“The universe,” the ethnologist was told by his native informant, “rests on the back of a giant turtle.” And what, the anthropologist wanted to know, does the giant turtle stand on? “Another giant turtle”, his informant asserted. And that turtle? “Ah, I know what you’re getting at, and it’s very important”, said the informant, “but it’s no use: it’s turtles all the way down.”
The “Big Bang” model of the early universe has by now come to be referred to as the “standard model” for cosmologists. But this cannot be taken to mean that all major objections to this model have been overcome. A number of serious difficulties have yet to be dealt with, if the phrase “standard model” is to mean anything more than “the best we have just now, but still a long way from being acceptable.”
These objections include problems of observation, of theory, and of philosophy. One example of each type:
1. The 3° K. background radiation, which is interpreted as evidence supportive of the Big Bang theory, has been found to be homogeneous, whereas the large-scale distribution of matter in the universe has been found to be heterogeneous. If at the time of the Big Bang matter was unevenly distributed then the background radiation should reflect this. If it was not unevenly distributed, then how did it come to be so?
2. Theory predicts that when the primordial universe cooled sufficiently for sub-atomic particles to form, exactly as many anti-particles should have emerged as particles. In our own part of the universe there is clearly a preponderance—to say the least—of matter to anti-matter. No counterbalancing preponderance of anti-matter has been detected elsewhere (and even if it were to be detected, further serious problems regarding distribution would remain). Although the preponderance of matter is theoretically minute (the vast bulk of matter and antimatter having combined, it seems, to form various higher-level particles), this is no reply: the question must be addressed.
3. Physicists, in exploring smaller-than-visible phenomena, have never been content to say “This is small enough, we shall ignore anything smaller.” Instead, they have delved from the molecule to the atom, from the atom to the electron, proton, and neutron, and thence to baryons and other short-lived minisculities, always seeking the “bottom level”, if such a level exists. At present the barrier is the still-theoretical quark. So too, in exploring the past, physicists have never been content to say, “This is sufficiently long ago, we shall ignore anything earlier.” The Big Bang view, as it now exists, fails to address itself to the question of how the universe got to be so compact, and it fails to address itself to the question of whether the question “before” in this context is even meaningful. Although these are philosophical questions they cannot be ignored by the scientist, for in the end the scientist’s questions and methodology are but a means to the end of resolving these questions.
The now-discarded Steady State theory of Hoyle, Bondi, and Gold achieved its popularity precisely because it was philosophically satisfying, and many physicists were disappointed that the evidence did not support it. Instead, it seemed, they were saddled with a theory, the Big Bang, which raised questions more serious than those it answered. However, it was quickly realized that there were two sub-categories of the Big Bang: the open universe, in which the mass of the universe is insufficient for gravitational attraction to eventually reverse the expansion produced by the Big Bang; and the closed universe, in which mass is sufficient.”1 Each view has various possible sub-routines, among which the most discussed is that if the universe is to eventually contract, that this might result in yet another massive explosion, another Big Bang, and thus an oscillating universe.
The attractiveness of such a model is probably due to its offering of the same philosophical satisfaction as the Steady State view, for it manages to avoid, as the “open universe” view does not, that horrible question, “What was the universe like before the Big Bang, Daddy?” For an oscillating universe (whatever the mechanism which drives it, and whatever its path of development) the question “What was it like before this?” is always answerable with “It’s always been like this”. And although ultimately that answer is not really more satisfying than the reply “we haven’t the foggiest…”, yet the “always” of “It’s always been like this” is no less powerful than the “ultimately” of “ultimately it is no more satisfying than…”, and “ultimately” is never quite achieved.
Yet the oscillating-universe view, however satisfactory it may be philosophically, has so far failed to achieve compatibility with both evidence and theory. The evidence to date suggests that the mass of the universe is only about 1/6 that is necessary to have a closed universe (whether or not it is oscillating), and although estimates of the mass of the universe have been increasing2 in both senses, it seems, not only do recent estimates propose more matter in the universe than earlier estimates, but also, recently there have been an increasing number of such estimates, there is still a long way to go (albeit, less than a single power of ten).
And, even more importantly, this question has not been answered: What force might there be which is so powerful as to be able to counter the momentum that would be developed over billions of years of accelerating contraction, to make the entire universe suddenly and dramatically stop contracting and begin expanding? If such a force has to be hypothesized then the result is not a theory but, precisely, a hypothesis.
This paper will propose, nevertheless, that a model of an oscillating universe can be constructed which will be entirely consonant with the evidence which currently supports the Big Bang theory; which addresses itself to the question of the mass of the universe (though, admittedly, not in a definitive manner); which describes a mechanism, a force, which could in fact cause a rapidly contracting universe, when sufficiently contracted, to reverse its momentum and begin expanding (a force already well known and not in the least theoretical); which accounts for the uneven large-scale distribution of matter in the universe; which considers the imbalance of matter over anti-matter; which proposes a fresh understanding of presently-puzzling phenomena such as quasars; and which suggests a number of experiments and surveys by which what is herein proposed could be tested. If these experiments were to be carried out successfully the evidence would be strong, albeit indirect, that there is in fact sufficient matter in the universe, most of it in black holes, to ensure that the universe is oscillating. In so doing it will also offer a view of our universe which will be found appealing to those who regret the collapse of the Steady State view.
In order to develop this view a number of disparate elements must first be introduced and what is known about them reviewed, as briefly as possible. Among these elements are the four universal forces, black holes, and particle pressure.
THE FOUR FORCES
The existence of four universal forces is recognized: strong nuclear, electromagnetic, weak nuclear, and gravitational. These forces are called ‘universal’, but in fact they each have their own spheres of dominance, outside of which their effect is virtually nil. The strong nuclear force is the most powerful, but its range is limited to the diameter of an atomic nucleus (approximately l0-13 cm.) or less—indeed, so limited is its range that large nucleii become increasingly unstable due to the growing influence of the next most powerful force, the electromagnetic. The electromagnetic force, though only about a thousandth the strength of the strong nuclear force, has a vastly greater range, as everyone knows who has ever handled a magnet or touched a live wire: its range can sometimes be measured on a human scale. The weak nuclear force is but a hundred million millionth the strength of the strong nuclear force (10-14). Its influence is on an atomic scale. The particles that respond to it (called leptons) are for the most part low-mass non-nuclear particles, whereas the particles that respond to the strong nuclear force (called hadrons) are the more massive particles ascribed to the nucleus of the atom. (Just as only electrically-charged particles respond to the electro-magnetic force, so too only certain particles respond to the strong and weak nuclear forces.) The weakest of the four universal forces is gravity, a mere million million million million million million millionth the strength of the strong nuclear force (10-42), but of vastly greater range: its influence is on large-scale matter, and it is irrelevant to small-scale systems. Even in large-scale systems, certain sub-atomic components are not affected by it. These four forces, then, can be called universal only insofar as they can be said to exert their influence everywhere in the universe within their range.
A FIFTH FORCE?
But are these four the only forces? Are there any compelling logical, philosophical, theoretical, or experimental reasons for necessarily limiting our roll-call of basic forces to four? It would seem not.
For instance, as ever-more tenuous sub-atomic particles are theoretically predicted or experimentally verified, and as explanatory theory becomes increasingly complex, it becomes reasonable to ask whether there might not exist a force which operates on a scale minute to that of the strong nuclear, and which would govern the interaction of at least some sub-atomic particles in such a way as to make the ever-increasing complexity of the sub-atomic world (as we conceive it) more comprehensible. Beyond a certain level of complexity it becomes increasingly difficult not to believe that there exists a simpler and more fundamental level out of which such complexity emerges.
So far, it seems, the existing experimental evidence has not been viewed in a way which would make a compelling argument for the existence of such a force, to parallel the philosophical argument sketched above; but there would seem to be no a priori reasons which would rule out the existence of such a force. True, quantum-level theory proposes the notion of absolute smallness; but physical theories, like universal forces, have their spheres of dominance. Just as earlier theories, though adequate for their scale, were found to be increasingly unsatisfactory descriptive tools as technological advances made it possible to examine (or create) situations ever-farther removed from everyday experience so too quantum theory seems to work as an explanatory tool, however imperfectly, only on the quantum level: any level smaller than the quantum level would not necessarily be constrained by the limitations and regularities, such as they are, which exist on the quantum level. Such a smaller-scale view would have its own limitations and regularities. Therefore the existence of a force with range of some magnitudes smaller than that of the strong nuclear force would be credible, provided that it could be described in such a way as to endow it with sufficient explanatory and predictive power.
There is the philosophical question of whether there will ‘always’ be an ever-smaller scale which underlies whatever scale we consider: just as the molecular level is supported by atoms, and atoms by a nucleus and orbiting electrons, and they in turn by (the still-theoretical) quarks—is there an infinite hierarchy of smallness to the universe, or is there, actually an end to it all? Do the turtles ever come to an end?
However, it is not the purpose of this paper to actually propose such a sub-nuclear force: these opening remarks are intended only to set forth some background.
Black holes, having caught the popular imagination, have been credited with various properties, most of which are merely fanciful. There is at present not even any direct observational evidence for the existence of black holes—for in their very nature black holes are not directly observable (although certain theoretically-consequential phenomena would be observable, if black holes do exist, and if we could get close enough to one to be able to observe those consequential phenomena). However, there are other sorts of evidence, including the notions of consistency and consequence, and if we are willing to accept that what we already know is consistent and has consequences, then there is a compelling reason to accept that black holes either exist or, at minimum, could exist.
But what exactly is a black hole? In brief, it is a mass which is both so great and so compact that the gravitational force totally overwhelms all three of the other forces. Against such dominance the forces which give structure on the molecular, atomic, and sub-atomic levels are ineffective: they no longer have a sphere of influence. One can then no longer speak of particles, for divorced from the forces which govern their behaviour, the word no longer refers to what we mean by “particle”. From a point of view outside the black hole what can be spoken of are two things: an event horizon and a singularity. We are not entitled, from our perspective, to speculate on what happens “on the inside”: from outside a black hole such a question is, strictly, meaningless.
What is an event horizon? The concept is related to the simpler one of escape velocity. We know that if a rocket achieves a speed of approximately 11 kilometers per second this will be sufficient for it to escape Earth’s gravity from the planet’s surface without the application of any additional force. From more massive planets escape velocity would be correspondingly greater: from the surface of Jupiter a velocity of 58 kilometers per second would be needed. From stellar masses escape velocity will be comparatively enormous: 618 kilometers per second from our own sun’s surface. We also know that escape velocity is a function not only of the mass of a body, but also of its volume. Seven miles per second is the escape velocity from the surface of the earth; but as we know, the escape velocity for a vehicle already in orbit around the earth is considerably less, since it is farther from the center of gravity. Thus, escape velocity from Jupiter is not as great as it would be if Jupiter were as dense as the Earth, i.e. if Jupiter’s mass were to remain the same but if that mass were to be more compact. And, on the other hand, if we were to find a planet with a mass identical to that of the Earth, but which was made entirely of iron, which is very dense, then from the surface of that planet escape velocity would be very much greater than seven miles per hour, since we would be taking off from a point much nearer to the center of gravity: the planet, though as massive as the Earth, would be smaller. A black hole is an object both massive enough and small enough so that escape velocity is greater than the speed of light. Since neither matter nor energy can go faster than the speed of light neither matter nor energy can escape from a black hole. The event horizon is the sphere which could be constructed around a black hole from which distance escape velocity exactly equals the speed of light. Outside of that event horizon light could escape;3 from within that event horizon no light can escape, nor can anything else: we are cut off from direct perception of anything happening within the event horizon, and from within the event horizon there could be no direct perception of anything happening beyond it. (It might seem at first that this latter statement did not apply, since light can get in from the outside: it might seem at first that we could send messages to the interior of a black hole—if, that is, we could but find one—but never receive an acknowledgement of our message; but there are compelling reasons, which we need not enter upon here, for rejecting such a view: although matter and energy can be [and necessarily are] entering into the black hole, they cannot do so in an organized form but can only do so already destroyed as far as their potential for containing information about ‘the outside world’.)
And what is a singularity? It is that which is within the event horizon. It cannot be called ‘matter’, as already pointed out. And as we cannot say that there is matter, so too we cannot ascribe to the singularity those qualities which differentiate what is matter from what is not; and this will include the quality of volume. We cannot say that this singularity takes up any space (although we also cannot say that it does not). The singularity certainly has mass, and it certainly has energy. We say it has mass because gravitational attraction is inseparable (as far as we know) from mass, and black holes, by having an escape velocity greater than the speed of light, exhibit gravitational attraction. Without gravity there could be no event horizon and no black hole. And since mass and energy are inseparable there must also be energy. Beyond this there is really very little we can say about this singularity.
Very little, but not nothing. For just as the existence (or at least the possibility of the existence) of black holes is necessarily consequential upon what we know of the observable universe, so too there are certain points consequential to the existence of gravity, mass and energy.
The first consequence is this: black holes grow. They can only get bigger, more massive, and can never get smaller.4 Whatever percentage of our universe is presently contained within black holes (and some findings have suggested that the figure may be well over 50%), we know that next year that figure will be more, and a billion years from now it will be substantially more.
Not only will every black hole become more massive, with an event horizon of increasing radius; but also, quite simply, there will be more black holes. Furthermore, their distribution throughout galactic volume will not be random and homogeneous for the simple reason that the distribution of stars is not random and homogeneous. There are more stars near the central portion of galaxies.
There is reason to believe that stars have a faster gestation period near the center of galactic bodies than in the less—dense nether regions, and that therefore there would have been more generations of stars near galactic centers. This would be particularly true of large stars, which are the types from which black holes result, for they have a shorter lifetime as normal healthy stars on the main line of development: burning ‘hotter’, they more quickly exhaust their nuclear fuel, consequent upon which the outward pressure of the nuclear fires can no longer counterbalance the inward pressure of gravitational attraction. Such stars, whether they explode or collapse, generate massive amounts of interstellar matter. This matter then forms a new generation of stars. Out here, in the backwaters of the galaxy, progress—if that’s the word for it—is slower. So we can expect that there would be more black holes near the centers of galaxies than on the fringes, and observations within our own galaxy suggest that this is indeed the case.
While reports are still sketchy, and more work is needed before confident statements can be issued, it would seem that there is a black hole in the, center of the Milky Way with a mass of approximately 5 million solar masses. Studies of the galaxy called Centaurus A suggest that it may contain a black hole of more than double this, mass, while galaxy M87 may have a black hole of more than 5 billion solar masses. A black hole of this size would have an event horizon great enough so that a solar mass could be swallowed without tidal forces destroying the star before it crossed the event horizon. This means that it would leave no luminous trace of its disappearance, no bursts of X-rays or cries of anguish. Not even a hiccup.
But how is it possible for a single black hole to attain to such enormous mass? Clearly not from the collapse of a single star, for no single star could be millions of times more massive than our sun, nor by gradually absorbing, like an amoeba, millions of its brighter neighbours. Not that it couldn’t do this, but simply, unless the universe is very much older than the most generous estimates there hasn’t been time; to swallow 5 million stars in 20 billion years requires swallowing one star every 4000 years—even the greediest black hole could not consume stars at such a pace, for stars are too far away from one another. The only possibility is from the coalescence of many less massive black holes. If indeed black holes are a common feature of the center of galaxies, then it is only to be expected that from time to time they will come within gravitational range of one another. And when this happens the result will be quite different from the approach of two stellar masses. In the latter case an actual collision would be extremely rare: near misses would be far more common; and in the case of a near miss there would be merely the loss of some mass by one or both stars. They would survive the encounter only slightly the worse for wear. But when black holes come within gravitational range of each other the consequences would be different, for neither black hole could lose any of its matter. As far as I know no theoretical study has been made to define parameters, limits, and likely pathways in such a collision; but even lacking such a study we can recognize that the result would be neither an exchange or loss of mass nor destructive crash. The only possibility is the merger of the two black holes into a single black hole with the combined mass of both.
And as black holes grow their gravitational reach will also grow, increasing their mass as well as the radius of their event horizon for as long as there is anything for them to gobble.
The minimum mass necessary for a star to collapse into a black hole has been calculated (it is approximately 1.5 solar masses). Might there not be a corresponding value for galaxies? In the case of galaxies there would be two functions: not only mass but also density. But given a galaxy of sufficient mass, wherein a sufficient part of that mass is near galactic center, black holes will combine until the galaxy, or the greater part of it, is contained within a single massive black hole.
Eventually, then, black holes will assume galactic-size masses. (Indeed, the 5-billion-solar-mass black hole of galaxy M87 begins to approach this: it is [if it actually exists] about 5% the mass of the Milky Way. Its radius, however, would be no more than about sixteen million kilometers, less than a light-minute.) There would be a halo of stellar and galactic matter—much of it dark, as in other galaxies—surrounding a black central core. There is so far no incontrovertible evidence for the existence of such black galaxies, and to that extent they remain hypothetical, as do black holes of any size. But this is not to say that there is no evidence at all. And even if we must regard such galactic-sized black holes as still hypothetical, it is a hypothesis which, being the inevitable consequence of there being black holes at all, would be difficult to dismiss.
How could such a galaxy be detected? For, a mature black galaxy would not give off enough radiation to suggest its actual mass; nor could it have an apparent disk sufficiently great to block radiation from behind it. However, such a dark galaxy would distort radiation passing near to it, and it may be possible to calculate the effects of such a distortion and to conduct a search for such distorted radiation. And, in addition, large amounts of radiation with unique characteristics will be generated at the event horizon. This is the result of oblique strikes which result in the partial engulfment of the matter or energy striking the event horizon and the generation of X-ray and other radiation which escapes being engulfed. Some of this materia will escape entirely, and be detectable, and some of it will, according to existing models, adhere to the event horizon (which therefore has also been called an ‘accretion disk’), forming an extraordinarily thin and dense bubble.
But if black holes begin with stellar masses, grow to multi-stellar masses, and eventually attain galactic-mass proportions, what is to prevent them (given sufficient time: a commodity with which our universe seems to be excellently well endowed) from growing still larger? Could there be—are there already—black holes which are as massive as many galaxies, yet which are but a few light-days in radius?
Some studies have been made of galaxies which are apparently interacting. Collide—the usual term—is certainly a dramatic description of such a meeting, if not the most accurate: apparently in such a ‘collision’ most stars escape totally unscathed, so dispersed are stars within the volume of any galaxy. However, since dust particles would collide and there would be a transfer of energy from velocity to heat the galaxies themselves, as coherent units, might be radically transformed. Inasmuch as galactic orbits, velocities, and other features could become greatly perturbed, we could perhaps in this sense speak of a collision.
When only one of the galaxies is white (or predominantly white: it may be that all or nearly all galaxies contain many black holes), and the other black we would expect that the event would not be much more dramatic than the meeting of two white galaxies. The event horizon of the black hole would be minute by galactic standards, and though its gravitational influence would be vast enough to fatally attract a large number of stars, gradually increasing the mass of the black-hole galaxy at the expense of the white galaxy, yet, compared to the mass already contained within the black galaxy the increase would probably not be significant, and we could still expect that a large, part of the white galaxy would survive the collision, even if somewhat perturbed.
But when black galaxies come within range of each other the word ‘collide’ would be more accurately used, for the result could be no different, except for scale, than the collision of smaller black holes. There is no way in which two black galaxies could ‘pass through’ each other. At a certain distance their mutual attraction would be such that they must indeed collide and merge into a single black hole with the combined mass of the two. And so as more and more of the universe goes black, more and more of the universe comes to be contained in fewer and fewer black holes, until, eventually, within a black hole the force of gravity approaches the limit wherein it will be counterbalanced by a force which holds sway in a more massive arena: the fifth force.
Particle pressure is a well-known phenomenon. One manifestation is the “solar wind”. A toy sometimes sold at the lobby shops of science museums consists of a light-weight four-leafed sail (each leaf at right angles to its two neighbours), one side of each leaf black and the other side silvered, the whole finely balanced on a spindle with minimum friction. When held up to a strong light source the sail will spin round on the spindle, the black side of each leaf being the tail. The explanation offered is that light, absorbed more readily by the darker surface, imparts energy which is dissipated in movement. It could as well be said that the pressure of the light—of the photons, that is—pushes the leafs much as wind propels a sailboat. Such a force, then, is commonly recognized. Under present-day conditions it is a marginal force, one which does not usually need to be taken into account.
So too, we have noted, the four recognized universal forces need to be considered only within their own sphere of influence: gravity is irrelevant to sub-atomic reactions, and the strong nuclear force is irrelevant to the motion of the planets round the sun. Could it be that particle pressure—by which is meant, specifically, the pressure exerted by high-velocity sub-atomic particles—has a sphere of influence in which it is dominant?
Though not so identified, such a sphere has been described by no less noted a scientist than Stephen Weinberg, in his well—received book, The First Three Minutes: it is a realm of such high mass and incredible density that, unlike the universe today, it is opaque to energy. Energy, in the form of sub-atomic particles, is so densely packed that any particle can barely move before colliding with one of its neighbours. In such a state matter cannot exist, for the particles have no opportunity to combine into stable configurations. The particles, or many of them, have mass, and so gravity is a feature of such a system; however gravity is not a (or, at least, the) significant feature: the significant feature is particle pressure, and it is (as are two like-charged electromagnetic particles) a repulsive force.
The evolution of such a massive and dense body can be calculated in statistical terms based entirely upon its present state: what it emerged from is irrelevant to what it will become. Although from static point of view such a system is, at any given moment, stable in terms of that moment, yet from a dynamic point of view it is, of course, highly unstable and could survive for only a short time. Within a few minutes particle pressure will have exerted such enormous repulsive force upon the body that it will be expanding at an enormous velocity and will then have emerged from energy-opacity to a state of energy-transparency. Particle pressure will no longer be a force—one of the five universal forces—greater than gravity. However, by that time such momentum will have been imparted to the body that it will take gravity billions of years to counteract the momentum and begin a contractive force if, indeed, it ever succeeds: whether it can do so will depend upon the now-expanding body having a sufficient mass—and, therefore, a sufficient gravitational strength—to reverse the momentum.
The necessary mass has been calculated to be, we will recall, some five or six times more than the presently-known mass of the universe. However, the mass necessary to begin the expansive process seems to have been not yet calculated. Clearly, though, the body could not have entered upon a state in which particle pressure could overwhelm gravitational attraction unless it had a mass sufficiently great (and sufficiently dense) to achieve particle opacity. Such a calculation would seem to be of great importance: a comparison with the contracting-universe minimum mass (five times the known mass) will determine the range of scenarios possible within the Big Bang context. It will also inform us how massive two super-galactic black holes must be in order that when they collide their merger will create a particle-opaque situation which will drive the singularity into an expansive phase.
THE ORIGIN OF THE PRIMORDIAL EGG
We now see how a situation could evolve that would produce a primordial egg (for such is the name that has been applied to the “thing” which “exploded” to form our universe). However, we now see that “explosion” is an entirely inappropriate term, implying, as it does, a force originating at one point and then pushing everything around it outwards. Rather, what happened was—it is now suggested—that when two gigantic black holes collided the resulting singularity had a mass and density so great that gravity, which has previously been totally dominant, was no longer so. The entire mass, then under the influence of particle pressure, began to expand, and, in fact, is still doing so some fifteen or twenty billion years on.
What happens when the fifth force overbalances gravity? Very simply, gravity ceases to hold sway. And since it was gravity which held together the whole shebang, when gravity ceases to hold sway the whole shebang comes apart. We can, if we wish, call ‘the whole shebang’ a ‘primordial egg’, and we can, if we wish, call this coming apart a ‘big bang’, but neither term is particularly appropriate, and the latter term, ‘big bang’, is particularly inappropriate, inasmuch as it suggests an explosion. What happens is by no means an explosion: it is simply the counterbalance of a force which becomes more influential than gravity. Gravity is no longer dominant, and therefore the singularity comes under the dominance of a new force, one which no longer prevents the singularity from ‘coming unstuck’; and as it comes unstuck it does so with increasing velocity (and here the image of a ‘big bang’ misleads, with its suggestion of a massive initial movement). Just as when a sufficient weight is placed on the raised end of a teeter-totter it will descend, and there is no need to describe such an event as a bang, so too, when a singularity becomes massive enough for the fifth force to become dominant, its basic characteristics will be altered from what they were.
However, there is one way in which the notion of a ‘big bang’ is not so far off the mark: it is extremely unlikely that this counterbalance will occur by the addition of a minute mass to that of the singularity—a back-breaking straw. By the time we arrive at a universe within which there exist black holes of a mass sufficient, upon collision, to produce an energy-opaque region it is highly probable that that universe will already be in the final stages of a contractive phase, wherein the volume of the universe as a whole is no longer so great as to make such a collision improbable beyond all reason. In fact, as the universe contracts the probability of such a collision increases, and eventually it must take place. By the time it does occur the contractive momentum of the universe will be so great that the sudden reversal of momentum could well be regarded as a “bang”. That part of the universe not involved in the big bang will, of course, continue briefly to contract; however, the particle-opaque mass of the universe will be dominant, and can be expected to soon overwhelm the remaining momentum of the residual matter, just as a wave can swamp a rowboat. From this view the term ‘big bang’ (with which, in any case, we are surely now stuck) is not wholly misleading, for the shift from a gravity-dominant era to a particle-pressure era are likely to be dramatic, and the consequence is impressive.
Black holes, of course, are objects wherein gravity is totally dominant, and therefore as soon as particle pressure became dominant the thing was no longer a black hole. All the difficulties inherent in describing what is “inside” a black hole were instantly removed, for there was, in an instant, no longer a black hole. The singularity was no longer a singularity but a rapidly—expanding particle-opaque body. And the event horizon, as an event horizon, also ceased to exist. However, we must remember that the event horizon has also been called an accretion disk because of the incredibly thin yet dense shell of particles which accumulates there. This shell, of course, would break up, just as a soap bubble collapses when the pressures stabilizing it are no longer equalized. [Or, if the dramatic shift in forces failed to destroy it, then the particle-opaque body, as it expanded, would quickly reach the perimeter defined by the accretion disk and shatter it.] Despite the metaphor, however, “collapse” would probably be as misleading a term here as “explode” was earlier; and in any case the accretion disk would not shatter into the nothingness of a burst soap bubble, because it is itself extremely massive. When conditions no longer supported its sphericity it would re-structure itself according to the demands of the new conditions. Possibly, this form might be describable in mathematical terms.
It is worth noting, in this regard, that Krauss, referring to the preliminary analysis of a deep—sky survey by Geller, Nuchra, et al [of the Harvard-Smithsonian Astrophysical Observatory], says: “…it seems that nearby galaxies are clustered in filmlike surfaces that surround nearly spherical voids—a structure resembling that of soapsuds or foam bubbles.” (The “bubble” metaphor seems hard to escape.) Later Krauss adds, “Recent data on the motions with respect to the microwave background of very large-scale regions of matter have provided evidence that these regions are moving, together, with an extremely large drift velocity. No current theory of large-scale structure can explain this apparent phenomenon.” But such a drift would not be out of accord with the large-scale movements of matter outside the region of the Big Bang; and the present view, which allows the existence of a region of the universe outside of (but affected by) the Big Bang-specifically, the accretion disk5 itself and all the matter outside the accretion disk, [which for convenience we can call “residual matter”] such matter being predominately contained within large-scale black holes—is able to accommodate both the drift velocity and the uneven large-scale distribution of matter which have been reported. [As the core universe expanded it would encounter the residual matter and this would introduce an unevenness in the flow of expansion which would be magnified over the aeons. It is also possible that the “spherical voids” reported by Geller et al are not void: each may contain residual matter in the form of a black hole which disrupted the expansion pattern of the Big Bang.]
A second possibility (not necessarily in exclusion to this) is that the accretion disk might at least partially be distorted into numerous strings, or worms, enormously long and thin, yet cohering because of their density. This suggestion is not pulled out of a hat. Very recent reports (see TIME of late last year, October or so) tell of photographing a strange object its discoverers have called “a cosmic string”. They offer an explanation unrelated to what is being developed in this paper, but the point here is that large-scale strands of enormously dense, extremely thin substance seem to exist, and may be—if mathematical support can be found—as real a remnant of the Big Bang as the three degree background radiation.
Also among the strange and unexplained large-scale phenomena are quasars. Briefly, quasars are the most energetic objects ever discovered. Most (though, according to recent observations, apparently not all) are among the most distant objects known (as measured by redshift calculations). And, astonishingly, they are very small—on the order of light-hours, or even light-minutes, in diameter; yet putting out more energy than entire galaxies measuring thousands of light-years in diameter. The diameter of such distant objects cannot, of course, be measured: it is arrived at, rather, through the “consistency and consequences” approach: some quasars are periodic; in order for the object, as a body, to exhibit periodicity there must be communication within the entire region of the body; this communication cannot proceed faster than 3×105 km. /sec. (the speed of light); the diameter of the body cannot be greater than the distance light can cover within a single pulse. If, for example, the period is five minutes the body can have a maximum diameter of five light-minutes, or 900 million kilometers.
One thinks immediately of black holes; and yet a quasar cannot simply be a black hole, for black holes do not give off energy: they take energy (and everything else) in. It has been suggested that a quasar might be a black hole in collision with a galaxy; but here too we find an obvious difficulty: an ordinary galaxy is substantially larger than a mere billion or so kilometers. How could such a volume be isolated so that it could act independently (by exhibiting periodicity) of its surrounding galactic matter? How could it produce such a vast outpouring of energy? The proposal introduces greater problems than it attempts to resolve.
Perhaps what has been developed already in this paper will suggest that a more likely explanation would be the interaction of two black holes, with the consequent merging of the two accretion disks and the release of a vast outpouring of energy. This suggestion, however, also raises several problems: why should quasars be observed mostly (or, if the recent reports are mistaken, entirely) at such great distances?; how can the merging of two black holes, of whatever mass, be an ongoing phenomenon? For it would be extraordinary to assume either that we happen to exist at a time when many black holes happen to be merging or that such mergers are so frequent that we could expect at any time in the life of the universe to be able to observe a substantial number of them. Yet the alternative view, that the merging of black holes takes a considerable period of time, seems no less improbable.
What would happen if a black hole met with a cosmic string? The image which comes to mind is that of sucking in an enormously long strand of spaghetti, with sauce flying from one’s lips onto the tablecloth and, possibly, one’s fellow diners. The image, ludicrous as it may be, is not therefore necessarily inappropriate. We know that when matter enters a black hole some energy escapes. A continuous signal from a black hole (and if quasars do not involve black-hole interaction then they are totally beyond the realm of anything presently known or theorized) requires a continuous input of matter. A periodic signal requires that that input not be haphazard. If cosmic strings exist (i.e. if the photographs are what they seem to be), and if they are remnants of the primordial accretion disk, then they would be found mainly in far distant reaches of the universe, and it is there that they would eventually meet with black holes. If they could retain their coherence as strings then they would indeed be sucked into the black hole rather like spaghetti. A lot of ifs, but they are not totally speculative ifs; rather they are ifs that could become distinct possibilities (or impossibilities) if the mathematics—which are beyond me—confirmed (or refuted) the suggestion, and which could become likelihoods if observational evidence further supported it.
The black holes which the cosmic strings met with would not necessarily have emerged from the cosmic egg: with the collapse of the event horizon, with the transfiguration of the singularity into an energy-opaque body, the two black holes, upon meeting, would cease to exist as black holes and would re-emerge into the universe from which they had been isolated. The bulk of this universe will now be found either within the expanding opaque body, within the cosmic strings (which, in this view, constitute a major body of objects in the universe), or within whatever other black holes existed, and which did not form part of the merger which led to the Big Bang; for as the universe contracted6 more and more of it came to be contained within in fewer and fewer ever-more-massive black holes. However, only two black holes could have merged to produce the critical mass necessary for the Big Bang to have occurred, and all other black holes existed outside of this event. Some of them would have been drowned in the tidal expansion of the primordial mass, but others, more distant, would now inhabit the fringes of the universe. lt is with these black holes that we would expect the cosmic strings to interact to produce the energy output known as quasars7
The matter which (apart from cosmic strings) exists outside the core-universe (i.e. the universe which emerged from the primordial egg) would be calculable. lf the mass which is sufficient, when in dense form, such that particle pressure is capable of overcoming gravity and initiating an expansive phase, be called a mass MO, then, when two black galaxies meet and form a single black unit of mass MO or greater, it clearly cannot be more than ZMO . The mass which lies outside the core-universe will be not less than the total mass of the universe less 2MO , and not more than the total mass of the universe less MO. (The minimum mass necessary for a singularity to evolve beyond the gravitational-dominant mode to a particle-pressure-dominant era should be calculable, though not by me. How does this compare with the mass necessary so that the universe will eventually cease expanding and begin contracting? If the first value is greater than the second then the universe must be closed. If it is less than the second then this does not rule out an open universe, although other considerations might.)
Another piece of potential observational evidence would be to do a survey of galactic distribution according to size. As noted earlier there may be minimum values of diameter and mass—i.e. density—for the creation of a black-hole galaxy, just as there is for the creation of a black-hole star (though in the case of stars the question of density would not be as relevant). If so, then it could be expected that as the universe ages more and more large galaxies will go black, leaving a proportionally larger number of smaller galaxies. Since more distant regions of the universe are seen in an earlier stage of evolution it can be expected that they will contain a larger proportion of large galaxies than regions close by. If a survey supported this, it would lend strength to much of what has been proposed in this paper. It is possible that the results could suggest the rate at which galactic-sized black holes form and, therefore, the amount of the universe presently contained in such high-mass objects.
Obviously a great deal more could be said on the subject of the birth, evolution, and death of the universe; but what has been presented here should be sufficient for a preliminary draft.
Since the universe is now expanding there must exist a repulsive force which operates on a scale sufficient to have started that expansion. There is no evidence that such a repulsive force is presently operative, at least on a sufficiently powerful scale, to counteract gravitational attraction, so it must have been operative under conditions which do not presently prevail. Those conditions existed during the first minutes of the universe which is described in the Big Bang view, when there was a mass of sufficient density to create a pressure-opaque era. However, this era could only have emerged given proper antecedent conditions. Those conditions could have been the collision of two black holes such that their combined mass was sufficient to initiate a region of the universe wherein a pressure-opaque era could arise. And the conditions which allowed black holes of such mass to form are those which are operative even today, but primarily in the closing stages of a contracting universe. Despite the absence of the absolute proof that our presently-expanding universe will eventually begin to contract, there is a great deal of indirect evidence to support the notion; and if this single assumption is allowed we find that it is possible to describe a cyclical universe, wherein the question of beginnings becomes meaningless.
Furthermore, such a view allows us ‘to address a number of other unresolved questions and either to propose solutions to them or at least to suggest that this cyclical view of the universe allows of approaches to solutions where previously no approach was apparent.
A number of ways—by experiment, by survey, by mathematical calculation—have been suggested whereby the views presented in this paper could be tested.
“The universe,” the ethnologist was told by his native informant, “was born out of the collision of two gigantic black holes.” And what, the anthropologist wanted to know, were those black holes born from? “From the previous universe,” his informant asserted. And what was that universe born from? “Ah,” said the informant, “that too is very important; but it’s no use: it’s black holes all the way down.”
1 There is a third possibility, the zero-state universe, where the mass is precisely balanced on the knife-edge between being open and closed. This view has its appeal, but nevertheless the universe must be either open or closed: ‘ajar’ is equivalent to open.
2 Since this was written, an essay (“Dark Matter in the Universe”, by Lawrence M. Krauss: Scientific American, December, 1986) has put the mass at one fifth that necessary for a closed universe.
3 So the matter is usually stated; but strictly speaking this is not the case: the speed of light in a vacuum has long been regarded as a constant, unaffected by gravity or anything else. Gravity affects not speed but wavelength. What should be said is that at the event horizon escape velocity is such that the wavelength of light becomes infinite, i.e. a straight line. The effect, of course, is the same: a wave of infinite length is no wave at all, in terms of a finite world. Presumably, light passing into the black hole would be infinitely contracted, of infinitesimal wavelength. Thus there can be no communication in either direction. Or, to put the matter in different words, we can have no knowledge of what goes on “inside” a black hole because there is no point where its co-ordinate system—if it has one—coincides with ours.
4 The existence has been proposed of black holes with an event horizon radius less than that of an electron and a mass of not more than 1015 grams. These could have been formed, if at all, only under conditions which prevailed when matter first ‘condensed’ out of the energy flux which followed immediately upon the Big Bang, and there are theoretical arguments that would force the conclusion that such microscopic black holes could and would deteriorate, the last of them disappearing during the present era. However these microscopic black holes, if they exist, are not relevant to the subject under discussion. When we consider black holes of solar masses there is apparently no mechanism whereby energy or mass could be lost.
5 Or, perhaps more accurately, two accretion disks: in the time between the entry of one singularity through the accretion disk of the second black hole and the evolution of the two singularities into a single energy-opaque arena the two accretion disks would be unlikely to have had sufficient opportunity to merge into a single unit.
6 In this draft paper I have failed to develop earlier the idea that the universe cannot be open. A study by Dicke and Peebles, reported by Krauss (op.cit., p. 62) points out that “any deviation from an exactly flat universe should tend to increase linearly with time. If the universe had had even a small non-zero curvature at the time of nucleo-synthesis, the deviation from flatness would by today have increased by a factor of about 1012.” If this study is reliable then an open universe is clearly ruled out already. Krauss takes this study as supportive of a zero-curvature universe (one which is flat, balanced between being open and closed); but this assumes first that a “flat universe” is a meaningful concept—see the first footnote on page 2—and second that there is not a substantial amount of mass still undiscovered, which is contrary to expectation: both black holes and cosmic strings must be added to the sum, and possibly other sources as well. I would argue that inasmuch as the known mass of the universe, like black holes, can only increase, that a closed universe is the most likely possibility based on present understanding; and that moreover the movement of present understanding, if it continues in the same direction, would make a closed universe even more probable. This notion of deviation increasing with time explains why the comparatively small deviation in distribution introduced by early encounters with residual black holes should lead to present-day large—scale uneven distribution of mass.
7 Krauss describes cosmic strings (p. 67) as “extended topological defects that might have arisen from symmetry breaking in the early universe. They would take the form of long, thin tubes of constant and very great energy density winding through the universe. …Even cosmic strings may soon be detectable, either by their direct gravitational effects on the light from distant quasars and the microwave background (concentrations of energy as dense as cosmic strings should create gravitational fields that would bend light appreciably) or indirectly by measurement of the gravity waves or other radiation they should emit as they evolve.” His article was written, apparently, before the report that such strings had in fact been detected.