CHAPTER I
THE REVERSE UNIVERSE

Among the physical laws it is a general characteristic
that there is reversibility in time; that is, should the whole
universe trace back the various positions that bodies in it
have passed through in a given interval of time, but in the
reverse order to that in which these positions actually
occurred, then the universe, in this imaginary case, would
still obey the same laws.
To test reversibility, we may imagine what we may call
"the reverse universe," that is to say, another, an imaginary
universe, in which the positions of all bodies at various
moments of time are the same as in our real universe, in
which those positions occur at tile same respective
intervals of time but in the reverse order. To assist in
imagining this reverse universe, we may remind ourselves
that, when we look in a mirror, the imaginary world that we
see in that mirror corresponds in every detail to the world
we are in, with the exception that one dimension of space
occurs in the reverse order, namely the direction
perpendicular to the plane of the mirror. If, now, we conceive
of time as a sort of additional dimension of the, universe,
then our "reverse universe" would be one in which there was
a similar reversal in that dimension, leaving the three
dimensions of space unaltered. Or, to put it in another way,
the series of images produced by running a motion-picture
reel backwards would give exactly the impression of such
a reverse universe.
With this auxiliary, imaginary universe, our test of the
reversibility of any given physical law or process would be,
whether that law holds good, whether that process still
subsists in the reverse universe. In order to see that in any
case, we may first find out how to translate any physical
occurrence into the corresponding occurrence in our reverse
universe. To start with, all positions in space remain
absolutely the same in the reverse universe as in the real
universe; intervals of time, however, remain the same in
magnitude but are reversed in direction. In other words,
though the absolute amount of an interval of time remains
unchanged, it is necessary, in translating into terms of the
reverse universe, to replace "before" by "after," and vice
versa.
The path of a moving body will remain the same in the
reverse universe because all the positions which constitute
that path will remain unchanged. Since, however, the positions
are reached in the reverse order of time, the body moves
along the path in the reverse direction. The absolute amount of
corresponding intervals of space and time in this motion
remaining unchanged, it follows that all velocities must, in the
reverse universe, be the same in amount but exactly reversed
in direction.
We come to a problem of greater difficulty in considering
what becomes of acceleration. Acceleration is the rate of
change of velocity with respect to time. If, to make this question
simpler, we assume uniform acceleration, then the acceleration
of a body is equal to the difference of velocity divided by the
interval of time required to produce this difference. If, for example,
in an interval of time T the velocity A is changed to the velocity B,
the acceleration (vectorially represented) would be (B-A)/T : In the
corresponding motion in the reverse universe, in the interval of
time T, the velocity changes from -B to -A, so that the acceleration
is ((-A)-(-B))/T, or (B-A)/T. In other words, the acceleration of a
body remains unchanged to the reverse universe, both in amount
and in direction, in translation into terms of the reverse universe.
The above reason assumes that the acceleration of the body is
uniform, but an extension of the same reasoning will show that the
same conclusion holds even when the acceleration is constantly
varying.
So much for pure kinematics. For dynamical terms. it is
necessary to find what happens to the mass of bodies. in the
reverse universe. Now, mass being merely amount of matter, and
unrelated to time, it follows that mass is not in the least changed
by reversal. From that it follows, by what we have seen, that all
moments are reversed In direction but unchanged in amount,
while, in the reverse universe, the force acting on a body, being
the product of two magnitudes that remain unchanged in the
reverse universe (namely, the mass of the body and the
acceleration, assuming no other force to act), must necessarily
remain unchanged in the reverse universe not only in amount
but also in direction. It might have been expected that, in the
reverse universe, forces would be reversed in direction; but
this is not so.
Energy, being entirely dependent on such things as
position and force (in the case of potential energy) or on mass
and the square of speed (in the case of kinetic energy), all of
which remain entirely unchanged in the reverse universe, must
manifestly remain entirely unchanged.
We come, however, to a more complicated problem in the
question of the causal relation. For this purpose it is necessary
to distinguish various kinds of causality. The true relation of
cause and effect is one of temporal sequence; e. g., the removal
of the support of an object is the cause of its falling. The force of
gravity has been there all the time; and it Is a logical consequence
of the existence of such force that the fall of an object should
follow the removal of its support. Strictly speaking, the force of
gravity is in this case not a cause, but an explanation, a reason
for the actual causation, which is itself merely a sequence with an
explanation. We have thus to distinguish between the relation
of reason and consequence, on the one hand, and, on the other
hand, the relation of cause and effect. The latter implies
sequence in time, the former is a pure relation of logical
deduction and essentially implies simultaneity, for the reason
and the consequence, one being a logical deduction from the
other, must both subsist together.
Now, in the reverse universe, we must suppose that all
logical relations of facts remain the same. This does not imply
anything concerning mental phenomena; of that we shall find
out later In our investigation. In fact, logical relations of facts
must of necessity subsist apart from the question whether or
not a mind exists In the universe. Logical relations may be said
to be simply the most general external facts in existence. If A is
B and B is C, the rule then is, not that I think that A Is C; it Is a
fact verifiable by observation that A Is C. Hence, even should
the reverse universe destroy completely all mental phenomena,
logical relations must remain unchanged. and consequently
also the relation of reason and consequence.
But with true physical causality, it is otherwise. If some
general law or some particular force resulting therefrom has for
its consequence, in the real universe, that event A should be
followed by event B, then the corresponding law or, force in the
reverse universe must result in the corresponding events A' and
B' following one another in the reverse order. That is to say, if
one physical event causes another in the real universe, then the
event corresponding in the reverse universe to the effect will, in
general, cause the event corresponding in the reverse universe
to the cause. That is to say, in translating into terms of the reverse
universe, "cause" is to be translated by "effect," and vice versa.
This, however, is not an accurate rule, there being exceptions, a
causal relation being sometimes altogether severed or else
unrecognizably altered by the reversal of time.
Again in the reverse universe, such properties as density,
specific heat, elasticity, amount of heat, temperature, etc., also
remain unchanged. It could also be shown that such properties
as electricity and magnetism remain unchanged, but that the
direction of an electric current would be reversed. Thus all
physical phenomena could readily be translated into terms of
the reverse universe. The various varieties of substance,
depending on the internal structure of the atom and molecule,
etc., also remain unchanged in the reverse universe.