THE QUANTUM THEORY
The theory of relativity has justly excited a great amount of public
attention. But, for all its importance, it has not been the topic which
has chiefly absorbed the recent interest of physicists. Without question
that position is held by the quantum theory. The point of interest in
this theory is that, according to it, some effects which appear
essentially capable of gradual increase or gradual diminution are in
reality to be increased or decreased only by certain definite jumps. It
is as though you could walk at three miles per hour or at four miles per
hour, but not at three and a half miles per hour.
The effects in question are concerned with the radiation of light from a
molecule which has been excited by some collision. Light consists of
waves of vibration in the electromagnetic field. After a complete wave
has passed a given point everything at that point is restored to its
original state and is ready for the next wave which follows on. Picture
to yourselves the waves on the ocean, and reckon from crest to crest of
successive waves. The number of waves which pass a given point in one
second is called the frequency of that system of waves. A system of
light-waves of definite frequency corresponds to a definite colour in
the spectrum. Now a molecule, when excited, vibrates with a certain
number of definite frequencies. In other words, there are a definite set
of modes of vibration of the molecule, and each mode of vibration has
one definite frequency. Each mode of vibration can stir up in the
electromagnetic field waves of its own frequency. These waves carry away
the energy of the vibration; so that finally (when such waves are in
being) the molecule loses the energy of its excitement and the waves
cease. Thus a molecule can radiate light of certain definite colours,
that is to say, of certain definite frequencies.
You would think that each mode of vibration could be excited to any
intensity, so that the energy carried away by light of that frequency
could be of any amount. But this is not the case. There appear to be
certain minimum amounts of energy which cannot be subdivided. The case
is analogous to that of a citizen of the United States who, in paying
his debts in the currency of his country, cannot subdivide a cent so as
to correspond to some minute subdivision of the goods obtained. The cent
corresponds to the minimum quantity of the light energy, and the goods
obtained correspond to the energy of the exciting cause. This exciting
cause is either strong enough to procure the emission of one cent of
energy, or fails to procure the emission of any energy whatsoever. In
any case the molecule will only emit an integral number of cents of
energy. There is a further peculiarity which we can illustrate by
bringing an Englishman onto the scene. He pays his debts in English
currency, and his smallest unit is a farthing which differs in value
from the cent. The farthing is in fact about half a cent, to a very
rough approximation. In the molecule, different modes of vibration have
different frequencies. Compare each mode to a nation. One mode
corresponds to the United States, and another mode corresponds to
England. One mode can only radiate its energy in an integral number of
cents, so that a cent of energy is the least it can pay out; whereas the
other mode can only radiate its energy in an integral number of
farthings, so that a farthing of energy is the least that it can pay
out. Also a rule can be found to tell us the relative value of the cent
of energy of one mode to the farthing of energy of another mode. The
rule is childishly simple: Each smallest coin of energy has a value in
strict proportion to the frequency belonging to that mode. By this rule,
and comparing farthings with cents, the frequency of an American would
be about twice that of an Englishman. In other words, the American would
do about twice as many things in a second as an Englishman. I must leave
you to judge whether this corresponds to the reputed characters of the
two nations. Also I suggest that there are merits attaching to both ends
of the solar spectrum. Sometimes you want red light and sometimes violet
light.
There has been, I hope, no great difficulty in comprehending what the
quantum theory asserts about molecules. The perplexity arises from the
effort to fit the theory into the current scientific picture of what is
going on in the molecule or atom.
It has been the basis of the materialistic theory, that the happenings
of nature are to be explained in terms of the locomotion of material. In
accordance with this principle, the waves of light were explained in
terms of the locomotion of a material ether, and the internal happenings
of a molecule are now explained in terms of the locomotion of separate
material parts. In respect to waves of light, the material ether has
retreated to an indeterminate position in the background, and is rarely
talked about. But the principle is unquestioned as regards its
application to the atom. For example a neutral hydrogen atom is assumed
to consist of at least two lumps of material; one lump is the nucleus
consisting of a material called positive electricity, and the other is a
single electron which is negative electricity. The nucleus shows signs
of being complex, and of being subdivisible into smaller lumps, some of
positive electricity and others electronic. The assumption is, that
whatever vibration takes place in the atom is to be attributed to the
vibratory locomotion of some bit of material, detachable from the
remainder. The difficulty with the quantum theory is that, on this
hypothesis, we have to picture the atom as providing a limited number of
definite grooves, which are the sole tracks along which vibration can
take place, whereas the classical scientific picture provides none of
these grooves. The quantum theory wants trolley-cars with a limited
number of routes, and the scientific picture provides horses galloping
over prairies. The result is that the physical doctrine of the atom has
got into a state which is strongly suggestive of the epicycles of
astronomy before Copernicus.
On the organic theory of nature there are two sorts of vibrations which
radically differ from each other. There is vibratory locomotion, and
there is vibratory organic deformation; and the conditions for the two
types of change are of a different character. In other words, there is
vibratory locomotion of a given pattern as one whole, and there is
vibratory change of pattern.
A complete organism in the organic theory is what corresponds to a bit
of material on the materialistic theory. There will be a primary genus,
comprising a number of species of organisms, such that each primary
organism, belonging to a species of the primary genus, is not
decomposable into subordinate organisms. I will call any organism of the
primary genus a primate. There may be different species of primates.
It must be kept in mind that we are dealing with the abstractions of
physics. Accordingly, we are not thinking of what a primate is in
itself, as a pattern arising from the prehension of the concrete
aspects; nor are we thinking of what a primate is for its environment,
in respect to its concrete aspects prehended therein. We are thinking of
these various aspects merely in so far as their effects on patterns and
on locomotion are expressible in spatio-temporal terms. Accordingly, in
the language of physics, the aspects of a primate are merely its
contributions to the electromagnetic field. This is in fact exactly what
we know of electrons and protons. An electron for us is merely the
pattern of its aspects in its environment, so far as those aspects are
relevant to the electromagnetic field.
Now in discussing the theory of relativity, we saw that the relative
motion of two primates means simply that their organic patterns are
utilising diverse space-time systems. If two primates do not continue
either mutually at rest, or mutually in uniform relative motion, at
least one of them is changing its intrinsic space-time system. The laws
of motion express the conditions under which these changes of space-time
systems are effected. The conditions for vibratory _locomotion_ are
founded upon these general laws of motion.
But it is possible that certain species of primates are apt to go to
pieces under conditions which lead them to effect changes of space-time
systems. Such species would only experience a long range of endurance,
if they had succeeded in forming a favourable association among primates
of different species, such that in this association the tendency to
collapse is neutralised by the environment of the association. We can
imagine the atomic nucleus as composed of a large number of primates of
differing species, and perhaps with many primates of the same species,
the whole association being such as to favour stability. An example of
such an association is afforded by the association of a positive nucleus
with negative electrons to obtain a neutral atom. The neutral atom is
thereby shielded from any electric field which would otherwise produce
changes in the space-time system of the atom.
The requirements of physics now suggest an idea which is very consonant
with the organic philosophical theory. I put it in the form of a
question: Has our organic theory of endurance been tainted by the
materialistic theory in so far as it assumes without question that
endurance must mean undifferentiated sameness throughout the
life-history concerned? Perhaps you noticed that (in a previous chapter)
I used the word ‘reiteration’ as a synonym of ‘endurance.’ It obviously
is not quite synonymous in its meaning; and now I want to suggest that
_reiteration_ where it differs from _endurance_ is more nearly what the
organic theory requires. The difference is very analogous to that
between the Galileans and the Aristotelians: Aristotle said ‘rest’ where
Galileo added ‘or uniform motion in a straight line.’ Thus in the
organic theory, a pattern need not endure in undifferentiated sameness
through time. The pattern may be essentially one of aesthetic contrasts
requiring a lapse of time for its unfolding. A tune is an example of
such a pattern. Thus the endurance of the pattern now means the
reiteration of its succession of contrasts. This is obviously the most
general notion of endurance on the organic theory, and ‘reiteration’ is
perhaps the word which expresses it with most directness. But when we
translate this notion into the abstractions of physics, it at once
becomes the technical notion of ‘vibration.’ This vibration is not the
vibratory locomotion: it is the vibration of organic deformation. There
are certain indications in modern physics that for the rôle of
corpuscular organisms at the base of the physical field, we require
vibratory entities. Such corpuscles would be the corpuscles detected as
expelled from the nuclei of atoms, which then dissolve into waves of
light. We may conjecture that such a corpuscular body has no great
stability of endurance, when in isolation. Accordingly, an unfavourable
environment leading to rapid changes in its proper space-time system,
that is to say, an environment jolting it into violent accelerations,
causes the corpuscles to go to pieces and dissolve into light-waves of
the same period of vibration.
A proton, and perhaps an electron, would be an association of such
primates, superposed on each other, with their frequencies and spatial
dimensions so arranged as to promote the stability of the complex
organism, when jolted into accelerations of locomotion. The conditions
for stability would give the associations of periods possible for
protons. The expulsion of a primate would come from a jolt which leads
the proton either to settle down into an alternative association, or to
generate a new primate by the aid of the energy received.
A primate must be associated with a definite frequency of vibratory
organic deformation so that when it goes to pieces it dissolves into
light waves of the same frequency, which then carry off all its average
energy. It is quite easy (as a particular hypothesis) to imagine
stationary vibrations of the electromagnetic field of definite
frequency, and directed radially to and from a centre, which, in
accordance with the accepted electromagnetic laws, would consist of a
vibratory spherical nucleus satisfying one set of conditions and a
vibratory external field satisfying another set of conditions. This is
an example of vibratory organic deformation. Further [on this particular
hypothesis], there are two ways of determining the subsidiary conditions
so as to satisfy the ordinary requirements of mathematical physics. The
total energy, according to one of these ways, would satisfy the quantum
condition; so that it consists of an integral number of units or cents,
which are such that the cent of energy of any primate is proportional to
its frequency. I have not worked out the conditions for stability or for
a stable association. I have mentioned the particular hypothesis by way
of showing by example that the organic theory of nature affords
possibilities for the reconsideration of ultimate physical laws, which
are not open to the opposed materialistic theory.
In this particular hypothesis of vibratory primates, the Maxwellian
equations are supposed to hold throughout all space, including the
interior of a proton. They express the laws governing the vibratory
production and absorption of energy. The whole process for each primate
issues in a certain average energy characteristic of the primate, and
proportional to its mass. In fact the energy is the mass. There are
vibratory radial streams of energy, both without and within a primate.
Within the primate, there are vibratory distributions of electric
density. On the materialistic theory such density marks the presence of
material: on the organic theory of vibration, it marks the vibratory
production of energy. Such production is restricted to the interior of
the primate.
All science must start with some assumptions as to the ultimate analysis
of the facts with which it deals. These assumptions are justified partly
by their adherence to the types of occurrence of which we are directly
conscious, and partly by their success in representing the observed
facts with a certain generality, devoid of _ad hoc_ suppositions. The
general theory of the vibration of primates, which I have outlined, is
merely given as an example of the sort of possibilities which the
organic theory leaves open for physical science. The point is that it
adds the possibility of organic deformation to that of mere locomotion.
Light waves form one great example of organic deformation.
At any epoch the assumptions of a science are giving way, when they
exhibit symptoms of the epicyclic state from which astronomy was rescued
in the sixteenth century. Physical science is now exhibiting such
symptoms. In order to reconsider its foundations, it must recur to a
more concrete view of the character of real things, and must conceive
its fundamental notions as abstractions derived from this direct
intuition. It is in this way that it surveys the general possibilities
of revision which are open to it.
The discontinuities introduced by the quantum theory require revision of
physical concepts in order to meet them. In particular, it has been
pointed out that some theory of discontinuous existence is required.
What is asked from such a theory, is that an orbit of an electron can be
regarded as a series of detached positions, and not as a continuous
line.
The theory of a primate or a vibrating pattern, given above, together
with the distinction between temporality and extensiveness in the
previous chapter, yields exactly this result. It will be remembered that
the continuity of the complex of events arises from the relationships of
extensiveness; whereas the temporality arises from the realisation in a
subject-event of a pattern which requires for its display that the whole
of a duration be spatialised (_i.e._, arrested), as given by its aspects
in the event. Thus realization proceeds _viâ_ a succession of epochal
durations; and the continuous transition, _i.e._, the organic
deformation, is within the duration which is already given. The
vibratory organic deformation is in fact the reiteration of the pattern.
One complete period defines the duration required for the complete
pattern. Thus the primate is realised atomically in a succession of
durations, each duration to be measured from one maximum to another.
Accordingly, so far as the primate as one enduring whole entity is to be
taken account of, it is to be assigned to these durations successively.
If it is considered as one thing, its orbit is to be diagrammatically
exhibited by a series of detached dots. Thus the locomotion of the
primate is discontinuous in space and time. If we go below the quanta of
time which are the successive vibratory periods of the primate, we find
a succession of vibratory electromagnetic fields, each stationary in the
space-time of its own duration. Each of these fields exhibits a single
complete period of the electromagnetic vibration which constitutes the
primate. This vibration is not to be thought of as the becoming of
reality; it is what the primate is in one of its discontinuous
realisations. Also the successive durations in which the primate is
realised are contiguous; it follows that the life history of the primate
can be exhibited as being the continuous development of occurrences in
the electromagnetic field. But these occurrences enter into realisation
as whole atomic blocks, occupying definite periods of time.
There is no need to conceive that time is atomic in the sense that all
patterns must be realised in the same successive durations. In the first
place, even if the periods were the same in the case of two primates,
the durations of realisation may not be the same. In other words, the
two primates may be out of phase. Also if the periods are different, the
atomism of any one duration of one primate is necessarily subdivided by
the boundary moments of durations of the other primate.
The laws of the locomotion of primates express under what conditions any
primate will change its space-time system.
It is unnecessary to pursue this conception further. The justification
of the concept of vibratory existence must be purely experimental. The
point illustrated by this example is that the cosmological outlook,
which is here adopted, is perfectly consistent with the demands for
discontinuity which have been urged from the side of physics. Also if
this concept of temporalisation as a successive realisation of epochal
durations be adopted, the difficulty of Zeno is evaded. The particular
form, which has been given here to this concept, is purely for that
purpose of illustration and must necessarily require recasting before it
can be adapted to the results of experimental physics.