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 The Animate and the Inanimate   William James Sidis

CHAPTER II

REVERSIBLE LAWS

Now we shall attempt to find out what are the physical laws which subsist in this imaginary "reverse universe." To start with the simple laws of mechanics, we have it given in the real universe that a body retains its velocity unless there is some external force to change that velocity. Now, as there can be no change of velocity in the reverse universe without a corresponding change of the reverse velocity in the real universe, and since all forces in both universes are respectively equal, it follows that this same law of motion applies also in the reverse universe. In other words, the law of inertia is unchanged by the reversal in time, and is therefore what we may call a reversible physical law.

The second law of motion is that change of momentum is proportional to force impressed. Now, following the reasoning which we have already followed in the case of accelerations, the rate of change of momentum remains unchanged in our reverse universe. Furthermore, we have already seen that, in the reverse universe, the force impressed on a body remains unchanged. Hence it follows that the second law of motion subsists in the reverse universe, and is therefore reversible.

The third law of motion is that to every action (force) there is as also an equal and opposite reaction. This law is also obviously reversible, since in the reverse universe neither the magnitude nor the direction of forces is altered.

Energy being the same in the reverse as in the real universe, it similarly follows that the law of the conservation of energy holds in the reverse universe, and is therefore reversible in time. The same holds true of the law of the conservation of matter.

One of the principal methods by which motion can be changed is by impact. An impact may be elastic or inelastic. In the case of the very smallest particles of matter, that kind of collision only is possible which loses no energy, but in which the kinetic energy remains the same as before, that is to say, an elastic collision; for, in the case of ultimate particles, none of the original energy can be changed into internal motion of the particles. Hence only elastic collision is possible in the case of ultimate particles; and it is not difficult to show that, in the case of elastic collision, the reversed final velocities of the same masses will cause, as an effect of the impact, the reversed initial velocities. Now, since all matter is made up of these particles, whatever they may be, and therefore all collisions of bodies of matter are made up of countless elastic collisions of ultimate particles, it follows that, in the reverse universe, where impact occurs, all particles of matter follow the same course as they would in the real universe under the same initial conditions. Hence the laws of impact, when brought down to ultimate particles, are perfectly reversible and also remain unaltered in the reverse universe.

The various laws of attraction and repulsion that are found to subsist in the objective universe, such as gravitation, electrical and magnetic attraction and repulsion, etc., dealing as they do with the directions of forces, must also remain unchanged in the reverse universe. Similarly with many other general physical laws.

Even the laws of reflection and refraction of light will remain unaltered in the reverse universe, and are therefore perfectly reversible.

As a result, we may say in general that, looking to the ultimate particles of matter, enough physical laws subsist in the reverse universe to determine, from the positions and velocities of all particles of matter at a given instant, the entire past and future of the universe. The result is that, given those physical laws which we assume to remain always true, if we should imagine that, in the real universe, at one given moment, all particles of matter should, while retaining their respective positions, reverse their velocities, it would follow that this would be enough, of itself, to make all particles of matter trace back their previous positions in the reverse order and thus, as it were, create a reverse universe.

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