TOWARDS A UNIFIED COSMOLOGY

by     Reginald O. Kapp

PART II - THE PAST AND FUTURE DURATION OF MATTER

Chapter 6 - The Conservation Laws


The question arises whether the Hypothesis of the Symmetrical Impermanence of Matter violates the great principle of conservation of energy and the other conservation laws. At first sight it certainly does seem as though both continuous origin and continuous extinction do so.

6.1: Change in the Mass Content of an Isolated Region
Let us imagine that a region of space can be isolated from its surroundings in such a way that no mass and no energy can pass its boundary in either direction. According to (Al) the total mass and the total energy in this region will then remain constant. According to (A2) they will remain constant now, but would not have done so during that period of the remote past while the material universe was in process of originating. According to (A3) they do not necessarily remain constant at any time; at unpredictable moments new elementary components may originate within the region. If these do not themselves possess inertial mass, it is implicit in the hypothesis that they will eventually synthesize into particles that do possess it. So (A3) implies without doubt that the total mass within the isolated region may increase. Similarly (B3) implies that the total mass may decrease, and as the rates of increase and decrease are assumed to be random the amount of inertial mass in the region at any moment must be indeterminate.

If the region be enlarged until it becomes a fair sample of the whole material universe the argument that its content is not constant in spite of the isolation still holds, of course, but the content is no longer so in- determinate. Like the future activity of a lump of radium, the future content of the region can be predicted, though not from knowledge of external circumstances. It can be predicted only from knowledge of the net rate of random increases.

6.2: Change in the Energy Content of an Isolated Region
What is true for mass is also true for energy. But here the situation is more complicated; for the energy that accompanies each individual origin or extinction is a composite affair.

One part of it is represented by the inertial mass itself. For mass and energy are interchangeable, and conversions of the one into the other are today a commonplace of nuclear physics. Hence some of the newly formed mass may sooner or later reappear as the energy of a photon. If, for instance, hydrogen atoms form from the newly originated elemental components, they may in due course combine into atoms of helium, with some loss of mass and release of energy as happens in the sun.

Another part of the newly originating energy is in the electrical fields that surround any charges that are formed. If a negative charge originates in one place and a positive charge in another the configuration formed by the two new charges will contain a certain amount of energy by virtue of the distance between them. The greater this is, the greater the energy in the electrostatic field. So this component of the energy is a variable quantity Its value depends on a fortuitous circumstance, namely, the places in which the two charges happen to originate.

A third part of the energy of each new inertial particle is that possessed by virtue of the position of the particle in a gravitational field. Wherever the particle may originate it must have a store of such potential energy; for it must be within the field of gravitational force of some, though perhaps far distant, accumulation of inertial mass. It can fall on to this, gaining kinetic at the expense of potential energy as it does so, until it can fall no further.

This third part of the total energy must vary enormously between different new particles. Those that originate near a star can fall only a little way and are thus credited at birth with only a little potential energy, while those that originate far out in interstellar space begin their existence with a large store of energy. The kinetic energy with which they eventually arrive at the source of the particular gravitational field in which they have originated will be correspondingly great.

Thus, each origin and each extinction not only adds energy to, or subtracts it from, an isolated region, but the amount of the energy is both an extremely variable and a fortuitous quantity.

What holds for an isolated region of space or an isolated system holds also for the whole material universe. According to both (A3) alone and a combination of (A3) with (B3) the total mass and energy of the universe is continuously increasing. Is this conclusion consistent with the great conservation laws? If it were not, I think that (A3) and (B3) would have to be abandoned. For the conservation laws are too well established, their practical value is too great, for their sacrifice to be contemplated with equanimity. But there is no cause for alarm. All that has to be surrendered are certain misconceptions and certain careless ways of formulating the conservation laws.

6.3: A Correct Form oj the Principle of Conservation of Energy
A correct and precise formulation is: In any system the total energy is not changed by any change in the relation between the component parts of the system.

It is not, of course, the same for other physical quantities. The total amount of acid in a system may well be changed by a change in the relation between its component parts. Chemical reactions may increase or decrease the amount of acid. Similarly the total potential energy in a system may be changed when the relation between the component parts changes; for some of it may be converted into kinetic energy.

It is in the above formulation that physicists and engineers regard the principle of conservation of energy when they make practical use of it. The would-be inventor of a perpetual motion machine tries to increase the energy obtainable from a system by changing in some ingenious way the relation between its component parts. The principle foredooms his attempt to failure. A scientist knows that changes in the system can influence only the form and distribution of the energy contained in it and not its total quantity, and this knowledge makes it possible for him to work with a balance-sheet and an income and loss account for energy. He does this in effect when he sets up his energy equations.

The principle of conservation of energy tells us that energy income must balance expenditure if capital is to remain constant, but it says nothing about the source of the income or about the recipient of the expenditure. In our experience the income always arrives across the spatial boundary of the system. In a steam engine, for instance, it enters with the steam at the stop-valve. The expenditure is also across the spatial boundary. Some of it leaves through the connecting rod and does useful work in driving whatever machinery is being operated. A larger quantity leaves with the low-grade steam through the engine exhaust. A further part leaves through the hot surface of the engine as heat carried away. All of it was at one moment within space inside the system and is at a later moment within space outside it. The boundary of the system has been crossed.

Such observations have led people to form the following hypothesis: Energy cannot enter or leave a system except by crossing its boundary. But this is not commonly recognized as an hypothesis. It is regarded as a proved and irrefutable fact, which only shows how difficult it is to recognize an hypothesis when one sees one.

6.4: An Incorrect Form of the Principle of Conservation of Energy
People have unfortunately combined this unproven hypothesis with the Principle of Conservation of Energy in such a way as to give the principle the following unjustifiable and imprecise form: The total energy in a system changes only when energy crosses the boundary of the system. This would be acceptable if one could justify the hypothesis that energy can enter or leave a system only by crossing its boundary, but if energy can enter or leave without doing so the formulation just given is not necessarily true, and is certainly not a correct inference from the Principle of Conservation of Energy.

The choice is therefore not between the Principle of Conservation of Energy and the Hypothesis of the Symmetrical Impermanence of Matter. It is between the hypothesis that energy can enter or leave a system only by the specific process of crossing its boundary and that it can do so without crossing the boundary. Both hypotheses are equally compatible with the Principle of Conservation of Energy.

6.5: A Second Correct Form of the Principle of Conservation of Energy
Let this principle be given a second, and also correct, formulation: The total energy in a self-contained system is constant. For the purpose of this formulation a self-contained system is defined as one into which no energy enters and out of which no energy departs. The second correct formulation says, in effect, the same as the first one. But its interpretation depends on a correct understanding of the concept 'self-contained'.

A correct understanding would, I think, be helped if a distinction were made between a self-contained system and an isolated one. An isolated system would then be defined as one across the boundary of which energy did not pass. Every self-contained system would, by these definitions, also be an isolated one, but every isolated system would not necessarily be a self-contained one. While the Principle of Conservation of Energy asserts that the total energy in a self-contained system is constant, it does not necessarily assert this for an isolated system. It would do so only if 'self- contained' and 'isolated' were synonyms. But to claim that they are is to adopt the unproven hypothesis to which I have already referred.

6.6: An Isolated System is not Necessarily Self-Contained
By taking the necessary precautions one can ensure that a system prepared in the laboratory can be treated as an isolated one. To do so one must shield the system from external influences and provide its boundary, for instance, with adequate heat insulation. The isolation may not be theoretically perfect, but one makes it as nearly perfect as may be needed for practical purposes. But if the hypothesis of continuous, random, uncontrolled and uncaused origins and extinctions is correct, one cannot ensure that the system will be self-contained, even in theory. For origins and extinctions may occur within it at any moment.

The maximum changes to the total energy content of any system built to the laboratory scale would, however, be too small to be measurable. For practical purposes one can consider any isolated system as though it were also a self-contained one.

This would be far from true on the astronomical scale. There the difference between an isolated and a self-contained system could be very large. Supporters of (A3) interpret the red shift as a measure of this difference.

According to the Hypothesis of Symmetrical Impermanence the whole material universe can be regarded as an isolated system, but it does not meet the definition of a self-contained one. It has, however, been so readily taken for granted that the whole material universe must of necessity be a self-contained system that the notion of continuous origin and extinction has become difficult to accept. It must, nevertheless, be appreciated that it is no more than an unproven hypothesis to assert that the material universe is, by the definition given above, a self-contained system. This is just one of the many sly hypotheses that cause misconceptions. They enter our deliberations so unobtrusively that their entry passes unobserved. Thereupon they clothe themselves in the garments of an irrefutable fact. The disguise is often so excellent that even the most critical do not penetrate it.

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