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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 the 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 the 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 in 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 momenta 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