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
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
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
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
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
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
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