The most popular cosmological theory at present, the “Big Bang”, is not particularly satisfactory. No wonder the Pope himself praised it: it supposedly fits Church doctrine perfectly—there was nothing, and then God brought about that very “Bang!” That makes things simpler for the Pope. Scientists, however, are not all happy with it. For even if we allow for the existence of a Creator, the question immediately arises: what, then, is God himself, and where did he come from? So, for science, God is persona non grata.
After the explosion, however, from the very first microseconds onward, apart from one small “but”, to which we shall return later, it is more or less clear how the Universe acquired its structure (S. Weinberg. The first three minutes, a modern view of the origin of the Universe, New York: Basic Books, 1993). On the whole, there is nothing supernatural about it: entropy increases overall, but, owing to the energy acquired at the moment of the “explosion”, a system displaced from equilibrium and developing nonlinearly (P. Covency and R. Highfield. The arrow of time, 1990) gives rise to self-organizing “subsystems”—from atoms and galaxies to living organisms, including thinking ones.
And yet it remains unclear where that colossal energy of the “Big Bang” came from.
It seems that things happen as follows:
The Universe and the Anti-Universe exist eternally. This is not a “static” state, but their periodic appearance and disappearance—annihilation, “mutual destruction”—at moments corresponding to the “Big Bang” and/or the “Big Crunch”.
A similar process is well known in quantum mechanics. S. Hawking, for example, writes that in so-called “empty space”, pairs of virtual particles and antiparticles continually appear and disappear: they arise together, move apart, and come together again to annihilate, releasing a certain amount of energy (S. Hawking. The illustrated a brief history of time, Bantam Books, 1997). “Since energy cannot be created out of nothing,” Hawking goes on to write, “one partner in a particle-antiparticle pair has positive energy and the other has negative energy.”
Apparently, the same is true of the “Universe–Anti-Universe” system. It is precisely the force of attraction between these two worlds that gives rise to gravity, which opposes the expansion of the Universe that began with the “Big Bang”, “draws together” all its objects, and curves space and time, ultimately leading to the inevitable “Big Crunch” at the end of each cycle. Annihilation then once again supplies the colossal energy with which the Universe begins to develop in a new cycle—and so on “ad infinito”. Thus, of the three Friedmann models hitherto considered equally probable, Model I, that of a closed Universe, is the valid one; but the “Big Crunch” it predicts is not the end of everything, merely a new beginning.
Let us return to quantum mechanics. There is a complex relationship between matter/antimatter, spatial symmetry, and the two directions of time. It consists in the following: if particles are replaced with antiparticles, spatial coordinates with their mirror images, and the direction of time is reversed—from the future to the past—the physical laws governing such an object remain unchanged (C, P, T-invariance) (P. Covency and R. Highfield. The arrow of time, 1990).
Similar relationships apparently exist within the “Universe–Anti-Universe” pair: the Anti-Universe consists of antimatter (for a definition, see S. Weinberg. The first three minutes), has negative energy, is a “mirror image” of our Universe, and moves—develops, exists—backward in time, ensuring that all physical laws are preserved within the system. In the “singularity” prescribed by the “Big Bang” theory, by contrast, all laws break down.
Indeed, the “total sum” of matter and energy in the “Universe–Anti-Universe” pair, as in a “particle-antiparticle” pair, remains unchanged and equal to zero. That is, in accordance with the first law of thermodynamics—the fundamental law of nature—energy and matter are neither created out of nothing nor lost. The system exists eternally and requires no Creator.
As for the second law of thermodynamics, concerning the increase of entropy in the Universe, it too is, of course, valid—for the Universe, where irreversible processes occur, characterized by the positive direction of time, from the past to the future. “Irreversibility is the unidirectional development of a system with its inherent direction of time” (P. Covency and R. Highfield. The arrow of time, 1990).
As is known, both classical and modern physical theories allow for both directions of time—the “law of time symmetry” (P. Covency and R. Highfield. The arrow of time, 1990). Entropy is a function of time: when time runs from the past to the future, entropy increases with time; when time “changes sign”, running from the future to the past, entropy correspondingly decreases. That is, in the Anti-Universe, which consists of antimatter and exists backward in time, entropy gradually decreases, thus maintaining the perfect symmetry of all parameters of the “Universe–Anti-Universe” pair at every moment.
Thus, time, which according to Einstein can “slow down”, evidently “stops” at the moment of the “Big Bang”/“Big Crunch” and reverses its direction in the Anti-Universe. In other words, time, like the other coordinates, has two directions, extending both ways from zero. It is possible—and logical—that the curvature of space, too, upon reaching its maximum at the “singularity”, can acquire a “negative value” in the Anti-Universe, where space is, as it were, “turned inside out”, curving not like the surface of a sphere but like a “saddle surface”—or, more precisely, like the inner surface of a sphere, a “mirror image” of the configuration of the Universe. Interestingly, it is precisely such “saddle-shaped” curvature of space that, according to a number of authors, including S. Hawking, is required for travel “backward in time”.
Here is a translation of Hawking’s limerick:
“A lady nicknamed ‘Clever’
Wanted to travel down the street,
But she was rushing
Faster than light,
And here was the penalty:
The lady was back at her own front door,
Long, alas, before setting off.”
Since material objects cannot exceed the speed of light, such “effects” are apparently the prerogative of the Anti-Universe, its virtual particles, and the formations composed of them. Yet in the Universe, too, some very interesting phenomena occur at speeds close to the speed of light.
As is known from quantum mechanics, a wave and a particle are two different descriptions of the same entity. The dual nature of particles is demonstrated in the so-called “double-slit experiment”: if light—electromagnetic waves—passes through two narrow slits in a barrier onto a detecting screen, interference fringes appear on it, as would be expected of wave processes. It was also discovered that if the light source is replaced with a source of particles, such as electrons, sent strictly one at a time, interference fringes again appear on the screen, although one would naturally expect each electron to pass through either one slit or the other. The interference pattern, however, indicates that the electron passes through both slits simultaneously! From this it was concluded that the electron is not only a particle but also a wave.
What could explain such a phenomenon?
As is known from “thought experiments”, at speeds exceeding the speed of light an object can “overtake itself” (“A lady nicknamed…”). Apparently, at speeds equal to the speed of light, one can “catch up with oneself”. “Any particle with zero rest mass,” writes S. Weinberg, “such as a photon, neutrino, or graviton, moves at the speed of light. Material particles approach the speed of light if their energy is to a considerable extent comparable to the rest energy mc², where m is the mass of the particle” (S. Weinberg. The first three minutes). Perhaps such a particle, moving at a speed close to that of light and “catching up with itself”, as it were “doubles”, being in “two places at once”, alongside itself. It thus acquires the ability to pass through both slits simultaneously, creating an interference pattern, for which it is accorded the “status” of a wave. As is known, wavelength is inversely proportional to the mass of the particle, which is quite logical, since particles of greater mass are harder to “accelerate” to the speed of light.
The quantization of energy—that is, the fact that energy (electromagnetic waves—light, for example) is emitted not in a continuous stream but, as it were, in separate portions, “quanta”—is a natural consequence of the fact that a photon is first and foremost a particle, even though, having zero rest mass, it moves at the speed of light, where wave properties are most pronounced.
And now, back to cosmology.
The existence of the Anti-Universe does not seem so improbable if we recall the description of conditions in the primordial Universe, in the first moments after the “Big Bang”. “At first,” write I. Nicolson and P. Moore (I. Nicolson and P. Moore. The universe. Equinox, Oxford, 1985), “particles and antiparticles were constantly being created and mutually annihilated. Then … a tiny excess of particles over antiparticles arose—for reasons that are not yet entirely clear”—the very small “but” mentioned on the first page.
To understand the reasons for this excess, let us turn once again to quantum mechanics. Quantum mechanics states that every particle has a partner—an antiparticle. This evidently refers to each “class of particles”. But if we take this statement more literally—that each individual particle has its own “partner”, an antiparticle, which is precisely what was happening at the beginning, in the “homogeneous soup” of the primordial Universe (see, for example, S. Weinberg; I. Nicolson and P. Moore)—we may suppose that if an excess of particles forms in the Universe, an equal excess of antiparticles must be accumulating somewhere. That is, when, as the temperature fell after the “Big Bang”, the Universe began to acquire structure and material particles combined into increasingly complex assemblies, antiparticles likewise conglomerated into antimatter, into the Anti-Universe. Such structuring—combining with “one’s own kind”—prevents the immediate annihilation of particles with antiparticles, postponing it for billions of years, from the “Big Bang” to the “Big Crunch”!
On the basis of the above, it seems logical to conclude that the Universe—the sum of all particles—must inevitably have its partner: the sum of all antiparticles, the Anti-Universe. There is nothing “supernatural” about such an object, the “Anti-Universe”. The virtual particles of which it consists are, as is known, not picked up by detectors. But the existence of antiparticles is confirmed by their influence on material particles—a very noticeable influence indeed, extending to the annihilation of the latter.
Likewise, the Anti-Universe—the cause of the future “Big Crunch”—is real because it has a determining influence on our Universe: its emergence, its development down to the smallest details, the motion of all its objects along geodesic baskets in the curved four-dimensional space-time continuum, its end, and the subsequent repetition of the cycle. There are rigid reciprocal connections between the Universe and the Anti-Universe. Because time runs in opposite directions in them, an event that is to occur in the Universe “tomorrow” has already occurred in the Anti-Universe “yesterday”, and vice versa. In other words, our world determines the past of the virtual world with the same inevitability with which the virtual world determines the future of ours.
In this virtual, “imaginary” world, which exists backward in time, the use of imaginary numbers in calculations becomes justified. “Imaginary time is time measured using imaginary numbers” (S. Hawking, The illustrated a brief history of time). Mathematicians have long used imaginary numbers to solve cosmological problems—S. Hawking, R. Penrose, and others—but until now this method has been regarded as artificial, although S. Hawking notes: “Perhaps what we call imaginary time is actually more fundamental than real time” (S. Hawking, The illustrated a brief history of time).
On the basis of the above, it would be more accurate to conclude that imaginary time is, at any rate, no less fundamental than real time. The world simply turns out to be more complex than we have imagined it until now—exactly “twice” as complex, by the addition of the Anti-Universe. It is then eternal, indestructible, self-contained, and requires no Creator, but merely repeats an endless cycle of states.
Perhaps the Anti-Universe, where entropy decreases and, consequently, negentropy—in other words, information—increases (C. Shannon, I. Prigogine, L. Brillouin), may be regarded as an informational world. Some may find it tempting to call this informational, virtual world a “divine” substance, a kind of Higher Intelligence in which our future is supposedly determined. Well, that is a matter of taste. I would only point out that praying to such a God is useless: these reciprocal connections between the “world” and the “anti-world” are simply a consequence of the way the system exists, are governed by precise and immutable physical laws, and admit of no “appeal”.
One may, of course, regret that our “free will” is, strictly speaking, merely an illusion in this world rigidly determined by cause-and-effect relationships. Yet because it is utterly impossible for us to predict coming events, this “illusion” should be taken quite seriously. For my part, I would simply repeat after Spinoza: “God is Nature.” There is no point in looking for anything outside it.
Why, then, have the bodies of the Anti-Universe not yet been detected by scientists? Let us try to understand this question.
It is known that on the cosmic scale, the concepts of space and time are inseparably linked: we measure the distance between celestial bodies by the time light needs to cover it. It is also known that a light wave spreading from a source travels both toward the observer—the forward light cone—and away from the observer—the reverse light cone.
If we take the moment of an individual flash as the reference point, it is natural to regard the direction of photon motion in the forward cone as positive and that in the reverse cone as negative. Time undergoes corresponding changes: in the reverse cone, unlike the forward one, it takes on negative values, since each successive point lies further in the past than the preceding one—at a greater distance in light-years from the observer. That is, in the reverse cone, photons move backward in time, from the future to the past, on a negative time scale.
Indeed, any object moving away from the observer can be regarded as moving backward in time: this is precisely why an astronaut’s time slows down. But will the astronaut enter negative time? Let us conduct a thought experiment. Suppose the astronaut’s speed is half the speed of light—in a thought experiment, anything is possible. Then, moving backward in time for, say, ten years, the astronaut covers a distance of five light-years, that is, goes five years into the past relative to Earth time, and must therefore set the clock back five years:
This means that the astronaut’s time has remained positive, although it has slowed by a factor of two.
If, however, the astronaut’s speed is equal to the speed of light, then, travelling backward in time, the astronaut must set the clock back by exactly as many years as the journey has lasted:
that is, time has, as it were, stopped for the astronaut: at the end of the flight, the astronaut will be at the point where the vertices of the forward and reverse cones meet, at the epicentre of the wave. Finally, if the astronaut’s speed exceeds the speed of light—say, by a factor of two—the astronaut will enter the reverse light cone, negative time! The astronaut’s time is inverted and runs backward, since over ten years of travel the clock is set back twenty years:
Thus, the notion of unidirectional time apparently persists only because material objects cannot reach the speed of light, still less exceed it. Any object moving at a speed lower than that of light will sooner or later be overtaken by a light wave, which, after being reflected from it, will return to the observer. We can perceive only light travelling toward us, reaching the retina of the eye. Light from the reverse cone can be detected by the observer only if it is reflected from some object encountered along its path. It will then once again be a forward cone of light, but from a different source: as is known, all celestial bodies shine either by their own light or by reflected light and, in this sense, are independent sources of light for the observer.
Is it surprising that, considering only light travelling in one direction, we also regard time as a unidirectional quantity? But does this mean that there are no objects in the cosmos capable of moving in negative time? Not at all. It means only that such objects cannot be detected by astronomers: since their speed exceeds the speed of light, a light wave will never catch up with them or be reflected from them, however long ago their motion began or however long it continues. The existence of such objects is confirmed only by indirect evidence (see above). There is, however, no doubt that the antiparticles formed in the primordial Universe cannot simply disappear. Their annihilation with their partners, material particles, proved impossible, since the latter still exist today in the objects of the material Universe. The antiparticles could only follow their example, group together, and form the bodies of the Anti-Universe. But whereas mass is a measure of inertia, antimatter objects apparently acquired the necessary mobility that allows them successfully to evade the close scrutiny of astronomers tirelessly searching for dark matter in the Universe.
Objects moving at a speed exceeding the speed of light always remain in the reverse light cone and therefore cannot, in principle, be detected by an observer on Earth. It is precisely the totality of these objects that constitutes the Anti-Universe.
It must be emphasized that, when dealing with objects of quantum mechanics, where the observer is, as it were, outside the system and can, under certain conditions, detect what happens in both the forward and reverse cones, particular care should be taken in classifying particles. Perhaps a clue may be found in whether or not the object has rest mass, as well as in properties such as the particle’s charge and spin. And finally, might photons, this boundary substance, be their own antiparticles precisely because they can visit both these worlds?
15 December 2000