by     Reginald O. Kapp


Chapter 7 - Disappearance Without Trace

7.1: Introduction
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 turn.

7.2: Radiation
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 finite.

(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 invented.

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 finite velocity.

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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