CHAPTER IV
THE PARADOX

The second law of thermodynamics is, as we have seen,
an irreversible physical law, and seems to be the one
distinguishing characteristic between the real universe and
the reverse universe. At the same time, that law is of such a
nature, that, for the ultimate particles of matter. it dues not
exist; It Is essentially a law concerning transformations of
energy of large masses. And yet all large bodies are made
up of countless numbers of the ultimate particles of matter,
the laws of whose motion are all perfectly reversible. Ail phen-
of the reverse universe, however strange they may look, are
perfectly explicable in terms of the ordinary physical laws as
applied to the smallest material particles. It would seem,
then, as though there must be some reason in terms of the
reversible physical laws why the second law of
thermodynamics must be true; that is, the second law of
thermodynamics, if true, should be a consequence of the
reversible physical laws applicable to ultimate particles. We
are, then, confronted with the paradox of having to deduce an
Irreversible law from perfectly reversible ones.
And yet, since the reverse universe consists of a perfectly
consistent series of positions, obeying all reversible
physical laws, it follows that any logical deduction from
premises which are reversible laws must Inevitably apply to
the reverse universe, and that therefore the conclusion
must be true in the reverse universe as well as in the real
physical universe. That is to say, any deduc-

tive conclusion from reversible laws must itself be
reversible. And yet, in the case of the second law of
thermodynamics, the reversible laws which govern the
motions of ultimate particles of matter seem to compound
themselves somehow into the best possible example of an
irreversible law governing the motions of large masses.
We are, therefore, inevitably led to the conclusion that the
second law of thermodynamics cannot be deduced from the
reversible laws by strict deductive reasoning.The reversible
laws must of necessity leave some room for the possibility
of the truth of the reverse of the second law of
thermodynamics. But, since the second law of
thermodynamics simply represents a general tendency, we
come to the conclusion that the only possibility that the
second law of thermodynamics represents a correct
physical law, is, that it is to be deduced from the reversible
laws not as a strict logical consequence, but as a great, or
even an overwhelming probability. Such a solution of this
paradox of the second law was propounded by Clerk
Maxwell and other physicists of the middle of the nineteenth
century.
Let us, then, examine the reasoning by which Clerk
Maxwell was enabled to reconcile reversible premises with
an irreversible conclusion. According to his reasoning, both
processes are physically possible, concentration and
diffusion of energy. The one process obeys the second law
of thermodynamics, the other reverses it. Under the second
law of thermodynamics, a collision of large masses will
generate heat (conversion of molar energy into heat-energy)
; under its reversal, the heat generates molor motion in and
of itself. Now, says Clerk Maxwell, if particles move In a.
group, .or rather in two approaching groups, the particles
are likely to strike one another at all sorts of angles, so that,
after the
Impact, the resulting velocities will become scattered, which
means that some of the energy will be converted into heat.
On the contrary, a reversal of the process means a
concentration of the motions, of the particles at the very
point and time of the impact, which is a very much more
improbable combination, and, requiring as it does that this
concentration should happen in a particular direction, at a
particular point, at a particular time, in order to have the
desired effect, it follows that such a reversal of the second
law of thermodynamics is so overwhelmingly improbable as
to be almost impossible. The second law of
thermodynamics is thus based not on necessity but on
extreme probability. A reversal of the second law is possible
under the reversible physical laws, as we have seen, but this
reasoning tends to prove that it is overwhelmingly
improbable, and therefore would almost never happen.
But, again, if the premises of the reasoning are, as we
suppose, reversible physical laws, it must be possible to
apply the same reasoning to the reverse universe.
Consequently, a similar line of reasoning, which must be
exactly as correct logically, can be followed by tracing
events backwards from effect to cause instead of tracing
from cause to effect, as Clerk Maxwell has done.
Any momentary condition, of the universe may be regarded
either as the cause of all future conditions of the universe or
as the effect of all past conditions. And not only can a given
momentary condition of all particles in the universe determine
one and only one possible effect, one and only one possible
future; that same given momentary condition (position and
velocity of every particle) could only have been caused by one
possible past series of conditions. Hence it is just as possible
to trace our causal relations step by step backwards, as it is to
trace them similarly forwards.

Now, tracing causation thus backwards, we find that molar
motions, when traced backwards into the past, Will, in all
probability, bring us to a time when two masses which are
now in motion have been together, in contact. Following
Clerk Maxwell's reasoning, we must say that, when two
particles move away from contact with each other, an impact
must have been the cause, at least some form of impact of
particles, but it is a form of impact which produced molar
motion. In all probability, those two particular masses will not
have motions which trace back to a rebound of all particles
at the same angle; which necessitates, according to the
rules of elastic collision, that before the impact the motions
of the particles must have been scattered. Thus, tracing the
reasoning backwards, we arrive at the probability that the
molar motions must have been partially at least caused by
heat, that is, to the probability of a reversal of the second law
of thermodynamics On the contrary, In order to have a case
in accordance with the second law of thermodynamics, on
this analogous reasoning, it would be necessary to suppose
two bodies being traced back to contact at some particular
time, and that the heat-motions of those bodies, when thus
traced back, should suddenly, at the particular moment and
point of contact, trace back to a concentration of motion of
the particles of each body away from th other, for only such
concentration could be the effect of a molar motion bringing
the bodies into collision. Now, the probability of such a
combination is extremely small, so that, by merely shifting our
reasoning gear into reverse, the very same reasoning tells
us that the second law of thermodynamics is most-extremely
Improbable, but that, on the contrary, its reversal is an
overwhelming probability.
Tracing thus from a given momentary condition of
the universe, our forward and backward reasoning combined
might be interpreted, if such reasoning could be trusted. to
mean that the second law of thermodynamics holds good as
a probability as to the future, but that its reversal holds true
as to the past. Aside from this result being untrue In point of
fact, it is self-contradictory, for any given moment of time is
always future as to moments that precede it. and past as to
moments that follow it. It follows, then, that there must be
some fallacy in Clerk Maxwell's reasoning, which, when
extended, gives us the second law of thermodynamics in the
general form.
To take the special case that we have been using as an
illustration. Molar motion without heat, it is true, is likely, as a
matter of pure theory, to produce, after impact, less molar
motion and some heat (the total amount of energy remaining
invariable). But such an initial condition is, in itself, extremely
improbable. If initial velocities of particles may be selected
initially as in any direction: and in any amount, it is extremely
improbable that all the velocities will have the same direction
and amount, or even approximately so. The smaller the
number of particles, the greater the probability of a
concentrated motion resulting. Also, the smaller the mass,
the greater the probable average velocity of the mass at a
given time, when the particles are moving at random. Hence,
when there is impact of bodies in which particles move at
random, the probabilities are that, at that moment, at the
point of contact, the small mass of particles in the immediate
vicinity will have a greater speed in all probability than the
entire mass. Thus, when the collision occurs, the force
available for producing molar motion will consist, in the
immediate vicinity of the point of contact, of two average
speeds greater than those of the respective masses. If those

greater speeds lend to be more towards one another than
the masses as a whole, then it would be most probable that
some of the heat-energy of the two bodies will be converted
into molar motion. On the other hand, if the respective
speeds in the vicinity of the point of contact are more away
from each other than the velocities of the masses
themselves, the reverse will happen. Besides, while we have
this possibility of heat turning into molar energy or into some
other form of energy, and of differences of energy
concentration building themselves up in this manner, we
have the contrary tendency supplied by Clerk Maxwell's
reasoning. The result is, that we as yet can form no
conclusions as to which tendency Is more likely.
If, furthermore, we consider that we must regard for a
given moment of time, all positions and velocities as equally
likely, and that for all such initial positions and velocities
which will give a universe obeying the second law of
thermodynamics, there is a reverse universe, equally
probable; reversing that law, we come to the conclusion that
the second law and its reverse are equally probable. If this is
true for any given event, then the probability of the observed
facts, that is to say, that all events obey the second law, must
be infinitesimally small. So that, again, we are forced to the
conclusion that the second law of thermodynamics, being an
observed fact which can only be explained as an extremely
probable result of the reversible physical laws is, on the
contrary, most extremely improbable.
Not merely that, but the second law of thermodynamics,
when pushed to its logical conclusion, produces rather
absurd results. In the first place, we have, seen that it
involves a sort of death of the universe in the remote future, a
time when all 'will be one dead level of heat; though all this
will, in all probability, come about
slowly. But the rate of decrease of the available energy under
this second law is approximately proportional to the amount of
available energy In the universe; therefore the rate of the
running down of energy into the unavailable form must
be'constantly decreasing. Tracing backwards, we find that, in
the past, the farther back we go, the more we get a larger
percentage of available energy in the universe, Increasing at
an ever greater rate. Therefore it follows that we must arrive at
some definite time in the past---and that not at an infinite time
back---when the available energy was 100% of the total
energy of the universe. At a time probably not much farther
back, all the motion in the universe must have consisted of
molar motion of masses which, as we go back, must have
increased In size till we arrive at a time when all the energy
must have consisted of the energy of two halves of the
universe moving together, each half of the universe being at a
temperature of absolute zero and all its parts moving side by
side at exactly the same velocity. This possibility, it is true, is
somewhat corroborated by the fact that at present the stars
are moving in two opposite directions, in two opposite
currents, as It were, which may be supposed to 4e the
remnants of ilia two original large groups of stars whose
collision formed the present universe ac, cording to this
hypothesis.
At the same time the two original halves of the universe
cannot have been altogether mutually Impenetrable, for in
that case the result of the collision would but have made
them rebound, though producing a great amount of internal
heat-energy in each, and possibly breaking some small
pieces off each. It would seem, then, as though the original
halves of the universe must have consisted of separate dark
stars, with a structure somewhat similar to the present
universe. At the time

of the collision, all the stars, even all the particles, In each
semi-universe must all be moving together at the same
speed and in the same direction.
The second law of thermodynamics, then, must date from
some sort of Great Collision out of which the present
universe evolved. .But what happened before this Great
Collision? The answer would have to be, everything was at a
temperature of absolute zero, there were two semi-
universes which were moving towards each other, in each
of which there was not even a trace of relative motion.
Although each of the two semi-universes were in motion, yet
within each there was no motion, no internal energy.
But if such was the situation at the time of the Great
Collision, it cannot have been so for an eternity past, unless
we conceive of the law of gravitational attraction not to have
been true in those times. Taking each semi-universe by
itself, its reverse universe will also show the same
conditions as we have already described, except that the
semi-universes are moving away from each other, so that
we can proceed in peace without danger from the
impending Great Collision. Each semi-universe may, for the
purpose of internal occurrences, be regarded as at rest.
Gravitation will then draw all the stars of each semi-universe
towards its center of gravity, till all of them fall in there.
Reversing once more, so as to obtain the process as it
must have bean supposed to happen, we get the following
result: Each semi-universe originally consisted of one great
body; suddenly, somehow, that body exploded into pieces,
which formed stars, each piece, though, remaining at a
temperature of absolute zero. Finally, in each semi-
universe. mutual gravitation of the stars slowed them down
to relative rest. Just when this relative rest was reached, the
two semi-universes collided, and
Out of this collision came our present universe. Thus we
trace a little farther back to the Great Explosions; but these
explosions cannot possibly be traced back any farther
according to the known physical laws without violating the
second law of thermodynamics. In consequence, if we wish
to preserve the second law of thermodynamics, we must
either dispense with some of the other physical laws, or as
some physicists have done. intersperse a creation. In other
words, the second law of thermodynamics cannot have
been true for an eternity past, though it may be true for on
eternity in the future. And even the assumption of a creation
would be assuming a process different from the processes
coming under the ordinary physical laws.
In other words. we come to the inevitable conclusion that
the subsistence of the irreversible second law of
thermodynamics in the same universe is the reversable
laws concerning the motion of particles is a paradox, both
from that point of view and from the fact that this second
law, pushed to its logical conclusion, leads back to a
mysterious creation which denies all physical laws
whatever.