Part Four
The Opposition
XIII
”The history of theoretical physics,” says Jeans,
“is a record of the clothing of mathematical formulae which were
right, or very nearly right, with physical interpretations which were
often very badly wrong.”^{47} The Special Theory of Relativity
adds another page of the same kind of history. In essence this theory
is simply a mathematical system of compensating for the error introduced
into relations at high velocities by the failure to recognize the existence
of coordinate time. It can easily be seen that a generally applicable
mathematical scheme of this kind is impossible, since no conceivable
mathematical system can accurately describe a threedimensional relationship
in onedimensional terms. If we limit the field of application to unidirectional
transnational velocities, however, we are dealing with only one of the
three dimensions of coordinate time, and in this special situation a mathematical
compensation for the conceptual error is possible. The Einstein theory
is an ingenious and carefully developed system of this nature and in relatively
simple applications it gives consistently accurate results, but because
of its inherent limitations it quickly runs into complications as soon
as it attempts to go beyond these simple applications.
In spite of its shortcomings, Relativity Theory has been
the accepted physical doctrine in its field for more than a half century
and consequently any new theory that is presented must indicate where
and to what extent it differs from Relativity, as a matter of facilitating
tile task of grasping the content of the new theoretical structure, if
for no other reason. A general picture of this situation can be obtained
by considering first, the postulates on which Relativity is based, and
second, the experimental and observational evidence which is offered in
support of the theory.
Relativity theory utilizes many principles and relations
drawn from the general body of physical knowledge. Except in the one case
of the basic concept of the nature of time, there is no point of conflict
in this area, and a discussion of these items will not be necessary in
the present connection. In addition, the theory sets up four postulates
of its own. Two of these appear in the Special Theory: (1) a denial of
the existence of absolute velocity, and (2) the constant velocity of light.
The General Theory adds two more: (3) the equivalence of gravitational
and inertial mass, and (4) the socalled postulate of “covariance.”
The constant velocity of light is a necessary and direct
consequence of the Fundamental Postulates of this present work. The same
is true of the equivalence of gravitational and inertial mass. The Reciprocal
System is therefore in full agreement with the Relativity Theory so far
as postulates (2) and (3) are concerned. Furthermore, there is no definite
disagreement concerning postulate (4). It is true that the implications
of the Reciprocal System tend to reinforce the opinions of those who doubt
whether there is any actual meaning in this postulate. Bridgman claims
that “any assumed law of nature whatever can be expressed in covariant
form,”^{48} and states that this was admitted
by Einstein in 1918. Bondi brings out the same point very forcibly: “Thus
whereas the special principle has physical content, the general principle
is void of all physical meaning and is merely a mathematical challenge,
a challenge to the ingenuity of mathematicians to find the same form for
the laws of nature in all systems of coordinates, however different the
content of these laws might be. Given sufficient high ingenuity on the
part of the mathematician the principle places no restriction whatever
oil the laws.”^{49} But
in any event, whatever physical significance the postulate does have in
the Relativity Theory, if any, is equally valid in the Reciprocal System;
indeed, the problem of maintaining the “forminvariance’ is
less acute in the new system as the theory itself and the mathematical
expression thereof are both much simpler.
The area of disagreement between the Reciprocal System and
the Relativity Theory, so far as the basic assumptions are concerned,
therefore reduces to the difference in the respective concepts of the
nature of time, and to a question as to the validity of postulate (1):
the denial of the existence of absolute motion.
In setting up his Special Theory of 1905, Einstein took
as his starting point the experimentally established constancy of the
velocity of light, and expressed this as a postulate: a law of nature
which we must accept, however strange and illogical it may seem in the
light of preexisting thought. This immediately led to a direct conflict
with the definition of velocity as s/t, space traversed divided
by elapsed time, but Einstein found that the discrepancy, in the special
case of uniform translational velocities, is a function of the velocity.
He therefore deduced that the correct mathematical results could
be obtained by denying the existence of absolute space and time and eliminating
the discrepancy through an appropriate modification of the numerical values
of the space and time terms.
This First Postulate which denies the existence of absolute
motion, together with absolute space and time magnitudes, and thereby
gives the Relativity Theory its name, is a purely negative proposition.
It is sometimes stated in a positive manner; that is, the assertion is
made that motion is relative rather than that it is not absolute. But
absolute motion is also relative to any reference system which we may
wish to set up, and the relativity assertion is therefore meaningless
unless it is intended to signify that motion is relative only, which
is just another way of saying that it is not absolute. As a negative proposition,
this postulate cannot contribute anything positive to the theoretical
structure. Herbert Dingle says flatly, “The principle of relativity
in itself tells us nothing whatever about anything...”^{50} It merely serves the purpose of
evading the contradiction which would otherwise exist, and it is somewhat
analogous to the legal principle that prevents a wife from testifying
against her husband. This prohibition does not strengthen the husband’s
affirmative case in the least, but it may be extremely important in blocking
the opposition. So it is with the First Postulate. When this postulate
has eliminated the necessity of conforming to the space and time magnitudes
determined by measurement, the way is left clear for the mathematical
manipulation that is necessary in order to force an agreement with the
constant velocity of light.
The First Postulate of Relativity is incompatible with the
Reciprocal System described herein, as all physical magnitudes in this
system are absolute, but as long as the only accomplishment of the postulate
is to evade a contradiction, the new system arrives at exactly the same
result without the postulate, since no contradiction develops in this
system; the absolute space and time magnitudes on the new basis are in
full agreement with the observed constant velocity of light.
We thus find that the Reciprocal System is in agreement
with three of the four basic postulates of the Relativity Theory and it
achieves the same results without the remaining postulate that Relativity
Theory does with it. It is therefore appropriate to conclude that if these
four postulates correctly represent the content of the theory, as Tolman
and many others contend, any results which can legitimately be
derived from the Relativity Theory will also be reached by the Reciprocal
System. Other conclusions which result from attempts to apply the mathematical
methods of Relativity to areas outside of their scope of applicability
(that is, to areas in which the error due to the use of clock time rather
than total time is not a function of the velocity alone) or which result
from inferences drawn from the language in which the postulates are expressed
will not be in agreement with the results obtained from the new system.
In this connection, it should be noted that there is no
observational evidence to support the First Postulate, the only one of
the basic postulates of the Relativity Theory with which the Reciprocal
System is in conflict, whereas there is evidence that tends to
contradict it. It is true that all attempts to measure a translatory velocity
relative to a hypothetical ether or to the general framework of space
have failed, but this does not necessarily mean that absolute motion does
not exist; it is equally consistent with the hypothesis that such motion
exists but our present facilities are incapable of detecting it. Heisenberg
views the situation in this manner: “This is sometimes stated by
saying that the idea of absolute space has been abandoned. But such a
statement has to be accepted with great caution... The equations of motion
for material bodies or fields still take a different form in a ’normal’
system of reference from another one which rotates or is in a nonuniform
motion with respect to the ’normal’ one.”^{51} Bergmann expresses the same thought:
“It. appears as if general relativity contained within itself the
seeds of its own conceptual destruction, because we can construct ’preferred’
coordinate systems.”^{52}
The most that can legitimately be contended, therefore,
is that the experimental evidence leaves the question of the existence
of absolute translational motion open. As indicated in the foregoing statements,
absolute rotational motion can be detected. It is possible, for
instance, to determine that the galaxies are rotating and even to get
a rough idea as to the magnitude of the rotational velocity in each case
simply by looking at them. All attempts that have been made to reconcile
these facts with the First Postulate have been extremely awkward and farfetched.
In the words of Eddington, “We see at once that a relativity theory
of translation is on a different footing from a relativity theory of rotation.
The duty of the former is to explain facts; the duty of the latter is
to explain away facts.”^{53}
The inapplicability of the First Postulate to rotational
motion not only invalidates its claim to the status of a general physical
principle; hut also creates a strong doubt as to its applicability to
translational motion. The existence of absolute rotational motion and
“preferred coordinate systems” strongly suggests that absolute
translational motion also exists, since rotational and translational motion
are interconnectertible, and it is rather difficult to accept the idea
that absolute motion can be converted to motion which has no absolute
magnitude. It is, in fact, just this point that has made the proponents
of the Relativity Theory so desperate in their attempt to “explain
away” the physical evidence of absolute rotation.
The findings of this present work make these considerations
somewhat academic, however, as these findings not only eliminate the reason
for questioning the existence of absolute motion, but also indicated
that absolute translational motion can be detected and measured.
We cannot regard our usual measurements relative to the earth as absolute,
since we know that the earth revolves around the sun; we cannot regard
measurements relative to the sun or the solar system as absolute, since
we know that the sun takes part in the rotation of the galaxy; we cannot
regard measurements relative to the galactic center or to the galaxy as
absolute, since we know that the galaxies have random motions of their
own and are also receding from each other. Up to now there has also been
the possibility that the galaxies are in motion as component parts of
some larger unit. An extensive development of the consequences of the
Fundamental Postulates of the Reciprocal System indicates, how ever, that
the galaxy constitutes the maximum aggregation of matter, the socalled
clusters of galaxies being merely temporary associations of no major significance
which will ultimately disappear either by dispersion or by agglomeration.
An absolute system of reference can therefore be obtained by correcting
the galactic positions for the effects of the recession and the random
movements of the individual galaxies. Such a system constitutes the general
spatial framework of our physical universe and since we know only one
universe, motion relative to this general framework is absolute motion.
The principal problem involved in establishing this absolute system of
reference lies in evaluating the random movements, as the correction for
the recession due to the spacetime progression is a straightforward operation,
but available statistical methods should he adequate for this purpose.
XIV
The ultimate test of the validity of any physical theory
is agreement with the results of observation, and measurement. An actual
proof of validity is, however, extremely difficult to achieve.
In order to constitute a proof, the correlation between theory and observation
must be comprehensive enough to reduce the possibility of a hidden conflict
somewhere in the system to the point where it is negligible and, as previously
pointed out, this means that there must be an exact correspondence in
a large number of cases throughout the area affected, without exception,
and without the use of contrived methods of evading contradictions or
inconsistencies.
Because of the extraordinary difficulties that stand in
the way of achieving a valid proof, it is necessary to relax the standards
to some extent for practical purposes and to accept on a provisional basis
a great many laws and principles which are far from qualifying as established
truths under any reasonably rigid standards. Strictly speaking, such principles
should be recognized as merely tentative, and in referring to them the
words “We think...” should be used rather than “We know...”
but the human mind is reluctant to admit ignorance and there is a very
general tendency to regard today’s best guess as the equivalent of
established fact. The individual who is firmly convinced of the truth
of the currently accepted doctrines in his field is inclined to take at
face value anything which tends to reinforce the position to which he
is committed, but to be very critical of anything to the contrary. As
a result, the meaning of the word “proof” is badly distorted
in current usage.
One very common practice, for instance, is to present evidence
in favor of some particular portion of a theory as proof of the validity
of the theory as a whole. A great deal of publicity has recently been
given to some new “proofs” of the Relativity Theory that have
been made possible by modern technological developments. One of the most
significant of the recent experiments of this kind was carried out at
Columbia University by C. H. Townes and associates; another at Harvard
University by R. V. Pound and G. A. Rebka, Jr. The results of this work
were immediately reported in the news journals of the scientific world
with headlines such as “YearLong Tests Confirm Einstein’s Theory,”
followed by unequivocal statements that these tests “have confirmed...
that Einstein’s special theory of relativity is correct.”^{54} But when we look behind the facade
to see just what was actually accomplished, we find that the Columbia
group simply produced some additional verification of one of the postulates
of the Relativity Theory: the constant velocity of light, whereas
the Harvard investigators verified another of the postulates: the
equivalence of gravitational and inertial mass.
To the extent that this additional evidence constitutes
proof of anything, it is proof of these two postulates, not of the Relativity
Theory as a whole. Furthermore, these particular postulates are not actually
assumptions at all; they are experimental facts whose validity most physicists
were willing to concede before Einstein incorporated them into
his Relativity Theory. When we get down to bedrock, there fore, we find
that these widely publicized “proofs” of the Relativity Theory
simply verify knowledge that existed before the theory was born; they
tell us nothing about the new ideas that Einstein put into the theory.
An even more serious threat to the integrity of scientific
knowledge is the widespread tendency to accept evidence, which is consistent
with a theory as proof of that theory. The situation with respect
to the First Postulate of Relativity has already been discussed. Teriestrial
experiments of many kinds have failed to disclose any effects that can
be attributed to absolute translational motion of the earth. This is consistent
with the hypothesis that no such absolute motion exists, to be sure, but
by no stretch of the imagination can it qualify as proof, since the contrary
hypothesis that such motion exists but cannot be detected by available
methods is equally consistent with the facts. But Relativity is the currently
fashionable doctrine, and it is standard practice to accept contentions
favorable to the orthodox doctrine at their face value hence, as Herbert
Dingle states the case, “A theoretical demonstration that the theory
contains no internal contradictions—that it could be right—has
frequently been regarded as a proof that it is right.”^{55}
Another striking illustration of the current trend is furnished
by the concept of an increase in mass at high velocities. Everywhere we
turn, we find references to the “proof” of this relation derived
from experiment, and to our “knowledge” of the rate of increase
of the mass. Here again the evidence is clearly consistent with the popular
hypothesis, but even a very casual consideration is sufficient to show
that this evidence is equally consistent with any one of several other
explanations, and hence is no proof of any of them. The almost universal
habit of treating this evidence as proof of the hypothesis of an increase
in mass is scientifically indefensible.
Equally common is the thoroughly unsound practice of accepting
a hypothesis as an established truth simply because it happens to be the
best explanation available at the moment, even if the confirmatory evidence
is wholly inadequate This is the situation which exists today with reference
to the Relativity Theory as a whole. In order to verify this statement,
we will next proceed to summarize the evidence in favor of the theory
and then to analyze the extent to which this evidence is sufficient to
justify the two assertions that are now commonly made on behalf of Einstein’s
ideas: (1) that tile Relativity Theory is superior to the Newtonian system,
and (2) that the Relativity Theory is a correct representation of the
physical relationships.
The following are the points that are generally advanced
in support of the theory:
 It reduces to Newton’s system at low velocities and hence is
in agreement with all of the great mass of experimental and observational
data that supports Newton’s generalizations.
 It is in agreement with the observed fact that the velocity of light
is constant and independent of the reference system.
 It accounts for the advance of the perhelion of Mercury.
 It predicts the interconvertibility of mass and energy and furnishes
the correct mathematical expression for this conversion.
 It supplies an explanation for the deviation from the Newtonian
relation F = ma that is observed at high velocities.
Einstein proposed two other tests of the theory: bending
of a light ray in passing a massive body and a shift of atomic spectra
toward the red in a strong gravitational field. The first observations
made after the original publication of the theory were interpreted as
confirming these theoretical predictions, and for many years these correlations
were accepted as proofs of the validity of the theory. More recently,
however, skepticism has been growing, and what may be regarded as the
“official” opinion at present is that the status of both of
these tests is doubtful. A statement by H. P. Robertson at a conference
on “Experimental Tests of Theories of Relativity” held at Stanford
University in July 1961 contains the following conclusions, as reported
by L. I. Schiff: “the deflection of light by the sun has not been
measured with great precision,” “the red shift follows from
more elementary considerations and is not really a test of general relativity,”
and “only the precession of the perhelion of the orbit of the planet
Mercury provides an accurate test of Einstein’s theory.”^{56} In view of the existing uncertainties,
we are not justified in taking the deflection of light and the gravitational
red shift into consideration in the present analysis.
If we examine the five points listed in the foregoing tabulation
from the standpoint of their relevance to the question as to the relative
merits of Newton’s and Einstein’s theories, it is apparent that
the verdict is definitely in favor of Einstein. Newton’s theory gives
the wrong answer in the case of item 2, the constant velocity of light
and also item 5, the decrease in acceleration at high velocities, and
it provides no explanation of the observed facts concerning item 3, the
advance of the perhelion of Mercury. It is likewise silent on item 4.
’This latter cannot be counted against Newton, as this subject is
not specifically within the scope of his theories, but the ability to
cover a larger field is a point in favor of Einstein’s theory. On
the other side of the picture, Newton can claim no offsetting advantage
over Einstein because of item 1, which means that all of the positive
evidence in favor of Newton’s system is equally favorable to the
Relativity Theory. This statement should perhaps be qualified to some
extent, as the ability of Einstein’s theory (the General Theory,
in particular) to achieve the same results as Newton’s system cannot
be definitely checked in the more complex applications because the mathematics
become too difficult to handle by any means now available. Mc Vittie comments
on this point as follows: “But whether it (General Relativity) can
also embrace the phenomena associated with the idea of rotation—the
tides, for example—which presented little difficulty to Newtonian
theory, is still an unsolved problem.”^{57}
The early history of the Relativity Theory is commonly portrayed,
in presentday writings, as a contest between Einstein and Newton in which
the points outlined in the foregoing paragraphs were gradually recognized
by the scientific profession, so that the decision ultimately went to
Einstein. Actually, however, Michelson and Morley destroyed the validity
of Newton’s Laws as physical principles of general application in
conjunction with existing ideas of space and time in 1887, not by Einstein,
who first published his theory in 1905. As soon as the authenticity of
the results of the MichelsonMorley experiment was conceded, the generality
of Newton’s Laws was automatically invalidated, even though it took
some years to overcome the reluctance of the scientific profession to
accept this distasteful fact. There was now a direct conflict between
the Newtonian concept of motion and the experimentally verified constancy
of the velocity of light. Something in the fabric of physical theory obviously
had to be altered, and the issue facing the scientific community was essentially
a question as to what this should be. Not recognizing the incomplete nature
of the existing ideas of time, tile scientists of this era selected the
concept of absolute magnitudes of space, time and motion as the item to
be sacrificed. Fitzgerald first advanced the idea of a contraction of
space in the direction of motion, Lorentz enlarged and improved the concept,
and finally Einstein put the whole development on a firm mathematical
and theoretical footing.
Between 1887 and 1905 there was no general theory of motion
that could even claim validity. Thus the Relativity Theory did
not attain its present position by triumph over an opposing idea; it simply
filled a conceptual vacuum, and its general acceptance in spite of its
many weaknesses is due primarily to this fact. Because of these numerous
and serious weaknesses powerful voices were raised against it in its youth.
P. W. Bridgman, for example, once predicted (referring particularly to
the General Theory) that “the arguments which have led up to the
theory and the whole state of mind of most physicists with regard to it
may some day become one of the puzzles of history.”^{26} Paul R. Heyl was equally critical.
“Here,” he says, speaking of rotational motion, “the relativity
concept shows plainly its nature: a hollow mathematical shell, with no
real content; useful as far as it fits the facts, useless where it does
not.”^{58} But the battle was won by default.
Bridgman, Heyl and their fellow critics were ultimately silenced because
they had no alternative to offer; they could only attack the shortcomings
of the theory itself and, as the politicians so aptly put it, “You
cannot beat something with nothing.”
But when we turn to the second issue, the question as to
whether the Relativity Theory is a correct representation of the actual
physical relationships, all of the deficiencies and shortcomings pointed
out by these early critics to no avail once more become pertinent. Here
the theory has much more difficult requirements to meet; it must be so
strongly supported that the possibility of an error of any consequence
in the structure of the theory is negligible. As previously stated, this
means that it must agree with the observed and measured facts in a large
number of individual applications throughout the area affected, without
exception, and without the use of contrived methods of evading inconsistencies
or contradictions. Obviously the theory does not even begin to meet these
requirements. Aside from the fact that it claims to incorporate Newton’s
low velocity relations, which are firmly established, the Relativity Theory
can point to only a very few instances of agreement with the established
facts, and in the most important of these, the situation with respect
to the constant velocity of light, the agreement has been reached only
by means of one of those evasive devices which vitiate any attempt at
proof.
The use of principles of impotence or other evasive devices
has become such a commonplace feature of presentday physical theory that
their true character has been to a large extent obscured. What these devices
actually accomplish is to dispose of a contradiction or inconsistency
by postulating that this discrepancy shall not be counted as a discrepancy.
It is, of course, possible that the device may be entirely legitimate;
the universe may actually be constructed in some such weird manner. But
there is no way in which we can determine whether or not it is legitimate
in any particular case, and hence the use of such a device precludes any
possibility of proof, irrespective of whether or not the contentions are
wellfounded. If we have to utilize a device of this kind to arrive at
the truth, then we can never be certain that it is the truth. As Einstein
himself has pointed out, “For it is often, perhaps even always, possible
to adhere to a general theoretical foundation by securing the adaptation
of the theory to the facts by means of artificial additional assumptions.”^{59}
Either of these deficiencies, the lack of adequate observational
confirmation or the use of the unsupported assumption of the “rubber
yardstick,” is sufficient to stamp the Relativity Theory as unproved,
hence our second question, the question as to whether the theory is a
correct representation of the physical facts, will have to receive an
inconclusive answer for the moment. There are no instances where the theory
is definitely in conflict with established facts, aside from such bearing
as the existence of absolute rotation may have on the issue, but the theory
becomes more and more vague as it passes from general principles to details,
and there is ample justification for a suspicion that it is only the concealment
thus provided that prevents recognition of many conflicts with the physical
facts. Einstein tacitly admits this when he speaks of “...the ever
widening logical gap between the basic concepts and laws on one side and
the consequences to be correlated with our experience on the other—a
gap which widens progressively with the developing unification of the
logical structure.”^{60}
XV
The development of the Reciprocal System now confronts the
Relativity Theory with the kind of an acid test which it has never had
to meet before: a direct item by item comparison with a new theoretical
structure that agrees with the facts of observation and experiment in
an easy and natural way, without the use of evasive devices such as the
First Postulate of Special Relativity or vague and obscure “artificial
additional assumptions” of the kind that are employed so freely in
the development of the General Relativity Theory. The presentation in
this volume advances two contentions on behalf of the Reciprocal System
similar to those, which have previously been offered on behalf of the
Relativity Theory. These are (1) that the Reciprocal System is superior
to the Relativity Theory, and (2) that this system is a correct representation
of the physical facts. The second contention includes the first and it
would actually be sufficient to establish this point alone, but it will
help to clarify several significant issues if the two questions are considered
separately.
In beginning an analysis of these two questions, let us
first summarize the position of the Reciprocal System with respect to
the five points raised in support of the Relativity
 This system also reduces to Newton’s system at low velocities.
 It is also in agreement with the observed constant velocity of light.
 It furnishes a different, but equally accurate, explanation of the
advance of the perhelion of Mercury.
 It arrives at the same mathematical expression for the interconversion
of mass and energy.
 It furnishes a different, but equally consistent, explanation of
the deviation from the relation
F = ma at high velocities.
From this tabulation it can be seen that the points which
led to the triumph of Relativity over Newton’s system are not available
as arguments in the contest with the Reciprocal System. On the contrary,
unless it can be shown that Relativity Theory furnishes a better explanation
in one or more of those cases where the two theories arrive at the same
results by different routes, the Relativity Theory has no argument at
all to support a contention that it is superior to the Reciprocal System.
Let us therefore examine the differences between the two theories in these
particular areas.
So far as the agreement with Newton’s Laws at low velocities
is concerned, the Reciprocal System is in much the better position. The
adherents of the Relativity Theory claim that the equations of this theory
give the same results as Newton’s Laws at low velocities but, as
pointed out earlier, this claim cannot be vitrified in any other than
the very simplest applications, as the mathematics of the theory are too
complicated to be workable elsewhere. The Reciprocal System does not merely
give the same results as Newton’s Laws; at low velocities
the equations of this system are Newton’s expressions, hence there
cannot be any question as to the kind of results which this system
produces in the low velocity field.
The comparison in the field of motion at high velocities
is also very definitely favorable to the Reciprocal System, as Relativity
Theory is confronted with a contradiction between the constant velocity
of light and the definition of velocity which the theory utilizes: a contradiction
that is removed only by the use of an arbitrary assumption of a wholly
unsupported nature. In the Reciprocal System, on the other hand, no such
contradiction exists and no evasive assumption is required. The constant
velocity of light emerges easily and naturally from the development of
the basic postulates of this system.
Closely connected with this question of the constant velocity
of light is the advance of the perhelion of Mercury. It has been known
since the time of Leverrier that the orbit of this planet is constantly
moving ahead of the position calculated on the basis of Newton’s
Laws, the unexplained increment being almost twenty miles per revolution
or something over 40 seconds of arc per century. According to the Reciprocal
System, this is merely another effect of the same factors that are responsible
for the negative result of the MichelsonMorley experiment. As long as
the orbital velocity is low, the difference between clock time and total
time is negligible, but the velocity of Mercury is great enough to introduce
an appreciable amount of coordinate time and during this added time the
planet travels through an additional distance.
Einstein’s massenergy equation E = mc^{2}
is entirely in accord with the relations derived from the Reciprocal System.
In the previous publication mass was identified as the reciprocal of threedimensional
velocity, t^{3}/s^{3},
and energy as the reciprocal of onedimensional velocity, t/s. When
reduced to the spacetime terms of the new system, the massenergy equation
becomes
t/s = t^{3}/s^{3}
x s^{2}/t^{2}
As this is a valid equality, the equation E = mc^{2}
hold good in the Reciprocal System just as it does in the Relativity Theory.
But this agreement as to the mathematical form of
the relationship does not signify agreement as to the meaning of
the equation accepted l y both systems. Einstein claims that a body at
rest possesses a quantity of energy equivalent to its mass, and that kinetic
energy of motion likewise corresponds to an equivalent amount of mass.
A body in motion therefore acquires an additional mass, which “varies
with changes in its energy” and “becomes infinite when q (the
velocity) approaches 1, the velocity of light.”^{61} “According to the theory of
relativity,” Einstein says, “there is no essential distinction
between mass and energy. Energy has mass and mass represents energy.”^{62}
The Reciprocal System is in direct conflict with this interpretation
of the equation. From the Fundamental Postulates of this system we
find that energy is a onedimensional displacement of spacetime, whereas
mass is a threedimensional displacement (rotational). Under appropriate
conditions the dimensions of the displacement can be altered, hence mass
is convertible to energy and vice versa. The displacement can exist either
as mass or as energy (that is, either in three dimensions or in one
dimension) but obviously not as both simultaneously. Mass is not
associated with energy; it is convertible to energy, and
the massenergy equation merely indicates the relation between the magnitudes
involved when and if the conversion takes place. Energy is mass
only if it is converted to mass, and when such a conversion takes place
so that a quantity of mass makes its appearance, the equivalent quantity
of kinetic energy ceases to exist.
As Bridgrnan has pointed out, many of Einstein’s conclusions
have been accepted without adequate critical scrutiny, and this massenergy
relation definitely falls in this category. If this relationship is examined
from the standpoint of logic, it is apparent that Einstein’s contentions
are internally inconsistent and must eventually fall of their own weight,
irrespective of what any other theory may say. Mass cannot be something
that is associated with energy (and therefore increases as the energy
increases) and at the same time something that is convertible to energy
(and therefore decreases as the energy increases). But this obvious conceptual
contradiction is one of the things that Relativity Theory expects us to
accept. If “mass and energy, are only different expressions for the
same thing,”^{61} as Einstein declares, then we cannot
have a conversion of one to the other; we cannot convert anything into
itself. But such a conversion clearly does take place. An atomic
explosion, for example, is not a mere alteration in terminology or a conceptual
reorientation; it is an actual physical event, and hence Einstein’s
viewpoint cannot be correct. It does not meet the requirements of elementary
logic.
It is generally believed that the hypothesis of an increase
in mass accompanying increased velocity is firmly established by experiment,
and scientific literature is full of positive statements to that effect:
statements which emanate not only from rank and file physicists, but also
from the most eminent leaders of science. Louis de Broglie states unequivocally,
“...the variation of mass with velocity deduced by Einstein... is
verified daily by observation of the motion of the highspeed particles
of which nuclear physics currently makes such extensive use.”^{63} Planck was equally positive: “The
theory of relativist mechanics was verified by experiment in the case
of rapidly moving electrons, for this experiment showed that mass is not
independent of velocity,”^{64} and Eddington tells us flatly,
“...the mass depends on the velocity—a fact unknown in Newton’s
day.”^{65}
Yet, oddly enough, while a host of scientific authorities
of the highest rank are thus proclaiming that the postulated increase
of mass with velocity has been proved by experiments with highvelocity
electrons and verified by the successful use of the theory in the design
and construction of the particle accelerators, almost every elementary
physics textbook admits, explicitly or tacitly, that this hypothesis of
an increase in mass is only an arbitrary selection from among several
possible explanations of the observed facts. Richard Schlegel even manages
to put both points of view into the same sentence. “Even before Einstein’s
first paper on special relativity,” he tells us, “W. Kaufmann
had observed an increase in the mass of electrons moving with very high
velocities—or more precisely he had found a decrease in the e/m ratio
of electrons, where e is the electron charge, a magnitude unaffected by
relative velocity.”^{66} Still more precisely, we may say
that Schlegel’s final comment about the effect of velocity on the
magnitude of the charge is pure assumption. The truth is that the experiments
with high velocity particles and the experience with the particle accelerators
merely show that if a specific force is applied to a specific mass, the
acceleration decreases at high velocities, following a pattern which indicates
that it will reach zero at the velocity of light. II we are to maintain
the relation a = F/m it then necessarily follows that either
the mass increases or the force decreases, or both. Certainly the hypothesis
of an increase in mass is consistent with the observed facts, but
this is by no means the equivalent of the proof that is claimed. The door
is wide open for ally alternative explanation which calls for a decrease
in the effective force: either a decrease in the magnitude of the entity
responsible for the force (an electric charge, in the usual case) or a
reduction in the effective component of the force. The latter is the explanation
that we obtain from the Reciprocal System.
In this system mass is absolute in magnitude, and it therefore
remains constant irrespective of velocity. I Here, however, force is not
constant. Force, according to the principles of the Reciprocal System,
is simply a special way of looking at motion. If we assume a velocity
v_{1} acting in a certain direction
and then superimpose an equal velocity v_{2}
acting in the opposite direction, the net velocity is v_{1}–v_{2}
= 0. In describing this situation we may take the stand that both velocities
actually exist and that the null result is due to the fact that one cancels
the other, or alternatively, we may say that there is a force F_{1}
tending to produce velocity v_{1}
and an oppositely directed force F_{2}
tending to produce velocity v_{2},
but that, since the resultant of the two forces is zero, no motion takes
place.
It is clear from the development in Part Three that the
motions actually do exist and that the concept of force is simply an artificial
way of looking at the situation. This does not mean that there is anything
inherently wrong in the use of such a concept. If there is an element
of convenience in utilizing an artificial contrivance of this kind, as
there certainly is in this particular case, it is perfectly legitimate
to take advantage of this more convenient mode of expression, providing
that the concept is recognized for what it really is, and its limitations
are taken into account. But if this true status is not recognized and
the limitations are ignored, it is inevitable that this artificial contrivance
will lead us astray sooner or later.
From the standpoint of the force concept itself, the idea
of a constant force seems entirely logical, and up to now the existence
of forces of constant magnitude has not been questioned. On the basis
of the explanation of the nature of force given in the preceding paragraphs,
however, there can be no such thing as a constant force. The spacetime
progression, for instance, tends to cause objects to acquire unit velocity
and we therefore say that it exerts unit force. But a tendency to impart
unit velocity to a mass, which is already at a high velocity, is not equivalent
to a tendency to impart unit velocity to a body at rest. The effective
force is a function of the difference between the velocities, and
the full effect of any force is only attained when that force is exerted
on a body at rest. As velocity increases the velocity difference decreases
and hence the effective force also decreases. In the limiting condition,
when tile mass already has unit velocity, the force (the tendency to cause
unit velocity) has no effect at all and the effective force component
is zero. The acceleration is then also zero, as the experimental results
indicate.
The foregoing discussion shows that the Reciprocal System
provides a consistent and logical explanation for each of the five points
on which Relativity Theory rests its case. Since this is true, there is
no scientific basis on which Relativity can claim any superiority. On
the contrary, whatever advantage does exist favors the Reciprocal System,
since this system does not have to utilize any principle of impotence
such as the First Postulate of Relativity, nor does it contain any internal
inconsistency such as giving mass both the status of something associated
with energy and the status of something convertible to energy. Even when
it meets the Relativity Theory on that theory’s own ground, therefore,
the Reciprocal System makes a very favorable showing. But the facts brought
out for this purpose represent only a minor portion of the evidence supporting
the validity of the new system. Unlike the Relativity Theory, which can
be checked against experiment and observation in only a few cases and
which, as Einstein says, confronts us with an “ever widening gap”
between the theoretical concepts and the facts of experience as the theory
is extended into additional areas, the consequences of the Reciprocal
System are clearly and sharply defined at all points, and they can be
checked against experience in a multitude of applications, not only in
the areas which Relativity Theory purports to cover, but also in many
additional fields which have hitherto been considered totally unrelated
to the gravitational phenomenon.
In presenting the case in favor of the broader contention
that the gravitational theory derived from the Fundamental Postulates
of the Reciprocal System is a correct representation of the physical facts,
we will limit the discussion to gravitation, the specific subject under
consideration in this present work, rather than dealing with the Reciprocal
System as a whole. No attempt will be made, therefore, to present all
of the immense volume of data confirming the validity of the system in
general. Enough of these data were included in the previous publication
The Structure of the Physical Universe to establish the solid factual
status of the system, which may be described by the statement that the
necessary consequences of the Fundamental Postulates of this system, without
the aid of subsidiary or supplemental assumptions, and without the use
of any contrived or artificial methods of evading contradictions, constitute
a complete theoretical system of physical entities and relationships which
is in agreement with observations and measurements in thousands of applications
throughout the physical universe, and thus far has not been found inconsistent
with the established facts in any instance. Just because of the validity
of these postulates, and without the intervention of any other factor,
radiation, matter, electrical and magnetic phenomena, and the other major
features of the observed universe must exist in the theoretical
universe, and the primary characteristics which these phenomena theoretically
must have are identical with the characteristics of the corresponding
observed phenomena.
In its general aspects, therefore, the Reciprocal System
meets all of the requirements for proof of its validity; that is, it agrees
with the observed and measured facts in a large number of individual cases
throughout all of the general areas in which such facts are available,
there are no known cases in which positively established facts are inconsistent
with the theoretical conclusions, and no use has been made anywhere in
the theoretical development of principles of impotence or other artificially
contrived devices for evading such inconsistencies. It is true, of course,
that the new system is in conflict with much of the currently accepted
thought of the scientific profession, but in every case where such conflicts
occur, it can be shown that the existing ideas, however firmly entrenched
they may be, are not established facts; they are extrapolations of, interpretations
of, or inferences drawn from these facts, or else they are pure assumptions
not connected with the facts at all. If the issue is squarely faced, therefore,
it must be conceded that the validity of the system in general has been
established.
It does not follow, however, that every deduction, which
may be made from the Fundamental Postulates of the Reciprocal System necessarily,
participates in the proof of the validity of the system as a general proposition.
As pointed out in Part One, once the validity of general principles of
this kind has been established, it is possible to prove the validity of
certain other conclusions by deductive methods; that is, by showing that
these conclusions are necessary and unavoidable consequences of the principles
already established, or of these principles taken together with certain
known facts. The extent to which this kind of proof can be carried is
somewhat limited; however, as one can rarely, if ever, be absolutely certain
that a long line of reasoning is entirely free from error. Because of
this situation the method of deductive proof is not ordinarily sufficient
in itself; the purpose that it normally serves is reduce the number of
correlation’s with established facts that are required in order to
bring the possibility of a concealed error down to the vanishing point.
A theoretical relation that is definitely in conflict with positively
established facts is wrong regardless of its derivation, but w here there
is no contradiction or inconsistency, a relation that is derived in a
straightforward manner from principles whose validity has already been
proved is obviously in a much better initial position than a relation
that is purely hypothetical. What we have done here is to reduce the general
question of the possible existence of some contradictory fact to the more
limited question of the validity of the deductive process, and hence a
smaller number of factual correlation’s is sufficient to reduce the
probability of a hidden error to the neighborhood of zero.
The extent to which the deductive proof is effective in
this respect naturally depends upon the length of the chain of reasoning
involved in deducing the conclusion from the previously established principles.
If the connection is immediate and direct, comparatively little factual
corroboration should be required; the absence of any contradiction or
inconsistency should be almost enough in itself under these circumstances.
As the number and complexity of the steps in the process of deduction
increases, the chance of a logical or mathematical error somewhere in
the process likewise increases, and the need for more factual corroboration
increases accordingly. In the limiting condition, where the deductive
chain is extremely long and involved, the requirements for proof are essentially
no different than in the case of a pure hypothesis.
On this basis, there is abundant proof of the validity of
the gravitational theory presented herein. To begin with, this theory
is an immediate and direct consequence of the Fundamental Postulates of
the Reciprocal System, the validity of which, as has been stated, is confirmed
by a great mass of evidence that meets all of the requirements of proof.
In view of this status as a direct deduction from principles already established,
a relatively small amount of factual corroboration should be adequate
to complete the proof, and since everything that is actually known about
gravitation is in full agreement with the theory, this should be sufficient
for the purpose, even though it is true that the existing knowledge in
this field is quite limited.
Furthermore, a very substantial amount of additional support
is developed in fields, which have not hitherto been recognized as falling
within the scope of gravitational theory. As the previous discussion has
indicated, the new gravitational theory not only explains the origin of
this phenomenon and the characteristics which it manifests in the generally
recognized aspects of the gravitational action, but also goes on to provide
explanations for other phenomena, such as the recession of the distant
galaxies, the cohesion of solids, and the abnormal distances between the
stars, which have heretofore been considered as totally unrelated to gravitation.
The agreement between theory and established facts in these additional
fields not only constitutes a major addition to the rather meager number
of factual correlation’s which it is possible to obtain in the narrow
field hitherto connected with gravitation, but also has another very significant
aspect, in that such an extension of the field of application is a recognized
indication of merit in a new theory of any kind. In this case the extension
that has been achieved is extremely farreaching and it adds substantial
additional weight to the already strong case in favor of the new gravitational
theory
The question as to just how far it is necessary to go before
we can say that the remaining probability of the existence of a hidden
error is essentially zero is a matter of opinion, but if the new gravitational
theory does not actually qualify, it is certainly not far away from qualification.
In any event, it is much closer to positive proof than most physical theories,
and far superior in this respect to the current favorite, Einstein’s
General Theory of Relativity, which has not achieved its present standing
on its own merits, but because of the fact that nothing better has hitherto
been available.
XVI
In spite of the status of gravitation as the primary subject
of this volume, the foregoing discussion of the Relativity Theory has
been directed largely at the Special ’Theory since the General Theory,
which actually deals with gravitation, is supposed to be an extension
of the principles of the Special Theory to the wider field of nonuniform
motion, and a full understanding of the true nature of the Special Theory
gives us a better indication of the position of the General Theory than
we can obtain by making a detailed analysis of the rather confused structure
of the latter. It has been shown in the preceding pages that the Special
Theory is simply a mathematical device which compensates for the error
introduced into the relations of moving bodies by the failure to recognize
the existence of coordinate time. The General Theory represents an attempt
to extend this compensating mechanism into the field of nonuniform motion.
The Special Theory is mathematically correct even though
it is expressed in terms of totally erroneous concepts, because its mathematical
content is empirical and independent of the language in which it is described
by the theory (in fact, this mathematical content antedates the theory
itself). The validity of the empirical relations is dependent, however,
on restricting their application to those cases where the error due to
using clock time instead of total time is a definite function of the velocity.
It is evident, therefore, that when the relations of the Special Theory
are extended to rotational and other accelerated motion, where this error
is normally not a specific function of the velocity, for reasons
that have been detailed in the preceding discussion, the derived relations
cannot be correct. Thus it is impossible for the General Theory to supply
us with mathematical expressions which will serve the same purpose with
respect to nonuniform motion that the equations of the special theory
(the Lorentz transformations, etc.) do for uniform translational motion.
No mathematical system, regardless of how complex and sophisticated it
may be, can provide an accurate representation of the relations between
quantities which, in truth, are not definitely related in any mathematical
way. Any theory, which attempts to achieve this objective, must inevitably
bog down in unworkable mathematical complexities and conceptual confusion,
just as has actually happened in the case of the General Theory.
”In physics,” said Herbert Dangler twentyfive
years ago, “the name of Relativity is notorious: if one claims to
understand it he is looked at askance, and his subsequent statements are
received with suspicion.”^{67} Another quarter of a century in
which Relativity has had the field all to itself without serious competition
has silenced most of the critics, but it has not lessened the real force
of their criticism. The General Theory is just as full of inconsistencies
and loose ends today as it was in that earlier era; it has made no appreciable
advance in the interim. If we examine the two postulates, which Tolman
tells us contain the essence of the General Theory, the reason for this
sterility is evident. The objective of the theory, its originator asserts,
is an extension of the findings of the Special Theory into the area of
nonuniform motion, particularly accelerated motion. Now let us ask, just
what does the Principle of Equivalence contribute toward this objective?
The answer must be—nothing. This postulated principle merely asserts
that gravitational mass and inertial mass are equivalent, and hence gravitation
can be treated as the equivalent of an accelerated motion. The present
work has no quarrel with this conclusion; on the contrary, it goes a step
farther and says that gravitation is an accelerated motion. But
this simply means that we have only one problem—accelerated motion;
we do not have two problems—gravitation and accelerated motion—as
had been thought previously. All that the equivalence postulate does is
to establish this point; it makes no contribution whatever to the solution
of the one problem which does exist.
When we turn to the second of the two postulates of General
Relativity, the postulate of covariance, we encounter a very odd situation.
It was pointed out originally by Kretschmann, emphasized by Bridgman and
others, and admitted both by Tolman and by Einstein, that this postulate
actually imposes no restriction on physical theory, yet we find some of
the most farreaching conclusions of General Relativity ostensibly based
upon it. This strange situation is the subject of a very penetrating comment
by Bridgman: “It must, I think, strike one on reflection as paradoxical
to attempt to get information about nature from the requirement of covariance,
for this is at bottom merely an attempt to get information about nature
from an analysis of the language in terms of which we describe it, whereas
the fundamental idea back of the argument as it is worked out in detail
is that the sort of language with which we describe nature must be a matter
of indifference.”^{48}
The two postulates, which are supposed to express the content
of General Relativity thus, turn out to have no bearing on the primary
problem of extending the application of Special Relativity to accelerated
systems. “The astonishing thing about Einstein’s equations is
that they appear to have come out of nothing,”^{68} says one observer. Even the status
of the General Theory as an extension of the Special Theory is open to
serious question. Peter G. Bergmann states categorically, “It is
quite true that the general theory of relativity is not consistent with
the special theory any more than the special theory is with Newton’s
mechanics—each of these theories discards, in a sense, the conceptual
framework of its predecessor.”^{69}
The question therefore arises, just how does General
Relativity come to grips with this problem? Einstein himself supplies
the answer to this question. He tells us that he had completed his analysis
of the factors involved in gravitation and accelerated motion in general
by 1908, and then goes on to say, “Why were another seven years required
for the construction of the general theory of relativity? The main reason
lies in the fact that it is not so easy to free oneself from the idea
that coordinates must have an immediate metrical meaning.”^{70} He later defines this expression
“a metrical meaning” as the existence of a specific relationship
between differences of coordinates and measurable lengths and times.
Here we have the real essence of General Relativity.
Special Relativity accomplished its objective of providing a mathematical
correction for the conceptual error in the conventional view of time by
abandoning the idea that the magnitudes of time and space intervals measured
with respect to coordinate systems of reference have fixed values, and
introducing a fictitious variability in these magnitudes. To meet the
additional problem of accelerated motion, Einstein simply prescribed a
bigger dose of the same medicine. It took him seven years to figure out
where the additional flexibility could be introduced, but finally he created
more latitude for numerical variation by depriving the coordinates themselves
of any meaning so far as mensuration is concerned. As Moller sums up the
new picture, “In accelerated systems of reference the spatial and
temporal coordinates thus lose every physical significance; they simply
represent a certain arbitrary, but unambiguous, numbering of the physical
events.”^{71}
If the situation were one which could be reconciled
with the conventional views of time by purely mathematical means, this
strategy might have been successful (to the extent that constructing a
theory that is mathematically right but conceptually wrong can be considered
a success) just as Special Relativity is able to compensate for an error
in its concept of the nature of time by introducing a counterbalancing
error in its treatment of space. But since no general mathematical relationships
of this kind exist once we get away from uniform translational velocity,
General Relativity cannot expect to do anything in the field of motion
beyond the little that has already been accomplished; that is, to provide
complicated and rather vague solutions for certain very limited and mainly
hypothetical problems.
Strangely enough, the reputation of the General Theory of
Relativity, which is essentially, a theory of motion (gravitational and
other) rests primarily on items which are only indirectly connected with
motion. If this theory had to rely on its achievements in the field of
motion alone (that is, on what it has accomplished in extending the relations
of Special Relativity to accelerated motion) it would be in a very sorry
state. But other, somewhat incidental, conclusions derived from or suggested
by the Relativity Theory have had a spectacular success, and the success
in these collateral areas has had the effect of sidetracking any critical
scrutiny either of the extent to which the theory has accomplished its
primary objective or the extent to which these widely publicized collateral
derivatives are legitimate products of the Relativity Theory. “Though
this treatment gets over some difficulties,” says Sir George Thomson,
“it does so at the cost of considerable violence to commonsense.
It may be doubted if it would have received the full acceptance that it
in fact has but for the remarkable applications to mechanics... leading
to predictions concerning the identity of mass and energy which have been
brilliantly verified in nuclear physics.”^{72}
When the originator of a new theory tells us that his theory
leads to the (at that time) astonishing conclusion that mass and energy
are equivalent and interconvertible, and subsequently the conversion of
mass to energy is demonstrated in an aweinspiring manner; when he also
tells us that the mass of a body in motion increases with the velocity,
becoming infinite at the velocity of light, and that this mass increase
will decrease the acceleration of high speed particles subjected to constant
forces, and subsequently it is found that particles traveling at high
velocities behave in exactly the manner predicted, this practically closes
the door to any attempt at a critical analysis of the theoretical background.
Few investigators are willing to attack such a strongly entrenched position,
and little attention is paid to those who do have the temerity to make
the attempt.
As a result, no one seems to have given any consideration
to the fact that, while each of these two conclusions alleged to have
been derived from the Relativity Theory makes an impressive showing by
itself, they are mutually contradictory, and if either one is valid, the
other is necessarily wrong. At least one of these impressive successes
of the theory is fictitious. Mass cannot be an accompaniment of
energy, as demanded by the aspect of the theory that explains the operation
of the particle accelerators, and also something that can be converted
into energy, as demanded by the aspect of the theory that explains
the atomic bomb. These two concepts are incompatible and it is obvious
that a theory, which claims to have derived both results from the same
basic source, is in error somewhere. A thorough examination of the whole
development is therefore very much in order.
Unfortunately, such an examination encounters major obstacles.
One of the principal items of this kind, a factor that has played an important
part in preventing the emergence of any fullscale attempts at a critical
analysis of the alleged achievements of the Relativity Theory is the extreme
difficulty of getting at the real essence of the theory. The situation
that faces anyone who attempts to find out where the conclusions of the
theory actually come from has already been mentioned. The mathematical
basis of the theory is equally elusive. In the words of H. Bondi, “The
equations describing general relativity are, in all but the simplest applications,
exceedingly complex and difficult to unravel.”^{3}
When it is extremely difficult to determine just what is in a theory,
it is an almost hopeless task to arrive at a critical judgment as to the
legitimacy of conclusions, which the originator and his supporters claim
to have obtained out of the theory.
However, now that the Reciprocal System has provided us
with a complete and consistent theoretical structure that is in agreement
with the observed facts at all points, it is possible to examine the General
Theory in the light of this new information and to get a more intelligible
picture of the status of the points at issue, as has been done in the
preceding pages. The conclusions of the foregoing analysis may be summarized
as follows:
 As to the general objective. The real, even though unrecognized,
purpose of the theory (as interpreted in the context of the new information
now available) is to provide a mathematical means of correcting for
the error introduced into calculations involving nonuniform motion
by the failure to recognize the existence of coordinate time. However,
the magnitude of the required correction, unlike that for uniform
translatory motion, is not a specific function of the velocity, hence
the primary objective of the General Theory is an impossible goal.
 As to the postulates of the theory. The Principle of Equivalence
is fully in accord with the newly developed information; indeed, the
Reciprocal System goes a step farther and asserts that gravitation
is an accelerated motion, not merely the equivalent of an accelerated
motion. The Principle of Covariance is also accepted by the new system,
although the significance of this principle is minimized. Most of
the conclusions purporting to be derived from it have actually been
introduced into the General Theory ad hoc.
 As to the correlation’s with observation. The equivalence
of mass and energy (more properly the interconvertibility of mass
and energy) deduced from the Relativity principles is verified by
the Reciprocal System, but the hypothetical increase in mass accompanying
an increase in velocity is inconsistent with the interconvertibility
and is erroneous. The observed decrease in acceleration at high velocities
is due to a decrease in the effective component of the presumably
“constant” force, instead of an increase in mass. The advance
of the perhelion of Mercury is a consequence of the same factors that
are responsible for the negative result of the MichelsonMorley experiment
and it is therefore related to the Special Theory, even though it
involves nonuniform motion, rather than to the General Theory.
 General conclusion. Unlike the Special Theory, which is mathematically
correct, even though conceptually wrong, the General Theory must be
considered erroneous in all of its basic aspects. The tangible achievements
that it can claim, such as the prediction of the interconvertibility
of mass and energy, have only a very tenuous connection with the theory
itself, and rest primarily on ad hoc assumptions suggested
by the theory. The widespread acceptance of the General Theory
is based primarily on the achievements of the Special Theory, which
is definitely superior to Newton’s Laws of Motion in application
to bodies moving at high velocities. The argument here is that if
the Relativity principles are correct in application to uniform translatory
motion, as the mathematical results seem to indicate, then they are
probably also correct, and therefore superior to Newton’s system,
in application to nonuniform motion. In view of the admitted lack
of consistency between the General Theory and the Special Theory this
reasoning is clearly invalid, but in any event the issue being examined
in this work is not between the Relativity Theory and Newton’s
system, but between the Relativity Theory and the newly developed
Reciprocal System, and here the Relativity Theory is badly outperformed.
The Reciprocal System is not only superior on an item by item basis
in every instance where there is any significant difference between
the too, but it also makes out a very good case when matched against
the requirements for positive proof of its validity: something that
the Relativity Theory cannot even approach.
The many glaring deficiencies and weaknesses that show up
in the structure of the Relativity Theory as soon as it is subjected to
a critical examination and judged on its own merits rather than merely
on the basis of a comparison with Newton’s system, indicate very
clearly wily Bridgman was troubled by “the whole state of mind of
most physicists with regard to it.” We do not necessarily have to
go along with his opinion that this will “some day become one of
the puzzles of history,” however, as it is actually quite evident
that this is simply another manifestation of the psychological trait which
makes the scientist (in common with his fellow human beings in other pursuits)
unwilling to admit ignorance and leads him to treat today’s best
guess as the equivalent of an established fact, however weak and vulnerable
that guess may be. Relativity has been, in reality, merely a makeshift:
something to which the physicist could cling temporarily rather than drifting
in a sea of uncertainty. It has survived only because of the lack of any
serious competition, coupled with a general feeling that something is
better than nothing: that even a poor theory is better than none at all.
