orbits of the multiple star systems, which are comparable in dimensions to the planetary orbits and involve distances that, in terms of the velocity of light, are measured in minutes or hours, there are no stars at all until we get out to distances measured in years. The star nearest the earth is 4.2 light years distant and there is no evidence that any two stars in the solar neighborhood, aside from those in multiple star systems, are appreciably closer together. The average separation of the stars in this region is estimated at 2 parsecs or 6.5 light years.
Even where conditions would be expected to be the most favorable for the development of powerful gravitational forces, in the interiors of the globular clusters and the nuclei of the giant spiral galaxies, the weight of evidence indicates that the minimum separation must still be measured in light years. The average density of the globular clusters is estimated at only about five times the density of the local star system, and although the central regions of the spiral galaxies are too far away for detailed observations there are indications that they are no more densely populated than the globular clusters. “The average density of matter in the nuclear region (of our galaxy) is probably about twice that for the vicinity of the sun…”38 reports Bok.
The existence of this immense gap from light hours to light years completely void of stars is completely inconsistent with the theories of Newton and Einstein in their existing forms, regardless of what assumptions may be made as to the age of the universe or the elapsed time since gravitation first took effect. The fact that stars do not enter this immense region, which should be well populated on the basis of existing gravitational theory, strongly suggests that they can not enter, and that unless stars have a common origin (as those in multiple star systems presumably do) the gravitational pattern is such that they cannot approach each other within a distance of the order of light years. A satisfactory gravitational theory must therefore contain such a pattern, or alternatively, must provide some other plausible explanation of this very peculiar star distribution.
Again moving inward toward the shorter distances, we find another major discrepancy when we get to the point where we are dealing with individual atoms. There is nothing in gravitational theory, as it now stands, to indicate that the gravitational force is any less applicable to atoms than to any other masses, but the observed behavior at inter-atomic distances comparable to those existing in the solid state is totally different from that envisioned by existing theory. On the basis of either the Newton or the Einstein version of the theory the atoms should continue to move toward each other under the influence of the gravitational forces until they are in actual contact, after which they should be held together by these same forces. Until rather recently it was assumed that the atoms are actually in contact in the condensed states, but this concept is no longer tenable in the light of present-day knowledge, and as matters now stand it is evident that the inter-atomic distance in the solid state merely represents a point of equilibrium at which the attractive and repulsive forces acting between the atoms are in balance. Furthermore, it is now clear that the gravitational force, if it follows the same mathematical pattern as at greater distances, is far too small to account for the observed cohesion in the solid structure. At this level, then, existing gravitational theory contributes nothing toward an explanation of the observed situation.
We thus find that Newton’s “Law of Universal Gravitation,” with or without Einstein’s modification, is far from being universal. There are at least three important regions in the universe where the actual behavior of matter is entirely different from that specified by the allegedly “universal” law, and a complete and correct theory of gravitation must necessarily explain the gravitational pattern in these regions as well as the more conventional behavior.