THE ASTRONOMICAL UNIVERSE
The consideration of the question of the origin of life and the various theories formed on that question has led us into astronomical considerations, so that it may be worth while to examine the astronomical aspects of our theory of the reversibility of the universe. And we may well, after dealing both with objects of ordinary size and with very small and even ultimate particles, turn to the consideration of objects of a different, a larger scale of magnitude: the heavenly bodies. We shall therefore consider our theory in connection with such objects. Astronomy deals not only with individual planets in our solar system as a whole, but also with the almost inconceivably vast extents of space which stand between the various stars and their special systems, and, finally, with the theory of that general group of all stars which is known to astronomers as the stellar universe, or simply as the universe. Accordingly one of the first things we should investigate should be the astronomical theories of the universe, especially since our theory of reversibility is essentially a theory of the universe.
When we come to examine the astronomical theories of the universe, we find that they divide themselves into two groups. Just as the biological theories of the nature of life are, generally speaking, to be divided into the mechanistic and the vitalistic, so the astronomical theories of the nature of the universe may be divided into the theories of the finite universe and the theories of the infinite universe. And, as our theory effects a compromise between the two kinds of theories of life, we may try to see whether our theory cannot also reconcile the two kinds of theories of the universe. Let us, therefore, examine more in detail each of the two kinds of astronomical theories of the universe and the various arguments that can be adduced in support of both kinds of theories.
Let us take the theories of an infinite universe. The general idea of these theories is, that space is infinite, and there is no special reason why matter should be confined to one portion—and, at that, only an infinitesimal portion compared to the infinity of space. Thus we get the picture of an infinite geometrical space filled with stars, here to a somewhat greater density, there somewhat less densely, but, on the whole, with a certain average density. This reasoning on the basis of the theory of probability is a perfectly good one, and it is, furthermore, not the only argument in favor of an infinite universe. There are arguments that are based not on theory but on actual observation.
The most important of these is the gravitational consideration. If the universe is infinite, and matter approximately uniformly distributed throughout the universe, then, on the average, the gravitational pulls on a given stellar system should, on the whole, completely balance each other, so that gravitation would not tend to pull any stellar system in any particular direction, and the proper motion of any star should be, in accordance with the law of inertia, a uniform motion in a straight line. But, on the contrary, if there were in the universe a center of density, and especially if there were a finite universe, then all stellar systems would tend to be pulled on towards that center of density and, in general, revolve round that center. The facts indicate that the proper motion of stars is actually uniform motion in a straight line, and that there is no center about which all stars move; so that this argument would point most distinctly to an infinite universe, with matter distributed throughout space approximately uniformly, one part of space being in this respect no different from another.
But there is one outstanding objection to this theory that the stellar universe is infinite. There may be supposed to be no reason why the average brightness of stars should be any different in one part of space from what it is in any other part; multiplying this average brightness by the average number of stars per unit volume (the average star-density that we suppose for the infinite universe), we will get the average amount of light issuing from a unit volume anywhere in space; let us call this product L. Now, as the apparent brightness of any source of light is inversely proportional to the square of the distance between that source and the observer, then, if we call that distance d, the average apparent brightness of a unit of volume at distance d from the observer could be represented as L/d˛. If we divide space into an infinite number of concentric spherical shells, with the observer at the center, each with equal thickness, let us say the unit distance divided by 4π, then, especially when the sphere is very large, the volume of each shell is approximately d˛. Multiplying the average apparent brightness of a unit volume at distance d by the volume of the shell of distance d, we find that the volume of each such shell is a constant, l. Since the stellar universe consists of an infinite number of such shells, each of which has the same apparent brightness, it follows that the brightness of the sky, or indeed of the smallest part of it, must be altogether infinite. The consequence of the theory of an infinite universe is obviously contradicted by facts.
On account of this objection to the universe being infinite, there arose the theories of the finite universe, which seem to depend mainly on the observed distribution of light in the sky (outside of the light from the sun, moon, and other members of the solar system). These theories of the finite universe started with the great observer, Sir William Herschel (one of the three originators of the Nebular Hypothesis), whose theory is that of the so-called "drum universe." According to Herschel's theory, the universe is in the shape of a very flat circular drum, or, in other words, a thin, wide circular slab, with possibly another secondary slab at a plane inclined a few degrees to the first, the two slabs being concentric, and the center being—the sun! It seems that even Herschel had the idea that our solar system is the center of all things, which is somewhat a survival of the ancient doctrine that the earth is the center of the universe. In fact, we may say that Herschel's theory of the universe is a modernized version of the ancient primum mobile containing the stars and having the earth for a center. However, the drum (or double-drum) shape of the universe is intended to explain the distribution of light; for, in a plane of the drum, we should have to look through such an immensely greater amount of stars than in a direction with any considerable inclination to the plane, so that we should have the appearance of a white streak running all around the sky, which we actually have under the name of the Milky Way; the double-drum shape would require a bifurcation of this white streak at two opposite parts; which again is strictly in accord with observed facts. Herschel was perfectly willing to believe that there are other similar drum-shaped universes, two of which, according to him, are visible to us, and known as the Magellanic Clouds. These "clouds" were first discovered by the famous explorer Magellan, and are circular patches in the sky of the southern hemisphere which look like detached portions of the Milky Way, though at a considerable distance from the Milky Way.
The modern theories of the finite universe, though not accepting Herschel's explanation as to the Magellanic Clouds (rather tending to suppose that those objects are within our own stellar universe), are very similar to Herschel's drum theory in general outline, and all have the same characteristic of being attempted explanations of the distribution of light actually found in the sky. The tendency, however, is not to suppose that the solar system is at the center of the universe, but rather to suppose that the solar system is considerably south of the center, being almost on the southern side of the drum, and much nearer the southern part of the drum edge than it is to the northern. There is, further, a tendency to suppose that this stellar universe is the result of a collision of two semi-universes, which is what we have seen would be the result of pushing the second law of thermodynamics to its logical conclusion, it being an observed fact that the stars seem to move in two general currents. However, just as the theory of the infinite universe cannot be supported on the grounds of the distribution of light, so similarly the theories of the finite universe cannot be supported on the grounds of the consideration of gravitational attraction.
We thus find that considerations of gravitational attraction lead us to suppose an infinite universe with stars approximately uniformly distributed throughout space; similarly with considerations of probability, which lead us to the same conclusion. But, on the contrary, the observed distribution of light in the sky leads us to the directly opposite conclusion, that our stellar universe is finite, though there may be stray stars outside that universe that occasionally come in, and though similarly some stars may occasionally stray out of the limits of the universe. There may be other such finite universes, in which case we may conceive of things in such a series as the following:
Electrons are the particles that make up atoms;
Atoms are the particles that make up molecules;
Molecules are the particles that make up masses;
Masses are the particles that make up planets, etc;
Planets, etc., are the particles that make up stellar systems;
Stellar systems are the particles that make up universes;
Universes are the particles that make up existence.
All of which sounds perfectly reasonable; but the gravitational consideration spoils this simple series; and it is a consideration that cannot easily be disposed of. It would seem, then, as if there was gravitationally an infinite universe, while in relation to light the shape of the universe is something like Herschel's drum. In other words, stars are uniformly distributed throughout the whole of infinite space, so that the gravitational phenomena will be like those of an infinite universe; while somehow or other, beyond Herschel's drum, stars do not give out light. This phenomenon cannot be explained by a partial opaqueness of ether; for then the apparent shape of the universe would be spherical, with ourselves at the center, instead of double-drum-shaped, with ourselves on the southern side. Hence there must be some other explanation, especially since this same question of probability indicates that ether is likely to be uniformly distributed through infinite space.
Some other explanation, then, must be found. Beyond the boundaries of Herschel's drum, for some unknown reason or other, stars fail to give out light. Either they are all cold or they are hot but not bright. And furthermore, stars must be constantly entering and leaving the limits of this Herschel drum. We may easily suppose that a star, after having passed all the way across this part of space, has cooled down so much as to give no light; but on entering, they are much hotter than later on, because stars constantly lose heat to the surrounding ether; hence, if these stars were cold before entering the Herschel drum, something must have happened to them near the boundary to heat them up suddenly. If there is, around the boundary of the drum, any material which would heat up a star by collision, friction, or contact, then it would follow that cold stars leaving the drum would be similarly affected; which is hardly in accordance with the theory, as deduced from observation. Hence we conclude that the stars which enter the Herschel drum are, to a great extent at least, hot, but give out no radiant energy (light). Thus, outside the limits of the Herschel drum, as far as we can judge, stars exist, and many of them are even hotter than the stars within our observation, and it would seem that the ether is there to receive radiant energy from them, but no radiant energy is forthcoming.
The result, then, is, that we do indeed have an infinite stellar universe, but that Herschel's drum has the peculiarity that, within it, stellar heat is converted into radiant energy, while no such conversion takes place outside the Herschel drum. There may, furthermore, be other Herschel drums in other parts of space having similar peculiarities. In order to understand the special peculiarity of these Herschel drums, let us examine why stellar heat is converted into radiant energy at all.
In the first place, the ether of interstellar space is at a very low temperature, while, in general, a star is at an extremely high temperature, many stars being much hotter than our sun. According to the second law of thermodynamics, the energy should tend to run down towards a common level; that is, the star's heat energy would radiate into the surrounding space and appear in the form of ether-vibrations, that is, in the form of radiant energy, under which heading is included light. If, then, outside Herschel's drums, there are many hot stars, hot enough to give out light of all vibration-periods (white hot), but which do not issue any radiant energy, it follows that somehow the second law of thermodynamics applies only within the Herschel drums but is somehow suspended or even reversed outside them. In other words, the actual stellar universe, as manifested by gravitational phenomena, is infinite, and stars are approximately uniformly distributed throughout infinite space; but we can only see the stars in that section of space where the second law of thermodynamics prevails, and therefore the section of the stellar universe that is visible is, after all, only finite.
We thus come to the conclusion that the boundary of the Herschel drum is really the limiting surface between positive and negative sections of the universe. And now we come to the question whether, starting with our theory of the positive or the negative tendency prevailing in different parts of space and time according to the theory of probability, we can draw any more detailed conclusions in respect to the exact appearance of the stellar universe.
In the first place, we have come to the conclusion that, taking any given moment of time, the positive and the negative parts of the universe should be approximately equal, as a matter of probability; in fact that, if we take the whole of space and time, the positive and negative sections bear towards one another a ratio of exactly 1. Since we are dealing with only the present time (or times near the present) in dealing with the present appearance of the universe, we may confine ourselves to the statement that, in a given portion of time, there should be approximately equal positive and negative sections of space; and, if matter is approximately uniformly distributed throughout space, that the volumes of the two kinds of sections should be approximately equal. The next question is, in what way the negative section of space can be distinguished from the positive section.
Our previous consideration on the production of radiant energy from the stars indicates that such production of radiant energy is only possible where the second law of thermodynamics is followed, that is, in a positive section of the universe. In a negative section of the universe the reverse process must take place; namely, space is full of radiant energy, presumably produced in the positive section of space, and the stars use this radiant energy to build up a higher level of heat. All radiant energy in that section of space would tend to be absorbed by the stars, which would thus constitute perfectly black bodies; and very little radiant energy would be produced in that section of space, but would mostly come from beyond the boundary surface. What little radiant energy would be produced in the negative section of space would be pseudo-teleologically directed only towards stars which have enough activity to absorb it, and no radiant energy, or almost none, would actually leave the negative section of space. The peculiarity of the boundary surface between the positive and negative sections of space, then, is, that practically all light that crosses it, crosses it in one direction, namely, from the positive side to the negative side. If we were on the positive side, as seems to be the case, then we could not see beyond such surface, though we might easily have gravitational or other evidence of bodies existing beyond that surface.
Furthermore, just as, in the positive section of space, light is given out uniformly in all directions, so, in the negative section, light must be absorbed by a star equally from all directions. Thus, to any star in the negative section, light must come in about the same amount from all directions; and, since most of this light comes from the positive sections, it follows that the negative sections must be completely surrounded by positive sections and must therefore be finite in all directions. By reversing this (since we have seen that all physical laws are reversible), it follows that any positive section must also be finite in all directions, and be completely surrounded by negative sections. We thus find the universe to be made up of a number of what we may call bricks, alternately positive and negative, all of approximately the same volume; a sort of three-dimensional checkerboard, the positive spaces counting as white (giving out light), and the negative spaces as black (absorbing light).
Thus what we see is simply the white space that we are in. The surrounding black spaces are invisible, and in addition, absorb the light from the white spaces beyond, so that even those cannot be seen, and, if we judge from the distribution of light in the sky, we get an idea merely of the size and shape of our special white space.
Let us try, now, to get a theoretical idea as to approximately what should be the shape of these white and black spaces, so that it can be compared with observation. For developing the theory in this direction, we must remember that the proportion of positive matter in any part of space should, according to probability, be about 50%. But this same theory of probability will tell us that it is extremely improbable in any given part of space that this proportion should be exactly 50%, but that there should be a discrepancy between the percentage of positive and that of negative phenomena, this discrepancy becoming increasingly improbable the greater the discrepancy is. Accordingly we may suppose that there are surfaces where the proportion of positive events is 50% (our boundaries), and other similar surfaces where there are other special proportions, while, in the middle of the positive "bricks," there will be a maximum percentage point, and in the middle of the negative "bricks" there will be a minimum percentage point. Around these maximum and minimum points our white and black spaces will be built, the fundamental variation of the percentage away from these points being presumably based on three principal directions or dimensions, of which the variation in other directions will be compounded.
Proceeding from, let us say, one of the maximum points (center of a positive section of the universe) in any direction, the discrepancy from the normal of 50% should become first positive, then negative, in a sort of vibrationary form. This vibration should be irregular, according to the theory of error, though with a certain average; but in the three principal directions, approximately perpendicular to each other, we should expect to find them more uniformly periodic.
If these "vibrations" were regular and perfectly periodic in these three directions, the boundary surfaces would be planes midway between the maximum and minimum points, and the sections of the universe would take the shape of rectangular parallelopipeds. With such shape, the sections of the universe would indeed be "bricks." But such regular uniform vibrations are hardly to be expected. The theory of error would lead us to expect irregularities from even that; but the volume of the sections should remain unaltered. Furthermore, a positive section must touch another positive section along an edge, or else at that edge two negative sections will form a continuous section, and we are thus liable to get a continuous line of negative space to perhaps an infinite extent, which is contrary to anything that we should expect. Hence we must expect that, in the irregularities, both the edges and the volume would be but slightly changed.
The faces of the parallelopiped, however, may, even under these conditions, be considerably changed. We may, for instance, expect that the vibrations of the percentage, instead of being the simple-harmonic vibrations which would produce plane boundary surfaces midway between the maximum and minimum points, may be compounded with its "harmonics," that is, may be compounded with vibrations of multiple frequency, of which the double frequency is the most important. The double frequency would be likely to make a whole face of the parallelopiped either cave in or bulge out, the higher frequencies will simply introduce further irregularities. Since there is to be little alteration of volume of the sections, two of the opposite pairs of surfaces must be changed in one direction, and the third in the other. The longer dimensions of the parallelopiped are those in which more irregularity is likely to show itself, so that the biggest alteration would show itself on one of the two smaller pairs of opposite faces. The other two pairs of faces will then have to be altered in the opposite way to make up for this; presumably the largest and the smallest, the medium pairs of faces showing the greatest irregularity. The irregularity may thus be of two varieties: either the medium pair of faces is caved in, and the largest and smallest bulged out somewhat less; or the largest and smallest pairs of faces are caved in slightly, and the medium pair of faces extremely bulged out.
Taking each of those two shapes (and they are liable to alternate to some extent, some sections of the universe being of one kind of shape, and some of the other), we can suppose of each one that it represented a positive section of the universe, and attempt to predict the distribution of light in the sky as seen from somewhere near the maximum point. If the parallelopipeds are comparatively flat (as they are likely to be, the three dimensions of these figures probably being widely different), it follows that in the sky, the plane parallel to the largest pair of faces would seem to be filled with a thick white strip. According to which of the forms of irregularities we suppose, the shape of the strip will vary. If the largest and smallest faces are bulged out, this white strip would be much less conspicuous, there being in other directions a good distribution of stars visible, but the strip would still be visible, and the hollow in one pair of faces would mean that, in one place on the strip, as well as in the opposite part, there would be a widening (due to the medium pair of faces being nearer than the smallest, and consequently, appearing wider) with a dark space in the middle of this widening. Midway between these dark spaces the strip becomes narrow, due to the fact that there the surface bounding the section of the universe recedes to a great distance. If the other shape of the positive section were adopted, we should have something similar, except that the strip would tend more to be of uniform width, and, if anything, the "coal-sacks" would be in the narrow part of the strip. We may represent the two forms of the strip somewhat as follows:
These "coal-sacks" would tend to be oval in shape, instead of pointed at the ends, as Herschel's double drum would lead us to suppose. If we are on the southern side of the positive section, then on the southern side more irregularities would be seen, such as striations of the strip, occasionally small "coal-sacks" in other parts than where expected, while some of the irregular wavy variations on the largest face of the "brick" on the south side would result in our seeing, near this strip, apparently detached sections, presumably approximately circular. As a matter of fact, the so-called Galaxy or Milky Way has the shape indicated in the first of the two above diagrams, with exactly such irregularities as we have predicted. The shape of the coal-sacks is indeed approximately oval, and not pointed, as Herschel's theory would lead us to expect. Furthermore, such circular detached sections of the Milky Way actually do appear in the southern hemisphere, and have been phenomena which have always been difficult to explain; they are called the Magellanic Clouds, and we can see that, according to our theory, they are exactly what they look like: detached sections of the Milky Way. And, if they result from what we suppose, namely, the largest of the three southern faces of the "brick" becoming wavy and extending suddenly a great distance out, it follows that the neighboring regions, which are the opposite phase of the same waves, should be so near us that there should theoretically, around the Magellanic Clouds, be very few stars visible. This is indeed the case; the Magellanic Clouds are found in a region of the sky that is almost completely devoid of stars.
We thus find that not only does our theory of a reversible universe actually reconcile the theories of the infinite universe with the theories of the finite universe, but it actually enables us to predict the distribution of light in the sky much more accurately than any theory has yet been able to do. We thus see that the universe is infinite, but divided into alternately positive and negative spaces of approximately equal volume, and that the apparent stellar universe is merely the positive section in which we are. The Galaxy consists merely of the distant sides of the irregular "brick" that constitutes this positive section.
To get an approximate idea of the size of this "brick," the temporary star, Nova Persei, which appeared in 1902, was in the Milky Way, and was probably as distant. Its distance has been estimated at about 3400 light-years, so that this gives us the length of the "brick" as about 7000 light-years. The Milky Way near the coal-sacks being about twice as wide as here, the width of the "brick" would be about 4000 light-years. And, the greatest width of the Milky Way being about 15 degrees, that gives the thickness of the brick at about 1000 light-years. In reducing to ordinary measurement, we may notice that a light-year is about 5.8 trillion miles.