To many people, unaccustomed to dialectical thinking, the notion of infinity is difficult to accept. It is so far at variance with the finite world of everyday objects, where everything has a beginning and an end, that it seems strange and unaccountable. Moreover, it is at variance with the teachings of most of the main world religions. Most of the ancient religions had their creation myth. Medieval Jewish scholars put the date of Creation at 3760 B.C., and in fact, the Jewish calendar dates from then. In 1658, Bishop Ussher worked out that the universe was created in 4004 B.C. Throughout the 18th century, the universe was considered to be six or seven thousand years old at most.
But—you might object—20th century science has nothing in common with all these creation myths! With modern scientific methods we can get an exact picture of the size and origins of the universe. Unfortunately, things are not as simple as that. Firstly, despite colossal advances our knowledge of the observable universe is limited by the power of even the largest telescopes, radio signals and space probes, to provide information. Secondly, and more seriously, is the way in which these results and observations are interpreted in a highly speculative manner, frequently bordering on mere mysticism. All too often, one has the impression that we have indeed regressed to the world of the creation myth (the “Big Bang”), complete with its inseparable companion, the Day of the Final Judgement (the “Big Crunch”).
Gradually, beginning with the invention of the telescope, the advance of technology has pushed the boundaries of the universe further and further away. The crystal spheres which ever since Aristotle and Ptolemy had hemmed in the minds of men, were finally shattered, along with all the other barriers that the religious prejudices of the Middle Ages had placed in the way of progress.
In 1755, Kant postulated the existence of distant collections of stars, which he called “island universes”. Yet as late as 1924, the entire universe was estimated to be only 200,000 light years in diameter, and consisted of just three galaxies—our own and the two neighbouring ones. Then the American cosmologist, Edwin Powell Hubble (1889-1953), using the new 100-inch telescope at Mount Wilson, in Southern California, showed the Andromeda nebula to be far outside our own galaxy. Later, other galaxies were discovered still further away. Kant's “island universes” hypothesis was shown to be correct. Thus the universe was rapidly “expanded”—in the minds of men—and has continued to expand ever since, as more and more distant objects are discovered. Instead of 200,000 light years, it is now thought to measure tens of billions of light years across, and time will show that even the present calculations are nowhere near big enough. For the universe, as Nicolas of Cusa and others thought, is infinite. Before the Second World War, it was thought that the age of the universe was only two billion years. That is slightly better than Bishop Ussher's calculation. But it was still hopelessly wrong. At present there is a fierce dispute among the supporters of the big bang concerning the supposed age of the universe. We shall return to that later.
The big bang theory is really a creation myth (just like the first book of Genesis). It states that the universe came into being about 15 billion years ago. Before that, according to this theory, there was no universe, no matter, no space, and, if you please, no time. At that time, all the matter in the universe is alleged to have been concentrated at a single point. This invisible dot, known to big bang aficionados as a singularity, then exploded, with such a force that it instantly filled the entire universe, which is still expanding as a result. Oh, by the way, this was the moment when “time began”. In case you are wondering whether this is some kind of joke, forget it. This is precisely what the big bang theory states. This is what the great majority of university professors with long strings of letters after their name actually believe. There is the clearest evidence of a drift towards mysticism in the writings of a section of the scientific community. In recent years, we have seen a flood of books about science, which, under the guise of popular accounts of the latest theories of the universe, attempt to smuggle in religious notions of all kinds, in particular, in connection with the so-called theory of the big bang.
The New Scientist (7th May 1994) published an article entitled In the Beginning Was the Bang. The author, Colin Price, trained and worked as a scientist, but is now a Congregationalist minister. He begins by asking: “Is the big bang theory disconcertingly biblical? Or to put it another way, is the Genesis story disconcertingly scientific?” And he ends with the confident assertion: “No one would have appreciated the big bang story more than the authors of the first two chapters of the book of Genesis.” This is quite typical of the mystical philosophy that lies behind what Mr. Price, no doubt with tongue in cheek, but quite accurately describes as the big bang story.
The Doppler effect
In 1915, Albert Einstein put forward his general theory of relativity. Before this, the general view of the universe was derived from the classical mechanistic model worked out in the 18th century by Sir Isaac Newton. For Newton, the universe was like a vast clockwork mechanism, obeying a number of fixed laws of motion. It was infinite in extent, but essentially unchanging. This vision of the universe suffered from the defect of all mechanistic, non-dialectical theories. It was static.
In 1929, Edwin Hubble, using a powerful new telescope, showed that the universe was far bigger than had been previously thought. Moreover, he noticed a previously unobserved phenomenon. When light reaches our eyes from a moving source, it creates a change in frequency. This may be expressed in terms of the colours of the spectrum. When a source is travelling towards us, its light is perceived to shift towards the high frequency (violet) end of the spectrum. When it moves away, we perceive a shift towards the low frequence (red) end of the spectrum. This theory, first worked out by the Austrian Christian Doppler, and called the “Doppler effect” after him, had major implications for astronomy. The stars appear to observers as a pattern of lights against a dark background. Noticing that most of the stars showed a shift towards the red end of the spectrum, Hubble's observations gave rise to the idea that the galaxies were moving away from us at a speed proportionate to the distance of the galaxy. This became known as Hubble's Law, although Hubble himself did not think that the universe was expanding.
Hubble observed that there was a correlation between the redshift and distance, as measured by the apparent brightness of the galaxies. It appeared that the most distant galaxies then observable were moving away at 25,000 miles per second. With the advent of the new 200-inch telescope in the 1960s, even more distant objects were detected, moving away at 150,000 miles per second. Upon these observations, the hypothesis of the “expanding universe” was built. In addition, the “field equations” of Einstein's general theory of relativity could be interpreted in such a way as to make them conform to this idea. By extension, it was argued that, if the universe was expanded, it must have been smaller in the past than now. The consequence of this was the hypothesis that the universe must have begun as a single dense core of matter. This was not originally Hubble's idea. It had already been advanced in 1922 by the Russian mathematician, Alexander Friedmann. Then in 1927, Georges-Henri Lemaître first put forward his idea of the “cosmic egg”. From the standpoint of dialectical materialism, the idea of an eternally unchanging, closed universe, in a state of permanent equilibrium, is clearly incorrect. Therefore, the abandonment of this standpoint was undoubtedly a step forward.
The theories of Friedmann were given an important boost by the observations of Hubble and Wirtz. These appeared to indicate that the universe, or at least the part of it we can observe, was expanding. This was seized upon by Lemaître, a Belgian priest, who attempted to prove that, if the universe was finite in space, it must also be finite in time—it must have had a beginning. The usefulness of such a theory to the Catholic Church is beyond all doubt. It leaves the door wide open to the idea of a Creator, who, after being ignominiously expelled from the universe by science, now prepares his triumphal comeback as the Cosmic Ju-ju Man. “I felt at the time,” said Hannes Alfvén years later, “that the motivation for his theory was Lemaître’s need to reconcile his physics with the Church's doctrine of creation ex nihilo.” 54 Lemaître was later rewarded by being made director of the Pontifical Academy of Science.
How the theory evolved
It is not actually correct to refer to “the big bang theory”. In fact, there have been at least five different theories, each of which has run into trouble. The first, as we have seen, was put forward in 1927 by Lemaître. This was soon refuted on a number of different grounds—incorrect conclusions drawn from general relativity and thermodynamics, a false theory of cosmic rays and stellar evolution, etc. After the Second World War, the discredited theory was revived by George Gamow and others in a new form. A number of calculations were advanced by Gamow and others, (incidentally, not without a certain amount of scientific “creative accountancy”) to explain the different phenomena which would flow from the big bang—density of matter, temperature, radiation levels, and so on. George Gamow's brilliant style of writing ensured that the big bang captured the popular imagination. Once again, the theory ran up against serious problems.
A whole number of discrepancies were found which invalidated, not only Gamow's model, but the “oscillating universe” model subsequently worked out by Robert Dicke and others, in an attempt to get round the problem of what happened before the big bang, by making the universe oscillate in a never-ending cycle. But Gamow had made one important prediction—that such an immense explosion would leave behind evidence in the form of “background radiation”, a kind of echo of the big bang in space. This was used to revive the theory some years later.
From the beginning there was opposition to the idea. In 1948, Austrian astronomers Thomas Gold and Hermann Bondi advanced the “steady state” as an alternative, later popularised by Fred Hoyle. While accepting the expanding universe, it attempted to explain it by the “continuous creation of matter from nothing”. This was alleged to be happening all the time, but at a rate too slow to be detected by present-day technology. This means that the universe remains essentially the same for all time, hence the “steady state” theory. Thus matters went from bad to worse. From the “cosmic egg” to matter created out of nothing! The two rival theories slugged it out for over a decade.
The very fact that so many serious scientists were prepared to accept Hoyle's fantastic notion that matter was being created out of nothing is itself absolutely astonishing. In the event, this theory was shown to be false. The steady state theory assumed the universe to be homogeneous in time and space. If the universe were in a “steady state” for all time, the density of a radio-emitting object ought to be constant, since the further we look out into space, the further back in time we see. However, observations showed that this was not the case; the further they looked out into space, the greater the intensity of the radio waves. This proved conclusively that the universe was in a constant state of change and evolution. It had not always been the same. The steady state theory was wrong.
In 1964, the steady state theory received the coup de grace with the discovery by two young astronomers in the USA, Arnas Penzias and Robert Wilson, of background radiation in space. This was immediately taken to be the “after-echo” of the big bang, predicted by Gamow. Even so, there were inconsistencies. The temperature of the radiation was found to be only 3.5°K, not the 20°K predicted by Gamow, or the 30°K predicted by his successor, Philip J.E. Peebles. This result is even worse than it looks. Since the amount of energy in a field is proportional to the 4th power of its temperature, the energy of the observed radiation was actually several thousand times less than that predicted.
American astrophysicist Robert Dicke and his Canadian counterpart Peebles took over the theory where Gamow had left off. Dicke realised that there was a handy way of getting round the sticky question of what happened before the big bang, if only they could get back to Einstein's idea of a closed universe. It could then be argued that the universe would expand for a time, then collapse to a single point (a “singularity”), or something near it, and then bounce back into expansion, in a kind of everlasting cosmic ping-pong game. The trouble was that Gamow had calculated the energy and density of the universe at levels just short of what would be needed to close the universe. The density was about two atoms per cubic meter of space; and the energy density, expressed as the predicted temperature of the background radiation, supposed to represent the remnants of the big bang, 20°K, i.e., 20 degrees above absolute zero. In fact, Gamow had fixed these figures in order to prove that the big bang produced heavy elements, something nobody now accepted. So Dicke unceremoniously ditched them, and selected new and equally arbitrary figures, which would fit in with his theory of a closed universe.
Dicke and Peebles predicted that the universe would be filled with radiation, mainly radio waves, with a temperature of 30°K. Later, Dicke claimed his group had predicted a temperature of 10°K, although this figure does not appear anywhere in his published notes, and is anyway a 100 times more than the observed result. This showed that the universe was more diffuse than Gamow had thought, with less gravity, which aggravated the basic problem of where all the energy for the big bang came from. As Eric Lerner points out:
“Far from confirming the Peebles-Dicke model, the Penzias-Wilson discovery clearly ruled out the closed oscillating model.” 55 Thus arose a third version of the big bang—which became known as the standard model—an open universe in a permanent state of expansion.
Fred Hoyle did some detailed calculations, and announced that a big bang would produce only light elements—helium, deuterium and lithium (the latter two are actually quite rare). He calculated that if the density of the universe were about one atom per eight cubic metres, the amounts of these three light elements would be quite close to those actually observed. In this way, a new version of the theory was put forward which was nothing like the older theories. This no longer mentioned the cosmic rays of Lemaître, or the heavy elements of Gamow. Instead, the evidence put forward was the microwave background and three light elements. Yet none of this constitutes conclusive proof for the big bang. A major problem was the extreme smoothness of the background microwave radiation. The so-called irregularities in the background are so small that these fluctuations would not have had time to grow into galaxies—not unless there was a lot more matter (and therefore a lot more gravity) around than appears to be the case.
There were other problems, too. How does it come about that bits of matter flying in opposite directions all managed to reach the same temperature, and all at the same time (the “horizon” problem)? The partisans of the theory present the alleged origins of the universe as a model of mathematical perfection, all perfectly regular, a regular “Eden of symmetry whose characteristics conform to pure reason,” as Lerner puts it. But the present universe is anything but perfectly symmetrical. It is irregular, contradictory, “lumpy”. Not at all the stuff that well-mannered equations are made of down at Cambridge! One of the problems is why did the big bang not produce a smooth universe? Why did not the original simple material and energy just spread out evenly in space as an immense haze of dust and gas? Why is the present universe so “lumpy”? Where did all these galaxies and stars come from? So how did we get from A to B? How did the pure symmetry of the early universe give rise to the present irregular one we see before our eyes?
The 'inflation' theory
To get round this and other problems, Alan Guth, the American physicist, advanced his theory of the “inflationary universe”. (It may be no coincidence that this idea was put forward in the 1970s, when the capitalist world was going through an inflationary crisis!) According to this theory, the temperature dropped so rapidly that there was no time for the different fields to separate out or for different particles to form. The differentiation took place only later, when the universe was much larger. This, then, is the most recent version of the big bang. It asserts that, at the time of the big bang, the universe experienced an exponential expansion, in which it doubled in size every 10–35 seconds (hence “inflation”). Whereas the earlier versions of the “standard model” envisaged the whole of the universe squashed to the size of a grapefruit, Guth went one better. He calculated that the universe did not begin as a grapefruit, but instead, it would be a billion times smaller than the nucleus of a hydrogen atom. Then it would expand at an incredible speed—many times the speed of light, which is 186,000 miles per second—until it reached a size 1090 times its initial volume, that is, 1 with 90 zeros after it!
Let us examine the implications of this theory. Like all the other big bang theories, it sets out from the hypothesis that all the matter in the universe was concentrated in a single spot. The fundamental mistake here is to imagine that the universe is equal to the observable universe, and that it is possible to reconstruct the entire history of the universe, as a linear process, without taking into account all the different phases, transitions, and different states through which matter passes.
Dialectical materialism conceives of the universe as infinite, but not static or in a permanent state of “equilibrium”, as both Einstein and Newton did. Matter and energy cannot be created or destroyed, but are in a continual process of movement and change, which involves periodic explosions, expansion and contraction, attraction and repulsion, life and death. There is nothing intrinsically improbable about the idea of one, or many, great explosions. The problem here is a different one—a mystical interpretation of certain observed phenomena, such as the Hubble red shift, and an attempt to smuggle the religious idea of the creation of the universe into science by the back door.
To begin with, it is unthinkable that all the matter in the universe should be concentrated in a single point “of infinite density”. Let us be clear what this means. Firstly, it is impossible to place an infinite amount of matter and energy in a finite space. Just to pose the question is sufficient to answer it. “Ah! say the big bangers, but the universe is not infinite, but finite, according to Einstein's general theory of relativity.” In his book, Eric Lerner points out that an infinite number of different universes are allowed by Einstein's equations. Friedmann and Lemaître showed that many equations led to universal expansion. But by no means all of them imply a state of “singularity”. Yet this is the one variant that is dogmatically advanced by Guth and co.
Even if we accept that the universe is finite, the notion of “singularity” leads us to conclusions of a clearly fantastic character. If we take the tiny corner of the universe which we are able to see as being the whole universe—an arbitrary assumption with no logical or scientific basis whatsoever—then we are talking about more than 100 billion galaxies, each containing about 100 billion main sequence stars (like our own sun). According to Guth, all this matter was concentrated in a space smaller than a single proton. When it had existed for a millionth of a trillionth of a trillionth, of a trillionth of a second with a temperature of trillions of trillions of trillions of degrees, there was only one field and only one kind of particle interaction. As the universe expanded and the temperature fell, the different fields are supposed to have “condensed” out of the original state of simplicity.
The question arises where all the energy came from to propel such an unprecedented expansion. In order to solve this riddle, Guth resorted to a hypothetical omnipresent force field (a “Higgs field”), the existence of which is predicted by some theoretical physicists, but for which there is not a shred of empirical evidence. “In Guth's theory,” comments Eric Lerner, “the Higgs field which exists in a vacuum generates all the needed energy from nothing— ex nihilo. The universe, as he puts it, is one big 'free lunch', courtesy of the Higgs field.” 56
Every time the big bang hypothesis runs into trouble, instead of abandoning it, its supporters just move the goal posts, introducing new and ever more arbitrary assumptions in order to shore it up. For example, the theory requires a certain amount of matter in the universe. If the universe was created 15 billion years ago, as the model predicts, there has simply not been enough time for the matter we observe to have congealed into galaxies like the Milky Way, without the help of invisible “dark matter”. According to the big bang cosmologists, in order for galaxies to have been formed from the big bang, there must have been sufficient matter in the universe to bring about an eventual halt to its expansion through the law of gravitation. This would mean a density of approximately ten atoms per cubic metre of space. In reality, the amount of matter present in the observable universe is about one atom per ten cubic metres—a hundred times less than the amount predicted by the theory.
The cosmologists decided to represent the density of the universe as a ratio of the density needed to bring the expansion to a halt. They call this ratio omega. Thus, if omega equals 1, it would just be sufficient to halt the expansion. Unfortunately, the actual ratio was observed to be around .01 or .02. Approximately 99 per cent of the required matter had somehow “gone missing”. How to solve the conundrum? Very simply. Since the theory demanded that the matter be there, they arbitrarily fixed the value of omega at close to 1, and then began a frantic search for the missing matter! The first problem facing the big bang was the origin of the galaxies. How did the extremely smooth background radiation produce such a “lumpy” irregular universe? The so-called ripples (anisotropies) in the radiation were supposed to have been a reflection of the formation of the clumps of matter around which the early galaxies coalesced. But the irregularities observed were too small to have been responsible for the formation of galaxies, unless there was a lot more matter, and therefore gravity, present than seems to be the case. To be exact, there needed to be 99 per cent more matter, which just wasn't there.
This is where the notion of “cold dark matter” comes in. It is important to realise that no one has ever seen this stuff. Its existence was put forward in the early 1980s, in order to fill up an embarrassing hole in the theory. Since only 1 or 2 per cent of the universe can actually be seen, the remaining 99 per cent or so was alleged to consist of invisible matter, which is dark and cold, emitting no radiation at all. Such strange particles, after a decade of searching for them, remain unobserved. But they nevertheless occupy a central place in the theory, simply because it demands that they should exist.
Fortunately, it is possible to work out quite accurately the amount of matter in the observable universe. As we have already pointed out, it is about one atom for every ten cubic metres of space, a mere one per cent of what is required by the big bang theory. But, as the journalists like to say, don't let the facts spoil a good story! If there is not enough matter in the universe to square with the theory, then there must be an awful lot of matter there which we can't see. As Brent Tully put it, “It's disturbing to see that there is a new theory every time there's a new observation.”
At this stage, the defenders of the big bang decided to call on the aid of the Seventh Cavalry, in the person of particle physicists. The mission they were called upon to carry out puts all the exploits of John Wayne completely in the shade. The most he ever had to do was to find some unfortunate women and children carried off by the Indians. But when the cosmologists called in their colleagues who were busy investigating the mysteries of “inner space”, their request was a trifle more ambitious. They wanted them to find the 99 per cent or so of the universe which had inconsiderately “gone missing”. Unless they could find this missing matter, their equations would just not add up, and the standard theory of the origin of the universe would be in trouble!
In his book, The Big Bang Never Happened, Eric Lerner details a whole series of observations, the results of which have been published in scientific journals, which completely refute the idea of dark matter. Yet, in the teeth of all the evidence, the advocates of the big bang continue to behave like the learned professor who refused to look through the telescope to test the correctness of Galileo's theories. Lerner claims dark matter must exist —because our theory demands it!
“The test of scientific theory, is the correspondence of predictions and observation, and the big bang has flunked. It predicts that there should be no objects in the universe older than twenty billion years and larger than 150 million light-years across. There are. It predicts that the universe, on such a large scale, should be smooth and homogeneous. The universe isn't. The theory predicts that, to produce the galaxies we see around us from the tiny fluctuations evident in the microwave background, there must be a hundred times as much dark matter as visible matter. There's no evidence that there's any dark matter at all. And if there is no dark matter, the theory predicts, no galaxies will form. Yet there they are, scattered across the sky. We live in one.” 57
Alan Guth succeeded in removing some of the objections to the big bang, but only by advancing the most fantastic and arbitrary version of the theory yet seen. It did not say what the “dark matter” was, but merely provided the cosmologists with a theoretical justification for it. The real significance was that it established the link between cosmology and particle physics that has lasted ever since. The problem is that the general tendency of theoretical physics, as in cosmology, has been to resort increasingly to a priori mathematical assumptions to justify their theories, making very few predictions that can be tested in practice. The resulting theories have an ever more arbitrary and fantastic character, and frequently seem to have more in common with science fiction than anything else.
In point of fact, the particle physicists who rushed to the aid of cosmology had plenty of problems of their own. Alan Guth and others were trying to discover a Grand Universal Theory (GUT), which would unify the three basic forces that operate on the small scale in nature—electromagnetism, the weak force (which causes radioactive decay), and the strong force (which holds the nucleus together, and is responsible for the release of nuclear energy). They hoped to repeat the success of Maxwell, a hundred years earlier, who had proved that electricity and magnetism were one and the same force. The particle physicists were only too willing to enter an alliance with the cosmologists, in the hope of finding the answer in the heavens for the difficulties they had found themselves in. In reality, their whole approach was similar. With scarcely any reference to observation, they based themselves on a series of mathematical models, and completely arbitrary assumptions, which were often little more than mere speculation. Theories have emerged thick and fast, each more incredible than the last. “Inflation” theory is mixed up with all this.
The neutrino to the rescue!
The determination with which the supporters of the big bang cling to their positions frequently leads them to perform the most amusing somersaults. Having searched in vain for the 99 per cent of missing “cold dark matter”, they failed to find anything like the quantities required by the theory, to prevent the universe from expanding forever. On 18th December 1993, The New Scientist published an article entitled Universe Will Expand Forever. Here it was admitted that “a group of galaxies in the constellation of Cepheus contains far less invisible matter than had been thought a few months ago,” and that the claims made earlier by American astronomers was “based on faulty analysis”. A lot of scientific reputations are at stake, not to mention hundreds of millions of dollars in research grants. Could this fact have some connection with the fanaticism with which the big bang is defended? As usual, they saw what they wanted to see. The facts had to conform to the theory!
The evident failure to find the “cold dark matter”, the existence of which is essential to the survival of the theory, was causing unease in the more thinking sections of the scientific community. An editorial of The New Scientist, published on the 4th June 1994 with the suggestive title A Folly of Our Time? compared the idea of dark matter with the discredited Victorian concept of the “ether”, an invisible medium, by which light waves were believed to travel through space:
“It was invisible, ubiquitous, and, in the late 19th century, every physicist believed in it. It was, of course, the aether, the medium in which they thought light propagated, and it turned out to be a phantom. Light does not need a medium in which to propagate, unlike sound.
“Now, at the close of the 20th century, physicists find themselves in a curiously similar situation to their Victorian counterparts. Once again they are putting their faith in something which is invisible and ubiquitous. This time it is dark matter.”
At this point, one would expect a serious scientist to begin to ask himself whether there was not something basically wrong with his theory. The same editorial adds:
“In cosmology, free parameters seem to be proliferating like wildfire. If the observations do not fit the theory, cosmologists seem happy to simply add new variables. By continually patching up the theory, we may be missing out on some Big Idea.”
Indeed. But, don't let the “facts” get in the way. Like a conjurer pulling a rabbit out of a hat, they suddenly discovered— the neutrino!
The neutrino, which is a subatomic particle, is described by Hoffmann as “fluctuating uncertainly between existence and non-existence.” That is to say, in the language of dialectics, “it is and is not”. How can such a phenomenon be reconciled with the law of identity, which categorically asserts that a thing either is or is not? Faced with such dilemmas, which reappear at every step in the world of subatomic particles described by quantum mechanics, there is frequently a tendency to resort to formulations such as the idea that the neutrino is a particle with neither mass nor charge. The initial opinion, still held by many scientists, was that the neutrino had no mass, and since electric charge cannot exist without mass, the inescapable conclusion was that the neutrino had neither.
Neutrinos are extremely small particles, and therefore difficult to detect. The existence of the neutrino was first postulated to explain a discrepancy in the amount of energy present in particles emitted from the nucleus. A certain amount of energy appeared to be lost, which could not be accounted for. Since the law of the conservation of energy states that energy can neither be created nor destroyed, this phenomenon required another explanation. Although it seems that the idealist physicist Niels Bohr was quite prepared to throw the law of conservation of energy overboard in 1930, this proved to be slightly premature! The discrepancy was explained by the discovery of a previously unknown particle—the neutrino.
Neutrinos formed in the sun's core at a temperature of 15 million degrees centigrade moving at the speed of light reach the sun's surface in three seconds. Floods of them stream through the universe, passing through solid matter, apparently without interacting on it. Neutrinos are so small that they pass straight through the earth. So tiny are these elusive particles that their interaction with other forms of matter is minimal. They can pass through the earth, and even through solid lead, leaving no trace. Indeed, trillions of neutrinos are passing through your body even as you read these lines. But the likelihood that one could be trapped there is negligible, so you needn't worry. It has been estimated that a neutrino can pass through solid lead with a thickness of 100 light-years, with only a 50 per cent chance of being absorbed. That is why it remained undetected for so long. Indeed, it is difficult to imagine how a particle, which is so small that it was thought to have neither mass nor charge, and can pass through 100 light-years of lead, could ever be detected. But detected it was.
It seems that some neutrinos can be stopped by the equivalent of one tenth of an inch of lead. In 1956, using an ingenious experiment, American scientists succeeded in trapping an anti-neutrino. Then in 1968, they discovered neutrinos from the sun, although only one-third of the amount predicted by the current theories. Undoubtedly the neutrino possessed properties that could not immediately be detected. Given its extreme smallness, that was not surprising. But the idea of a form of matter that lacked the most basic properties of matter was clearly a contradiction in terms. In the event, the problem appears to have been resolved from two completely different sources. First, one of the discoverers of the neutrino, Nobel Prize winning physicist Frederick Reines, announced in 1980 that he had discovered the existence of neutrino oscillation in an experiment. This would indicate that the neutrino does have mass, but Reines' results were not seen as conclusive.
However, Soviet physicists, involved in an entirely separate experiment, showed that electron-neutrinos have a mass, which could be as much as 40 electron volts. Since this is only 1/13,000th of the mass of an electron, which in turn is only 1/2,000th of a proton, it is hardly surprising that the neutrino was for so long believed to have no mass.
Up till recently, the general view of the scientific establishment was that the neutrino had no mass and no charge. Now, all of a sudden, they have changed their mind and declared that the neutrino does indeed have mass—and, perhaps, quite a lot of it. This is the most astonishing conversion since Saint Paul fell off his horse on the road to Damascus! Indeed, such indecent haste must raise serious doubts about the motivation behind this miraculous conversion. Can it be that they were so desperate at their signal failure to deliver the goods with “cold dark matter” that they finally decided to do an about-turn on the neutrino? One can just imagine what Sherlock Holmes would have said to Doctor Watson!
Despite the enormous advances in the field of particle research, the present situation is confused. Hundreds of new particles have been discovered, but as yet there is no satisfactory general theory capable of introducing some order, as Mendeleyev did in the field of chemistry. At present, there is an attempt to unify the fundamental forces of nature by grouping them under four headings: gravity, electromagnetism, and the “weak” and “strong” nuclear forces, each of which functions at a different level.
Gravitation works on the cosmological scale, holding the stars, planets and galaxies together. Electromagnetism binds atoms into molecules, transports photons from the sun and stars, and fires the synapses of the brain. The strong force binds together protons and neutrons inside the nuclei of atoms. The weak force is expressed in the transmutation of unstable atoms during radioactive decay. Both the latter forces only operate at very short range. However, there is no reason to suppose that this arrangement represents the last word on the subject, in some respects it is an arbitrary notion.
There are big differences between these forces. Gravitation affects all forms of matter and energy, whereas the strong force only affects one class of particles. Yet gravitation is one hundred million trillion trillion trillion times weaker than the strong nuclear force. More importantly, it is not evident why there should be no opposite force to gravity, whereas electromagnetism is manifested both as positive and negative electrical charge. This problem, the solution of which was attempted by Einstein, remains to be solved, and has a vital bearing on the entire discussion about the nature of the universe. Each force is accounted for by a different set of equations, involving some twenty different parameters. These give results, but nobody knows why.
The so-called Grand Unified Theories (“GUTs”) put forward the idea that matter itself might only be a passing phase in the evolution of the universe. However, the prediction made by the GUTs that protons decay has not been borne out, thus invalidating at least the simplest version of the GUTs. In an attempt to make sense of their own discoveries, some physicists have got entangled in ever more weird and wonderful theories, like the so-called supersymmetry theories (“SUSYs”) which purport that the universe was originally built on more than four dimensions. According to this notion, the universe could have started with, for example, ten dimensions, but unfortunately all but four of them collapsed during the big bang, and are now too small to be noticed.
Apparently, these objects are the subatomic particles themselves, which are alleged to be quanta of matter and energy that condensed out of pure space. Thus they stagger from one metaphysical speculation to the next in a vain attempt to explain the fundamental phenomena of the universe. Supersymmetry postulates the universe as beginning in a state of absolute perfection. In the words of Stephen Hawking, “the early universe was simpler, and it was a lot more appealing, because it was a lot simpler.” Some scientists even try to justify this kind of mystical speculation on aesthetic grounds. Absolute symmetry is alleged to be beautiful. Thus we find ourselves back in the rarefied atmosphere of Plato's idealism.
In reality, nature is not characterised by absolute symmetry, but is full of contradictions, irregularities, cataclysms, and sudden breaks of continuity. Life itself is a proof of this assertion. In any living system, absolute equilibrium signifies death. The contradiction that we observe here is as old as the history of human thought. It is the contradiction between the “perfect” abstractions of thought and the necessary irregularities and “imperfections” which characterise the real material world. The whole problem stems from the fact that the abstract formulae of mathematics, which may or may not be beautiful, most certainly do not adequately represent the real world of nature. To suppose such a thing is a methodological error of the first magnitude, and necessarily leads us to draw wrong conclusions.
Constant headaches, or Hubble trouble
At present there is a fierce dispute among the supporters of the big bang concerning the supposed age of the universe. In fact, the entire “standard model” is in crisis. We are treated to the spectacle of respectable people of science attacking each other in public with the most ungentlemanly language. And all over something called the Hubble Constant. This is the formula that measures the speed at which things are moving in the universe. This is of great importance for those who wish to discover the age and size of the universe. The trouble is that nobody knows what it is!
Edwin Hubble asserted that the speed with which the galaxies are moving apart was proportional to their distance from us—the further away, the faster they are moving. This expressed in Hubble's Law: v(elocity) = H x d(istance). In this equation, the H is known as Hubble's Constant. In order to measure this, we need to know two things: the speed and distance away of a particular galaxy. The speed can be calculated by the red shift. But the distance between galaxies cannot be measured with a slide-rule. In fact, no reliable instruments exist for measuring such immense distances. And here lies the rub! The experts cannot agree on the real value of the Hubble Constant, as was comically revealed in a Channel 4 TV programme:
“Michael Pierce says that, without doubt, the Hubble Constant is 85, Gustaf Tamman asserts 50, George Jacoby 80, Brian Schmidt 70, Michael Rowan Robinson 50, and John Tonry 80. The difference between 50 and 80 may not sound like much,” says the accompanying Channel Four booklet, “but it is crucial to the age of the Universe. If the Hubble is high, astronomers could be in the process of disproving their most important theory."
The importance of this is that the higher the “Hubble”, the faster things are moving, and the sooner in the past was the moment when the big bang was supposed to have occurred. In recent years, new techniques of measuring the distance of galaxies have been applied, which have led astronomers to revise earlier estimates drastically. This has provoked consternation in the scientific community, since the estimates for the Hubble Constant have been getting higher all the time. The latest estimate puts the age of the universe at just 8 billion years. This would mean that there are stars that are older than the universe itself! This is a glaring contradiction—not a dialectical one, but simply nonsense. Carlos Frank, quoted in the same booklet, concludes:
“Well, if it turns out that the ages of the stars are greater than the expansion time of the universe, as inferred by the measurement of the Hubble Constant and the measurement of the density of the universe, then there is a genuine crisis. You only have one option: you have to drop the basic assumptions upon which the model of the Universe is based. In this case, you have to drop some, perhaps all, of the basic assumptions on which the big bang theory is based." 58
There is virtually no empirical evidence to bear out the big bang theory. Most of the work done to support it is of a purely theoretical character, leaning heavily on abstruse and esoteric mathematical formulae. The numerous contradictions between the preconceived “big bang” schema and the observable evidence have been covered up by constantly moving the goal posts in order to preserve at all costs a theory upon which so many academic reputations have been built.
According to this theory, there can be nothing in the universe older than 15 billion years. But there is evidence that contradicts this proposition. In 1986, Brent Tully of Hawaii University discovered huge agglomerations of galaxies (“superclusters”) about a billion light years long, three hundred million light years wide and one hundred million light-years thick. In order for such vast objects to form, it would have taken between eighty and a hundred billion years, that is to say four or five times longer than what would be allowed by the “big bangers”. Since then there have been other results that tend to confirm these observations.
The New Scientist (5th February, 1994) carried a report of the discovery of a cluster of galaxies by Charles Steidel of the Massachusetts Institute of Technology and Donald Hamilton of the California Institute of Technology in Pasadena with big implications for the big bang theory:
“The discovery of such a cluster spells trouble for theories of cold dark matter, which assume that a large fraction of the mass of the universe is in cold, dark objects such as planets or black holes. The theories predict that material in the early universe clumped together from the 'bottom up', so that galaxies formed first, then only later clumped to form clusters.”
As usual, the initial reaction of astronomers is to resort to “move the goal posts”, adjusting the theory to get round awkward facts. Mauro Giavalisco of the Baltimore Space Telescope Science Institute “believes it might just be possible to explain the birth of the first galaxy cluster at a red shift of 3.4 by fine-tuning the cold dark matter theory. But he adds a warning. 'If you found ten clusters at red shift 3.5, it would kill cold dark matter theories'.”
We may take for granted that not just ten but a far larger number of these vast clusters exist and will be discovered. And these, in turn, will only represent a minute proportion of all the matter that stretches far beyond the limits of the observable universe and reaches out to infinity. All attempts to place a limit on the material universe are doomed to fail. Matter is boundless, both at the subatomic level, and with regard to time and space.
Big crunch and superbrain
“Dies irae, dies illa
Solvet saeclum in favilla.”
(Thomas of Celano, Dies Irae)
(“That day, the day of wrath,
will turn the universe to ashes.”
—Mediaeval Church chant for the dead.)
In the same way they cannot agree on the origin of the universe, so they also disagree on how it is all supposed to end up—except that they all agree that it will end badly! According to one school of thought, the expanding universe will eventually be brought to a halt by the force of gravity, whereupon the whole thing will collapse in on itself, leading to a “big crunch”, where we will all end up just where we started, back inside the cosmic egg. Not so! exclaims another school of big bangers. Gravity is not strong enough to do this. The universe will simply keep on expanding indefinitely, getting thinner and thinner, like “Augustus who would not have any soup”, until eventually it fades away into the black night of nothingness.
Decades ago, Ted Grant, using the method of dialectical materialism, showed the unsoundness both of the big bang theory of the origin of the universe and the alternative steady state theory put forward by Fred Hoyle and Herman Bondi. Subsequently, the steady state theory, which was based on the continuous creation of matter (from nothing), was shown to be false. The big bang theory therefore “won” by default, and is still defended by the majority of the scientific establishment. From the standpoint of dialectical materialism, it is arrant nonsense to talk about the “beginning of time”, or the “creation of matter”. Time, space, and motion are the mode of existence of matter, which can neither be created nor destroyed. The universe has existed for all time, as constantly changing, moving, evolving matter and (which is the same thing) energy. All attempts to find a “beginning” or an “end” to the material universe will inevitably fail. But how is one to explain this strange regression to a mediaeval view of the fate of the universe?
While it is pointless to look for a direct causal link between the processes at work in society, politics and the economy, and the development of science (the relationship is neither automatic nor direct, but far more subtle), it is hard to resist the conclusion that the pessimistic outlook of some scientists in relation to the future of the universe is not accidental, but somehow related to a general feeling that society has reached an impasse. The end of the world is nigh. This is not a new phenomenon. The same doom-laden outlook was present in the period of decline of the Roman Empire and at the close of the Middle Ages. In each case, the idea that the world was coming to an end reflected the fact that a particular system of society had become exhausted and was on the point of extinction. What was imminent was not the end of the world, but the collapse of slavery and feudalism.
Just take the following quote from The First Three Minutes by Nobel Prize winner Steven Weinberg:
“It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more or less farcical outcome of a chain of accidents reaching back to the first three minutes, but that we were somehow built in from the beginning. As I write this I happen to be in an aeroplane at 30,000 feet, flying over Wyoming en route home from San Francisco to Boston. Below, the earth looks very soft and comfortable—fluffy clouds here and there, snow turning pink as the sunsets, roads stretching straight across the country from one town to another. It is very hard to realise that this all is just a tiny part of an overwhelmingly hostile universe. It is even harder to realise that this present universe has evolved from an unspeakably unfamiliar early condition, and faces a future extinction of endless cold or intolerable heat. The more the universe seems comprehensible, the more it also seems pointless.” 59
We have already seen how the big bang theory opens the door to religion and all kinds of mystical ideas. To blur the distinction between science and mysticism is to put back the clock 400 years. It is a reflection of the current irrational mood of society. And it invariably leads to conclusions of a thoroughly reactionary nature. Let us take just one apparently remote and obscure question: “Do protons decay?” As we have said, this is one of the predictions of one of the branches of modern particle physics known as the GUTs. All kinds of sophisticated experiments were conducted to test this. All ended in complete failure. Yet they persist in putting forward the same idea.
Here is a typical example of the type of literature issued by the advocates of the big crunch theory:
“In the final moments, gravity becomes the all-dominant force, mercilessly crushing matter and space. The curvature of space-time increases ever faster. Larger and larger regions of space are compressed into smaller and smaller volumes. According to conventional theory, the implosion becomes infinitely powerful, crushing all matter out of existence and obliterating every physical thing, including space and time themselves, at a space-time singularity.
“This is the end
“The 'big crunch', as far as we understand it, is not just the end of matter. It is the end of everything. Because time itself ceases at the big crunch, it is meaningless to ask what happens next, just as it is meaningless to ask what happened before the big bang. There is no 'next' for anything at all to happen—no time even for inactivity or space for emptiness. A universe that came from nothing in the big bang will disappear into nothing at the big crunch, its glorious few zillion years of existence not even a memory.”
The question that follows is a classic of unconscious humour: “Should we be depressed by such a prospect?” Paul Davies asks, presumably expecting a serious answer! He then proceeds to cheer us up by speculating on various means whereby humankind might escape destruction. Inevitably, we immediately find ourselves in a kind of never-never land half way between religion and science fiction.
“One might wonder whether a superbeing inhabiting the collapsing universe in its final moments could have an infinite number of distinct thoughts and experiences in the finite time available.” So, before the final three minutes are up, humanity casts off its crude material body, and becomes pure spirit, able to survive the ending of everything by transforming itself into a superbrain.
“Any superbrain would need to be quick-witted and switch communications from one direction to another as the oscillations brought more rapid collapse in one direction and then another. If the being can keep pace, the oscillations could themselves provide the necessary energy to drive the thought processes. Furthermore, in simple mathematical models there appears to be an infinite number of oscillations in the finite duration terminating in the big crunch. This provides for an infinite amount of information processing, hence, by hypothesis, an infinite subjective time for the superbeing. Thus the mental world may never end, even though the physical world comes to an abrupt cessation at the big crunch.” 60
One really needs a superbrain to make head or tail of this! It would be nice to think that the author is joking. Unfortunately, we have read too many passages of this kind recently to be sure of this. If the Big Crunch signifies “the end of everything”, where does this leave our friend the superbrain? To begin with, only an incorrigible idealist could conceive of a brain without a body. Of course, we are here in the presence, not of any old brain, but a superbrain. But even so, we assume that the presence of a spinal cord and a central nervous system would be of some use to it; that such a nervous system ought in all fairness, to posses a body; and that a body (even a superbody) generally requires some kind of sustenance, specially since the brain is known to be somewhat greedy, and absorbs a very high percentage of the total calories consumed even by a mere mortal. A superbrain would logically possess a superappetite! Sadly, since the big crunch is the end of everything, our unfortunate superbrain will evidently be placed in a rather strict diet for the rest of eternity. We can only hope that, being quick-witted, it will have had time to snatch a quick meal before its three minutes was up. With this edifying thought, we take our leave of the superbrain, and return to reality.
Is it not astonishing that, after two thousand years of the greatest advances of human culture and science, we find ourselves back in the world of the Book of Revelations? Engels warned more than a hundred years ago that, by turning their backs on philosophy, scientists would inevitably end up in the “spirit world”. Unfortunately, his prediction has proven to be all too accurate.
A 'plasma universe'?
The standard model of the universe has led us into a scientific, philosophical, and moral dead-end. The theory itself is full of holes. Yet it still remains on its feet, though badly shaken, mainly for the lack of an alternative. Nevertheless, something is stirring in the world of science. New ideas are beginning to take shape, which not only reject the big bang, but which set out from the idea of an infinite, constantly changing universe. It is far too early to say which of these theories will be vindicated. One interesting hypothesis, that of the “plasma universe”, has been put forward by the Swedish Nobel Prize winning physicist Hannes Alfvén. While we cannot deal with the theory in detail, we feel we should at least mention some of Alfvén's ideas.
Alfvén passed from the investigation of plasma in the laboratory to a study of how the universe evolves. Plasma consists of hot, electrically conducting gases. It is now known that 99 per cent of the matter in the universe is plasma. Whereas in normal gases, electrons are bound to an atom and cannot move easily, in a plasma, the electrons are stripped off by intense heat, allowing them to move freely. Plasma cosmologists envisage a universe “crisscrossed by vast electrical currents and powerful magnetic fields, ordered by the cosmic counterpoint of electromagnetism and gravity.” 61 In the 1970s, the Pioneer and Voyager spacecrafts detected the presence of electrical currents and magnetic fields filled with plasma filaments around Jupiter, Saturn and Uranus.
Scientists like Hannes Alfvén, Anthony Peratt and others, have elaborated a model of the universe which is dynamic, not static, but which does not require a beginning in time. The phenomenon of the Hubble expansion needs an explanation. But the big bang is not necessarily it. A big bang will certainly produce an expansion, but an expansion does not require a big bang. As Alfvén puts it: “This is like saying that because all dogs are animals, all animals are dogs.” The problem is not the idea of an explosion, which at some point gave rise to an expansion of part of the universe. There is nothing intrinsically improbable in this. The problem is the idea that all the matter in the universe was concentrated at a single point, and that the universe and time itself was born in a single instant called the big bang.
The alternative model suggested by Hannes Alfvén and fellow Swedish physicist Oskar Klein accepts that there could have been an explosion, caused by the combination of large amounts of matter and antimatter in one small corner of the visible universe, which generated huge quantities of energetic electrons and positrons. Trapped in magnetic fields, these particles drove the plasma apart for hundreds of millions of years.
“The explosion of this epoch, some ten or twenty billion years ago, sent the plasma from which the galaxies then condensed flying outward—in the Hubble expansion. But this was in no way a big bang that created matter, space, and time. It was just a big bang, an explosion in one part of the universe. Alfvén is the first to admit that this explanation is not the only possible one. 'The significant point,' he stresses, 'is that there are alternatives to the big bang'.”
At a time when almost all other scientists believed that space was an empty vacuum, Alfvén showed that this was not the case. Alfvén pointed out that the entire universe is pervaded by plasma currents and magnetic fields. Alfvén did pioneering work in the field of sunspots and magnetic fields. Later, Alfvén proved that when a current flows through a plasma in the laboratory, it assumes the form of a filament in order to move along magnetic field lines. Starting out from this observation, he then concluded that the same phenomenon takes place in plasma in space. It is a general property of plasma throughout the universe. Thus, we have immense electrical currents flowing along naturally formed plasma filaments, which crisscross the cosmos.
“By forming the filamentary structures observed on the smallest and largest scales, matter and energy can be compressed in space. But it is clear that energy can be compressed in time as well—the universe is filled with sudden, explosive releases of energy. One example that Alfvén was familiar with is the solar flare, the sudden release of energy on the sun's surface, which generates the streams of particles that produce magnetic storms on earth. His 'generator' models of cosmic phenomena showed how energy could be produced gradually, as in a well-behaved power station, but not explosively, as in the flares. Understanding the explosive release of energy was the key to the dynamics of the cosmos.”
Alfvén had proved the correctness of the Kant-Laplace Nebular Hypothesis. Now, if the stars and planets can be formed by the action of huge filamentary currents, there is no reason why whole solar systems cannot be formed in the same way:
“Again, the process is identical, but this time immensely larger: filaments sweeping through a protogalactic nebula pinch plasma into the building materials of the sun and other stars. Once the material is initially pinched, gravitation will draw some of it together, especially slower-moving dust and ice particles, which will then create a seed for the growth of a central body. Moreover, the filament's vortex motion will provide angular momentum to each of the smaller agglomerations within it, generating a new, smaller set of currents carrying filaments and a new cycle of compression that forms a solar system. (In 1989, this hypothesis now widely accepted, was definitively confirmed when scientists observed that the rotation axes of all the stars in a given cloud are aligned with the cloud's magnetic field—clearly, a magnetic-field-controlled stellar formation.)”
Alfvén's theories were, of course, rejected by the cosmologists, since they challenged not only the standard model, but even called into question the existence of black holes, which were then all the rage. He had already correctly explained the cosmic rays, not as the remnants of the big bang, but as the products of electromagnetic acceleration.
“Thus, in Alfvén and Klein's scenario, only a small part of the universe—that which we see—will have first collapsed and then exploded. Instead of coming from a singular point, the explosion comes from a vast region hundreds of millions of light-years across and takes hundreds of millions of years to develop—no 'origin of the universe' is required.” 62
Whether this particular theory is shown to be correct only time will tell. The important thing, as Alfvén himself points out, is that other alternative hypotheses to the big bang are possible. Whatever happens, we are sure that the model of the universe which is finally corroborated by science will have nothing in common with a closed universe with a big bang at one end and a big crunch at the other. The discovery of the telescope in 1609 was a decisive turning point in the history of astronomy. Since then, the horizon of the universe has been pushed further and further back. Today powerful radio telescopes probe deep into space. All the time new objects are being discovered, bigger and further away, with absolutely no end in sight. Yet man's obsession with the finite creates the persistent urge to place a “final limit” on everything. We see this same phenomenon repeated time and again in the history of astronomy.
It is ironic that, at a time when technology enables us to penetrate further than ever into the vastness of the universe, we witness a psychological regression to the mediaeval world of a finite universe, beginning with Creation and ending in the total annihilation of space, time and matter. An impassable line is drawn at this point, beyond which the human mind is not meant to enquire, since “we cannot know” what is there. It is the 20th century equivalent of the old maps, which showed the edge of the world, marked with the stern warning, “Here be Monsters”.
Einstein and the big bang
In recent decades the prejudice has become deeply rooted that “pure” science, especially theoretical physics is the product of abstract thought and mathematical deduction alone. As Eric Lerner points out, Einstein was partly responsible for this tendency. Unlike earlier theories, such as Maxwell's laws of electromagnetism, or Newton's laws of gravity, which were firmly based on experiment, and soon confirmed by hundreds of thousands of independent observations, Einstein's theories were initially confirmed on the basis of only two—the deflection of starlight by the sun's gravitational field and a slight deviation in the orbit of Mercury.
The fact that relativity theory was subsequently shown to be correct has led others, possibly not quite up to Einstein's level of genius, to assume that this is the way to proceed. Why bother with time-consuming experiments and tedious observations? Indeed, why depend upon the evidence of the senses at all, when we can get straight to the truth through the method of pure deduction?
We see a steadily increasing tendency towards a purely abstract theoretical approach to cosmology, based almost exclusively on mathematical calculations and relativity theory. “The annual number of cosmology papers published skyrocketed from sixty in 1965 to over five hundred in 1980, yet this growth was almost solely in purely theoretical work: by 1980 roughly 95 per cent of these papers were devoted to various mathematical models, such as the 'Bianchi type XI universe'. By the mid-seventies, cosmologists' confidence was such that they felt able to describe in intimate detail events of the first one-hundredth second of time, several billion years ago. Theory increasingly took on the characteristic of myth—absolute, exact knowledge about events in the distant past but an increasingly hazy understanding of how they led to the cosmos we now see, and an increasing rejection of observation.”
The Achilles' heel of Einstein's static, closed universe is that it would inevitably collapse in on itself because of the force of gravity. In order to get round this problem, he advanced the hypothesis of the “cosmological constant”, a repulsive force that would counteract that of gravity, thus preventing the universe from collapse. For a time the idea of a static universe, held forever in a state of equilibrium by the twin forces of gravity and the “cosmological constant” received support—at least from the very small number of scientists who claimed to understand the extremely abstract and complicated theories of Einstein.
In 1970, in an article in Science, Gerard de Vaucouleur showed that, as objects in the universe get larger, so their density gets less. An object ten times bigger, for example, will be 100 times less dense. This has serious implications for the attempts to establish the average density of the universe, which is necessary to obtain in order to establish whether there is enough gravity to halt the Hubble Expansion. If the average density drops with increases in size, it will be impossible to define the average density for the universe as a whole. If De Vaucouleur is right, the density of the observed universe will be far less than had been thought, and the value of omega could be as little as .0002. In a universe with so little matter, the effects of gravity will be so weak that the difference between general relativity and Newtonian gravity will be insignificant and, therefore, “for all practical purposes, general relativity, the foundation of conventional cosmology, can be ignored!” Lerner continues: “De Vaucouleur's discovery shows that nowhere in the universe—except perhaps near a few ultradense neutron stars—is general relativity more than a subtle correction.” 63
The difficulties involved in grasping what Einstein “really meant” are proverbial. When some journalist asked the English scientist Eddington, whose work gave the first direct confirmation of Einstein’s general theory of relativity, if it was true that there were only three people in the world who understood relativity, the latter replied, “Oh, really? And who is the third?” However, the Russian mathematician Alexander Friedmann in the early 1920s showed that Einstein's model of the universe was only one of an infinite number of possible cosmologies, some expanding, some contracting, depending on the value of the cosmological constant, and the “initial conditions” of the universe. This was a purely mathematical result, derived from Einstein's equations. The real significance of Friedmann's work was that it called into question the idea of a closed static universe, and showed that other models were possible.
Contrary to the idea of Antiquity that the stars were eternal and changeless, modern astronomy has shown that stars and other heavenly bodies have a history, a birth and life and a death—gigantic, rarefied and red in youth; blue, hot and radiant in middle life; shrunken, dense and red once more in old age. An immense amount of information has been accumulated from astronomical observations involving powerful telescopes. At Harvard alone, a quarter of a million stars had already been arranged in forty classes before the Second World War through the work of Annie J. Cannon. Now a great deal more is known as a result of radio telescopes and space exploration.
The British astronomer Fred Hoyle has made a detailed investigation of the life and death of stars. The stars are fuelled by the fusion of hydrogen into helium at the core. A star in its early stages changes little in size or temperature. This is the present position of our own sun. Sooner or later, however, the hydrogen that is being consumed at the hot centre is turned into helium. This accumulates at the core until, when it reaches a certain size, quantity changes into quality. A dramatic change occurs, causing a sudden variation in size and temperature. The star expands enormously, while its surface loses heat. It becomes a red giant.
According to this theory, the helium core contracts, raising the temperature to the point where the helium nuclei can fuse to form carbon, releasing new energy. As it heats, it contracts still further. At this stage, the life of the star draws rapidly to a close, for the energy produced by helium fusion is far less than that produced by hydrogen fusion. At a given point, the energy required to keep the star's expansion against the pull of its own gravitational field begins to fail. The star contracts rapidly, collapsing in on itself to become a white dwarf, surrounded by a halo of gas, the remnant of the outer layers blown out by the heat of contraction. These are the basis of planetary nebulae. Stars may remain in this state for a long time, slowly cooling, until they no longer possess enough heat to glow. They then end up as black dwarves.
However, such processes seem relatively sedate in comparison to the scenario mapped out by Hoyle for bigger stars. When a large star reaches a late stage of development, in which its internal temperature reaches 3-4 billion degrees, iron begins to form at the core. At a certain stage, the temperature reaches such a point that the iron atoms are driven apart to form helium. At this point, the star collapses in on itself in about one second. Such a terrific collapse causes a violent explosion, which blasts all the outer material away from the star's centre. This is what is known as a supernova, like the one that astonished Chinese astronomers in the 11th century.
The question arises of what happens if a large star continues to collapse inwards under the pressure of its own gravity. Unimaginable gravitational forces would squeeze the electrons into the space already occupied by protons. According to a law of quantum mechanics known as the Pauli exclusion principle, no two electrons can occupy the same energy state in an atom. It is this principle acting on the neutrons that prevents further collapse. At this stage the star is now mainly composed of neutrons, hence its name. Such a star has a tiny radius, maybe only 10 km, or about 1/700th of the radius of a white dwarf, and with a density of more than a 100 million times that of the latter, which was already extremely high. A single matchbox full of such material would weigh as much as an asteroid a mile in diameter.
With such staggering concentrations of mass, the gravitational pull of a neutron star would absorb everything in the surrounding space. The existence of such neutron stars was theoretically predicted in 1932 by the Soviet physicist and Nobel Prize winner Lev D. Landau, and later studied in detail by J.R. Oppenheimer and others. For some time it was doubted whether such stars could exist. However, in 1967 the discovery of pulsars inside the remnants of supernova such as the Crab Nebula gave rise to the theory that pulsars are really neutron stars. There is nothing in all this that is inconsistent with the principles of materialism.
Pulsars are pulsating stars which gave out rapid bursts of energy at regular intervals. It is estimated that there may be 100,000 pulsars in our galaxy alone, of which hundreds have already been located. The source of these powerful radio waves was thought to be a neutron star. According to the theory, it would have to have an immensely strong magnetic field. In the grip of the neutron star's gravitational field, electrons could only emerge at the magnetic poles, losing energy in the form of radio waves in the process. The short bursts of radio waves could be explained by fact that the neutron star must be rotating. In 1969, it was noted that a light of a dim star in the Crab Nebula was flashing intermittently in line with the microwave pulses. This was the first sighting of a neutron star. Then, in 1982, a fast pulsar was discovered, with pulsations 20 times faster than those of the Crab Nebula—642 times a second.
In the 1960s, new objects were discovered by radio telescopes, the quasars. By the end of the decade, 150 were discovered—some of them estimated to be nine billion light years away, assuming the red-shift to be correct. To appear at all at such a vast distance must mean that these objects are 30 to 100 times more luminous than a normal galaxy. Yet they appeared to be small. This poses difficulties, which led some astronomers to refuse to accept that they could be so far away.
The discovery of quasars gave an unexpected boost to the big bang theory. The existence of collapsed stars with a tremendously strong gravitational field posed problems that could not be resolved by direct observation. This fact opened the door to a flood of speculations, involving the most peculiar interpretations of Einstein's general theory of relativity. As Eric Lerner points out:
“The glamour of the mysterious quasars quickly attracted young researchers to the arcane calculations of general relativity and thus to cosmological problems, especially those of a mathematical nature. After 1964 the number of papers published in cosmology leapt upward, but the growth was almost wholly in purely theoretical pieces—mathematical examinations of some problem in general relativity, which made no effort to compare results with observations. Already, in 1964, perhaps four out of five cosmology papers were theoretical, where only a third had been so a decade earlier.” 64
It is necessary to distinguish clearly between black holes, the existence of which has been derived from a particular interpretation of the general theory of relativity, and neutron stars, which have actually been observed. The idea of black holes has captured the imagination of millions through the writings of authors like Stephen Hawking. Roger Penrose, in an essay based on a BBC Radio lecture delivered in 1973, describes the theory of black holes as follows:
“What is a black hole? For astronomical purposes it behaves as a small, highly condensed dark 'body'. But it is not really a material body in the ordinary sense. It possesses no ponderable surface. A black hole is a region of empty space (albeit a strangely distorted one), which acts as a centre of gravitational attraction. At one time a material body was there. But the body collapsed inwards under its own gravitational pull. The more the body concentrated itself towards the centre the stronger became its gravitational field and the less was the body able to stop itself from yet further collapse. At a certain stage a point of no return was reached, and the body passed within its 'absolute event horizon'.
“I shall say more of this later, but for our present purposes, it is the absolute event horizon which acts as the boundary surface of the black hole. This surface is not material. It is merely a demarcation line drawn in space separating an interior from an exterior region. The interior region—into which the body has fallen—is defined by the fact that no matter, light, or signal of any kind can escape from it, while the exterior region is where it is still possible for signals or material particles to escape to the outside world. The matter which collapsed to form the black hole has fallen deep inside to attain incredible densities, apparently even to be crushed out of existence by reaching what is known as a 'space-time singularity'—a place where physical laws, as presently understood, must cease to apply.” 65
In 1970, Stephen Hawking put forward the idea that the energy content of a black hole might occasionally produce a pair of subatomic particles, one of which might escape. This implies that a black hole can evaporate, although this would take an unimaginably long period of time. In the end, according to this view, it would explode, producing a large amount of gamma rays. Hawking's theories have attracted a lot of attention. His well-written best seller A Brief History of Time, From the Big Bang to Black Holes, was perhaps the book that more than any other drew the attention of the new theories of cosmology to the public's attention. The author's lucid style made complicated ideas seem both simple and attractive. It makes for good reading, but so do many works of science fiction. Regrettably, it appears to have become fashionable for the authors of popular works about cosmology to sound as mystical as possible, and to put forward the most outlandish theories, based on the maximum amount of speculation and the minimum amount of facts. Mathematical models have displaced observation almost entirely. The central philosophy of this school of thought is summed up in Stephen Hawking's aphorism “one cannot really argue with a mathematical theorem.”
Hawking claims that he and Roger Penrose proved (mathematically) that the general theory of relativity “implied that the universe must have a beginning and, possibly, an end.” The basis of all this is that the general theory of relativity is taken as absolutely true. Yet, paradoxically, at the point of the big bang general relativity suddenly becomes irrelevant. It ceases to apply, just as all the laws of physics cease to apply, so that nothing whatsoever can be said about it. Nothing, that is, except metaphysical speculation of the worst sort. But we will return to this later.
According to this theory, time and space did not exist before the big bang, when all the matter in the universe was alleged to have been concentrated at a single infinitesimally small point, known to mathematicians as a singularity. Hawking himself points out the dimensions involved in this remarkable cosmological transaction:
“We now know that our galaxy is only one of some hundred thousand million that can be seen using modern telescopes, each galaxy itself containing some hundred thousand million stars…We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating; the stars in its spiral arms orbit around its centre about once every several hundred million years. Our sun is just an ordinary, average-sized, yellow star, near the inner edge of one of the spiral arms. We have certainly come a long way since Aristotle and Ptolemy, when we thought that the earth was the centre of the universe!” 66
In point of fact, the very large quantities of matter mentioned here give no real idea of the amount of matter in the universe. New galaxies and super-clusters are being discovered all the time, and there is no end to this process. We may have come a long way since Aristotle in some respects. But in others, it seems that we are far, far behind him. Aristotle would never have made the mistake of talking about a time before time existed, or claiming that the entire universe was, in effect, created from nothing. In order to find ideas like these one would have to go back several thousand years to the world of the Judaic-Babylonian creation myth.
Whenever someone attempts to protest against these proceedings, he is instantly ushered into the presence of the great Albert Einstein, as a naughty schoolboy is dragged to the headmaster's study, and given a stern lecture on the need to show greater respect to general relativity, informed that one cannot argue with mathematical theorems, and sent home duly chastened. The main difference is that most headmasters are alive, and Einstein is dead, and therefore unable to comment on this particular interpretation of his theories. In fact, one would look in vain in all the writings of Einstein for any reference to the big bang, black holes and the like. Einstein himself, although he initially tended towards philosophical idealism, was implacably opposed to mysticism in science. He spent the last decades of his life fighting against the subjective idealist views of Heisenberg and Bohr, and, in fact, moved close to a materialist position. He would certainly have been horrified that mystical conclusions should be drawn from his theories. The following is a good example:
“All of the Friedmann solutions have the feature that at some time in the past (between ten and twenty thousand million years ago) the distance between neighbouring galaxies must have been zero. At that time, which we call the big bang, the density of the universe and the curvature of space-time would have been infinite. Because mathematics cannot really handle infinite numbers, this means that the general theory of relativity (on which Friedmann's solutions are based) predicts that there is a point in the universe where the theory itself breaks down. Such a point is an example of what mathematicians call a singularity. In fact, all our theories of science are formulated on the assumption that space-time is smooth and nearly flat, so they break down at the big bang singularity, where the curvature of space-time is infinite. This means that even if there were events before the big bang, one could not use them to determine what would happen afterward, because predictability would break down at the big bang. Correspondingly, if, as is the case, we know only what has happened since the big bang, we could not determine what happened beforehand. As far as we are concerned, events before the big bang can have no consequences, so they should therefore cut them out of the model and say that time had a beginning at the big bang.”
Passages such as this forcefully remind one of the intellectual gymnastics of the Medieval Schoolmen, arguing about the number of angels who could dance on the end of a pin. This is not meant as an insult. If the validity of an argument is determined by its internal consistency, then the arguments of the Schoolmen were as valid as this. They were not fools, but highly skilled logicians and mathematicians, who erected theoretical constructs as elaborate and perfect in their way as medieval cathedrals. All that was necessary was to accept their premises, and everything fell into place. The problem is whether the original premise is valid or not. This is a general problem with all mathematics, and its central weakness. And this entire theory leans very heavily on mathematics.
“At the time which we call the big bang…” But if there was no time, how can we refer to it as “a time” at all? Time is said to have begun at that point. So what was there before time? A time when there was no time! The self-contradictory nature of this idea is glaringly obvious. Time and space are the mode of existence of matter. If there was neither time, nor space, nor matter, what was there? Energy? But energy, as Einstein explains, is just another manifestation of matter. A force field? But a force field is also energy, so the difficulty remains. The only way that time can be got rid of is if before the big bang there was— nothing.
The problem is: how is it possible to get from nothing to something? If one is religiously minded, there is no problem; God created the universe from nothing. This is the doctrine of the Catholic Church, of Creation ex nihilo. Hawking is uncomfortably aware of this fact, as he says in the very next line:
“Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention. (The Catholic Church, on the other hand, seized on the big bang model and in 1951 officially pronounced it to be in accordance with the Bible.)”
Hawking himself does not want to accept this conclusion. But it is unavoidable. The whole mess arises out of a philosophically incorrect concept of time. Einstein was partly responsible for this, since he appeared to introduce a subjective element by confusing the measurement of time with time itself. Here again the reaction against the old mechanical physics of Newton has been carried to an extreme. The question is not whether time is “relative” or “absolute”. The central issue to be addressed is whether time is objective or subjective; whether time is the mode of existence of matter or an entirely subjective concept existing in the mind and determined by the observer. Hawking clearly adopts a subjective view of time, when he writes:
“Newton's laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second. Thus, if they met again, one would be older than the other. In this case, the difference in ages would be very small, but it would be much larger if one of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned he would be much younger than the one who stayed on Earth. This is known as the twins paradox, but it is a paradox only if one has the idea of absolute time at the back of one's mind. In the theory of relativity there is no unique absolute measure of time that depends on where he is and how he is moving.” 67
That there is a subjective element in the measurement of time is not in dispute. We measure time according to a definite frame of reference, which can, and does, vary from one place to another. The time in London is different from the time in Sydney or New York. But this does not mean that time is purely subjective. The objective processes in the universe take place whether we are able to measure them or not. Time, space, and motion are objective to matter, and have no beginning and no end.
Here it is interesting to note what Engels had to say on the subject:
“Let us continue. So time had a beginning. What was there before this beginning? The universe, which was then in a self-identical, unchanging state. And as no changes succeed one another in this state, the more specialised idea of time transforms itself into the more general idea of being. In the first place, we are not in the least concerned here with what concepts change in Herr Dühring's head. The subject at issue is not the concept of time, but real time, which Herr Dühring will by no means rid himself of so cheaply. In the second place, however much the concept of time may be converted into the more general idea of being, this takes us not one step further. For the basic forms of all being are space and time, and being out of time is just as gross an absurdity as being out of space.
“The Hegelian 'timelessly past being' and the neo-Schellingian 'unpreconceivable being' are rational ideas compared with this being out of time. For this reason Herr Dühring sets to work very cautiously; actually it is of course time, but of such a kind as cannot really be called time; time does not in itself consist of real parts, and is only divided up arbitrarily by our understanding—only an actual filling of time with differentiable facts is susceptible of being counted—what the accumulation of empty duration means is quite unimaginable. What this accumulation is supposed to mean is immaterial here; the question is whether the world, in the state assumed here, has duration, passes through a duration in time. We have long known that we can get nothing by measuring such a duration without content, just as we can get nothing by measuring without aim or purpose in empty space; and Hegel calls this infinity bad precisely because of the tedium of this procedure.” 68
Do singularities exist?
A black hole and a singularity are not the same thing. There is nothing in principle that excludes the possible existence of stellar black holes, in the sense of a massive collapsed star where the force of gravity is so immense that not even light can escape from its surface. Even the idea is not new. It was predicted in the 18th century by John Mitchell who pointed out that a sufficiently massive star would trap light. He came to this conclusion on the basis of Newton's classical theory of gravitation. General relativity did not enter into it.
However, the theory advanced by Hawking and Penrose goes far beyond the observed facts, and, as we have seen, draws conclusions that lend themselves to all kinds of mysticism, even if this was not their intention. Eric Lerner considers the case for supermassive black holes at the centre of galaxies to be weak. Together with Anthony Peratt, he has shown how all the features associated with these supermassive black holes, quasars, etc., can be better explained by electromagnetic phenomena. However, he believes the evidence is considerably stronger for the existence of stellar sized black holes since this rests on detecting very intense X-ray sources which are too big to be neutron stars. But even here the observations are far from proving the case.
The abstractions of mathematics are useful tools for understanding the universe, on one condition: that we do not lose sight of the fact that even the best mathematical model is only a rough approximation of reality. The problems start when people begin confusing the model with the thing itself. Hawking himself unwittingly reveals the weakness of this method in the passage already quoted. He assumes that the density of the universe at the point of the big bang was infinite, without giving any reasons for this, and then adds, in a most peculiar line of argument, that “because mathematics cannot really handle infinite numbers” the theory of relativity breaks down at this point. To this, it is necessary to add, “and all the known laws of physics”, since it is not only general relativity which breaks down with the big bang, but all of science. It is not just that we do not know what occurred before this. It is that we cannot know.
This is a return to Kant's theory of the unknowable Thing-in-Itself. In the past, it was the role of religion and certain idealist philosophers, like Hume and Kant, to place a limit upon human understanding. Science was permitted to go so far, and no further. At the point where human intelligence was not allowed to proceed, mysticism, religion and irrationality commenced. Yet the whole history of science is the story of how one barrier after another was removed. What was supposed to be unknowable for one generation became an open book for the next. The whole of science is based on the notion that the universe can be known. Now, for the first time, scientists are placing limits on knowledge, an extraordinary state of affairs and a sad comment on the present situation in theoretical physics and cosmology.
Consider the implications of the above passage: a) since the laws of science, including general relativity (which is supposed to provide the basis for the whole theory) break down at the big bang, it is impossible to know what, if anything, occurred before it, b) even if there were events before the big bang, they have no relevance to what happened afterwards, c) we cannot know anything about it, and so, d) we should simply “cut it out of the model and say that time began at the big bang.”
The self-assurance with which these assertions are put forward is truly breathtaking. We are asked to accept an absolute limit on our ability to understand the most fundamental problems in cosmology, in effect, to ask no questions (because all questions about the time before there was time are meaningless) and that we should just accept without more ado that time began with the big bang. In this way, Stephen Hawking simply assumes what has to be proved. In the same way, the theologians assert that God created the universe, and when asked who created God, merely answer that such questions are beyond the minds of mortals. On one thing we can agree, however; the whole thing does indeed “smack of divine intervention”. More than that, it necessarily implies it.
In his polemic against Dühring, Engels points out that it is impossible that motion should arise out of immobility, that something should arise out of nothing: “Without an act of Creation we can never get from nothing to something, even if the something were as small as a mathematical differential.” 69 Hawking's principal defence seems to be that the alternative theory to the big bang, put forward by Fred Hoyle, Thomas Gold and Hermann Bondi—the so-called Steady State theory—was shown to be false. From the standpoint of dialectical materialism, there was never anything to choose between these two theories. One was as bad as the other. Indeed the Steady State theory, which suggested that matter was being continuously created in space out of nothing, was, if possible, even more mystical than its rival. The very fact that such an idea could be taken seriously by scientists is itself a damning comment on the philosophical confusion that has bedevilled science for so long.
The ancients already understood that “out of nothing comes nothing”. This fact is expressed in one of the most fundamental laws of physics, the law of the conservation of energy. Hoyle's claim that only a very small amount was involved makes no difference. It is a bit like the naïve young lady who, in order to placate her irate father who found out she was going to have a baby, assured him that it was “only a little one”. Not even the tiniest particle of matter (or energy, which is the same) can ever be created or destroyed, and therefore the Steady State theory was doomed from the outset.
Penrose's theory of a “singularity” was originally nothing to do with the origin of the universe. It merely predicted that a star collapsing under its own gravity would be trapped in a region whose surface eventually shrinks to zero size. In 1970, however, he and Hawking produced a joint paper in which they claimed to prove that the big bang itself was such a “singularity”, provided only that “general relativity is correct and the universe contains as much matter as we observe.”
“There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein's theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity.”
General relativity has proved a very powerful tool, but every theory has its limits, and one has the impression that it is being pushed to the limit here. How long it will be before it is replaced by a broader and more comprehensive set of ideas it is impossible to say, but it is clear that this particular application of it has led to a blind alley. As far as the amount of matter in the universe is concerned, the total amount will never be known, because it has no limit. Typically, they are so wrapped up in mathematical equations, that they forget reality. In practice, the equations have replaced reality.
Having succeeded in convincing a lot of people, on the basis that “one cannot really argue with a mathematical theorem,” Hawking then proceeded to have second thoughts: “It is perhaps ironic,” he says, “that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe—as we shall see later, it can disappear once quantum effects are taken into account.” The arbitrary nature of the whole method is shown in Hawking's extraordinary change of mind. He now says there is no singularity in the big bang. Why? What has changed? There is no more actual evidence than before. These twists and turns all take place in the world of mathematical abstractions.
Hawking's theory of black holes represents an extension of the idea of singularity to particular parts of the universe. It is full of the most contradictory and mystical elements. Take the following passage, which describes the extraordinary scenario of an astronaut falling into a black hole:
“The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must be a singularity of infinite density and space-time curvature within a black hole. This is rather like the big bang at the beginning of time, only it would be an end of time for the collapsing body and the astronaut. At this singularity the laws of science and our ability to predict the future would break down. However, any observer who remained outside the black hole would not be affected by this failure of predictability, because neither light nor any other signal could reach him from the singularity. This remarkable fact led Roger Penrose to propose the cosmic censorship hypothesis, which might be paraphrased as 'God abhors a naked singularity'. In other words, the singularities produced by gravitational collapse occur only in places, like black holes, where they are decently hidden from outside view by an event horizon. Strictly, this is what is known as the weak cosmic censorship hypothesis: it protects observers who remain outside the black hole from the consequences of the breakdown of predictability that occurs at the singularity, but it does nothing at all for the poor unfortunate astronaut who falls into the hole.” 70
What sense can one make of this? Not content with the beginning (and end) of time for the universe as a whole, Penrose and Hawking now discover numerous parts of the universe where time has already ended! It has now been demonstrated that black holes exist (probably the remnants of massive collapsed stars), and contain tremendous concentrations of matter and gravity. But it seems extremely doubtful that this gravitational collapse could ever reach the point of a singularity, much less remain in this state forever. Long before this point was reached, such a tremendous concentration of matter and energy would result in a massive explosion.
The entire universe is proof that the process of change is never-ending, at all levels. Vast tracts of the universe may be expanding, while others are contracting. Long periods of apparent equilibrium are disrupted by violent explosions, like supernovas, which in turn provide the raw material for the formation of new galaxies, which goes on all the time. There is no disappearance or creation of matter, but only its continuous, restless change from one state to another. There can therefore be no question of the “end of time” inside a black hole, or anywhere else.
An empty abstraction
The whole mystical notion derives from the subjectivist interpretation of time, which makes it dependent on (“relative to”) an observer. But time is an objective phenomenon, which is independent of any observer. The need to introduce the unfortunate astronaut into the picture does not arise from any scientific necessity, but is the product of a definite philosophical point of view, smuggled in under the banner of “relativity theory”. You see, for time to be “real”, it needs an observer, who can then interpret it from his or her point of view. Presumably, if there is no observer, there is no time! In a most peculiar piece of reasoning, this observer is protected against the malign influence of the black hole, by an arbitrary hypothesis, a “weak cosmic censorship”, whatever that might mean. Inside the hole, however, there is no time at all. So outside, time exists, but a little distance away, time does not exit. At the boundary between the two states, we have the mysterious event horizon, the nature of which is shrouded in obscurity.
At least, it would appear that we must abandon all hope of ever understanding what goes on beyond the event horizon, since, to quote Hawking, it is “decently hidden from outside view.” Here we have the 20th century equivalent of the Kantian Thing-in-Itself. And, like the Thing-in-Itself, it turns out to be not so difficult to understand after all. What we have here is a mystical idealist view of time and space, fed into a mathematical model, and mistaken for something real.
Time and space are the most fundamental properties of matter. More correctly, they are the mode of existence of matter. Kant already pointed out that, if we leave aside all the physical properties of matter, we are left with time and space. But this is, in fact, an empty abstraction. Time and space can no more exist separately from the physical properties of matter than one can consume “fruit” in general, as opposed to apples and oranges, or make love to Womankind. The accusation has been levelled against Marx without the slightest justification that he conceived of History as taking place without the conscious participation of men and women, as a result of Economic Forces, or some nonsense of the sort. In fact, Marx states quite clearly that History can do nothing, and that men and women make their own history, although they do not do so entirely according to their own “free will”.
Hawking, Penrose and many others are guilty precisely of the mistake that was falsely attributed to Marx. Instead of the empty abstraction History, which is, in effect, personified, and endowed with a life and a will of its own, we have the equally empty abstraction Time, envisaged as an independent entity which is born and dies, and generally gets up to all kinds of tricks, along with its friend, Space, which arises and collapses and bends, a bit like a cosmic drunkard, and ends up swallowing hapless astronauts in black holes.
Now this kind of thing is fine in science fiction, but is not very useful as a means of understanding the universe. Clearly, there are immense practical difficulties in obtaining precise information about, say, neutron stars. In a sense, in relation to the universe, we find ourselves in a position roughly analogous to early humans in relation to natural phenomena. Lacking adequate information, we seek a rational explanation of difficult and obscure things. We are thrown back on our own resources—the mind and the imagination. Things seem mysterious when they are not understood. In order to understand, it is necessary to make hypotheses. Some of these will be found to be wrong. That in itself presents no problem. The whole history of science is full of examples where the pursuit of an incorrect hypothesis led to important discoveries.
However, we have a duty to attempt to ensure that hypotheses have a reasonably rational character. Here the study of philosophy becomes indispensable. Do we really have to go back to primitive myths and religion in order to make sense of the universe? Do we need to revive the discredited notions of idealism, which, in fact, are closely related to the former? Is it really necessary to re-invent the wheel? “One cannot argue with a mathematical theorem.” Maybe not. But it is certainly possible to argue with false philosophical premises, and an idealist interpretation of time, which leads Hawking to conclusions like the following:
“There are some solutions of the equations of general relativity in which it is possible for our astronaut to see a naked singularity: he may be able to avoid hitting the singularity and instead fall through a 'wormhole' and come out in another region of the universe. This would offer great possibilities for travel in space and time, but unfortunately it seems that these solutions may all be highly unstable; the least disturbance, such as the presence of an astronaut, may change them so that the astronaut could not see the singularity until he hit it and his time came to an end. In other words, the singularity would always lie in his future and never in his past. The strong version of the cosmic censorship hypothesis states that in a realistic solution, the singularities would always lie either entirely in the future (like the singularities of gravitational collapse) or entirely in the past (like the big bang). It is greatly to be hoped that some version of the censorship hypothesis holds because close to naked singularities it may be possible to travel into the past. While this would be fine for writers of science fiction, it would mean that no one's life would ever be safe: someone might go into the past and kill your father or mother before you were conceived!” 71
“Time-travel” belongs to the pages of science fiction, where it can be a source of harmless amusement. But we are convinced that nobody ought to be afraid that their existence may be put at risk by some inconsiderate time-traveller doing away with their granny. Frankly, one only has to pose the question to realise that it is a patent absurdity. Time moves in only one direction, from past to future, and cannot be reversed. Whatever our friend the astronaut might find at the bottom of a black hole, he will not find that time has been reversed, or “stands still” (except in the sense that, since he would instantly be torn to pieces by the force of gravity, time would cease for him, along with a lot of other things).
We have already commented on the tendency to confuse science with science fiction. It is also noticeable that much of science fiction itself is permeated with a semi-religious, mystical and idealist spirit. Long ago, Engels pointed out that scientists who despised philosophy frequently fall victim to all kinds of mysticism. He wrote an article on the subject entitled Natural Science and the Spirit World, from which the following extract is taken:
“This school prevails in England. Its father, the much lauded Francis Bacon, already advanced the demand that his new empirical, inductive method should be pursued to attain, above all, by its means: longer life, rejuvenation—to a certain extent, alteration of stature and features, transformation of one body into another, the production of new species, power over the air and the production of storms. He complains that such investigations have been abandoned, and in his natural history he gives definite recipes for making gold and performing various miracles. Similarly Isaac Newton in his old age greatly busied himself with expounding the Revelation of St. John. So it is not to be wondered at if in recent years English empiricism in the person of some of its representatives—and not the worst of them—should seem to have fallen a hopeless victim to the spirit-rapping and spirit-seeing imported from America.” 72
There is no doubt that Stephen Hawking and Roger Penrose are brilliant scientists and mathematicians. The problem is that, if you begin with a wrong premise, you will inevitably draw the wrong conclusions. Hawking clearly feels uncomfortable with the idea that religious conclusions can be drawn from his theories. He mentions that in 1981 he attended a conference on cosmology in the Vatican, organised by the Jesuits, and comments:
“The Catholic Church had made a bad mistake with Galileo when it tried to lay down the law on a question of science, declaring that the sun went round the earth. Now, centuries later, it had decided to invite a number of experts to advise it on cosmology. At the end of the conference the participants were granted an audience with the Pope. He told us that it was all right to study the evolution of the universe after the big bang, but we should not inquire into the big bang itself because that was the moment of Creation and therefore the work of God. I was glad then that he did not know the subject of the talk I had just given at the conference—the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation. I had no desire to share the fate of Galileo, with whom I feel a strong sense of identity, partly because of the coincidence of having been born exactly 300 years after his death!” 73
Clearly, Hawking wishes to draw a line between himself and the Creationists. But the attempt is not very successful. How can the universe be finite, and yet have no boundaries? In mathematics, it is possible to have an infinite series of numbers which starts with one. But in practice, the idea of infinity cannot begin with one, or any other number. Infinity is not a mathematical concept. It cannot be counted. This one-sided “infinity” is what Hegel calls bad infinity. Engels deals with this question in his polemic with Dühring:
“But what of the contradiction of 'the counted infinite numerical series'? We shall be in a position to examine it more closely a soon as Herr Dühring has performed the clever trick of counting it for us. When he has completed the task of counting from minus infinity to 0, let him come again. It is certainly obvious that, wherever he begins to count, he will leave behind him an infinite series and, with it, the task which he has to fulfil. Just let him invert his own infinite series 1+2+3+4…and try to count from the infinite end back to 1; it would obviously only be attempted by a man who has not the faintest understanding of what the problem is. Still more. When Herr Dühring asserts that the infinite series of lapsed time has been counted, he is thereby asserting that time has a beginning; for otherwise he would have been unable to start 'counting' at all. Once again, therefore, he smuggles into the argument, as a premise, what he has to prove. The idea of an infinite series which has been counted, in other words, the world-encompassing Dühringian Law of Determinate Number, is therefore a contradiction in adjecto, contains within itself a contradiction, and indeed an absurd contradiction.
“It is clear that an infinity which has an end but no beginning is neither more nor less infinite than one with a beginning but no end. The slightest dialectical insight should have told Herr Dühring that beginning and end necessarily belong together, like the North Pole and the South Pole, and that if the end is left out, the beginning just becomes the end—the one end which the series has; and vice versa. The whole deception would be impossible but for the mathematical usage of working with infinite series. Because in mathematics it is necessary to start from determinate, finite terms in order to reach the indeterminate, the infinite, all mathematical series, positive or negative, must start with 1, or they cannot be used for calculation. But the logical need of the mathematician is far from being a compulsory law for the real world.” 74
Stephen Hawking carried this relativistic speculation to an extreme with his work on black holes, which leads us right into the realms of science fiction. In an attempt to get round the awkward question of what happened before the big bang, the idea was advanced of “baby universes”, coming into existence all the time, and connected by so-called wormholes. As Lerner ironically comments: “It is a vision that seems to beg for some form of cosmic birth control.” 75 It really is astounding that sober scientists could take such grotesque ideas for good coin.
The idea of a “finite universe with no boundaries” is yet another mathematical abstraction, which does not correspond to the reality of an eternal and infinite, constantly changing universe. Once we adopt this standpoint, there is no need for mystical speculations about “wormholes”, singularities, superstrings, and all the rest of it. An infinite universe does not require us to look for a beginning or an end, only to trace the endless process of movement, change and development. This dialectical conception leaves no room for Heaven or Hell, God or the Devil, Creation or the Last Judgement. The same cannot be said for Hawking who, quite predictably, ends up attempting to “know the mind of God”.
The reactionaries rub their hands at this spectacle, and use the prevailing current of obscurantism in science for their own ends. William Rees-Mogg, big business consultant, and James D. Davidson write:
“We think it is extremely likely that the religious movement we see at work in many societies across the globe will be strengthened if we go through a very difficult economic period. Religion will be strengthened because the current thrust of science no longer undermines the religious perception of reality. Indeed, for the first time in centuries, it actually buttresses it.” 76
Thoughts in a vacuum
“Why, sometimes, I've believed as many as six
impossible things before breakfast.” (Lewis Carroll)
“With men this is impossible; but with God all things are possible.” (Matthew, 19:26)
“Nothing can be created out of nothing.” (Lucretius)
Just before finishing writing this book, we came across the latest contribution to cosmology of the big bang, which appeared in The New Scientist on the 25th of February 1995. In an article by Robert Matthews entitled Nothing like a Vacuum, we read the following: “It is all around you, yet you cannot feel it. It is the source of everything, yet is nothing.”
What is this amazing thing? A vacuum. What is a vacuum? The Latin word vacuus, from which it comes, means quite simply empty. The dictionary defines it as “space empty, or devoid of all matter or content; any space unoccupied or unfilled; a void, blank.” This was the case up till now. But not any longer. The humble vacuum, in Mr. Matthews’ words, has become “one of the hottest topics in contemporary physics.”
“It is proving to be a wonderland of magical effects: force fields that emerge from nowhere, particles popping in and out of existence and energetic jitterings with no apparent power source.”
Thanks to Heisenberg and Einstein (poor Einstein!), we have the “astonishing realisation that all around us 'virtual' subatomic particles are perpetually popping up out of nothing, and then disappearing again within about 10–23 seconds. 'Empty space' is thus not really empty at all, but a seething sea of activity that pervades the entire Universe.” This is true and false. It is true that the whole universe is pervaded by matter and energy, and that “empty space” is not really empty, but full of particles, radiation and force-fields. It is true that particles are constantly changing, and that some have a life so fleeting that they are called “virtual” particles. There is absolutely nothing “astonishing” about these ideas, which were known decades ago. But it is entirely untrue that they pop “out of nothing”. We have already dealt with this misconception above, and it is not necessary to repeat what was said.
Like an old record with a repeating groove, those who wish to introduce idealism into physics constantly harp on the idea that you can get something from nothing. This idea contradicts all the known laws of physics, including quantum physics. Yet we find here the incredible notion that energy can be obtained literally from nothing! This is like the attempts to discover perpetual motion, which were rightly ridiculed in the past.
Modern physics begins with the rejection of the old idea of the ether, an invisible universal medium, through which light waves were thought to travel. Einstein's theory of special relativity proved that light could travel through a vacuum, and did not require any special medium. Incredibly, after citing Einstein as an authority (as obligatory nowadays as crossing yourself before leaving church, and about as meaningful) Mr. Matthews proceeds to smuggle the ether back into physics:
“This does not mean that a universal fluid cannot exist, but it does mean that such a fluid must conform to the dictates of special relativity. The vacuum is not forced to be mere quantum fluctuations around an average state of true nothingness. It can be a permanent, non-zero source of energy in the Universe.”
Now what precisely is one supposed to make of this? So far we have been told about “astonishing” new developments in physics, “wonderlands” of particles and have been assured that vacuums possess enough energy to solve all our needs. But the actual information provided by the article does not seem to say anything new. It is very long on assertions, but very short on facts. Perhaps it was the author's intention to make up for this by obscurity of expression. What is meant by a “ permanent non-zero source of energy” is anyone's guess. And what is an “ average state of true nothingness”? If what is meant is a true vacuum, then it would have been preferable to use two clear words instead of four unclear ones. This kind of deliberate obscurity is generally used to cover up muddled thinking, especially in this area. Why not speak plainly? Unless, of course, what is involved is a “true nothingness”—of content.
The whole thrust of the article is to show that a vacuum derives unlimited quantities of energy from nowhere. The only “proof” for this is a couple of references to the special and general theories of relativity, which are regularly used as a peg upon which to hang any arbitrary hypothesis.
“Special relativity demands that the vacuum's properties must appear the same for all observers, whatever their speed. For this to be true it turns out that the pressure of the vacuum 'sea' must exactly cancel out its energy density. It is a condition that sounds harmless enough, but it has some astounding consequences. It means, for example, that a given region of vacuum energy retains the same energy density, no matter how much the region expands. This is odd, to say the least. Compare it with the behaviour of an ordinary gas, whose energy density decreases as its volume increases. It is as if the vacuum can draw on a constant reservoir of energy.”
In the first place, we note that what was only a hypothetical “universal fluid” a couple of sentences ago has now become transformed into an actual vacuum “sea”, though where all the “water” came from, nobody is quite sure. This is odd to say the least. But leave it there. Let us, like the author, assume what was to be proved, and accept the existence of this vast ocean of nothingness. It turns out that this “nothing” is now not only something, but a very substantial “something”. As if by magic, it is filled with energy from a “constant reservoir”. This is the cosmological equivalent of the cornucopia, the “horn of plenty” of Greek and Irish mythology, a mysterious drinking horn or cauldron that, however much one drank from it, was never empty. This was a gift from the gods. Now Mr. Matthews wishes to present us with something that makes this look like child's play.
If energy enters a vacuum, it must come from somewhere outside the vacuum. This is plain enough, since a vacuum cannot exist in isolation from matter and energy. The idea of empty space without matter is as nonsensical as the idea of matter without space. There is no such thing as a perfect vacuum on earth. The nearest thing to a perfect vacuum is space. But in point of fact, space is not empty, either. Decades ago, Hannes Alfvén pointed out that space was alive with networks of electrical currents and magnetic fields filled with plasma filaments. This is not the results of speculation or appeals to relativity theory, but is borne out by observation, including those of the Voyager and Pioneer spacecrafts that detected these currents and filaments around Jupiter, Saturn and Uranus.
So there is, indeed, plenty of energy in space. But not the kind of energy Mr. Matthews is talking about. Not a bit of it. Having established his “vacuum sea” he means to get his energy directly from the vacuum. No matter required! This is much better than the conjurer who pulls a rabbit out of a hat. After all, we all know the rabbit actually comes from somewhere. This energy comes from nowhere at all. It comes from a vacuum, by courtesy of the general theory of relativity: “One of the key features of Einstein's general relativity theory is that mass is not the only source of gravitation. In particular, pressure, both positive and negative can also give rise to gravitational effects.”
By this point, the reader is thoroughly mystified. Now, however, all becomes clear (almost). “This feature of the vacuum,” we are now told, “lies at the heart of perhaps the most important new concept in cosmology of the past decade: cosmic inflation. Developed principally by Alan Guth at MIT and Andrei Linde, now at Stanford, the idea of cosmic inflation arises from the assumption that the very early Universe was packed with unstable vacuum energy whose 'antigravitational' effect expanded the Universe by a factor of perhaps 1050 in just 10–32 seconds. The vacuum energy died away, leaving random fluctuations whose energy turned into heat. Because energy and matter are interchangeable, the result was the matter creation we now call the big bang.”
So that's it! The whole arbitrary construction is meant to back up the inflationary theory of the big bang. As always, they move the goalposts continually, in order to prop up their hypothesis at all costs. It is like the supporters of the old Aristotle-Ptolemaic theory of the crystal spheres, which they continually revised, making it ever more complicated, in order to fit the facts. As we have seen, the theory has been having a bad time lately, what with the missing “cold dark matter” and the unholy mess about the Hubble constant. Badly in need of a little support, its supporters have obviously looked round for some explanation to one of the central problems of the theory—where did all the energy come from to cause the inflationary big bang. “The biggest free lunch of all time,” Alan Guth called it. Now they want to pass the bill to somebody, or something, and come up with—a vacuum. We doubt whether this particular bill will ever be paid. And, in the real world, people who don't pay their bills are usually unceremoniously shown the door, even if they offer to produce the general theory of relativity in lieu of cash.
“From nothing, through nothing, to nothing,” said Hegel. That is a fitting epitaph for the theory of inflation. There is actually only one way of getting something from nothing—by an act of Creation. And that is only possible through the intervention of a Creator. Try as they will, the supporters of the big bang will find that their footsteps will always lead them in this direction. Some will go quite happily, others protesting that they are not religious “in the conventional sense”. But the movement back to mysticism is the inevitable consequence of this modern creation myth. Fortunately, an increasing number of people are becoming dissatisfied with this state of affairs. Sooner or later, a breakthrough will occur at the level of observation that will enable a new theory to emerge, allowing the big bang to be laid decently to rest. The sooner the better.
The origins of the solar system
Space is not really empty. A perfect vacuum does not exist in nature. Space is filled by a thin gas—”interstellar gas” first detected in 1904 by Hartmann. The concentrations of gas and dust become much greater and denser in the neighbourhood of galaxies, which are surrounded by “fog”, mostly composed of atoms of hydrogen, ionised by radiation from the stars. Even this matter is not inert and lifeless, but is broken up into electrically-charged subatomic particles, subject to all kinds of movement, processes and change. These atoms occasionally collide and can change their energy state. Though an individual atom might only collide once every 11 million years, given the vast numbers involved, it is enough to give rise to a continuous and detectable emission, the “song of hydrogen”, first detected in 1951.
Almost all of this is hydrogen, but there is also deuterium, a more complex form of hydrogen, oxygen and helium. It might seem impossible that combination should occur, given the extremely sparse distribution of these elements in space. But occur it does, and to a remarkable degree of complexity. The water molecule (H2O), was found in space, as was that of ammonia (NH3), followed by formaldehyde (H2CO), and even more complex molecules, giving rise to a new science—astrochemistry. Finally, it has been proved that the basic molecules of life itself— amino acids—exist in space.
Kant (in 1755) and Laplace (in 1796) first advanced the nebular hypothesis of the formation of the solar system. According to this, the sun and planets were formed out of the condensation of an immense cloud of matter. This seemed to fit the facts, and, by the time Engels wrote The Dialectics of Nature, it was generally accepted. In 1900, however, Thomas C. Chamberlain and Forest Ray Moulton put forward an alternative theory—the planetesimal hypothesis. This was further developed by British scientists Sir James Hopwood Jeans and Sir Harold Jeffreys, who advanced the tidal hypothesis in 1918. This involved the idea that the solar system originated as a result of a collision of two stars. The problem with this theory is that, if it were true, planetary systems would be extremely rare phenomena. The vast distances separating stars mean that such collisions are 10,000 times less common than supernovae—themselves far from common occurrences. Once again, we see that, by attempting to solve a problem by resorting to an accidental external source like a stray star, we create more problems than we solve.
Eventually, the theory that was supposed to have displaced the Kant-Laplace model was shown to be mathematically unsound. Other attempts, like the “three-star collision” (Littleton) and Hoyle's supernova theory, were also ruled out in 1939, when it was proved that the material drawn from the sun in such a way would be too hot to condense into planets. It would merely expand into a thin gas. Thus, the catastrophe-planetesimal theory was overthrown. The nebular hypothesis has been reinstated, but on a higher level than before. It is not merely a repetition of the ideas of Kant and Laplace. For instance, it is now understood that the clouds of dust and gas envisaged in the model would have to be much bigger than they thought. On such huge scales, the cloud would experience turbulence, creating vast eddies, which would then condense into separate systems. This perfectly dialectical model was developed in 1944 by the German astronomer Carl F. von Weizsäcker, and perfected by the Swedish astrophysicist, Hannes Alfvén.
Weizsäcker calculated that there would be sufficient matter in the largest eddies to create galaxies in the process of a turbulent contraction, giving rise to sub-eddies. Each of these could produce solar systems and planets. Hannes Alfvén made a special study of the magnetic field of the sun. In the early stages, the sun was spinning at a great speed, but was eventually slowed down by its magnetic field. This passed on angular momentum to the planets. The new version of the Kant-Laplace theory, as developed by Alfvén and Weizsäcker, is now generally accepted as the most likely version of the origins of the solar system.
The birth and death of stars constitute a further example of the dialectical workings of nature. Before it runs out of nuclear fuel, the star experiences a prolonged period of peaceful evolution lasting millions of years. But on reaching the critical point, it experiences a violent end, collapsing under its own weight in less than a second. In the process, it gives off a colossal amount of energy in the form of light, emitting more in a few months than the sun emits in a billion years. Yet this light represents only a small fraction of the total energy of a supernova. The kinetic energy of the explosion is ten times greater. Perhaps ten times more than the latter is carried away in the form of neutrinos, emitted in a split-second flash. Most of the star's mass is scattered into space. Such a supernova explosion in the vicinity of the Milky Way hurled forth its mass, reduced to nuclear ashes, containing a large variety of elements. The earth and all that is in it, ourselves included, is entirely composed of this recycled stardust, the iron in our blood being a typical sample of recycled cosmic debris.
These cosmic revolutions, like the earthly variety, are rare events. In our own galaxy, only three supernovas have been recorded over the past 1000 years. The brightest of these, noted by Chinese observers in 1054, produced the Crab Nebula. Moreover, the classification of stars has led to the conclusion that there is no new kind of matter in the universe. The same matter exists everywhere. The main features of the spectra of all stars can be accounted for in terms of substances that exist on earth. The development of infrared astronomy provided the means of exploring the interior of dark interstellar clouds, which are probably where most new stars are formed. Radio astronomy has begun to reveal the composition of these clouds—mainly hydrogen and dust, but with an admixture of some surprisingly complex molecules, many of them organic.
And so the birth of our solar system some 4.6 billion years ago developed out of a cloud of shattered debris of a now extinct star. The present sun coalesced at the centre of the revolving flat cloud, whereas the planets developed at different points encircling the sun. It is believed that the outer planets—Jupiter, Saturn, Uranus and Pluto—are a sample of the original cloud: hydrogen, helium, methane, ammonia and water. The smaller inner planets—Mercury, Venus, Earth and Mars—are richer in heavier elements and poorer in gases like helium and neon, which were able to escape their weaker gravities.
Aristotle thought that everything on earth was perishable, but that the heavens themselves were changeless and immortal. Now we know differently. As we gaze with wonder at the immensity of the night sky, we know that every one of these heavenly bodies that light up the darkness will one day be extinguished. Not only mortal men and women, but the stars themselves that bear the names of Gods experience the agony and the ecstasy of change, birth and death. And, in some strange way, this knowledge brings us closer to the great universe of nature, from which we came and to which we must one day return. Our sun has at present enough hydrogen to last for billions of years in its present state. Eventually, however, it will increase its temperature to the point where life on earth will become impossible. All individual beings must perish, but the wonderful diversity of the material universe in all its myriad manifestations is eternal and indestructible. Life arises, passes away, and arises again and again. Thus it has been. Thus it will ever be.
54. Quoted by Lerner, E., op. cit., p. 214.↩
55. Lerner, E., op. cit., p. 152↩
56. Lerner, E., op. cit., p. 158.↩
57. Lerner, E., op. cit., pp. 39-40.↩
58. The Rubber Universe, pp. 11 and 14, our emphasis (Channel 4 publication, 1995).↩
59. Quoted in Lerner, E., op. cit., pp. 164-5.↩
60. Davies, P. op. cit., pp. 123, 124-5 and 126.↩
61. Lerner, E., op. cit., p. 14↩
62. Lerner, E., op. cit., pp. 52, 196, 209 and 217-8.↩
63. Lerner, E., op. cit., pp. 153-4, 221 and 222.↩
64. Lerner, E., op. cit., p. 149.↩
65. Ferris, T. op. cit., p. 204.↩
66. Hawking, S. A Brief History of Time, From the Big Bang to Black Holes, p. 34.↩
67. Hawking, S. op. cit., pp. 46-7 and 33.↩
68. Engels, F. Anti-Dühring, pp. 64-5.↩
69. Engels, F. Anti-Dühring, p. 68.↩
70. Hawking, S. op. cit., pp. 50 and 88-9.↩
71. Hawking, S. op. cit., p. 89.↩
72. Engels, F. The Dialectics of Nature, pp. 68-9.↩
73. Hawking, S. op. cit., p. 116.↩
74. Engels, F. Anti-Dühring, pp. 62-3.↩
75. Lerner, E., op. cit., p. 161.↩
76. Rees-Mogg, W. and Davidson, J. The Great Reckoning: How the World Will Change in the Depression of the 1990s, p. 447.↩