Copyright © 2000 by Scott Teresi
www.teresi.us/writing

The Beginning

        Every bit of matter we see around us was born from stars, including the material of our actual bodies. This can be an astonishing realization, yet it is not hard to understand if one can simply accept that everything was formed out of the same material, evolving from a common past event. What is the origin of all the matter in the universe? What is the nature of an event which could create seemingly everything? Could something have existed before this event?

        Human life has existed on earth for a very short time compared to the age of our solar system. Our sun and solar system were formed from a rotating disc of matter which collapsed from its own gravitational pull, distributing its angular momentum among the orbiting planets and a spinning central star. This original nebula of matter was made up of the remnants of supernovae or other types of clouds of matter, the byproduct of dead stars. Similar cycles of decay and rebirth of stars continue within galaxies throughout the universe. How did these galaxies form? What were they born from?

        The most widely-accepted view of the origin of the universe holds that all matter was born in a gigantic event kind of like an explosion–the big bang. This event left a chaotic cloud of matter out of which irregularities accumulated over time and more defined clouds of matter accreted, collapsed, and spun into disc shapes, creating the first galaxies. How can scientists make such claims? Does the big bang mean that time has a beginning? Einstein’s theory of relativity predicts that the big bang would have to be a singularity, a realistic manifestation of a mathematical infinity. Does the possibility of infinite matter in an infinitesimally small point contradict some aspects of currently-trusted physical theories? How far can we turn back the clocks before current theories begin to lose their predictive power? While thoroughly examining the big bang, we will also examine singularities in general and the ensuing expansion of spacetime. What evidence supports these theories? What do they mean? How do they affect the way we think of the constituents of reality–space, time, and matter? What problems exist if we accept them?

        Two reasons we can trust that a theory of the big bang is valid are the existence of cosmic background radiation and the proportions of hydrogen, helium, and other light elements of matter. The latter evidence is predicted very precisely by big bang theory; the abundance of the elements in the universe can be derived from formulas which describe how a nuclear soup which would exist just after the big bang would condense into atoms and molecules as it cooled down. The ratios of the elements which would be formed happen to closely match what is observed in the universe. Hence, the mathematics of big bang theory predict a testable aspect of reality.

        A glow of about 2.7 Kelvins radiates from empty space in every direction and is called cosmic background radiation. This indicates the existence of a quickly receding wall of hot matter (in the opaque plasma phase) left over from the big bang. Since this matter is receding from us at nearly the speed of light, its radiation is red-shifted so much that it does not appear directly as something "hot" which gives off radiation in the visible electromagnetic spectrum but as something much cooler but still detectable. Its presence is predicted by the big bang model.

        Much of big bang theory is left beyond the realm of direct empirical evidence, guided by our formulas for general relativity up to a point. Let’s follow the universe’s history backwards through time up to this event. At a billion years after the universe’s formation, quasars began to form, the oldest cosmic objects still observable in the distant sky. From there matter began to condense into the stars and galaxies which are present today. On a smaller time scale, when the universe was about 300,000 years old, the primordial soup of elementary particles cooled enough to allow nuclei to reign in electrons and form atoms. The edge of the plasma era is seen as the cosmic background radiation. Out of this plasma, radiation and matter separated from each other and no longer closely interacted as before. This is an easy calculation for physicists, since they know what temperature can slightly overcome the electromagnetic pull between a proton and electron.

        At three minutes old, the universe began to cool enough to allow the strong nuclear force to take control and pull together atomic nuclei. The same conditions can be easily reproduced in a particle accelerator to allow the particle interactions to be observed. Models for big bang theory beyond a hundredth of a second, when many types of unknown atomic particles were created and destroyed, must rely solely on experiments and theories in particle physics. Quarks combined into neutrons and protons at an age of approximately 10^-6 seconds. Before this point, something called the quark soup model is used to describe the universe. However, since the strong nuclear force increases with distance, these tightly-packed quarks interact very little with one another. A simplified description of what happens to the universe before this moment is that the matter density and the temperature keep building up until the moment of the big bang, which occurs before the Planck wall at 10^-43 seconds, the point at which already questionable physics calculations totally break down and no longer apply.

        Near the age of 10^-10 seconds evidence of the unification of some of the forces can be seen. Before this point, the weak and electromagnetic forces were combined. The presence of neutral currents in particle accelerators are neatly predicted by the unified theory of the electroweak force. Around 10^-20 seconds, theoreticians can no longer rely on particle physicists’ empirical results and experiments cannot directly verify claims. Still, evidence of other sorts can be obtained. Even further back, at 10^-35 second, less substantiated speculation must be made. A grand unified theory would attempt to explain how the strong force and electroweak force were one and the same during this period of time. Finally, before 10^-43 second, physicists’ formulas for space, time, and matter break down. There is yet to be formed a theory which can describe the breaking of gravity’s connection with the rest of the forces which occurred at this moment. Within this superdense material, gravitational fields are so strong that quantum effects must be taken into account. Normally gravitational forces appear very weak on small scales and are easily ignored in quantum mechanics because of the tiny amounts of relatively sparse matter involved. Gravity is currently isolated within the separate realm of relativity.

        Does the existence of a big bang mean that time has a beginning? It’s not simply that clocks suddenly began ticking at a certain moment, but that during the first 10^-43 second of the birth of the universe was also the birth of time (and space) itself. This conclusion can be drawn from what we can say about singularities: all laws of physics as we know them will tend to collapse as the limit of a singularity is reached.

Singularities and Spacetime Expansion

        Einstein’s theory of relativity is considered one of the greatest single accomplishments of man’s intellect.

It builds the world out of pure geometry and arranges it according to mathematical laws that could scarcely be simpler or more powerful. Few scientists would deny that its aesthetic appeal is the most persuasive evidence in its favor (Davies, Infinity, 176).

When infinity is reached in physics, theories begin to break down or become questionable. On extremely small scales, relativity leads to one tremendously distasteful conclusion for many physicists. It cannot escape concluding that on smaller and smaller scales of distance, the force of gravity will become great enough that it becomes infinite at a single point, opposable by no other force in the universe. This is a singularity, or, in one of its natural forms, a black hole. A star which is destined to form a black hole might collapse into an ever-decreasing volume of space until it reaches a mathematical point and its density becomes infinite. The curvature of spacetime itself–in other words, gravity–becomes very steep and finally pinches off at a point. (This is surely what would happen had the original star been a perfect sphere.) As a consequence, the notion of spacetime completely "stops" for material which has reached the point of a singularity.

        Unfortunately, relativity by itself cannot be used to describe the formation of a singularity because its conclusions are somewhat irreconcilable with quantum mechanics. The uncertainty principle, which states that the position and velocity of a quantum particle cannot both be known at the same instant, would be violated in a singularity. Some theory must be devised which can incorporate the effects of gravity into the world of quantum particles, and bridge the gap between the physics of relativity and quantum mechanics. This is sometimes termed "the theory of everything," as it would unify gravity with the remaining elementary forces and tie together several apparently unrelated variables as a result.

        It is much more likely, however, that a star would contain some irregularities and not undergo a perfectly uniform collapse as a perfect sphere would. In this case, its constituent particles would collapse toward different centers of gravity, plunge into and through themselves, and then "bounce" back and expand out again (Davies, Infinity, 70). However, once matter is engulfed in a black hole and passes the "event horizon," it can never escape back into the universe. To an outside observer, whatever matter has fallen toward a black hole will appear to be frozen on the event horizon forever as a result of its tremendous, near-light-speed velocity, and it will appear to take an infinite amount of time to fall in. (However, light rays which could possibly leave the objects near the event horizon may be so red shifted as a result of the strong gravitational field that they will only be detectable in a lower portion of the electromagnetic spectrum.) So where could the material which has collapsed into the black hole "bounce back" into? If it re-entered the universe it came from, it would in effect be reappearing before it ever disappeared, and backward time travel violates causality.

        Curiously, black holes do lose material (energy) over time by emitting what is called Hawking radiation. This can occur because particle-antiparticle pairs are continually forming and disappearing within the fabric of space, and if one particle happens to appear at a point slightly closer to a black hole, it may fall in while the other escapes, appearing to have been radiated from the black hole. While it is true that this depletes some of the gravitational energy of the black hole, Hawking radiation cannot carry any information about the contents of the black hole or causality truly would be violated.

        What other possibilities exist for the fate of matter which has fallen into a black hole? This question remains a vague philosophical one rather than one which can be answered by current physical theories. As spacetime succumbs to the monstrous effects of infinite gravity, the matter caught in this infinite curvature could be pinched off from the rest of the universe. In some respect, this matter might be meeting the end of its existence; it could be entering an area where space and time no longer exist. However, some evidence seems to suggest that remnants of matter can endure the ripping and crushing intact, and survive the entrance to a singularity. Unfortunately, the matter inside a singularity must concede to new laws totally unlike our currently trusted physical theories, for physics cannot solve equations once they have produced an answer of infinity. New methods of analysis must be developed, beyond traditional physical formulas. The matter can no longer be matter as we know it, but some other decomposed entity possibly devoid of any space or time and cut off from the physical universe. Further, since no causal influence can even escape a singularity, a singularity may present a real limit to anything we can know and anything which is meaningful to the rest of the universe. These somewhat unbridled conjectures had best remain tempered, however, until a theory of quantum gravity can supply answers with more physical basis.

        Physicists will continue to make conjectures, however. The possibility of a discontinuity of time has long been a topic of discussion. Many physicists do not believe a true singularity can actually exist. Instead, at certain high values of spacetime curvature, the general theory of relativity simply can no longer supply an accurate description of reality. Such talk of matter and spacetime may cease to have meaning; we have reached a discontinuity of spacetime. One theory of this sort speculates that spacetime could be made up of a tiny discrete latticework, many times smaller than a subatomic particle, beyond the scale of quantum effects. These ideas have been supported in certain ways by the continual discovery of smaller and smaller scales of matter where quantization already begins to occur. Given that we know so little about the behavior of matter under such extremely compressed conditions, on what grounds should we suppose that gravity will always overcome the rigidity of matter, however much it is compressed? Until a theory of quantum gravity can reconcile relativity with quantum mechanics, it appears that quantum effects will completely overpower gravity as quantum energy uncertainty increases in an ever decreasing volume of space. For instance, across the width of an atom, energy fluctuates only slightly, but at scales within a tiny fraction of the size of an electron, energy uncertainty will become so large as to overcome gravitational effects and result in a seething froth of strange spacetime effects such as tiny wormholes and bridges existing for tiny fractions of a second (Davies, Infinity, 90). This view of a singularity may offer solace to some, since while spacetime may have reached the edge of its existence at a point, it is in most respects still a part of our physical universe, a less drastic finale than if it were to have disappeared altogether or been siphoned off into another universe.

        Unfortunately, strong evidence exists to suggest it is impossible for matter to reach a point of sufficiently compressed rigidity which can withstand the gravitational collapse occurring within a black hole. One reason for this is simply the behavior of sound waves. Sound propagates by vibrating an accompanying material, which means the material must have some flexibility or elasticity. The more rigid a material, the most vigorously and rapidly it will fight compression and decompression and the faster sound will propagate through it. Mathematical models have shown that any mass which is stiff enough to withstand the gravitational collapse of, say, a neutron star of several solar masses will have to propagate sound waves faster than the speed of light. Of course, no information can possibly travel faster than the speed of light, so such a material should not be able to exist, even within a highly rigid neutron star. To accept such a possibility would be to abandon causality it seems. These conflicting theories of singularities will remain irreconcilable until quantum gravitational effects are understood.

        Since the moment of the big bang, the universe has been expanding. This expansion of space has left the contents of the universe spread out in a rather smooth and uniform fashion. Relativity and quantum mechanics allowed matter to be created out of "empty" space. The energy it took to create this mass was then stored in the mass’ gravitational pull, slowing the expansion. However, new findings seem to suggest that the universe is expanding faster now than it was several billions years ago. Current evidence seems to suggest that the universe’s expansion rate is increasing rather than slowing. What mechanism could control this rate of this expansion? A fifth force has been postulated–the vacuum of space could contain enough energy to exert outward pressure on the rest of the universe. Curiously, Einstein once believed in this idea, the idea of the cosmological constant, but later called it his biggest mistake.

        Previously held theories predicted that the gravitational attraction between galaxies and large structures was sort of keeping a grip on spacetime expansion and slowing it ever so slightly. However, tabulation of the visible matter in the universe would indicate that it is not nearly dense enough to stop the expansion but could only slow it down asymptotically toward zero without ever quite allowing collapse. The density of matter involved in the latter scenario is known as the critical value. While the density of visible matter (stars, galaxies, and luminous clouds) accounts for only one percent of the critical value, more matter, "dark matter," can be shown to exist by indirect evidence. For instance, spiral galaxies display a rotational velocity much greater than what would seem allowable for their visible mass. If dark matter were not part of these galaxies’ constitutions, they would completely fly apart under their own angular momentum. Furthermore, just as stars have gravitated toward each other and formed galaxies, so do galaxies gather together and form superclusters. Hence, the movements of these superclusters can be observed and measured, and they do show a kind of rotation and interaction which would indicate that a sizeable quantity of unseen mass must be present. Unfortunately, all of this observational evidence taken together, probably including black holes and neutrinos as dark matter, suggests the universe only contains ten to twenty percent of the critical density (Davies, Runaway Universe, 168). More recent estimates indicate as much as thirty percent can be accounted for (Horgan, 18). Much more tenuous theory must take over from this point in postulating where the missing dark matter could be hiding.

        Why do physicists prefer a universe with exactly the critical density? Actually, a figure of ten to twenty percent is considered extraordinarily close to the value of the critical density. To achieve exactly this density requires an incredibly careful "choice" in initial density and expansion rate. If the density of the universe only one second after the big bang had been ever so slightly greater (by an amount of one part in a thousand billion), the universe could have collapsed after only ten years. Conversely, had the density of the universe been ever so slightly smaller, the universe would practically have been empty since the time it was ten years old (Hawking, Black Holes, 150).

        Because the matter in the universe is still spreading out and expanding, spacetime is still growing. It is not matter which is expanding into an infinite void, however, but the actual space in which the matter is "pinned" is expanding. Of course, gravity holds galaxies together and superclusters within their general shapes, but more loosely-coupled structures are growing in size with the underlying spacetime expansion. There is no center of the expansion, no center for a glob of matter. It’s as if the topology of the universe were placed on a balloon which is being inflated. That analogy implies no edge to the universe which is true to some extent, however it should not be possible for a straight line to "wrap around" the universe. Because spacetime is not expanding into anything, there can be no edge of the matter in the universe.

        Within an even larger context, our universe may be one of many, spawned by inflation. Within the extreme conditions of the primordial universe, an extremely dense speck of energy present in the vacuum of space could have triggered the inflation of our particular universe (and possibly many other totally separated universes). Inflation fits surprisingly well with much of today’s evidence, for instance the apparent flatness of space indicating continued expansion. Also, the cosmic background radiation appears to be extremely smooth which can be explained by how the universe must have exploded to monstrous proportions almost instantaneously. Beginning at 10^-33 second old and lasting only about 10^-32 seconds, the universe would have inflated and quickly reached thermal equilibrium (Watson, 1455). Also, the lumpiness of matter is attributable to the same process–small atomic-sized fluctuations were quickly scaled up and could provide the seeds for the formation of galaxies. With new evidence for the cosmological constant, reducing the great need to find dark matter, inflation theory has looked even more promising.

Philosophy of the Big Bang

        Examining the exact moment of the big bang puts us again upon the edge of existence. However, its singularity lives in reverse, starting in the past and then disappearing after its matter has spewn forth. A singularity like the big bang may not be of the same type as a black hole but instead something called a naked singularity. Naked singularities are highly chaotic and as such have a "surface" so complex and fluctuating that they cannot have event horizons.

        The naked singularity that was the big bang occurred for just a fraction of a second, left its effects, and then disappeared. As is usual for naked singularities, apparently unexplainable and chaotic phenomena occurred during the instant in time in which spacetime and matter were produced. However, since the singularity quickly dispersed, law and order could soon settle down and take over from there, in a rather undisturbed state. It is important to realize that this singularity meant the origination of the physical universe, and not simply the creation of matter. Time as we know it most likely could not continue further into the past before the big bang. Neither would there be space in which any matter could exist.

        Was the big bang really a singularity and the beginning of all of space, time, and matter? Is it impossible for something to have existed before? Consider the foamy spacetime which might comprise the heart of a modified singularity, following from some quantum mechanics’ predictions. Something obviously exists as its ingredients in a reality governed by laws which we do not understand. The big bang could have sprung out of this same kind of reality, something outside of our framework of spacetime, a geometry for geometries. Abstract mathematical ideas such as string theory have been created to provide something like the building blocks for spacetime. It is hoped that this can be used to derive basic topological properties such as the reason why our space has exactly three space dimensions plus one time dimension.

        If some aspect of space and time had existed before the big bang, then this might mean this universe is one of several in a cycle. Or it could mean the universe is the result of one of many exploding singularities yet still encompassed within a spacetime completely separate from other possible universes. Just as matter entering a black hole must either cease to exist (ignoring Hawking radiation’s slow effects of evaporation) or enter another universe altogether, the matter which exited the big bang must have either been formed at that moment or have gone through foamy spacetime and come from a singularity in a previous universe. In other words, our universe could simply be another universe, recycled.

        However, if "nothing" exists without spacetime, then there would be no past which could exist before the big bang. The singularity would be a complete temporal boundary in the past; time itself would have come into existence then. It would hence be meaningless to talk of what came "before," in the same way in which it would be meaningless to ask what caused the big bang, since causality requires time, and time did not exist until the big bang occurred.

        If there is no physical cause, then why is the universe the way we observe it? What events in the past have our current reality stemmed from? What if certain quantum particles were just slightly different and the balance of elements in the universe had changed? Life may not have developed and we may not have come into existence. Is it enough to say that things are the way they are because we are? One version of this "anthropic principle" holds that there may exist or could have existed many universes with slightly different physical parameters and initial conditions, but most of these scenarios would not have provided the right conditions for life to have formed to ask the anthropic question. However, this argument dodges the need to explain things which may very well have an explanation. It ignores the point of scientific investigation altogether. For instance, a person might ask, "Why does it rain?" and someone could answer "Because if it didn’t rain, we humans would not exist." In this case there definitely are deeper explanations and apparently hidden relations which science can explain but the anthropic principle sweeps under the rug, so to speak. Instead, a theory of everything, while still elusive, could tie together somewhat the apparently arbitrarily but fortunately-chosen parameters of the basic building blocks of the universe. Still, what could have chosen the big bang’s initial conditions? Could they have been the only possible byproduct of a harmonious set of physical laws? Or were many universes created, and humans came into existence in the only one in which it was possible? Or, more troubling, might there have been no cause at all, because nothing came before? Many philosophers see this as the last chance to invoke God as a creator and still be completely compatible with science. In the end, there may be no possible physical law to explain the creation of the big bang. As a result, science may not be able to be used to discover it.

About this paper

I wrote this paper while earning my Masters of Computer Science degree at the University of Illinois at Urbana-Champaign, Dec. 1998. This was my final assignment for Physics 319: "Philosophy of Physics: Space, Time, and Matter," taught by Prof. Mike Weissman.

© 2000 Scott Teresi. This paper is available on my web site: http://www.teresi.us

Notify me before you re-distribute this paper. I would be glad to hear it!

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