I'M LOOKING OVER A FOUR-LEAF CLOVER
by Isaac Asimov

     History is full of apocryphal stories; stories about people saying and doing things they never really said and did—like George Washington chopping down the cherry tree, or Galileo dropping weights off the Leaning Tower of Pisa. Unfortunately, apocryphal stories are so much more interesting than the truth that it is impossible to kill them. And what's even more unfortunate for me, specifically, is that my memory is so selective that I never forget an apocryphal story, even though I frequently have trouble remembering facts.
     For instance, here's a story, probably apocryphal (or I wouldn't remember it so tenaciously) about St. Augustine.
     He was asked once, by a scoffer, "What did God spend His time doing before He created Heaven and Earth?"
     And St. Augustine roared back, without hesitation, "Creating Hell, for those who ask questions like that!"
     But I hope St. Augustine was just joshing when he said that, for having talked about the conservation laws in Chapter 1, and about the expanding Universe in Chapter 2, I want to go on to discuss my theories as to the birth and development of the Universe in the light of the conservation laws; and to do that I will (among other things) have to ask that unaskable question —what came before the beginning?
     I ended Chapter 2 with the picture of an oscillating Universe; one that first expands, then contracts, then expands, then contracts, and so on over and over again, with each cycle of expansion and contraction taking some eighty billion years, and with an extremely dense "cosmic egg" at the point of maximum contraction in each cycle.
     In continuing the discussion, let's begin by asking whether all the cycles are identical, or whether there is some change from cycle to cycle; perhaps a steady, one-way change.
     For instance, we might argue that as the Universe expands, it radiates massless particles - photons and neutrinos - constantly. These photons and neutrinos, we can say, move outward and are forever lost. When the Universe contracts again, the mass that comes together into a cosmic egg is smaller by the loss of the mass-equivalent of the energy represented by the lost radiation. This would continue with each cycle, each cosmic egg being less massive than the one before, until finally a cosmic egg is formed that possesses so little mass that it can no longer explode properly. When that happens the entire Universe is represented by one extremely large but slowly dying mass of condensed matter.
     In that case, we would be living not merely in an oscillating Universe but in a damped oscillating one. The Universe, in that view, would be like a bouncing ball that is not very elastic. Each bounce is lower than the one before and finally the ball does not bounce at all but just lies there.
     That is rather a neat picture for it produces a logical end, the kind of an end we are familiar with in ordinary life and one we might therefore be disposed to accept. But suppose we look backward in time? What about the cosmic egg that existed before the one that started the present expansion? That earlier one had to be larger than ours, and the one before that had to be even larger, and the one before that still larger. To move back in time and find ever-larger cosmic eggs, exploding with ever-greater violence is troublesome, for an endlessly increasing mass may be hard to handle. The damped oscillating Universe produces a neat overall end but no neat overall beginning.
     Fortunately we don't have to complicate matters by picturing such a damped oscillation. Photons and neutrinos are not "forever lost." To be sure, they move outward from their source of radiation in a "straight line" but what do we mean by a "straight line"? Suppose we draw a straight line on the surface of the Earth. It might seem to us that if we extend that line with perfect straightness, it will go on and on forever and that a point traveling along it will be "forever lost" to anyone standing at the place of origin of the line. However, you know and I know that the Earth's surface is curved and that the "straight line" will eventually (if we assume the Earth to be a perfect sphere) come back to the place of origin.
     In the same way, photons and neutrinos, in traveling a "straight line" by our local-neighborhood-of-the-Universe definition, are actually traveling in a grand circle and will return, roughly speaking, to the point of origin. The Universe of "curved space" has a finite volume and all it contains, matter and energy, must remain within that volume.
     As the Universe contracts, not only matter, but also photons and neutrinos must be crowded together. The massless particles are still traveling in "straight lines" but these "straight lines" curve ever more sharply; and in the end all the contents of the previous cosmic egg are brought back into another cosmic egg, with nothing lost. Each cosmic egg is precisely like the one before and the one that will come after and there is no damping. In a strictly oscillating Universe of this sort, there is neither beginning nor end, nor, on the whole, any change. If this faces us with the uncomfortable concept of eternity, it is at least an essentially unchanging eternity.
     Within a single cycle of the oscillation, of course, there is a beginning at one cosmic egg, an end at the next, and colossal change in between.
     But what is the nature of the cosmic egg? That depends on the nature of the Universe. On the subatomic scale, our portion of the Universe is made up, in the main, of six kinds of particles: protons, electrons, neutrons, photons, neutrinos, and anti-neutrinos. The other particles that exist are present in vanishingly small traces on the whole and may be ignored.
     The subatomic particles are associated into atoms at the moment and these atoms are associated into stars and galaxies. We can assume that the six kinds of particles that make up our part of the Universe make up all of it and that even the farthest galaxy is essentially similar in fundamental makeup to our own bodies.
     As all the mass and energy of the Universe crunch together into the cosmic egg, the levels of organization of the Universe break down, one by one. The galaxies and stars come together in one contracting mass. The more complicated atoms decompose into hydrogen, absorbing neutrinos and photons as they do so. The hydrogen atoms break apart into protons and electrons, absorbing photons as they do so. The protons and electrons combine to form neutrons, absorbing antineutrinos as they do so.
     In the end, the Universe has been converted into a cosmic egg made up of a mass of hard-packed neutrons—a mass of "neutronium."
     Well-packed neutronium would have a density of about 400,000,000,000,000 grams per cubic centimeter, so that if the mass of the Sun were packed into neutronium, it would form a sphere with a radius of about 6.6 miles.
     If we consider that the mass of the Milky Way Galaxy is about 135,000,000,000 times that of the Sun, then the whole of our Galaxy, converted into neutronium, would form a sphere with a radius of about 33,600 miles.
     If we consider the Universe to contain a mass, 100,000,000,000 times that of our Galaxy, then the cosmic egg would have a radius of 156,000,000 miles. If the center of such a cosmic egg were made to coincide with the center of our Sun, the surface of the cosmic egg would almost coincide with the orbit of Mars. And even if the mass of the Universe were twenty thousand times as large as the mass I have cited, the cosmic egg, if it were composed of pure, well-packed neutronium, would be no larger than the orbit of Pluto.
     How does the cosmic egg fit in with the conservation laws discussed in Chapter 1?
     One can easily imagine that the momentum of the cosmic egg as a whole is zero, by defining the egg as motionless. When the cosmic egg explodes and expands, the individual portions have momentum in one direction or another, but all the momenta add up to zero. In the same way, the angular momentum of the cosmic egg can be defined as zero and while the parts of the expanding universe have individual angular momenta that are not zero, the total is zero.
     In short, it is tempting to try to establish a rule that for any conserved quantity, the value of that quantity in the cosmic egg is zero, or is capable of being defined as zero without logical difficulties.
     Since this notion is, as far as I know, original with me - especially in the manner I intend to develop it in the course of this article - I shall throw modesty to the dogs and speak of it as "Asimov's Cosmogonic Principle."
     The most economical way of expressing the principle is, "In the Beginning, there was Nothing."
     For instance, how about the conservation of electric charge? Of the six particles making up the Universe, one (the proton) has a positive charge and one (the electron) has a negative charge. These cannot combine and cancel electric charge under ordinary conditions (see Chapter 1), but in forming the cosmic egg, conditions may be extreme enough to make the two combine to form neutrons. The electric charge of the cosmic egg is then zero. (In the Beginning, there was No Charge.)
     In the course of the explosion and expansion of the cosmic egg, charge appears, to be sure, but in equal quantities of positive and negative so that the total remains zero.
     And what about lepton number (see "Balancing the Books"). Of the six particles making up the Universe, three are leptons. The electron and the neutrino have lepton numbers of +1, while the antineutrino has a lepton number of -1. In the formation of neutrons, all three disappear, and it is not unreasonable to suppose that the manner of the disappearance is such as to cancel out the lepton number and leave the cosmic egg with a lepton number of zero.
     On the whole, one can arrange matters to show that the values of all but two of the conserved quantities known to physicists are zero in the cosmic egg, or can logically be defined as zero. The two exceptions are baryon number and energy.
     Let's begin with the baryon number.
     Of the six particles making up the Universe, two are baryons, the proton and the neutron. Each has a baryon number of +1. Since there is no particle with a baryon number of -1 in the list of those making up the Universe, there is no chance of cancellation of baryon number, and no chance (or so it would now appear) of a cosmic egg possessing a baryon number of zero. In the process of cosmic egg formation, the protons disappear, to be sure, but for each proton that disappears, a neutron is formed and the baryon number remains positive.
     Indeed, if the cosmic egg contains the mass of 100,000,000,000 galaxies the size of ours, then it is made up of 1.6x10⁷⁸ baryons and its baryon number is +16,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000, 000,000,000,000,000,000,000,000,000,000,000.
     This is a terribly long way from zero and makes hash of Asimov's Cosmogonic Principle.
     There's a way out. There are particles with negative baryon numbers, even if those do not seem to occur in any but the tiniest traces in our neck of the woods. The antineutron, for instance, has a baryon number of -1. Well, suppose that the cosmic egg does not consist of neutrons only, but of neutrons and antineutrons, half and half. The baryon number would then be zero, as the Principle requires.
     The neutron half of the cosmic egg would explode to formprotons and electrons which would combine to form atoms. The antineutron half would explode to from antiprotons and anti-electrons (positrons) which would combine to form antiatoms.
     In short, we have now talked ourselves into supposing that the Universe is made up of equal quantities of matter and antimatter - but is it? It is absolutely inconceivable that the Universe be made up of matter and antimatter all mixed up, for if it were, the two would interact at once to produce photons. (That's exactly what happens when we, by might and main, produce a trifling quantity of antimatter in the laboratory.) A Universe composed of equal quantities of matter and antimatter, all mixed up, would actually be composed of a mass of photons, which are neither matter nor antimatter. The cosmic egg would be nothing more than compacted photons.
     But the Universe is not made up of photons only. If, then, it is made up of equal quantities of matter and antimatter, those must be separated - effectively separated - so that they do not interact to form photons. The only separation that is separate enough would be on the galactic scale. In other words, there may be galaxies made up of matter, and other galaxies made up of antimatter. Galaxies and antigalaxies, so to speak.
     We have no way of telling, so far, whether the Universe actually contains galaxies and antigalaxies. If a galaxy and an antigalaxy met, enormous quantities of energy would be formed as matter-antimatter annihilation took place. No clear-cut case of such an event has yet been detected, though there are some suspicious cases. Secondly, galaxies produce vast quantities of neutrinos as the hydrogen atoms are built up to helium in the stars they contain; while antigalaxies produce vast quantities of antineutrinos by way of the analogous process involving antimatter. When the day comes that astronomers can detect neutrinos and antineutrinos from distant galaxies, and pinpoint their sources, the galaxies and antigalaxies may be identified.
     In a Universe made up of galaxies and antigalaxies, we can picture the crunching together of the cosmic egg in a new way. Neutrons and antineutrons would be formed and these would undergo mutual annihilation to form photons. We would have "photonium" in the cosmic egg, rather than neutronium. What the properties of photonium would be like, I can't imagine.
     But what causes the photonium to break up into matter and antimatter in such a way that separate galaxies of each kind can be formed? Why doesn't the photonium break up into neutrons and antineutrons so well mixed that they annihilate each other at once? In short, why isn't the photonium stable? Why doesn't it remain photonium?
     Well, there are theories that an antiparticle is merely a particle that is moving backward in time. If you take a film of a positron in a magnetic field, it seems to curve, let us say, leftward, rather than rightward, as an electron would under similar conditions. However, if the film is run backward, then the positron curves rightward, like an electron.
     On the subatomic scale, it makes no difference whether time moves "forward" or "backward" as far as the laws of nature are concerned and consistent pictures of subatomic events can be drawn up in which particles move forward in time and anti-particles move backward.
     Could it be, then, that the photonium cosmic egg, with a baryon number of zero, breaks up into two smaller eggs, one of neutronium and one of antineutronium, and that the former moves forward in time and the latter backward, so that the two are out of reach of each other before they can interact? The neutronium egg with a positive baryon number can be called a "cosmon," while the antineutronium egg with a negative baryon number can be called an "anticosmon."
     We can picture the cosmon and anticosmon as both undergoing expansion and as continuing to separate along the time axis. We begin with a tiny cosmon and anticosmon, both close to the zero point on the time axis. As they move apart, they grow larger and larger and more and more separated.*
     (* Since this chapter first appeared in print, I have discovered that F. R. Stannard of University College, London, is speculating on the existence of such a "negative-time" universe on a more rigorous basis than any I can handle.)
     For the moment let's concentrate on the cosmon (our Universe). As it expands, the various forms of energy are spread out within it more and more evenly. We express this fact by saying that entropy increases and, indeed, entropy has sometimes been called "time's arrow." If entropy increases, you know time is moving forward.
     But when the cosmon begins to contract, all the atomic and subatomic processes that took place during expansion begin to reverse. Entropy then begins to decrease and time begins to run backward.
     In other words the cosmon moves forward in time when it is expanding, and backward when it is contracting. The anticosmon (behaving symmetrically) moves backward in time when it is expanding, and forward in time when it is contracting. Each does this over and over again.
     Instead of an oscillating Universe, we have an oscillating double-Universe, the two oscillations being exactly in phase, and both Universes coming together to form a combined cosmic egg of photonium.
     But if this picture takes care of baryon number, it does not take care of energy. The law of conservation of energy is the most fundamental generalization we know and no matter how I have sliced things so far, the Universe, cosmon and anticosmon combined, is made up of energy.
     If the cosmon consists of 1.6x10⁷⁹ neutrons and their descendant particles, and the anticosmon consists of 1.6x10⁷⁹ antineutrons and their descendant particles, then the total energy content of the photonium cosmic egg formed by the coming together of the cosmon and anticosmon must be something like 4.8 X1076 ergs, and that must always exist, at all stages of the cosmon-anticosmon separation, expansion, contraction, and coalescence.
     That is the final hurdle for Asimov's Cosmogonic Principle, for in the photonium cosmic egg all conserved quantities, except energy, can be set equal to zero.
     How, then, can one set the energy equal to zero as well? To do so, one must postulate something we might call negative-energy.
     There is no such thing as far as we know. It has never been observed. Nevertheless, the Principle makes its existence necessary.
     In a Universe consisting only of negative-energy, all the manifestations would be broadly identical with those in our own Universe consisting of ordinary energy. However, if a sample of ordinary energy and of negative-energy were brought together they would cancel each other and produce Nothing.
     There are familiar cases of partial cancellation of physical properties. Two billiard balls moving in opposite directions at equal speeds, and coated with glue to make them stick on collision, will, if they collide head-on, come to a dead halt. Momentum will have been canceled out (but the energy of motion of the billiard balls will be converted to heat). Two sound beams, or light beams, exactly out of phase, will combine to form silence, or darkness (but the energy content of the wave forms will be converted into heat).
     In all these partial cancellations, the energy - most fundamental of all - always remains. Well, in the case of the combination of energy and negative-energy, cancellation will be complete. There will be left Nothing!
     Negative-energy is made up of negative-photons, which can break down to form negative-neutrons and negative-antineutrons. The negative-neutrons can break down to form negative-matter which can be built up to negative-stars and negative-galaxies, forming a negative-cosmon. Negative-antineutrons can break down to form negative-antimatter which will build up to a negative-anticosmon.
     Suppose a cosmon and anticosmon contract and combine to form a photonium cosmic egg. A negative-cosmon and a negative-anticosmon can contract to form an antiphotonium cosmic egg. The two cosmic eggs, photonium and antiphotonium can then combine to form Nothing!
     We are then left with no cosmic egg at all! We are left with Nothing!
     In the beginning was Nothing and this Nothing formed a photonium cosmic egg and an antiphotonium cosmic egg. The photonium cosmic egg behaved as already described, forming a cosmon moving forward in time and an anticosmon moving backward in time. The antiphotonium cosmic egg must behave analogously, forming a negative-cosmon moving forward in time and a negative-anticosmon moving backward in time.
     But if the cosmon and negative-cosmon are both moving forward in time why don't they combine and cancel out to Nothing? It seems to me they must remain separate and this separation may come about through gravitational repulsion. So far, we know of gravitational attraction only, and there is no such thing (as far as we know) as gravitational repulsion. If, however, there is negative-energy, and if negative-matter is formed from it, perhaps a gravitational repulsion can also exist and be expressed between matter and negative-matter.
     As the cosmon and negative-cosmon expand, gravitational repulsion drives them steadily apart, perhaps, along the space axis (see Figure 1), while both move together up the time axis. Similarly, the anticosmon and negative-anticosmon drive steadily apart along the space axis as they move downward along the time axis.