22.1: Gravitation Appears to be an Isolated Phenomenon
One of the major problems presented by gravitation has been discussed in
the preceding Chapter 21. But there are others and these will now be
One of them is how to bring gravitation into association with other
natural phenomena. At present it appears curiously isolated from them.
In this it is unique. Mention has already been made in Chapter 1 of the
unification of the various branches of physical science that has been
achieved during the past few centuries. Heat, light and sound, electricity
and magnetism, mechanics, chemistry are now all under one common roof.
Quite a lot is known about the relation between them. One can often express
observations made in one of these branches in terms appropriate to another
one. Chemical processes are explained with reference to electrical forces.
Light is interpreted as an electromagnetic phenomenon. The effect of a
magnetic flux on the polarization of light is a subject for study. The temperature of a gas is attributed to the momentum of the constituent molecules, a mechanical effect. Wherever one turns in physical science one
meets this same close interlocking between its various branches. More and
more generalizations in physics are, let me repeat here, found to be logical
inferences from other, more basic, ones.
Gravitation is one of the few phenomena in physical science that have
entirely escaped this process of unification. It does not interlock with any
branch. It stands outside the roof that covers all the others. The few
generalizations that can be made about gravitation have not been found
to be logical inferences from any more basic generalizations. Gravitation
is, in a word, still one of the phenomena that cannot be explained.
I propose to show in this Part Four that it need not continue to be so.
Gravitation, like so many other natural phenomena, will be shown to be a
logical inference from the Principle of Minimum Assumption.
22.2: The Principle by which a Process Tends to Reduce its Cause
A third puzzling fact about gravitation is that it seems to violate one of
the most basic principles known to physics. This is that in a self-contained
system every process tends to be such as to reduce its cause. Something
has already been said about this principle in Chapter 3, when the reasons
for rejecting hypothesis (Al) were presented. It will be convenient to
repeat a little of this here.
The movement of electric charges in an electrostatic field provides an
example of a process that reduces its cause. At the origin of the field is an
accumulation of electrons. As like charges repel each other, any of those
that are free to move are propelled out of the field, thus weakening it. Any
unlike charges, on the other hand, that come into the field are attracted.
They neutralize the charge at the origin, again with the consequence that
the field is weakened. In this example the process is the movement of
electric charges; the cause is an electrostatic field; and the process reduces
the intensity of this field.
Another example is the transfer of heat between surfaces. The cause is
the difference in the temperature of the surfaces. As the process of transfer
continues, the temperature difference decreases and the rate of heat transfer
The principle can be further illustrated. Most chemical substances are
reactionable, which means that they enter into combination more or less
vigorously with other substances. But when they do so the resultant
products are always less reactionable; the process of chemical reaction
tends to reduce the capacity for reaction. Oxygen and iron, for instance,
combine with some vigour at certain temperatures, but rust, the product
of their combination, is comparatively inert.
Causes of physical change can be expressed in terms of gradients.
When an electric charge moves, it follows an electrical potential gradient.
When heat flows from one place to another it follows a temperature
gradient. In chemical reactions there are strong potential gradients between
atoms and molecules. According to the principle being discussed here, we
live in a world in which gradients are flattened out as time goes on.
If the opposite principle prevailed all causes would become more and
more pronounced in the course of time, gradients would become ever
steeper and steeper; the world would become a place of ever-increasing
contrasts. Every electrostatic field that had begun as a weak one would
have been becoming stronger and stronger in the course of timewithout
limit. Every hot surface would be getting hotter as it radiated heat and
every cold surface would be getting colder as it received it. We should be
living in a universe in which chemical processes were becoming ever
more violent. Such a universe would be unstable and so the principle
by which processes reduce their causes can be called the Principle of
Stabilization. As there will be occasion to refer to it again, this name will
This principle is, of course, only observable so long as the system is
self-contained. If, for instance, an electric generator supplies fresh electrons
as fast the old ones are removed or neutralized, there is no reduction in the
intensity of the electrostatic field.
The Principle of Stabilization is generally regarded as even more basic
than the first and second laws of thermodynamics, for it embodies both.
If starting a process sufficed to increase its cause, perpetual motion would
be possible and the first law would be refuted. If the transfer of heat caused
temperature differences to augment, every thermal change would be
accompanied by a decrease in the entropy of the system and the second law
would be refuted. To deny the Principle of Stabilization would be heresy
And yet! Gravitation has the appearance of violating it. When bodies
are free to move in a gravitational field they fall on to the attracting mass;
but they do not thereby reduce the intensity of the field, as electric charges
do when they fall in an electrostatic field. The bodies that fall in a gravitational field add to the mass at its centre and thereby increase its intensity.
We live in a world in which all gradients tend to become flatter in the course
of time with the exception of gravitational ones. These seem to tend to
The implications of this strange characteristic of gravitation cannot be
dismissed lightly. Every accumulation of matter must be attracting neighbouring bodies towards it and, in doing so, becoming increasingly powerful. It will be shown in Appendix B that, as a consequence, the cosmological
model that is based on Asymmetrical Impermanence does not resemble
actuality. In this model the whole of the matter in the universe would
eventually fall together into one single unit. The reason is that any two
neighbouring accumulations of matter may be regarded as in competition
for the substance that occurs between them. The larger accumulation will
always acquire a greater proportion of it and thereby become able to
compete still more successfully with its smaller neighbour. In the absence
of anything to counteract this tendency for the larger concentration
always to grow at the expense of the smaller ones, the largest of all must
eventually swallow the others one by one.
It would be easy to show that the models based on either hypothesis
(Al) or hypothesis (A2), as listed at the beginning of Chapter 3, would be
similar in this respect. Only the model based on the combination of (A3)
with (B3), on Symmetrical Impermanence, will, if the reasoning in Appendix
B is confirmed, continue to contain discrete concentrations at all times.
But the reason is, it will be found, that every large concentration, every
galaxy, finds itself at intervals of about three-and-a-half thousand million
years in a position where the loss rate from extinctions within its domain
exceeds the gain rate from new origins. The galaxy can, in consequence,
capture less new matter than it loses and so must dwindle for a while.
If one rejects Symmetrical Impermanence, one can only arrive at a
model that resembles actuality by inventing sundry ad hoc hypotheses.
Perhaps, one has to speculate, the expansion of space is effectively opposing
gravitational forces, a surmise that cannot easily be justified quantitatively.
Or perhaps some other, as yet unknown, force operates in extragalactic
space to keep the galaxies apart. Or perhaps such a force operated once-upon-a-time only in the remote past and caused all celestial bodies to
acquire a momentum away from each other. If quantitative reasoning
leads to an unwelcome conclusion one can always, as I have said repeatedly in these pages, save the favoured view with the help of sufficient
But those who adopt these, as also those who prefer to base their cosmological model on the Principle of Minimum Assumption, must all feel
some uneasiness at the apparent failure of gravitation to conform to so
basic a principle as that of stabilization. A single exception to a principle
that is otherwise absolutely universal calls for inquiry.
22.3. Gravitational Fields are Unidirectional
Gravitational fields always have the same sign. In this they differ from
other known fields. In electrostatics like charges repel and unlike ones
attract each other. Hence in some fields a given particle moves towards the
centre of the field and in others the same particle moves away from the
centre. This is expressed by saying that electric fields may be either positive
or negative. It is the same for magnetic fields. A north-seeking pole moves
in one direction in one kind of field and in the opposite direction in
another kind. But it is not the same with gravitation. Like gravitational
masses do not repel but attract each other, and unlike masses are not
known. In other words, electrostatic and magnetic fields are described
sometimes as positive and sometimes as negative, but one has no reason to
describe gravitational fields in similar terms. These are observed to be
unidirectional; bodies move always towards, and never away from, their
This does not appear to be the logical consequence of any other known
fact. It cannot be deduced from the definition of gravitation; it is not, so
far as can be ascertained, a tautology. No reason has been found why
inert masses should not do what electric charges do, sometimes attract
and sometimes repel others. Such explanations as have from time to time
been offered are far-fetched and by no means convincing. The uni-
directional nature of gravitational fields is just one of those stubborn facts
that have persistently defied explanation.
22.4: The Relative Intensities of Electrostatic and Gravitational Fields
Nearly all inert masses consist of protons, electrons and neutrons.
All protons have identical masses and identical positive charges. All
electrons also have identical masses and identical negative charges. All
neutrons also have identical masses and zero charge. Thus there are con-
stant ratios between charge and inert mass. As these ratios are not directly
concerned with gravitation they need not concern us here.
But it is generally assumed, rightly or wrongly, that each proton and
each electron has attracting as well as inert mass. On this assumption
a proton, for instance, is the centre of two fields of which one is electrostatic and the other gravitational. If it is so, one has to conclude that there
is a law according to which a motionless electrostatic field cannot occur
unless it is accompanied by a gravitational one. (The word 'motionless'
is necessary because the field that moves with the velocity of light and is
coupled with a magnetic one is not coupled with an attracting one.) One
has further to conclude that the ratio between the intensities of the electro-
static and gravitational fields around an elementary particle must be one of
a few constant values.
As already mentioned electrostatic fields, like gravitational ones, may
be regions in which the geometry of space-time is non-Euclidean. It is indeed difficult to imagine what else they could be. But if they are, their
geometry must be of a fundamentally different kind from that of the
gravitational field; for it does not affect the movement of inert masses; the
path of a neutron is the same whether it passes through an electrostatic
field or not. Correspondingly the path of a proton or an electron is not
influenced by a gravitational field except by virtue of its inert mass.
And yet, according to the generally accepted view, gravitational and
electrostatic fields invariably occur in association around every charged
particle. By what principle, one is led to ask, should two quite different
(and non-interacting) kinds of field be coupled in this way? By what
principle is the ratio of the intensities of the two fields limited to certain
constant values? Existing knowledge offers no hint of an answer to these
These are the questions that are being asked by those who are seeking
a unified field theory. They will not be further discussed in these pages.
But there is a further question about the ratio of the charge and attracting
mass that is, by traditional theory, attributed to elementary particles and
this question does have a place in the present inquiry.
Why, it may also be asked, are the two field intensities of such widely
different orders of magnitude? The electrostatic field around a proton is
large enough to be readily measurable. But its attracting field, if it has
one, is so weak that vast numbers of elementary particles, the numbers
that make up a sizeable leaden sphere, are needed to form a field of
It has been suggested that gravitation may be a differential effect; and
if a gravitational force were indeed simply the difference between a push
and a pull, the pull preponderating very slightly, one would, of course,
expect the force to be very weak. But that suggestion is pure speculation
and is not supported by any evidence. That the two fields associated with
the same particle should have such enormously different intensities has
yet to be accounted for.
22.5: Gravitation is Uncontrollable
A further puzzling feature of gravitation is that it is, in an absolute
sense, uncontrollable. This cannot be said about other natural phenomena.
Even radio-activity can be influenced by nuclear bombardment.
One can direct a beam of light in any desired direction. One can vary
its intensity and colour, reflect and refract it, break it down into the
component wave-lengths of its spectrum, polarize it. One can so control
temperature that a given substance may be nearly as cold as the absolute
zero or hotter than the sun. One can insulate a charged conductor and
thus prevent the charge from having an influence on bodies in its vicinity.
One can shield a magnetic pole and thus exclude magnetism from places
where it would interfere with an experiment. One can conduct electricity
along any desired path, vary at will its magnitude, vary its rate of change,
switch it on and off. One can arrange and rearrange the chemical elements
into a virtually unlimited number of different compounds, accelerate or
retard the speed with which they react, influence the physical properties of
substances. One can, in short, obtain in any given place any desired
amount and quality of light, heat, sound, electricity, magnetism, chemical
None of these things can be done with gravitation. One cannot direct,
reflect or refract it. One cannot vary its intensity. One cannot conduct
it. One cannot insulate or shield it. One cannot switch it on or off. Why not?
We have become so used to the uncontrollability of gravitation that we
tend to take it for granted and do not often ask questions about it. When a
writer of science fiction introduces into his story the notion of a substance
that intercepts gravitation or of a machine that controls it, we may smile
at the ignorance of those gullible readers who accept such an impossible
notion uncritically. But we should rather reflect on our own ignorance;
for there is not a scientist who can say why such an insulating substance
and such a controlling machine are but figments of an exuberant imagination, never to be implemented in the world of reality.
It is true enough that one cannot control the weather either. But its
uncontrollability is of a different kind from that of gravitation. The reason
is that the circumstances by which it is influenced are on a scale beyond
man's mastery. Changes in the weather are brought about by the movement of vast quantities of air, changes in the ionization of hundreds of
cubic miles of the upper atmosphere, changes in atmospheric pressure,
sunspots, in fact by all kinds of occurrence that, though uncontrollable
in practice, are not so in theory. If we disposed of unlimited resources, we
could control the weather. Even though meteorology is not a subject on
which much research can be done in the laboratories of our scientific
institutions, it is a suitable subject for study in what is sometimes rather
fantastically called nature's laboratory.
Many things happen in this laboratory to light, heat, sound, electricity,
magnetism, chemical compounds, the nuclei of elements. Circumstances,
great or small, may cause the same thing to become brighter or darker,
hotter or colder, to move faster or slower. The sun, like other objects,
undergoes many changes. A part of its surface sometimes experiences a
magnetic storm. Its surface is a region of turmoil.
Gravitation, on the other hand, is no more influenced by cosmic than
by man-made events. No circumstances ever cause the same body sometimes to exert an observably greater and sometimes a smaller gravitational
pull. The inert mass at the centre of a gravitational field may be hot or
cold, diffuse or concentrated, at rest or violently agitated, electrically
charged or neutral, it matters not. The steady field persists. There are magnetic storms on the sun but the sun is always quite free from gravitational
storms. The most shattering cosmic catastrophe does not send as much
as a faint tremor through any gravitational field. Gravitation is not
observed intermittently, but continuously, so that we never for a moment
lack evidence that there is such a phenomenon. We feel its steady influence
when we walk and when we lie down to sleep, when we raise an arm and
when we swallow our food. Gravitation is literally the only natural
phenomenon to assail our senses insistently and without interruption.
True, it is just possible to argue that the above statement may not be
quite strictly correct. If it could be proved that the attracting mass, Mg,
of a body increases with its velocity according to the law by which the
inert mass, M does so, one could control gravitation, be it to a limited
extent, by changing the velocity of the source of the field. If the leaden
sphere used to measure G were spun, a different value of this constant
would be obtained than if the sphere were at rest. If the sphere were
heated, moreover, the component molecules would have a greater velocity.
It is known that they would also have a greater inert mass. If they had a
greater attracting mass as well, a neighbouring sphere would be attracted
with a greater force.
But I have shown in Chapter 21 why such a conclusion is not implicit
in relativity theory. Those inclined to disagree with me about this should
remember that the relativity equations seem peculiarly difficult to interpret
in physical terms, which explains why experts sometimes differ about their
correct interpretation. In such interpretations as I have found there has
been no attempt to discuss the relation between attracting mass and
the other two kinds. The problem of understanding this relation has
not been solved by relativists; it has not even been tackled, it has
22.6: The Gravitational Field of a Body is Changeless
To say that gravitation is uncontrollable, even in nature's laboratory,
is to say that the gravitational field of a given body is changeless. In this
it is different from most other natural phenomena. These do change with
circumstances. Even the electrical field of a proton or an electron does so.
For it may be converted into a photon .This difference between the electro-
static and the gravitational field may, incidentally, explain why all attempts
at finding a unified field theory have failed.
But there is one other class of phenomena that are as changeless as
gravitation. The emission from a radio-active isotope is also a constant
quantity, no matter what is done to the emitting body. A given lump of
radium produces a known, constant amount of radiation and has a known,
constant gravitational field. But every other property that one may assign
to it varies with circumstances.
However, there is one significant difference between the changeless
radio-activity per unit mass and the changeless gravitational force per unit
mass. The former is attributed to a change in the material, namely to the
disintegration of atoms; but according to the traditional view the latter is
not attributed to any change at all.
The changelessness of the gravitational field is, incidentally, the reason
why there was no god of gravitation in the mythology of the ancient
Greeks. They believed that all natural phenomena that they could
recognize as such were controlled by some mythical being. All events
depended, in their mythology, on someone's conscious will just as events
in our laboratories do. The notion of nature's laboratory would not have
been remote from the Greek attitude. The Greeks saw the sea sometimes
tranquil and sometimes in violent turmoil and attributed the changes that
it underwent to the work of the sea-god Poseidon. They were alarmed by a
raging storm with flashes of lightning and peals of terrifying thunder and
explained it as a consequence of the anger of the god Zeus. They saw the
fruits of the field grow and ripen ready for the harvest and said that the
process was guided by the goddess Demeter. When a tree that began as a
sapling grew into a thing of grace and splendour, they concluded that a
charming dryad was the cause of the miraculous transformation.
But it was only changes, not steady states, that they attributed to their
gods. If the weight of things were to change from time to time, so that,
according to circumstances, a stone or a spear was sometimes heavier and
sometimes lighter, the ancient Greeks would, no doubt, have included a
god of gravitation in their pantheon. But the weight of a thing is the only
property that never changes. So there was no such god. Had there been he
would have had an idle time.
The remark is not as far off the point as one might think, for the
reason why there was no god of gravitation in the Greek pantheon is
fundamentally the same as the reason why there are no chairs of gravitation
in our universities. A phenomenon on which one cannot conduct experiments, on which experiments are not even conducted in nature's laboratory,
does not lend itself to much scientific study. Like a god of gravitation, a
professor of that subject would have an idle time, and a dull one.
22.7: Gravitational Effects do not seem to be Associated with Expenditure
It has already been pointed out that the sun expends vast
quantities of energy in sending its rays into space, but that, according to
the traditional view of gravitation, it does not expend any energy in keeping
the planets to their orbits. This important difference between gravitation
and other phenomena deserves some discussion.
One can speak of the energy in an electrostatic field. This is produced
when electrical charges are separated and the energy consists in the work
done to separate the charges. When the charges are allowed to fall together
again, the energy is released and appears in some other form.
The gravitational field is not analogous. While energy is expended in
creating the electrostatic field, none is expended, according to the traditional view, in creating the gravitational one. It is claimed instead that this
field just is. When, again, an object falls under the influence of the electrostatic field, when, for instance, a charged particle falls down the potential
gradient, the field is weakened. This is the reason why one says that the
energy is stored in the field. But it seems to be meaningless to say that
energy is stored in the gravitational field. One can speak of the energy
stored in the water of a mountain lake, for this, when released, flows over
stones and pebbles and the friction converts this energy into heat. But the
field that causes the water to flow down the valley is not in the least reduced
in the process; the earth's hold on the moon is as strong after, as before,
the water has flown out of the lake.
22.8: Action at a Distance
The earth is in one place and the meteor that is accelerated by it is in
another. Yet we attribute the acceleration to the earth. So the earth
exercises an influence in a place where it is not. How? This is yet another
of the facts about gravitation that have to be explained.
The problem is known as that of action at a distance. That it presents
itself in Newtonian mechanics is obvious, but strangely enough it has
sometimes been denied that it also presents itself in relativity theory.
However, the only difference is in the thing on which the earth is assumed
According to Newtonian mechanics the earth acts directly on the stone,
though it be from afar. But according to relativity theory the action of the
earth is indirect. The earth is claimed to act, not on the stone, but on space;
it causes this to be curved. It is the space that, in turn, acts on the stone. So
action at a distance is presumed in both theories; in the one it is between
the earth and the stone, and in the other between the earth and the part of
space where the stone is.
The expression 'action at a distance' is ambiguous. It could mean a
kind of action that does not puzzle us at all. When a person sends a letter
to someone in another town and asks him to do something he can be said
to be exercising an influence in a place where he is not. When a shell is
fired out of a gun and explodes some miles away one can say that the gun
is exercising an influence at a place where it is not. One can say the same of
a lamp in a photographer's studio. The lamp is in one place and the
photographic plate on which the light falls in another, and yet the lamp
exercises an influence on the plate.
In these examples the action at a distance is effected by means of a
transfer of energy; something moves from the one place to the other.
Action is between the writer and the letter that he is writing in one town
and between the letter and the recipient in the other. It is similarly between
the gun and the shell in one place and between the shell and the building
destroyed by it in the other place. It is between the lamp and the light rays
in one part of the photographer's studio and between the light rays and
the photographic plate in another part. In all these cases nothing separates
the cause and its immediate effect and the distance to the final effects is
spanned by something that moves from the one place to the other, be it a
letter, a shell, or light waves. Such movement involves the transfer of
energy from the one place to the other and so one can speak of the kind
of action at a distance that is effected by a transfer of energy.
This is not usually understood by the expression 'action at a distance'.
What is meant is action without an accompanying transfer of energy. It
is so understood in the generally accepted view of gravitation, both in
Newtonian mechanics and in relativity theory. At the moment when a
stone falls it is not assumed that something leaves the earth and travels
towards the stone. It is assumed in Newtonian mechanics that the falling
occurs without the simultaneous transfer of anything from the earth to
the place where the stone is.
The same assumption is usually made in relativity theory. It is assumed
that the mere presence of the earth causes space in remote places to be
curved. It is not assumed that to maintain this curvature anything leaves
the earth and produces its effect at the remote place. The earth is not said
to be depleted of anything by creating this curvature around itself. Once
again the analogy to radiation and other phenomena fails. When there is
action at a distance by the transmission of energy the action is the result of
something that happens. This is easy to accept. But it is not so easy to
accept the notion of action at a distance as the result of something that
merely is. A radiating body loses energy when it acts at a distance; but the
traditional view is that the earth acts gravitationally at a distance without
losing anything, be it repeated.
Here the mathematician is in an enviable position. He can write down
an expression for action at a distance and is not called upon to give it a
physical interpretation. But the physicist is in a quandary. His task is to
give meanings to the symbols with which the mathematician has provided
him. If the symbols say that there is action between distant places without
transfer of energy from one place to the other he is puzzled.
The questions discussed above remain to remind us that we do not
yet know as much about gravitation as we should like to know. For the
sake of convenience let them be repeated here. They are:
(1) Can gravitation be brought into association with the main body of
(2) Why do inert and attracting mass always occur in association? The
question can take the alternative form: Why does an accumulation of inert
mass cause the surrounding space to be curved?
(3) Why does gravitation seem to contradict the Principle of Stabilization according to which every process in a self-contained system tends to
reduce its cause?
(4) Why do gravitational fields always have the same sign?
(5) Why is there a limited number of constant ratios between unit
electric charge and the inert mass of the elementary particles? Why,
moreover, are the gravitational fields attributed to such particles vastly
weaker than the electrostatic ones?
(6) Why is gravitation uncontrollable?
(7) Why is gravitation the only phenomenon that does not seem to
require a transfer of energy?
(8) How can one reconcile what is known about gravitation with action
at a distance?
These are, I venture to claim, the kinds of question about natural
phenomena that scientists find it profitable to ask. Answers to this kind
of question usually lead to new insight into the nature of the physical
world. At least some of these questions have not been ignored in the past,
perhaps. But they have certainly not been asked with the insistence that
they require. It may be that the prospect of finding answers has seemed to
be too remote to justify the effort. But I hope to make it clear in the
following chapters that such defeatism is not warranted. There is an
excellent prospect that satisfactory answers to very nearly all the above
questions can be found by the same procedure that has served for answers
to questions about the spiral nebulae. No further hypothesis will be needed
than that of Minimum Assumption.
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