XVII
Although the description of the new theory of gravitation
given in Part Three is essentially complete as it stands, it may be helpful
to show how the new concepts of the Reciprocal System affect some of the
specific issues that have received special attention in previous studies
of the subject. The basic position occupied by the concept of a One of the major sources of confusion in the application
of the Relativity Theory is the conclusion, which follows logically from
Einstein’s basic assumptions (including the items that were simply
taken for granted, “without examination” as Tolman puts it,
as well as those that were expressly stated), that the clocks in a moving
system run at a different rate from those in a stationary system, if both
rates are measured in the same system of reference. When we recognize
the true nature of a clock, which is a device that measures the time progression
only, it is obvious that all accurate clocks are equivalent irrespective
of location or system of reference, just as the rate of recession of a
galaxy is the same for all points in the galaxy. But Einstein saw that
the This is the origin of many of the so-called “paradoxes” of Relativity including the famous Twin Paradox, in which the conclusions drawn from a straightforward application of the Relativity principles are so outrageous that many of the staunch supporters of the theory are reluctant to accept them, and they have occasioned a great deal of controversy within the ranks of the relativists themselves. In the usual statement of this paradox it is assumed that one of the twins remains on earth, whereas the other embarks on a journey into the far reaches of the Galaxy, traveling at a velocity approaching that of light. According to the Relativity Theory, the clocks by which the fast-moving twin lives are slowed down to a very low rate, hence he returns from his journey in what to him was a rather short time, and he comes back still a young man, while his twin brother has been subject to the faster-moving clocks on earth and has grown old in the meantime. Such fantastic conclusions are, of course, incompatible with the principles of the Reciprocal System. In this system the operation of clocks, the aging process, and all other such time-connected mechanisms in which no appreciable differences in coordinate time are involved, are determined by the relationships of the various factors as they exist in the local environment, and whether or not that environment is in motion, relatively or absolutely, is entirely irrelevant. Any change in position in time other than that resulting from the everpresent progression and registered on all clocks, affects only those relationships in which a significant difference in coordinate time is involved. A somewhat modified statement of the initial premises arrives at what is called the Clock Paradox. Here it is assumed that clock B is accelerated relative to clock A and that subsequently, after a period of time at a constant relative velocity, the acceleration is reversed and the clocks return to their initial locations. According to the principles of Special Relativity clock B. the moving clock, has been running more slowly than clock A, the stationary clock, and hence the time interval registered by B is less than that registered by A. But Special Relativity also tells us that we cannot distinguish between motion of clock B relative to clock A and motion of clock A relative to clock B. Thus it is equally correct to say that A is the moving clock and B is the stationary clock, in which case the time interval registered by clock A is less than that registered by clock B. Each clock therefore registers both more and less than the other: definitely a paradoxical situation. Tolman explains, “The apparent paradox is, however,
readily solved with the help of the general theory of relativity, if we
do not neglect the actual lack of symmetry between the treatment given
to the clock A which was at no time subjected to any force, and that given
to the clock B which was subjected to the successive forces F The alleged solution of the paradox does more than this;
it provides us with a “specially illuminating example” of the
way in which the originator of the Relativity Theory and his disciples
pass hastily over the weak points in their initial assumptions and concentrate
their c efforts on building up an invulnerable mathematical structure,
apparently oblivious to the fact that the right answers cannot be obtained
from the wrong premises, regardless of the power of the mathematical techniques.
Let us go back and take a good look at these initial assumptions Tolman
begins with the clocks in coincidence and subjects clock B to a temporary
force which produces an acceleration relative to clock A. Then follows
an extended period of time during which clock B has a velocity u relative
to clock A. The Relativity Theory insists that this velocity u Furthermore, if the end result is a purely relative motion
as the theory contends, then the acceleration that produced the motion
must be purely relative, since an absolute acceleration would not produce
a purely relative motion. It then follows that the force must also be
relative, in order to produce a relative acceleration. Tolman definitely
states that the “successive forces F If we hew to the line and apply the Relativity principles
consistently throughout the argument concerning the Clock Paradox, the
end result is an absurdity. Strictly according to these principles, it
is not possible to apply a force specifically to a particular mass. Force
is defined, by Einstein as well as by Newton, by means of the equation
F = Tolman does not specifically admit that he is violating
Relativity principles and giving clock B an absolute acceleration, but
Moller is more candid and concedes that the acceleration of clock B is
“relative to the fixed stars” : The truth of the matter is that the adherents of the Relativity
Theory have allowed themselves to be so carried away by their enthusiasm
for a theory which gives them plausible answers to But this situation cannot be explained away, and Eddington’s
attempt gets nowhere. The motion of the train past the station is something
of a totally different character than the motion of the station past the
train, however strongly Eddington and his colleagues, past and present,
may assert the contrary. We know that the accident causes a change in
the relative velocity of the station with respect to the train, but we
also know that this accident does not change the absolute velocity of
the station, because we have a system of essentially constant absolute
velocity, the surface of the earth, that we can use for reference. On
the other hand, we know from similar considerations that the train undergoes
an alteration of both its absolute velocity and its relative velocity
with respect to the station. This demonstrates that a change in The proponents of the Relativity Theory have simply taken
advantage of the prevailing strong desire for some kind of an explanation
of the experimentally verified deviations from Newton’s Laws of Motion
and have persuaded the scientific community to accept the extraordinary
reasoning that since uniform absolute velocity cannot be detected by a
This technique of dealing only with artificially simplified
systems, which is standard practice in explanations and discussions of
Relativity, arrives at conclusions which are, for all practical purposes,
meaningless. Conclusions with respect to “isolated systems”
have no meaning in relation to actual physical systems, all of which are
constituent parts of the physical universe as a whole. Just as soon as
we place the isolated system in its proper place in the universe, it becomes
obvious that we do have an absolute system of reference defined with the
aid of the fixed stars. As Moller admits, “Experience shows that
the fixed stars as a whole may be regarded as approximately at rest relative
to the ’absolute space’...” An extreme example of this sort of thing is provided by
the attempts that have been made to portray rotational motion as purely
relative. Tolman considers the case of a rotating platform and concludes
that “...we can with equal success treat the platform or the remainder
of the universe as subject to the rotation.” The paradoxes of Relativity are merely consequences of the fact that the entire theory is constructed on a false conceptual foundation: one which attempts to compensate for a basic error in its definition of the nature of time by the introduction of a fictitious variability in space and time magnitudes. Such paradoxes cannot be resolved on any logical basis; they are inherent in the structure of the theory itself.
Closely connected with the concept of the clock is that
of As brought out in the discussion of basic physical principles in Part Three, any object which has no independent motion of its own, and which must therefore stay in the same place indefinitely unless it is acted upon by some outside agency, actually moves outward at the constant velocity of one unit of space per unit of time. From the natural viewpoint, therefore, “the same place” is a thing in motion. In common usage, however, the term “the same place” means the same place with respect to some arbitrary reference system. For ordinary purposes the reference system is the earth; astronomers find it more convenient to use the sun, or in dealing with more distant regions, the Galaxy. In all cases the reference system that is selected is one that does not progress in space (although it is usually in motion) and “the same place” as defined by such a reference system is the same relative location in coordinate space. It is evident that “the same place” in clock space, the space of the progression, means the same point in the progression, and since the path of the progression can be identified in terms of the reference systems utilized for coordinate space, all points in a progressing system are in constant motion relative to our usual frames of reference. A distant galaxy which has no random motion does not remain at the same place relative to one of these conventional reference systems (our galaxy, for example); it occupies a specific place only momentarily and the progression then moves it along to another place. Our galaxy is similarly progressing outward away from the distant galaxies and from the overall standpoint, therefore, two events cannot occur at the same place unless they also occur at the same time. On first consideration this statement seems to outrage common sense. Surely if I walk across the intersection of First and Main Streets today, I can return to the same place and do the same thing again tomorrow. But a little reflection will tell us that, even without the progression, First and Main Streets will not be at the same location in the universe tomorrow that it is today. Of course, this intersection does remain at the same place with respect to our usual system of reference, the surface of the earth, but if we look at the situation from a broader viewpoint we will realize that in the meantime the earth will have traveled more than 1½ million miles in its orbit around the sun; it will have accompanied the sun and its fellow planets over a distance of some 15 million miles on the long path around the center of the Galaxy; and it will have been carried an unknown distance by the movement of the Galaxy itself. The progression merely adds one more motion to the many others that exist. No, we cannot return to the same location in the universe tomorrow. Whatever we wish to do at that same place (as thus defined) can only be done at the same time. So far as time is concerned, our reference system is analogous to a distant galaxy, as the progression of time continues unchecked in the material universe. In view of the symmetrical relation between space and time we may therefore invert the previous statement and say that two events cannot occur at the same time unless they occur at the same place. Events that take place at different locations cannot be simultaneous with reference to time in its totality. It is possible, however, to define “the same time” in the same manner as we normally define “the same place” ; that is, with respect to a reference system which is stationary in one of the two components of time. We could, for instance, define the expression “the same time” as meaning the same point in coordinate time, just as the usual meaning of the expression “the same place” is the same point in coordinate space. But this would require a reference system stationary in coordinate time, and since we have no such system in the material universe, the time referred to a system of this kind would be meaningless to us. It is also possible to define “the same time” as the same clock time; that is, the same point in the progression, and this is a more practical alternative, as in so doing we are conforming to the meaning of simultaneity as the term is used in common parlance.
Once again let us turn to the galactic recession as an aid in visualizing the time relations. Fig.5 represents a galaxy that is receding at approximately the velocity of light in the direction shown. The entire galaxy recedes or progresses in space as a unit, hence the particular point in the progression which it occupies at any instant, the clock space applicable to the galaxy as a whole, can be identified by utilizing the position of any specified location within the galaxy as a reference point. Let us take the center of the galaxy for convenience. When this center is at point A, the clock space for the entire galaxy is XA, the distance between A and some previous location X of the galactic center which will be taken as the origin of the coordinate system. At the same stage of the progression point B is at distance XB from the origin of the coordinates, but this does not mean that the clock space is any different at this location; the clock space is the distance which the galaxy has been moved by the progression during a certain interval of time, and since that distance is XA for one location within the galaxy, it is likewise XA for all other points in the galaxy. There is, however, a coordinate space AB intervening between A and B. hence the total distance from X to B. the position of point B in terms of the coordinates based on X, is XA plus AB, or XB. Similarly, the total distance between location C and the origin of the coordinates is XA minus AC, or XC. For a location such as D which is not collinear with A and X, it is necessary to convert the distance AD in three-dimensional coordinate space to the equivalent one-dimensional value in order to combine it with XA, but otherwise the situation here is identical with that applying to locations B and C. It is obvious, of course, that the relation of AD to its clock space equivalent depends on the spatial location assigned to point X since the galaxy is receding in all directions, whereas the line AD has a specific direction in coordinate space. Now let us give Fig.5 a new significance. Let us say that it represents our Milky Way galaxy instead of some distant galaxy, and that it is being depicted in coordinate time rather than coordinate space. The arrow now indicates the direction of progression of time from some assumed origin of time coordinates X. Points A, B. C, and D are locations in coordinate time within the galaxy, and are separated from one another by time intervals AB, AC, etc., which, in view of the equivalence of the unit of time and the unit of space, are commensurate with the corresponding space intervals AB, AC, etc. This equivalence enables us to measure the time intervals indirectly, but accurately, by measuring the space intervals and converting the results to the time equivalents. We now have an exact analogy with the original significance of the diagram as indicating a galactic recession. The clock time for our galaxy as a whole, and for any individual point within the galaxy, at the stage of the time progression portrayed in the diagram is XA. The time interval between X and B is the clock time XA plus the coordinate time interval AB, making a total of XB. The time interval between X and C is XA minus AC, or XC. The time interval between X and D is XA plus or minus the component of the coordinate time interval AD in the direction XA. The magnitude of this component depends on the location of the origin X of the coordinates; that is, on the direction XA of the time progression. This latter point is one which is somewhat difficult to
grasp if we look at the time situation only, without the aid of the analogy
provided by the galactic recession, because it is hard to think in terms
of a time concept totally different from the one which has been handed
down to us from past generations. But the recession of the galaxies, a
manifestation of the space phenomenon analogous to the progression of
time, is not nearly so hard to visualize. It is, indeed, quite easy to
get a clear mental picture of the observed situation in which the distant
galaxies are moving outward away from us in all spatial directions. The
further conclusion, which necessarily follows, that our galaxy is likewise
moving outward in The essential point here, so far as the matters now at issue
are concerned, is that the motion of the galactic recession is Similarly, the motion of the time progression is In earlier days when physical science dealt only with relatively
low velocities, the contribution of the coordinate time to the total time
interval in any physical process was negligible, and it was possible to
carry out all calculations involving motion on the basis of clock time
only. The advent of high velocity measurements, particularly those concerned
with the velocity of light, showed that there was an error somewhere in
the system, and it was a study of the background of this discrepancy that
led Einstein to his conclusion that, “There is no such thing as simultaneity
of distant events.” Einstein and his colleagues accepted the “operational”
point of view in this instance and rejected the concept of an objectively
real simultaneity because of its lack of an operational basis. As Moller
explains, “The concept of simultaneity between two events in different
places obviously has no exact objective meaning at all, since we cannot
give any experimental method by which this simultaneity could be ascertained.” It is worth mentioning that this case illustrates the validity of one of the principal objections that is advanced against the operational viewpoint. The operational school of thought contends that no physical concept should be employed in the formulation of theory unless there are specific operations by means of which the concept can be defined. The objective of setting up such a qualification is to prevent the use of vague and misleading concepts and ideas in the construction of theory. Such an aim is hardly open to criticism per se, but the weakness of operationalism is that it is necessary to assume that if “we cannot give any experimental method by which this... could be ascertained” as the present time, we will never be able to do so; that is, there is no such method. In the present case, this assumption has been proved wrong, and it could likewise be wrong in any other in stance. This does not necessarily mean that the operational idea has no merit, but it indicates that considerable care should be exercised in applying it.
Another concept which plays a major part in the detailed
development of the Relativity Theory, although it is by no means a necessary
consequence of the basic postulates of the theory, is that of the In view of the highly critical comments that have been made
and are being made about the theory of the ether, many of which imply
that the originators and supporters of that theory were almost incredibly
naive in believing in the physical reality of a purely hypothetical concept
of whose existence no observational evidence could be detected, it is
rather amusing to find the outspoken critics of the ether firmly convinced
of the physical reality of the gravitational field: another purely hypothetical
concept for which there is no observational evidence. The “field”
theory is, in fact, almost an exact duplicate of the “ether”
theory. In both cases we find matter and radiation exhibiting certain
patterns of behavior that are not explained, or not completely explained,
in terms of what is currently known. In order to provide some kind of
an explanation of these behavior characteristics there has been invented,
in each case, a purely imaginary entity having just those properties which
are necessary for the purpose. In neither case is there any But even though these two concepts are birds of a feather
almost down to the last detail, present-day theorists tell us that we
should discard the ether, because there is no evidence of its existence,
but that we should accept the physical reality of the field, even though
this is equally without observational support. The truth is that the theory
of the ether is not nearly as lacking in merit as the present-day appraisals
suggest; the fact that a physicist of the caliber of P.A.M. Dirac is seriously
proposing a return to the ether theory is enough to verify this point.
“...the failure of the world’s physicists to find such a (satisfactory)
theory, after many years of intensive research,” says Dirac, “leads
me to think that the aetherless basis of physical theory may have reached
the end of its capabilities and to see in the nether a new hope for the
future.” The need for these artificial constructs—mental crutches, we might call them—has resulted from unrecognized, but equally artificial, restrictions that have been placed on the viewpoint from which physical problems have been approached. In the case of gravitation it has been taken for granted that there are only two alternatives. Either we must concede the reality of action at a distance: some mysterious power, altogether foreign to physical relationships as we know them elsewhere, whereby one mass can exert an instantaneous influence on another distant mass without any connection between the two, or else we must have some kind of a medium, an ether or a deformable space (which is simply an ether under a different name) through which the gravitational effect is propagated at a finite velocity. In this way all thinking about gravitation has been restricted to the narrow field defined by these two concepts, and since the idea of action at a distance is repugnant to most physicists, the latitude for constructive thought has been reduced to the point where the only thing left for the theorists to do is to speculate about the nature and properties of the gravitational medium. Thus Einstein rejects the ether and gives space the properties of a medium. Then when Dirac is disillusioned with Einstein’s theories and concludes that they have arrived at a dead end, he sees no alternative but to return to the ether as “a new hope for the future.” But in spite of the unquestioning acceptance of the existence
of this dilemma in present-day science, these are This new explanation completely eliminates all justification
for postulating the existence of a gravitational field as “something
physically real.” It accounts for all aspects of the gravitational
phenomenon in terms of the motion of the individual mass units, without
any participation by either a medium or a field. It is legitimate to use
the term “field” to describe the region in which the gravitational
effect makes its appearance, and to call the magnitude of this effect
at any specific location the “strength of the field” at that
point. But this is merely an artificial method of expression adopted for
convenience: “nothing more than an aid in the calculations that have
to be performed,” When the concept of the gravitational field as a physically
real entity goes into the discard it automatically carries with it the
deformation of space which, according to current theory, creates the field.
Actually it is very difficult to distinguish the present-day concept of
“space” from that of the “field” or, for that matter,
from the concept of the “ether.” At first glance these appear
to be altogether different entities, but when a closer analysis is made,
to determine just how each of these concepts fits into the picture as
a whole, the differences tend to disappear. Eddington makes the following
comment, referring to the distinction between field and space: “The
distinction thus created is a rather artificial one which is unlikely
to be accepted permanently.” Two general concepts of the nature of space have come down
to us from the philosopher-scientists of antiquity. One viewpoint—that
held by Aristotle—regards space merely as a The principal weakness of the ether theory, aside from the
total lack of any independent evidence of the existence of anything of
this kind, is that when the ether is postulated to be a “substance”
it becomes identified with material substances, whereas the properties
which it must have in order to perform the functions for which it was
invented are incompatible with those of material substances. It must,
for example, be more rigid than steel, in order to account for the transverse
vibration of electromagnetic radiation, but at the same time it must be
even more fluid than the lightest gas, in order that material objects
may move through it without frictional effects. What Einstein and his
colleagues have done is to attribute to space all of the properties that
were previously conceived as properties of the ether. Thus the utility
of the ether as a medium is retained—space itself has now become
a medium—but inasmuch as this medium is no longer identified as a
“substance” there are no longer any restrictions on the kind
of properties that can be postulated. Who can say for instance, that a
rigid The difficulty of distinguishing between the concepts of
“space,” “field” and “ether” is a result
of the fact that, as currently employed, all three terms refer to the
same thing: the hypothetical universal medium. The significant properties
that are attributed to these entities, the properties that are actually
needed for the performance of their assumed physical functions, are the
same in all cases; the only differences between them are in connotations
of the language employed that are carried over from the sources from which
that language was derived, but have no meaning in the terms of reference
of current theory. The word “field,” for instance, calls up
a considerably different conceptual image than the word “space,”
yet if we examine the way in which each word is used The present confusion in this area is largely chargeable
to Einstein. Before his day the accepted world picture included an ether
located in and coextensive with space. It is commonly contended that Einstein’s
system eliminated the ether and accounts for gravitation as a product
of the geometry of space, but in reality what he did was to eliminate
the Even Einstein himself was forced to admit that the ether
still exists in his system: “...we may say that according to the
general theory of relativity space is endowed with physical qualities;
in this sense, therefore, there exists an ether.” In these three statements the contentions advanced in the preceding paragraph as to the true nature of the manipulation of space and ether in the Relativity Theory have been confirmed by the author of the theory. Einstein admits that it is only the name “ether” that he has discarded and that the functions of the ether have been transferred to space, thus making space a medium. The fact that he specifically uses the word “medium” is particularly significant. The view of space as the Then, to compound the confusion, Einstein insists that in the General Relativity Theory gravitation is solely a result of a deformation or curvature of this redefined space, resulting from the presence of mass, and he makes it clear that in his opinion he has reduced gravitation to a property of space-time. Yet he is equally insistent that the gravitational field is, as he puts it, “something physically real in the space.” Here again is a direct contradiction similar to the one pointed out in connection with the mass-energy relations. If gravitation is simply a geometrical effect, as Einstein claims, there can be no “physically real” entity which produces gravitational effects; if there is a physically real gravitational field “in the space” as Einstein also claims, then gravitation is not a purely geometrical affect. He cannot have it both ways. If it were not for the “exceedingly complex and difficult” nature of the General Theory, which has insulated it against effective criticism, both this and the equally glaring conflict in the mass-energy relations no doubt would have been recognized long ago. In retrospect it is clear that gravitational theory was diverted into the wrong channel at the very beginning of its development by the uncritical acceptance of the concept of gravitation as an action of one mass upon another. No subsequent skill or ingenuity could compensate for such a serious initial error, and the “failure” of the currently accepted theory to which Dirac refers in the statement previously quoted was inevitable from the start. Einstein presents one independent argument in support of
his “curved space” hypothesis which deserves special comment.
He points out that a gravitational force following the inverse square
law in an Euclidean universe is incompatible with a uniform or approximately
uniform density of matter. On such a basis, he says, “The stellar
universe ought to be a finite island in the infinite ocean of space.” It is evident that the observed universe does not conform
to this theoretical condition that would result from the assumed premises,
and Einstein therefore arrives at the conclusion that space must be curved
so that it is finite in extent even though unbounded. But this argument
contains a hidden assumption: the assumption that the gravitational force
of each individual mass is effective over infinite space. According to
the new information presented herein, this is not true. There is a gravitational
limit for each mass and a net gravitational force exists only within this
limit. Einstein’s argument is therefore valid only for the region
within the gravitational limit of each mass aggregate, and in each of
these regions the observed behavior is just what he claims it would be
if space is Euclidean; that is, each galaxy and each star system (single
star or multiple star system) is a “finite island in the ocean of
space” defined by the gravitational limits of that galaxy or star
system. Even before the true nature of the external galaxies was definitely
established, Kant and others were referring to these objects as “island
universes.” Einstein’s point therefore not only ceases to be
a valid argument
One of the most frequent comments offered by those who have become acquainted with the gravitational theory of this work through previous publications concerns the relatively minor use of mathematics in the development. “I am particularly puzzled about the lack of mathematics associated with your methods,” writes a British correspondent, “surely in order to show the superiority of your theory you must be able to predict all the experimental facts explained by present theories and more. It is difficult to see how you will do this without setting the whole thing on a rigorous mathematical basis.” Another correspondent asks, “Can you put your theories into a tensor formulation?” These comments reflect a general misconception that has developed in science, particularly in physics, within the present century, in which the “rigor” of the mathematical treatment is judged on the basis of its length and complexity, not on the basis of its adequacy for the task at hand. Following Einstein’s lead in calling upon complex mathematics in an attempt to compensate for conceptual errors, present-day physical theory has become largely a juggling of abstract mathematical relationships, the meaning of which (if any) “we do not ask,” as Eddington says. As so often happens when form is overemphasized, form rather than substance has come to be regarded as the essence. To arrive at a result in the realm of basic theory by plain arithmetic or simple algebra is today unthinkable; unless we can express that result in terms of tensors, or spinors, or matrix algebra, or some other currently fashionable mathematical device, it is automatically unacceptable. How far would Newton get today with his gravitational equation? Could such a simple expression as ever hope to receive any consideration from a generation
of physicists accustomed to tensors of the fourth rank? Obviously not.
But this simple and unpretentious equation is the only The gravitational theory derived from the postulates of the Reciprocal System is Newton’s gravitational law. The detailed development of this theory shows that the objections that have been lodged against Newton’s Law by modern investigators are based on erroneous conclusions, and that his gravitational equation is actually valid throughout the universe, precisely and with no exceptions. As has been pointed out previously, the only one of the items of evidence currently offered in support of Einstein’s proposed modification of Newton’s gravitational ideas that can stand up under critical scrutiny is the advance of the perhelion of Mercury, and the new information developed in this work shows that this is due to the high velocity of the planet and has no connection with gravitation. It is a result of the same factors which are responsible for the negative outcome of the Michelson-Morley experiment, not of any deficiency in the gravitational law. The other objections of a less tangible nature that have
been advanced against Newton’s theory have been similarly overthrown.
Eddington lists three such objections. Such a conclusion is fully justified by Eddington’s
next objection, which is that Newton’s theory is incompatible with
a finite velocity of propagation of the gravitational effect. “In
the theory given in this book,” he says, “gravitation is propagated
with the speed of light...” In other words, Newton is wrong because
his assumption does not agree with Eddington’s assumption. This present
work demonstrates that gravitation is not propagated with the speed of
light, nor is it propagated instantaneously; it is not propagated at all:
a fact which is fully compatible with Newton’s theory. Likewise this
work disposes of Eddington’s third objection: “Further, In the simple, completely understandable world of the Reciprocal System all of these present-day objections are swept away and Newton’s gravitational equation is valid throughout the universe, from the smallest region to the largest. Where, then, is there any place for complex mathematics? Do we need to call upon matrix algebra or tensors to restate the Newton equation? The whole idea of a more “rigorous” mathematical foundation is preposterous. If the mathematics at hand are fully adequate for their purpose there cannot be anything more complete or more rigorous, even if the mathematical formulation amounts to nothing more than a statement that two plus two equal four. Once it has been established that the Reciprocal System leads to Newton’s gravitational law and that it demolishes the objections that have hitherto been raised against the universal validity of that law, there is nothing further for mathematics to do. Newton’s equation cannot be made any simpler and nothing can be gained by expressing it in a more complex manner. Present-day basic physical theory does not need more mathematics—it is overflowing with mathematics already. What it needs is a conceptual clarification that will enable making full use of the physical knowledge and the mathematical tools already available. This is the objective of this present work: not to add to the profusion of abstruse mathematical speculations now in existence, but to identify the conceptual errors in the previous development of theory and to point the way to the changes in thinking that are necessary in order to make full use of the mathematical and theoretical equipment already on land. It is not contended here that At this point it should again be emphasized that the mathematical
aspects of Einstein’s Special Theory did not originate from that
theory; they are purely empirical relations which were current in physical
circles before the Relativity Theory was formulated. The Michelson-Morley
experiment showed that the velocity of light is independent of the reference
system. This made it clear that if the existing concepts of space, time
and motion were to be retained, a variation of distance (and perhaps time)
with velocity must be introduced, and the amount of the necessary variation
can be readily calculated in a straightforward manner from empirical data.
Such a calculation led to the conclusion that distance magnitudes are
reduced by the factor (1– This answer to the problem is Let us now examine the theoretical basis of this empirically determined correction factor. According to the principles of the Reciprocal System, the distance measured on the basis of Euclidean geometry is the true coordinate distance regardless of velocities and irrespective of the system of reference (as long as the reference system qualifies as a legitimate one on the basis of the criteria previously specified). In any application within our own galaxy, where we do not have to take the galactic recession into account, we are dealing with coordinate distance only, and hence this measured coordinate distance is also the total physical distance. Similarly, the time measured by any accurate clock is the true clock time irrespective of whether the system of reference in which the clock is located is stationary or in motion, and thus the clock time interval is also an absolute magnitude. But when an object is in motion it is not only moving in clock time, the quantitative expression of the motion of the progression, a motion that all material objects participate in, even when they are at rest in our usual system of reference, but is also moving in coordinate time, analogous to coordinate space. If we are dealing with the velocity of light, which is one unit of space per unit of time, any points which are separated by n units of coordinate space are also separated by n units of coordinate time. This coordinate time difference is separate and distinct from the clock time and must be added to the clock time to obtain the true physical time, just as we had to add the random motion of the distant galaxy to the motion of the galactic recession before we could determine where the galaxy would actually be found. It is evident that the velocity of light is always unity in such a system, but it is likewise clear that when we take the coordinate time into consideration as well as the clock time, there is no conflict between the constant velocity of light and the absolute magnitudes of the space and time intervals involved.
Inasmuch as any material particle is continually passing from one unit of space to another (since it is moving against the direction of the space-time progression) and the direction of the progression of each new unit is indeterminate, the motion of such a particle is distributed equally in all spatial directions. Radiation in free space, on the other hand, maintains the same spatial direction indefinitely, as the photon has no independent motion of its own. It follows that whether a particle is in motion or at rest relative to our usual reference system, and regardless of what direction in coordinate space any such motion may take, the particle is moving with the progression, and hence with the radiation, half of the distance that it travels and opposite to the direction of the radiation during the other half. We may therefore treat any movement of light or other radiation relative to material objects as if it involved a round trip, irrespective of the situation that may prevail in the usual system of reference. Let us assume that a light signal originates at point A on a rigid rod AB which is in motion toward the right of the diagram, Fig.6, with velocity v. The light signal travels to the point B. which in the meantime has moved forward to B’, and here it is reflected back. By the time it completes the round trip, point A has moved to A’, and the round trip is AB’A’ rather than ABA. If we analyze this situation on the basis of the assumption (accepted by both Newton and Einstein) that physical time consists of clock time only, the distance traveled by the signal is ct. since we have found from experiment that the velocity of light is constant irrespective of the reference system. The time t, according to Newtonian principles, is the distance AB, which we will call s, divided by the net velocity c-v on the outward trip and the same distance divided by the net velocity c+v on the return trip This gives us
Multiplying by c, we then have the distance traveled:
At rest, the round trip distance ABA is 2s. Now we find that if we insist on expressing our results in terms of clock time only, we must introduce a mathematical correction equivalent to reducing distances applying to objects in motion by the factor 1 – v,
in order to be consistent with the distances measured at rest. Since space
and time are reciprocally related in velocity, the correction does not
necessarily have to be applied to the distance; it can be applied either
to distance or to time or to both. In the light of the points developed
in this volume it would be most logical to apply the correction to time,
since it is through a misunderstanding of the nature of time that the
whole difficulty arises, but as the Relativity Theory actually developed,
the correction was divided equally between space and time, the distance
being reduced by the factor (1^{2}/c^{2} – v)^{2}/c^{2}^{¹/2}
and the time extended by the reciprocal of this factor.As indicated in the preceding discussion, the advance of
the perhelion of the planet Mercury, which is commonly interpreted as
indicating a deficiency in Newton’s gravitational law, is actually
a result of the same misconception of the nature of time that the Special
Theory tries to compensate for. The orbital velocity of Mercury is approximately
29.8 miles/sec, which, in terms of the velocity of light as unity, is
.00016. The correction for the coordinate time, ,
is then 2.56 x 10^{-8}; that is, the clock
time must be increased by this factor. Since the gravitational motion
is inward, the scalar space-time direction of the orbital motion is outward,
and the computed time increase is radial. To obtain the circumferential
space equivalent of this linear time increase, we multiply by p
obtaining 8.04 x 10^{-8}, or .1042 seconds
of arc per revolution. This amounts to 43.35 seconds per century, which
agrees with the observed advance of the perhelion, within the accuracy
of the measurements. Tolman reports 43.5 seconds per century as the observed
value and 42.9 seconds per century as the result obtained by calculations
based on the Relativity Theory.
In connection with this discussion of the incidental aspects of the gravitational situation, it may be in order to make some comments about the methods of approach to the problem which were utilized in the construction of the three theories that have been discussed: Newton’s Law, Einstein’s General Theory, and the gravitational theory derived from the Reciprocal System. Newton’s gravitational theory was developed during a relatively early scientific era in which basic physical concepts were simple and direct. When and if a theory became inadequate the corrective measures were applied to the basic concepts; these were drastically modified or else discarded and replaced by other simple and direct concepts. Einstein’s General Theory, on the other hand, is a product of the more sophisticated and ingenious modern school, which relies upon mathematical techniques to fit existing concepts to the observed facts rather than giving up basic ideas which encounter trouble. If a theory which agrees with the observed facts in a restricted area fails in application to a broader field there is, of course, a very strong probability that the theory is in error in some important respect. But abandonment of a cherished theory or concept is extremely distasteful, not only to the author of the theory, but also to those who have accepted it and have based their own thinking upon it, and in recent times the tendency has been to call upon an increasingly numerous assortment of devices whereby the theories can be made “looser” and accommodated more readily to a wider range of observational data, thus avoiding the painful necessity of parting with familiar and comfortable habits of thought. One of the easiest ways of avoiding conflict with the facts is to make the theory less specific. At the present time, for example, there is a great deal of activity that is directed toward the construction of semi-theoretical mathematical expressions designed to represent physical properties of matter. The usual practice is to start with some purely theoretical relation, such as the general gas law PV = RT. In order to secure better agreement with the experimental results this relation is then modified by additional terms and adjustable constants. In developing the first “equation of state” for gases from the general gas law, Van der Waals used two such constants. For a better fit with the experimental data, subsequent equation constructors have increased the number of these adjustable or “disposable” constants. The Beattie-Bridgeman equation has four; the Benedict-Webb-Rubin equation has eight. If the objective of this activity is the attainment of close
agreement with the experimental values for the purpose of facilitating
interpolation and extrapolation of the experimental results, the prevailing
policy has been successful, since the correlation is, in general, increasingly
better as the number of constants is increased. But if the objective is
to ascertain the In order to make progress toward the correct answers it is essential to reduce rather than increase the adjustability of the equation. As we move in this direction we must obviously keep the results of the calculations within the limits of experimental uncertainty, and we can move only as fast as we are able to devise new modifications that will stay within those limits, but as long as this requirement is met, every additional restriction that can be placed on the quantities entering into the calculations increases the mathematical probability that the values obtained from these calculations correctly represent the true physical magnitudes. The difficulty with this line of approach is that it is the hard road to follow. The prevailing practice of increasing the flexibility of the mathematical expressions through the addition of more adjustable constants or similar means follows a well-defined path: one which is almost certain to achieve results of some kind if sufficient time and effort are applied to the task. Most attempts to make progress toward the difficult goal of a more restrictive equation, on the contrary, will inevitably end in nothing but frustration and disappointment, and ordinarily no really significant advance can be made without discarding some cherished idea of long standing. The preference for the easy route is therefore quite understandable, but here, as in so many other lines of human endeavor, true forward progress can only be made in the hard way. The situation in such areas as gravitational theory is not
quite as obvious as that which results from the addition of successive
adjustable constants to the equations of state, but any measure that increases
the flexibility of a theoretical relationship so that it can more readily
accommodate itself to the experimental data produces the same results
as these added constants: it increases the number of possible situations
which can be made to agree with the postulated relation and hence decreases
the mathematical probability that the relationship is correct. A theory
such as Special Relativity which denies the constancy of the magnitudes
of space and time intervals has a smaller probability of being correct
than one which accepts fixed space and time magnitudes, providing that
neither is inconsistent with the observed facts. A theory such as General
Relativity which goes still farther in the same direction and eliminates
the “metrical meaning” of the coordinates that are employed
in describing these magnitudes has a still lower probability of being
correct, and if Einstein had succeeded in his attempt to devise a general
field theory by further loosening of the theoretical structure along similar
lines, the a In this connection, Bondi makes the comment, “...it
may justifiably be asked at this stage, when the mathematical complexity
of the theory emerges, why Einstein should require ten potentials of gravitation
where one was good enough for Newton.” Every The validity of the foregoing assertions is practically
self-evident. Such ideas are, however, given scant consideration in current
scientific thinking, not because of any disagreement in principle with
the contention that this is the true route toward a complete, logical
and understandable theory if such a theory exists, but rather on the ground
that such a goal is an impossible one. There is a very general tendency
to extrapolate From this premise he then reasons that we have two alternatives.
One possibility is to utilize some intelligible model as far as it will
go, and then set up additional, probably incompatible, models of the same
kind to cover the areas outside the scope of the original model. This
was the idea expressed by Jeans: “The most we can aspire to is a
model or picture which shall explain and account for some of the observed
properties of matter; where this fails, we must supplement it with some
other model or picture, which will in its turn fail with other properties
of matter, and so on.” When we subject Margenau’s conclusions to a critical
examination, however, it is apparent that the so-called trend toward abstraction
is not so much a matter of making the theory more But all this is a means of evading the issue, not of meeting it. If Newton’s Laws of Motion do not give the right answers in application to bodies moving at high velocities, the clear implication is that there is some error in the basic assumptions underlying these laws, as Einstein recognized. If the Special Theory of Relativity fails to give the right answers in application to non-uniform motion, the equally clear implication is that there is an error in the basic assumptions of this Special Theory, but Einstein was not willing to accept, in application to his own theory, the conclusion which seemed so clear to him so far as Newton’s system was concerned, and the introduction of more flexibility or abstraction was simply a way of avoiding the necessity of facing this uncomfortable situation. It is quite understandable that the author of a theory that has received general acceptance and widespread public acclaim should be reluctant to concede that there are fundamental defects in this theory and should resort to every possible expedient to save this invention that has brought him fame, but there is no good reason why the scientific profession as a whole should meekly acquiesce in a course of action dictated by proprietary pride rather than by scientific considerations, and Einstein should not have been permitted to run away from the problem. In order to arrive at the correct answer, it is obviously necessary to move in the opposite direction from Einstein’s course: to ascertain just where the basic assumptions are wrong and then to make the appropriate correction. As the findings of this work indicate, Einstein was right in his conclusion that there is an error in the basic assumptions of Newton’s Laws of Motion, but he was wrong in his conclusion as to the location of the error and the measures that were required in order to correct it, and his insistence on maintaining his original constructions intact at all costs has simply blocked all progress toward the correct answer. Actually both Newton’s Laws of Motion and the Special Theory of Relativity foundered on the same rock: an erroneous concept of the nature of time. No amount of additional “abstraction” can compensate for such a basic error, except in the very simplest situations. Modern theorists pride themselves on having eliminated the
“rigidity” of previously existing scientific concepts. Heisenberg
states the case in these words: “Coming back now to the contributions
of modern physics, one may say that the most important change brought
about by its results consists in the dissolution of this rigid frame of
concepts of the nineteenth century.” The development of the consequences of the postulates of
the Reciprocal System has now demonstrated that Newton was right: that
an explanation
In Newton’s era it was generally agreed that physical
theory was to be derived from experiment and observation in the first
instance, and that the development of such theory was essentially a matter
Einstein asserts, however, that we cannot get a true picture
in this way: by observation or by theoretical constructs based on observation.
“Since, however, sense perception only gives information of this
external world or of ’physical reality’ indirectly,” he
says, “we can only grasp the latter by speculative means,” In these statements Einstein is advancing the curious contention
that it is possible to derive from purely theoretical processes specific
information about the physical world that cannot be obtained, directly
or indirectly, from observations of the physical world itself. One might
hesitate to believe that he actually meant what these statements seem
to say, were it not for the fact that he repeats them over and over, and
acquiesces in interpretations of his views such as that of F. S. C. Northrop,
who states plainly, “It has been noted that the basic concepts of
deductively formulated scientific theory as conceived by him (Einstein)
are neither abstracted from nor deduced from empirically given data...
they are concepts of a kind fundamentally different from the nominalistic
particulars which denote data given empirically... And because the theoretic
term cannot be derived from the empirical term, theoretic physics contributes
something of its own to the scientific conception of nature and reality.” Here is strange doctrine indeed. Even the Kantian concept
of a The truth is that this contention that there are physical facts which are inherently beyond our ability to observe or measure, or to ascertain by mathematical or logical processes based on such observation or measurement is preposterous. Perhaps there are some facts which are beyond the capabilities of existing methods, but even this is a highly questionable assumption as there is little reason to believe that we are anywhere near the point of having exhausted the potentialities of the methods now available. Furthermore, the possibilities in the way of developing new methods are, so far as we are aware, essentially unlimited. We cannot say, therefore, in any particular case that it is impossible to devise a method that will serve our purpose. Hence, if the theoretical processes furnish “something of their own”—some information which cannot be “abstracted or deduced from experimentally given data”—this is not information about the physical world. If it has any meaning at all, it is simply information about the theory, or the model, which has been set up to represent the physical reality. It belongs to the dream world, not the real world. The question then naturally arises, how did a scientist
of Einstein’s competence ever come to formulate such an upside down
viewpoint as this: a viewpoint from which the data of experience are “fictitious”
and only the “free inventions of the human mind” can represent
“physical reality” ? Fortunately for the peace of mind of future
historians of science, who would otherwise be confronted with a baffling
enigma, he supplies the answer himself. “It was the General Theory
of Relativity which showed in a convincing manner the incorrectness of
this view,” he says, referring to his description of the 19 To Einstein, the lover of pure theory, already strongly
predisposed to regard his theories as something more than mere tools of
thought (”To him who is a discoverer in this field the products of
his imagination appear so necessary and natural that he regards them,
and would like to have them regarded by others, not as creations of thought
but as given realities” ), The most appropriate comment that can be made on this statement
is to repeat the previously quoted up-to-date opinion as to the true status
of the gravitational red shift: “the red shift follows from more
elementary considerations and is not really a test of general relativity.” The fatal weakness in Einstein’s concept of deriving
the basic laws of physics by “free inventions of the human mind”
is that this policy makes no provision for correcting any errors in the
premises, which are accepted as the foundation for the inventions. In
essence this puts the scientific investigator in the same position as
a mechanical computer. He can accomplish only those results, which are
obtainable by manipulation of the data that are put into the system in
the original program; if those data are erroneous then the answers that
are obtained are necessarily wrong. The validity of the Special Theory
of Relativity was programmed into Einstein’s mental analogue of the
mechanical computer. His development of General Relativity and his attempt
at development of a general field theory were therefore limited to what
could be done by building on the Special Theory. Had that theory been
conceptually correct, rather than merely a device, which attained mathematical
validity by counterbalancing, one conceptual error with another, this
procedure might well have been successful. But the The possibility that errors in the basic premises of physical
theory can be found and corrected by “free inventions of the human
mind” is quite remote. Any program such as Einstein’s which
relies on more and more abstraction definitely excludes any such possibility,
since the need for any correction becomes progressively less apparent
as the development of theory makes the conceptual structure progressively
more vague. Some other purely speculative program might be better adapted
to the purpose, but The explanation of gravitation outlined in this work is
a case in point. For hundreds of years the scientific world has accepted
without question the contention that there are only two possibilities
here: either we must admit the existence of action at a distance or we
must admit that the effect is propagated through something with the properties
of a medium (ether, field or deformable space). There is no reason to
believe that the “free inventions of the human mind” would have
produced any other possible explanation for many more hundreds of years;
the scientific mind was already convinced that it had thoroughly explored
the field. But the appeal to experience, which Einstein spurns as a “fictitious”
basis for theory, has This is by no means an isolated case. On the contrary, the
great majority of our basic physical laws were “abstracted or deduced
from experience” and were not “free inventions.” Whether
or not the story of the falling apple is apocryphal, there is no question
but that Newton’s Laws were distilled from experience. The same is
true of the first step, which Einstein took along the relativity route.
His Special Theory was not a “free invention” ; it was deliberately
designed to give a theoretical basis to a fact of experience: a mathematical
relation—the Lorentz transformation—which expressed the modification
of numerical values necessary to reconcile another fact of experience—the
constant velocity of light—with the accepted laws of motion. According
to the findings of this present work, the Special Theory was not It thus becomes evident that the difficulties which have
led to Margenau’s conclusion that a fully satisfactory physical theory
is impossible and that we must necessarily be content with something less
than the optimum are not inherent in the structure of nature itself, but
are a result of the fact that Einstein took the wrong road after his initial
success and carried the scientific world with him. His argument in favor
of the conclusion stated by Margenau cannot stand up under a cold-blooded
scrutiny. The mere fact that two different theories, or many different
theories, for that matter, achieve “a large measure of agreement
with experience” does not preclude the existence of another theory,
which agrees with The guideposts that have been set up in the preceding pages point out the true route the traditional scientific goal of a complete and understandable physical theory: a route which is almost diametrically opposite to the path toward increased flexibility (or abstraction) that has been followed by Einstein in the realm of the very large and by Bohr, Heisenberg and their associates in the realm of the very small. This opposite route is the one that has been taken in the development of the Reciprocal System. In this development Einstein’s dictum that we can only grasp “physical reality by speculative means” has been explicitly repudiated and the entire project has been devoted to accomplishing the very thing that Einstein claims is “doomed to failure” ; that is, to “derive the basic concepts” of physical science “from the ultimate data of experience.” The program that was followed in this work began with long
years of study of the experimental values of the physical properties of
thousands of different substances, directed toward the development of
more accurate and more generally applicable mathematical expressions to
represent the variability of these properties. After a number of such
expressions had been formulated, the next step, one which also extended
over many years, was an intensive study of these expressions, during the
course of which they were thrown into every conceivable mathematical form,
and each of the functions thus derived was subjected to an exhaustive
examination in an attempt to discover possible physical relationships
corresponding to the mathematical relations. Several of these lines of
approach finally converged to the reciprocal postulate, bringing the inductive
phase of the project to a conclusion. The second, or deductive phase of the project initially
involved the formulation of the collateral and supplementary assumptions
required in conjunction with the reciprocal postulate to form the fully
integrated set of postulates that underlies the Reciprocal System. The
development of the consequences of the postulates of this system then
followed. This is a gigantic task which is still under way and can be
expected to continue for a long time to come, gradually extending into
more and more detail. As can be seen from the foregoing description, the
Fundamental Postulates of the Reciprocal System were obtained inductively
from the empirical data, and all of the subsequent conclusions have been
derived deductively from these postulates. This entire system therefore
rests upon the facts of observation; it The final result of attacking the problem along this line
has been the achievement of the very thing that current scientific thought
assumes is unattainable: a complete and comprehensive theoretical structure
that is readily understandable in the terms of reference of everyday experience.
The present discussion covers only one of the many aspects of the Reciprocal
System, but in each of the other subsidiary areas the same result has
been obtained; that is, a development of the consequences of the Fundamental
Postulates of this system has established a complete and logical theory
for the phenomena included in the particular area: one which requires
no supplemental theories or XXIII In retrospect it is clear that overconfidence in the capabilities
of the theorists and in the validity of accepted modes of scientific thought
has been a major factor—perhaps the most important factor—in
diverting physical science from the straightforward path and into unproductive
side excursions. Over and over again we find that a proposition which
in reality is true only The current viewpoint with respect to the propagation of the gravitational effect is typical. Modern physicists have been able to visualize only two alternatives: propagation at a finite velocity through a medium or instantaneous action at a distance. Being unwilling to accept action at a distance and thoroughly convinced that their inability to conceive of any other alternative is definite proof that no such alternative exists, they have taken it for granted that the effect must be propagated through a medium at a finite velocity, even though there is not the slightest evidence to support this conclusion, whereas there is some significant evidence to the contrary, including the inescapable fact that energy which is determined by position in space cannot be propagated through space. Newton did not agree with the present-day viewpoint. He
was equally as opposed to accepting action at a distance as the modern
scientist, but he contended that the existence of gravitational effects
conforming to his gravitational equation should be accepted as an empirical
fact pending the discovery of some plausible explanation of the phenomenon
at some future time. The developments of this work have completely vindicated
Ncwton’s position. So far as this point is concerned, any judgment
that may be passed on the merits of the present work is entirely immaterial.
Whether or not the gravitational mechanism derived from the postulates
of the Reciprocal System is ultimately accepted as correct by the scientific
community, it cannot be denied that this does provide a third and totally
different alternative in this case where present-day thought contends
that no more than two alternatives are logically possible. The mere The situation with respect to the assumed contraction of
objects in motion is similar. The statements that are made in this connection
by modern authors are positive and categorical. “But the constancy
of c in different inertial systems,” says Margenau, “requires
that moving objects contract, that moving clocks be retarded, that there
can be no universal simultaneity, and so forth.” Whatever someone else may think about the work of modern
physical theorists, they have mode than ample confidence in their own
results. Here again it is immaterial whether or not the new explanation
presented in this work is accepted as correct. Whether correct or incorrect,
the new theory derived from the Reciprocal System provides a logical and
self-consistent explanation in which a constant velocity of light in all
systems of reference does It is not appropriate to enter into an extended consideration
of this aspect of modern science in a volume addressed to such a limited
subject as gravitation, but one can hardly refrain from making some comment
about the way in which the most astounding and fantastic conclusions are
accepted by the scientific community purely on the basis of what amounts
to an assumption that the collective opinion and judgment of the scientific
profession are infallible. One of the standard tools of logic is the Now let us bear in mind that no one is arguing that an absurd
and contradictory universe is a What has just been said with reference to Tolman and gravitational
theory applies with equal force to the scientific profession as a whole
and to physical theory in general. For example, the situation with respect
to atomic theory which was discussed in detail in Of course, a question such as that of the basic nature of time is not something that we can resolve by direct observation, and we have no option but to make an assumption of some kind. The fact remains, however, that when a development of the consequences of this and other basic assumptions ultimately leads to an absurdity, what we have proved is that one or more of the initial assumptions was in error, not that the universe is absurd and illogical. In arriving at the latter conclusion, the modern physicist is himself being absurd and illogical. It is quite evident that the “self-criticism” upon which physical science has relied to keep its progress headed in the right direction has failed in its appointed task, and that some more detached and less sympathetic analyses and appraisals of present-day physical theory are badly needed. As James R. Newman expresses it, the modern physicist has been allowed to “get away with murder,” and the consequences that have ensued make it clear that it is now high time that this unlimited license be revoked. No amount of sophistry or doubletalk can evade the cold, hard fact that the conclusions of modern physics as to the irrational and unpredictable behavior of the universe or portions thereof are nothing more than speculations; they are based on pure assumptions, not on solid knowledge. Actually the theoretical physicists themselves are somewhat uneasy about the tenability of the position which they now occupy in this connection. The concept of a universe, which is basically irrational and absurd, is definitely objectionable from a philosophical standpoint, and considerable thought has therefore been applied to devising some modifications of this idea, which the scientist can live with more comfortably. Thus Herbert Dingle gives us a “new estimate” of the situation that differs materially from the uncompromising viewpoint which he expressed in the statement previously quoted: The practice of physics has not changed, and the new estimate
of its discoveries is forced on it; it is not a matter of choice. When
we thought we were studying an external world our data were still simply
our observations; the world was an inference from them. Until this century
it was possible to make such an inference intelligibly... But now we
find that... we can no longer express them as the structure of an external
world unless we accept a world which is arbitrary, irrational and largely
unknowable. In this statement Dingle has shifted his position and he now attributes the irrationality and nintelligibility not to the universe itself but to the limitations inherent in our observations: limitations which, he contends, make it impossible to deal directly with the universe itself. Here is a strange new idea totally foreign to the traditional philosophy of science. From the very beginning of scientific inquiry the great majority of scientists have agreed that the subject of their investigations is a physical universe external to and independent of the observer. But now Dingle and those who share this same viewpoint are repudiating this long-standing concept of the fundamental nature of scientific knowledge and are taking the stand that science is merely “a method of correlating sense-data.” ”On this view of science,” McVittie explains,
“the Laws of Nature are simply the fundamental postulates lying at
the base of a theory and are to be regarded as free creations of the human
mind... Unobservable such as light, atoms, electromagnetic and gravitational
fields, etc., are not constituents of an independently existing rational
External World; are but concepts useful in the manufacture of the systems
of correlation.” Now let us ask, what justification does modern science advance for this drastic revision of its basic philosophy? By any logical standards we are certainly entitled to be given some compelling reason for any such far-reaching change: some outstanding new discovery, perhaps, or some significant clarification of the general scientific picture. But do we get anything of this kind? Positively not. The whole case for this extraordinary alteration of the underlying philosophy of science rests on the assumption that the failure of the scientific profession to attain the goals originally envisioned cannot be due to any shortcomings on their part; it must be due to the fact that these goals are non-existent. ”In short,” says McVittie, “if the doctrine
of a rational External World is accepted, past experience forces us to
conclude that science is everlastingly in error, a Kepler, a Newton or
an Einstein periodically ’proving’ that his predecessors severe
mistaken.” Dingle applies a similar type of reasoning in this statement: “...both relativity and quantum theory, the highlights of modern physics, are concerned not with an external world but with the operations of physicists and... they become nonsensical when they are presented as descriptions of external Nature.” If what Dingle asserts is true, then the most natural and logical conclusion is that these two “highlights of modern physics” are, in fact, nonsensical. But the present-day physicist refuses to recognize the possibility that the accepted pattern of thought of his profession may be wrong; he closes his eyes to this distressing prospect and pretends that it does not exist, thereby twisting Dingle’s point into another argument against the existence of a rational external world. Once a more realistic appraisal of the situation is made
and it is realized that it is no longer possible to avoid conceding that
modern science The new gravitational theory based on the postulates of
the Reciprocal System sacrifices neither traditional logic nor the external
world. Here again, as in the more specific situations previously discussed,
this new theory adheres to the simple and natural viewpoint rather than
introducing complicated and questionable
Another feature of current scientific thought, which has
been emphasized by the development of the Reciprocal System, is a strange
dichotomy in the prevailing viewpoint concerning the nature of scientific
proof. On the one hand, the possibility of the verification of a theory
is specifically and categorically denied. Northrop tells us, for instance,
“Thus no theory in mathematical physics can be established as true
for all time. Nor can the probability of the truth of any given theory
be scientifically formulated. For there is neither an empirical frequency
nor a theoretical Similar statements are quite common in present-day scientific literature, but Harrison’s words are particularly interesting because he lets the cat out of the bag, so to speak, by telling us specifically where this remarkable conclusion comes from. Modern scientists have “discovered” that there is no absolute truth by means of a chain of reasoning based on the assumption that the Theory of Relativity is absolutely true. The extraordinary nature of this reasoning is still further emphasized by the extremely liberal standards that have been applied in arriving at the “truth” of the Relativity Theory. Here is a theory whose factual supports are so flimsy that, as Bondi says in the statement quoted in Part One, a “substantial minority” of present-day theoretical physicists regard them as wholly inadequate, yet this theory is accepted as a solid foundation on which to base conclusions of the most far-reaching character. It cannot be denied that establishing the truth of a physical
principle or theory is a There is, of course, no definite rule by which we can say
specifically at what point the probability of a hidden error becomes negligible;
this will always be a matter of judgment. It is evident, however, that
where a very large number of correlations are made and these correlations
cover the entire field of application of the theory, so that the possibility
of an unrecognized limitation on the scope of the theory is ruled out,
there must be such a point somewhere along the line. Northrop’s contention
that wee cannot arrive at the probability of the truth of a theory is
thus manifestly erroneous in application to a theory which meets the requirements
specified in the preceding paragraph. Here the “empirical frequency”
and “definition of all the possibles” of which he speaks lose
their meaning because the actual numerical values of the probabilities
are no longer significant. After the term x in the function 1/ The present-day contention that positive proof is impossible
in principle is therefore untenable; the most that can be asserted on
any reasonable basis is that a rigid proof is not possible as a practical
matter, and even here the facts do not support such a contention. It is
true that most of the highly publicized physical theories of the current
era, those which are so widely hailed as having revolutionized our entire
scientific outlook, cannot be factually substantiated, since they are
not only deficient in the number of correlations with observation and
measurement, but are also inherently incapable of proof because they are
based in part on principles of impotence. But oddly enough, the prevailing
conclusions as to scientific proof in general are not applied here; in
current practice these cherished products of modern ingenuity are accorded
a status which puts them beyond the necessity of proof: a status which
even qualifies them as basic principles that can be used to “prove”
the validity of other conclusions, in the manner of Harrison’s contentions.
The amazing extent to which this strange exaltation of currently popular
theory has been carried is well demonstrated by the fact that no less
a scientist than Sir Arthur Eddingtonbegins one of his explanations with
the statement, “One proof rests on Einstein’s theory.” Obviously there is much confusion in current thinking on
this subject. With all due respect to Eddington, Harrison, and the many
others, who have said essentially the same thing, a The case for the gravitational theory presented herein, and for the entire Reciprocal System of which the gravitational theory is a part, is based on this same concept of the nature of proof; that is, we have achieved a proof when we have reduced the chance of error to the vanishing point. In elaborating, it will be convenient to draw an analogy between scientific theory, which is a concise representation of scientific knowledge, and a map, which is a concise representation of geographic knowledge. The traditional method of map making involves first a series of explorations, then a critical evaluation of the reports submitted by the explorers, and finally the construction of the map on the basis of those reports which the geographers consider correct. Similarly in the scientific field explorations are carried out by experiment and observation, reports of the findings and the conclusions based on these findings are submitted, these reports are evaluated by the scientific community and those which are judged to be authentic are added to the scientific map: the accepted body of factual and theoretical knowledge. But this traditional method of map making is not the only way in which a geographic map can be prepared. We may, for instance, devise some photographic system whereby we can secure a representation of an entire area in one operation by a single process. In either case, whether we are offered a map of the traditional kind or a photographic map we will want to make some tests to satisfy ourselves that the map is accurate before we use it for our purposes, but because of the difference in the manner in which the maps were produced the nature of these tests will be altogether different in the two cases. In checking a map of the traditional type we have no option but to verify each feature of the map individually, because aside from a relatively small amount of interrelation each feature is independent. Verification of the position shown for a mountain in one part of the map does not in any way guarantee the accuracy of the position shown for a river in another part of the map. The only way in which the position of the river can be verified is to compare what we see on the map with such other information as may be available concerning the river itself. Since these collateral data are often scanty or even entirely lacking, particularly along the frontiers of knowledge, the verification of a map of this kind in either the geographic field or the scientific field is primarily a matter of judgment and the final conclusion cannot be more than tentative at best. In the case of a photographic map, on the other hand, each test that is made is a test of the validity of the process and any verification of an individual feature is merely incidental. If there is even one place where an item that can definitely be seen on the map is in conflict with something that is positively known to be a fact, this is enough to show that the process is not accurate and it provides sufficient justification for discarding the map in its entirety. If no such conflict is found, however, the fact that every test is a test of the process means that each additional test that is made without finding a discrepancy reduces the mathematical probability that any conflict exists anywhere on the map. By making a suitably large number and variety of such tests the remaining uncertainty can be reduced to the point where it is negligible, thereby definitely establishing the accuracy of the map as a whole. In making these tests it is neither necessary nor advantageous to give any consideration to items which are in any degree doubtful. It serves no purpose because there is nothing to be gained by establishing the existence of a conflict if the significance of that conflict is unknown. It is not necessary because a map of this kind includes so many hundreds or thousands of individual features that there are ample opportunities for comparisons with facts that are not open to question, even if some areas are inaccessible. The whole operation of verifying a map of this kind is therefore a purely objective process in which features that can definitely be seen on the map are compared with facts that have been definitely established by other means. The final conclusion is an unequivocal yes or no. This is the kind of a map of the scientific field which
is presented in There is, however, one important precaution, which must
be observed: we must be certain of the validity of the alleged facts,
which we propose to use for test purposes. As has been emphasized previously,
the human mind is so constituted that it does not like to admit ignorance
and in those cases where we do not know there is a rather strong tendency
to dress our best guess in fine clothes and parade it as knowledge. For
example, one of the first items to emerge from the new theoretical development
is a new concept of the structure of the atom, and the general opinion
undoubtedly will be that this conflicts with a known fact: the nuclear
atom. But in reality we do not know that the atom has a nuclear structure.
On the contrary, the facts brought out in Similarly the new development finds normal hydrogen (H Development of the consequences of the fundamental postulates of this work results in many other conclusions which differ from currently accepted ideas but careful analysis has indicated that all of these cases are similar to those mentioned in the preceding paragraphs; that is, these popular ideas which are challenged by the new system are not factual; they are either inferences, hypotheses, or unsupported extensions of observational findings. In no case does this analysis disclose any conflict with genuine facts. Many of the theoretical conclusions cannot be tested at all, since they apply to areas in which no factual knowledge exists, but wherever and whenever the theory can be checked against solid facts the two are in agreement. It is perhaps inevitable that such statements in favor of
a new and revolutionary theory should be met with profound skepticism,
but the objective of this discussion is to bring out the point that the
appraisal of the new theoretical structure by the scientific community
can be, and therefore should be, a purely objective check of theory against
fact, without regard for the characteristically human but definitely unscientific
sentimental bias in favor of familiar ideas. Nor should it be in any way
surprising when this objective check does verify the validity of the new
theory. After all, the most conservative assumption that we can make about
the phenomena in the unknown regions of the universe, the assumption that
has by far the greatest |