Chapter I
The Fundamental Postulates
It is generally
recognized that presentday physical theory is no longer adequate to meet
the growing demands upon it. Those theoretical concepts which only a few
years ago were hailed as the keys to the innermost mysteries of nature
are now totally unable to cope with the flood of new discoveries emanating
from our laboratories and it has become obvious that some very different
approach to the problem is essential. As one observer, Ernest Hutten,
sums up the situation in a recently published book, "Most physicists feel
that the time is ripe, again, for a radical change in our ideas, and for
a new theory."
In retrospect
it is clear that this is not a new development but a recurring crisis;
each time a major advance is made in the observational field existing
physical theory finds itself unable to account for the newly discovered
facts and a drastic revision of the theory is necessary. But each successive
revision no more than takes shape before a new crisis is upon us; a new
set of facts is discovered which the revised theory does not anticipate
and cannot explain. A certain amount of modification and revision is no
doubt inevitable in the early stages of any theory but the same pattern
of helplessness in the face of new experimental advances has been repeated
so often that it becomes pertinent to inquire whether modern theory is
actually proceeding in the right direction. The continually renewed demand
for a "radical change in our ideas" strongly suggests that something more
than a minor reconstruction is required and that we should back up and
take a fresh start along a different path.
When we review
the evolution of modern physical theory to appraise the direction in which
we are now moving as a preliminary to charting a different course, it
is apparent that the outstanding general trend in the theoretical development
has been the gradual loosening of the ties between fundamental theory
and the facts of everyday life. Beginning with Einstein's introduction
of the concept of physical quantities whose actual magnitude varies with
the position of the observer, the divergence has increased at an ever
accelerating rate until the latest theoretical developments have passed
completely beyond the bounds of objective reality and have placed the
basic processes of nature in what Bridgman calls "a shadowy domain which
he (the physicist) cannot even mention without logical inconsistency."
In the scientific
field we are inclined to think that we have come a long way since the
days when all unexplained phenomena were attributed to demons and ogres,
but the current tendency to meet all difficult problems by assuming the
existence in the unobservable region of the universe of phenomena and
relationships totally unlike those which are found in the known world
is essentially the same pattern that was followed by primitive man: a
resort to the supernatural when ever explanation becomes difficult. Aside
from the personification of forces, which is no longer in vogue, it is
hard to detect any material difference between the mysterious unobservable
forces of modern science and the demons of old.
Of course we
must admit that when we are dealing with the unknown any assumption
may be valid, no matter how fantastic it may seem when judged by the standards
of our everyday experience, and if the bizarre theories of modern physics
were adequate to meet the demands upon them they would certainly be acceptable
regardless of the doubts with which their basic assumptions might have
been regarded initially. But when these theories are not adequate
and when insistent demands for revision are heard from all directions,
it is in order to suggest the possibility that an undue readiness to part
company with reality and to build the foundations of theory on unsupported
assumptions may be the root of the present difficulty. In this connection
it should be recognized that although we cannot arbitrarily reject any
fundamental assumption that is proposed, since we must concede that the
true relationships in the areas beyond the frontiers of knowledge are
unknown, there is in each case one possible assumption which is initially
so far superior to all others, so much more likely to represent the true
situation, that we are never justified in turning to anything else unless
and until we have established beyond a reasonable doubt that the consequences
of this assumption are not in accord with the facts. This greatly superior
hypothesis is, of course, the assumption that the relationships which
are found to apply in the regions accessible to observation also apply
in the unknown regions.
It will no doubt
be contended that in physical science the extrapolated relationships have
always been examined and their inapplicability has in each case been demonstrated
before any other assumptions were made. Someone is sure to point out that
relativity theory was formulated only alter Newton's Laws failed at high
velocities; that nonEuclidean geometry was developed only when Euclidean
geometry came to a dead end; that the concept of atomic events as happenings
which do not take place in space or time was devised as a last resort
only after all attempts to explain these phenomena by means of the laws
of the world of objective reality had proved fruitless, and so on. But
this present investigation has disclosed that the applicability of a theory
based wholly on extrapolated relations was never tested in any
of these instances, and that the supposed failures were not actually due
to deficiencies in the laws being examined but to the fact that in their
application these laws were always coupled with arbitrary and erroneous
assumptions as to the relation between space and time: a fatal handicap
for any theoretical structure.
Newton looked
upon space and time as two independent entities. Modern theory recognizes
that they are not independent, and regards them as components of a fourdimensional
structure in which there are three dimensions of space and one dimension
of time. But if we examine the bases of these two hypotheses it is apparent
that they are both purely arbitrary assumptions, and in view of the points
brought out in the preceding paragraphs neither of them should ever have
been given any consideration until after the consequences of extrapolating
the relation applicable in the known region had been thoroughly explored.
In this known region the relation between space and time is recognized
as motion. Motion is measured as velocity, and in velocity time and space
have a reciprocal relationship; that is, more space is the equivalent
of less time and vice versa. The most conservative assumption that we
can possibly make concerning the general relation of space and time, the
hypothesis that is by far the most probable representation of the underlying
truth, is that this relationship which holds good in the known phenomenon
also holds good in general. This hypothesis of a general reciprocal relation
between space and time has therefore been adopted as the first of the
assumptions of the new theory that will be developed in this work and
it may be regarded as the cornerstone of the entire theoretical structure.
When we thus
begin with a solid foundation based on extrapolation of an observed relationship
rather than starting with a purely arbitrary hypothesis, we will find
that the necessity for postulating that "things are different" in other
parts of the universe disappears, and we will be able to take the position
that the portion of the universe which is accessible to our observation
is a reasonably representative sample of the whole and that the physical
behavior of all other sectors of the universe can be deduced from the
relationships which we find in the observable regions. This means, of
course, that a large part of the existing structure of physical theory
must be discarded, regardless of the great skill and ingenuity that have
gone into its construction, as even the highest degree of competence cannot
derive the right answers from the wrong basic assumptions. Starting with
an untruth in physical theory is no different from making a false statement
in everyday life; in either case an ever widening structure of fabrication
is required in order to evade the contradictions which develop as a consequence
of the original deviation from the truth.
Having arrived
at a logical hypothesis as to the general relationship between space and
time, let us now apply the same extrapolation process to the formation
of the additional assumptions that will be necessary for a complete description
of spacetime. It is clear that when the reciprocal assumption is made
it must immediately be followed by another. If space and time are reciprocally
related they must have the same dimensions. We have very little specific
knowledge of time, either as to dimensions or otherwise, but we do know
from observation that there are at least three dimensions of space, and
the simplest assumption which is consistent with the reciprocal hypothesis
and the observed properties of space is that both space and time are threedimensional.
Here again the assumption is merely an extrapolation from the known to
the unknown. We observe space to be threedimensional where we are in
direct contact with it, and by extension we assume that this is a general
characteristic valid throughout the universe. The reciprocal hypothesis
then requires the further extension of this assumption to time, a step
which may also be regarded as simply a generalization of the geometrical
properties of the more readily observed component of spacetime.
The third assumption
of the new theory is that space and time exist in discrete units. This,
too, is an extrapolation from known facts into the region that is unknown.
In the early days of science it was generally believed that all of the
primary physical phenomena were continuous and infinitely divisible, but
as knowledge has grown during the succeeding centuries one after another
of these phenomena has been found to exist only in units. The atomic structure
of matter was the first to be demonstrated. Later the unit of electricity
was isolated and still more recently the work of Planck made it clear
that radiant energy follows the same pattern. There is also strong evidence
for the existence of basic units in other phenomena, such as magnetism
for instance. Since experience shows that as our knowledge widens more
and more physical phenomena are proved to exist only in discrete units,
it is merely a reasonable extrapolation to assume that if all of the facts
were known this would also be found to be true with respect to the basic
entities, space and time.
These three assumptions
constitute the definition of spacetime which will be used in this work.
For maximum economy of hypotheses it will be further postulated that spacetime
as thus defined is the sole constituent of the physical universe.
We may then express the assumptions as to the physical nature of the universe
as follows:
FIRST FUNDAMENTAL
POSTULATE
The physical universe
is composed entirely of one component, spacetime, existing in three
dimensions, in discrete units, and in two reciprocal forms, space and
time.
In developing
the consequences of this First Postulate it will be necessary to use some
mathematical processes and we must therefore make some assumptions as
to the mathematical behavior of the universe. Until comparatively recently
the validity of the relationships which will be assumed in this work was
generally considered axiomatic, but other systems have been devised in
the meantime and although we are unable to discover any physical reality
corresponding to these unorthodox systems they do put us in the position
where we must postulate the validity of the processes which we propose
to utilize.
The first of
this second group of assumptions will be that the physical universe conforms
to the relationships of what may be called ordinary mathematics, for want
of a better term. This means that two plus two equal four, the product
ab equals the product ba, multiplication is the inverse
of division, and so on. It is to be understood that probability mathematics
are specifically included. Next the validity of Euclidean geometry will
be assumed and finally it will be postulated that all primary physical
magnitudes are absolute.
Here again the
assumptions are merely generalizations of the relationships that are found
to be valid in the regions which are accessible to observation. It is
true that there are some experimental data which are currently accepted
as being in conflict with the third assumption but these are not direct
observations; they are merely inferences based on certain interpretations
of the observed facts. It will be shown later in the discussion that these
interpretations are not necessarily valid and that there are other equally
acceptable interpretations of the same observations which are entirely
consistent with the assumption of absolute magnitudes.
Combining these
assumptions we have the
SECOND FUNDAMENTAL
POSTULATE
The physical universe
conforms to the relations of ordinary mathematics, its magnitudes are
absolute and its geometry is Euclidean.
If these two
Fundamental Postulates are valid then a great many consequences necessarily
follow. The objective of this presentation is to develop these consequences
and to show that they describe a universe which is identical both qualitatively
and quantitatively with the observed physical universe wherever comparisons
can be made. It will be demonstrated that 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 physical universe must exist, matter
must exist in the form of a series of elements, these elements
must combine in certain ways and no others, the elements and
their compounds must have certain properties such as volume,
specific heat, etc., these properties must conform to
certain specific sets of numerical values, and so on.
