If, as is postulated by the Hypothesis of Asymmetrical as well as by that
of Symmetrical Impermanence, the content of the material universe is
always increasing, room must be found for the increase; otherwise the
quantity of matter per unit volume would have become infinite. But as, in
accordance with the theory of relativity, the extent of the material universe
increases with its content, no problem arises here. For a sufficiently large
sample of space, the quantity of matter per unit volume must remain
constant. In an expanding space matter, one may say, is removed to
distant regions as fast as it originates.
But ponderable matter is associated with its manifestations. When it
has been removed to some distance some of these can still be observed;
what is far away becomes known to us by the traces that it leaves with us.
If there were such traces of everything that is and has been, however
distant, the number of traces per unit volume here and now would be
infinite. It is not infinite and so one must conclude that, when ponderable
matter is removed, it disappears without trace.
For objects at astronomical distances only two kinds of trace need to
be considered; they are the radiation that the objects send out and the
gravitational fields that surround them. Let us consider each of these in
The radiation consists of electromagnetic waves and may or may not
be within the visible spectrum; but it is convenient always to speak of it
as light. It is caused by events in the microstructure of the objects in which
it is generated. A change in the state of an atom, for instance, associated
with a change in the orbit of an electron, will generate a pulse of light, a
photon, which then travels out into space. It may, on the rarest of occasions,
enter a telescope and deliver its message of what has happened to the atom.
Thus light from a distant object brings information just as a telegram
does, and for this reason a pulse of light is not inaptly called a signal.
But compared with the messages that are carried over telegraph wires,
those carried through space by photons can be described only as monotonous. Translated into words the story that they tell would be: 'Now an
electron has changed its orbit, now another electron has changed its orbit,
now another electron…' and so on, for many millions of years.
Of course we rarely read the signal in that way unless we happen
to be astrophysicists. We more often interpret the message as telling us:
‘I am a star and I am here'. But the astrophysicists are right and we are
wrong. The message is not of what is but of what happens. If there were
no changes in the microstructure of the star, we should not have any means
of seeing it or of discovering that it was there. As we receive a message to
say that something is happening we may safely believe that there is something that it is happening to, but we must not confuse events with things.
It is only the events that are observed. The things are inferred.
For much scientific work this philosophical distinction can be ignored
but not here. In the most general terms the event is always a conversion
of energy. When an electron changes its orbit and sends out a pulse of
light, energy is emitted with the pulse. Were it not so, the star would be
invisible. We see it only when it converts some of its energy into signals.
Physicists have thus come to regard it as axiomatic that what is perceived
has been acting prior to its perception as a source of energy and losing
energy while it did so. When the object is seen in reflected light, the energy
is borrowed. But the visible stars are self-luminous. So long as they signal
to us they are using up their capital.
The intensity of the light from a star is almost inversely proportional
to the square of the distance of the star and would be quite so if there were
no intervening substance to intercept some of it. In fact, less light is
received than would accord with the inverse square law, but that does not
alter the fact that the amount from each visible star is finite. If a finite
amount, however minute, reached us from every one of an infinite number
of stars, we should have here and now an infinite luminous intensity. It has
to be explained why it is not so.
The explanation is not difficult; it is implicit in the finite velocity of
light and the observed expansion of space. As the velocity with which
objects move away from one another in an expanding space is proportional
to how far they are separated from each other, there is a distance of
separation at which the rate of their mutual recession is equal to the
velocity of light. At this distance, or at a greater, a light signal emitted from
one of them can never reach the other. This limiting distance is called the
optical horizon. The radiation received here and now is only from objects
that are located within this horizon. Its intensity is finite because the number
of stars within the optical horizon and from which signals are received is
(A3), it is to be noted, has sufficient explanatory power to account for
the expansion of space and, therewith, for the finite value of the observed
luminous intensity here and now. No additional hypothesis need be
This can be put in another form. The matter that is removed by the
expansion of space can only disappear without trace because the traces
are signals of events, and all signals require transmission of energy at a
7.3: Gravitational Fields
Let us now consider the other kind of trace, the one left by the gravitational fields that surround all stars. Like the light intensity the gravitational
field conforms to the inverse square law. Though this field is very faint
when the distance is great, it is finite for a finite distance. The sum of all the
traces of gravitational pull from an infinite number of stars would be
infinite if they could all act in one place. The curvature of space, which in
relativity theory represents a gravitational field, would be such as corresponds to an infinite field intensity.
It is necessary to explain why it is not so. Why is the intensity of the
field such as would result from a finite number of sources?
If the gravitational field consisted of events, of signals, each of which
acted like a photon and transmitted energy, the answer would be easy. It
would be the same as has been found for the finite value of luminous
intensity. In that case no additional hypothesis would be needed; one could
then infer a gravitational horizon analogous to the optical horizon. Its
distance would depend on the velocity with which gravitational pulses
travelled. The gravitational effect experienced in any given place would
then be only that emanating from stars within the gravitational horizon.
But such an explanation would not be reached by logical reasoning
from the traditional hypothesis about gravitation, which is that gravitation
is the consequence not of what happens but of what is; that it is an
inherent property of every object with inertial mass and persists whether
something or nothing happens to the mass. According to this hypothesis
gravitation is not (as radiation is) a manifestation of any change at its
source. We are told that we should perceive the earth's gravitational pull if
nothing whatever were to change either in the earth's macrostructure or in
its microstructure. It is known that a luminous flux continues only for so
long as it is being renewed and that the renewal requires expenditure
of energy, but it is commonly assumed that the gravitational field is
kept going without the transfer of any energy whatever. While the amount
of energy that the sun is losing by radiation during every second is
enormous, the amount that is lost by the sun in keeping the planets to
their elliptical orbits is declared to be nil.
Such considerations are bound to lead to the suspicion that the
traditional hypothesis about gravitation is untenable and should be
replaced by a different one. If the gravitational field is, like the luminous
flux, a bundle of impulses, the finite value of the gravitational field is
explained, as has just been shown. In that case the sun does lose energy in
keeping the planets to their orbits; gravitation is in the same need of
continuous renewal as every other detectable manifestation of matter;
the axiom holds universally that what is perceived has been acting previously as a source of signals and losing energy while it did so.
It would not conform to the demands of scientific method to put
forward this as an alternative hypothesis to the traditional one about
gravitation if its sole purpose were to explain one single awkward fact.
But it will appear in due course that there is much more to justify the view
that the gravitational field does carry away energy and resembles radiation
in this respect. However, several further steps of reasoning will have to be
taken before this conclusion can be arrived at. So I propose at this moment
only to mention one of the many other hypotheses that might perhaps
occur rather readily to the mind as a possible means of explaining the
finiteness of observed gravitational fields.
Perhaps, it might be thought, the inverse square law requires a correction; perhaps it is only a first approximation to the truth and the real law
contains a term that is negligibly small at short distances, but becomes
appreciable when the distance is great. If this correcting term represented
a repulsion between inertial masses, those that were widely separated
would tend to move apart while those that were close together would tend
to move towards each other.
Such an hypothesis would provide an easy way out of the dilemma and
it might seem plausible at first sight. But, even if such a modification of the
inverse square law could be justified (which it cannot be, see Appendix F),
it would represent that undesirable thing mad hoc hypothesis designed to
surmount one particular difficulty. It will appear later that, if Symmetrical
Impermanence is accepted, no such desperate measures are necessary. The
reason why, in an expanding universe of infinite extent, the gravitational
field is constant here and now will emerge, without the need for additional
hypotheses, as a logical inference from Symmetrical Impermanence.
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