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Space and Time in Modern Cosmology

Dr. Carol Day
Tutor
Thomas Aquinas College
West Coast Meeting, Society for Aristotelian-Thomistic Studies
June 16, 2016

Introduction

I believe that there can and should be a friendly conversation between natural philosophy and the specialized sciences; it is with this in mind that I set out to write this paper about modern cosmology. In particular, I thought it would be worthwhile to ask some very simple questions about space, time and motion, as they are conceived in modern cosmology.  By simple I mean questions that may and do occur to non-professional readers of modern expositions of the subject; it does not follow that these questions will have simple answers. These questions tend to touch on fundamental matters, and these are often difficult to address in a simple manner. How exactly, for example, are we to understand Euclid’s account of why two triangles having two sides and the included angle equal are congruent? To think about this, issues prior to the science of geometry have to be considered. Similarly, cosmological answers to questions about space and time will involve us in prior considerations. These prior considerations fall under the scope of the Natural Philosopher.

One source of difficulty in addressing these questions is that the words used by the cosmologists may have meanings unfamiliar to the questioner, despite the familiarity of the word itself. The name “space” is a good example of this. Others have an application that may be familiar but which may not come to mind when the layperson hears the word. “Expansion,” as applied to the cosmos, is an example of this. Other names are seemingly well understood until one tries to give an account of them.  “Time” is a notorious example of such a name.[1]  One aim of this paper, then, is to explain the signification of these names in modern cosmology.

Another source of difficulty is that there is not a consensus among experts about the most likely answers to some of the questions. Different opinions about and interpretations of more fundamental parts of physics, which are presupposed by cosmology – I mean both General Relativity and Quantum Mechanics – make it impossible to be satisfied with the answers currently given to many of these questions, as judged from within physics as a whole. This should bring home to us the truth that the most general questions about the nature of the physical world, its constitution, its origin and its destiny, fall under natural philosophy and as such cannot be satisfactorily answered from within any specialized branch of science, especially one whose method makes use of such artifacts as mathematical models. The fact that these models and even the more basic theoretical structures which surround them undergo change from time to time shows the need for a more certain science, one which is capable of judging the principles of the more specialized sciences and of offering critiques of their conclusions in light of more general considerations.  This task belongs to natural philosophy. I hope to make a very small contribution to such an examination and critique in this paper by offering a dialectical discussion of the notions of space, time and cosmic expansion, as they are understood by contemporary cosmologists.

By cosmology I mean the branch of astrophysics that attempts to understand the nature, laws and motions of the universe, considered as a whole, in terms of received physical principles. The basic outline of cosmology as it is understood today arose from two very different sources, the attempts by mathematicians to work out the cosmic implications of the General Theory of Relativity and the discovery by astronomers of the recessional motions of the galaxies. These two developments converged to produce a new conception of the cosmos as different from that of the Scientific Revolution as the Newtonian conception of the universe was different from the cosmos of the ancients. In one important respect, however, the new cosmology marks a return to the ancient conception, however different it may be in most ways.

This most striking feature of contemporary cosmology is the recovery of the cosmos itself. I would like to give a brief account of how this came about. Post-Copernican thinkers assumed that the universe had only the unity of a heap. Newtonian dynamics was considered adequate to explain all the motions of celestial objects as well as the processes by which they could form under the influence of gravity. The universe was seen as a vast if not infinite expanse of void space in which stars are scattered around like molecules in a gas.

For long it was thought that the Milky Way was the entire universe. Although some early followers of Newton envisioned an infinite universe filled more or less uniformly with stars, Newtonian dynamics itself prohibits such a scenario. As Einstein expresses it, Newton’s theory “requires that the universe should have a kind of center in which the density of stars is a maximum, and that as we proceed outwards from this center the group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The universe ought to be a finite island in the infinite ocean of space.”[2] The reason is that if there were an average finite density of mass throughout an infinite cosmos, the intensity of the gravitational field would everywhere be infinite, which is absurd. Given a finite amount of matter, then, its eventual concentration towards a center would come about through the mutual gravitation of the parts. Moreover, according to Olber’s paradox, the night sky ought to be luminous in every direction, if there is a more or less uniform distribution of stars throughout infinite space. Although both problems could be solved by making ad hoc assumptions, most astronomers had no compelling reason to make such unfounded assumptions.

For these reasons, it seemed reasonable to most astronomers to hold that the Milky Way was the cosmos. But in the early years of the 20th century some began to speculate that certain of the faint nebulae visible in telescopes were “island universes” in their own right: collections of stars comparable to the Milky Way.[3]  The issue could be settled by finding out how far away from us and whether they formed coherent systems sharing a common motion.

A sound falls in pitch when it arrives from a source moving away from us, due to a lengthening of the wavelength. Similarly, there is a shift to the red of light coming to us from any source moving away from us. We can measure these shifts in the light coming to us from stars and other celestial objects. Sometimes shifts towards longer wavelengths are observed, sometimes shifts towards shorter ones. According to the most obvious interpretation of these observations, some celestial objects are moving towards us, some are moving away.  These observations indicate only the component of motion in a direct line between the source and the observer, which is called its radial velocity. For distant objects, the motion perpendicular to the line of sight is difficult or often impossible to detect. Celestial objects also have random motions, some towards us and some away, which have to be eliminated from the observations to reveal the general trend.

Th Velocity-Distance Relation for Extra-Galactic Nebulae

Making use of the best data he had available for galactic distances, Edwin Hubble found that more distant galaxies, ones therefore seen further back into the past, have larger red shifts than nearby galaxies.  Here is an examples from his book The Realm of the Nebulae.[4] These graphs plot logarithms of velocities calculated from red shifts versus magnitudes. Since magnitudes vary logarithmically with intensity of the light, and the intensity indicates distance, the horizontal axis is essentially an indication of logarithms of distance. The approximately linear relation between the logarithms indicates an approximately linear relation between the quantities themselves.

Example from his The Realm of the Nebulae

To get this graph, Hubble had to remove the effect of the sun’s proper motion, which he used as a stand-in for the proper motion of the Milky Way galaxy.[5]  You will notice that there is quite a bit of scatter in Hubble’s diagram, especially the one on the left. This is due to the random proper motions of the galaxies. The scatter is less when averages for various clusters of galaxies are used rather than individual galaxies. It seems clear, especially from the second graph, that there is at least a rough proportionality between the distances of galaxies and their recessional velocities.  Much of modern cosmology rests on attempts to explain, in as much detail as possible, this systematic relation between distances and red shifts. More extensive and more precise measurements supplied by the Hubble and Planck space telescopes have complicated the picture by showing departures from the simple linear function which I have just described. On this new evidence rest such speculative notions as Cosmological Inflation and Dark Energy. It is worth repeating: the raw data link red shifts and apparent brightness of celestial objects. All else rests on ideas about how to interpret these measurements.

So far, I have spoken as if the red shifts indicated recessional velocities in a literal sense, just as the falling pitch of a police siren indicates that the patrol car is moving away from your car and so you are safe from being pulled over. But this is not how the cosmologists have interpreted the red shifts, even in Hubble’s day. The expansion of the universe is not to be thought of as analogous to the expansion of a mob of people as they leave a club or ball-park into which they had been crowded.  Such an expansion is not, of course, a motion, but rather the increasing of a boundary enclosing all the moving people. Such a boundary is an artificial construct which may be useful in various ways but which does not itself have a physical meaning. The forces at work in causing such a per accidens expansion of the boundary enclosing the galaxies would be those of Newtonian dynamics: some sort of originating outward push and the subsequent inertial motion of the galaxies.  We need to see why this would not be a plausible account of what we observe.

There are a number of difficulties with a Newtonian explanation of the phenomena. If the galaxies formed prior to the expansion, what natural cause could possibly result in them flying apart from each other like so many projectiles while maintaining their beautiful internal symmetries? The required coordinated pushes on the individual stars and particles of gas and dust that constitute galaxies would require a sort of choreography unimaginable from the point of view of created nature. Granted that God could cause this, but that natural causes could do it is beyond belief. That the universe originally consisted of a symmetric collection of uniform particles which somehow acquired an outward movement and which later coalesced into stars and galaxies is not far-fetched, but even this account turns out to have serious technical difficulties and requires assumptions that conflict with classical physics.[6]  It is more reasonable to think that the unity of the effect points to a unity of the underlying subject. If we accept the evidence that Hubble’s constant is increasing with time, the Newtonian explanation is completely destroyed.

We are left with the idea, then, that the cosmos is a unified thing that is undergoing growth or something similar to growth. We naturally wonder what it is and how it is made one. It is interesting to note that this new conception of the universe as a cosmos was developing even before relativity theory was proposed by Einstein. The notion of a luminiferous ether pervading space, filled with electromagnetic radiation, became common in the nineteenth century, when developments in electrodynamics were beginning to push physics away from pure Newtonianism. This ether seemed like a physical embodiment of Newton’s absolute mathematical space, suggesting a unified cosmos at least in the sense that there is one physical continuum in which all things exist.

This idea is supported by Herman Bondi, one founders of modern cosmology:

“The first attempt to grapple with the cosmological problem as a whole was made during the nineteenth century, when the framework of Newtonian theory was accepted without question. It is a curious fact that these attempts were destined to fail not because of their Newtonian origin but because, in addition to the cosmological principle, the further assumption was made that the universe was static in the sense that there were no large-scale motions of matter. It will be seen in the course of this section that under these conditions there can be no solution in strictly Newtonian terms. This failure led to a diminution of interest in cosmology that lasted until Einstein began the exploration of the cosmological consequences of general relativity in his famous paper of 1916.”[7]

In this passage, Bondi mentions two difficulties with applying Newtonian theory to the unified cosmos. The two difficulties are related, in that one is a consequence of the other.  The first was the very generally accepted supposition that the universe looks the same, on a sufficiently large scale, to all observers at all times. This has been called the perfect cosmological principle.  The second difficulty mentioned by Bondi, is that the universe was seen as essentially static. Note that Bondi only says that these taken together pose a problem for Newtonian dynamics.  For if the universe (meaning the electromagnetic ether) is static, the matter within it will slowly be surely be coalescing into one mass under the influence of gravity, thus the cosmological principle would be violated.

Along with a few others, Bondi was a proponent of a relativistic steady state theory. In this, he rejected the static universe but kept the perfect cosmological principle. Today, the consensus is that Bondi kept the wrong principle. The universe is not static, and the perfect principle is replaced by a modified cosmological principle, namely, that the universe looks the same, on a sufficiently large scale, to all observers at a given time. (What is mean by a given time will have to be examined.) From now on, this is what I will mean by the cosmological principle. It is equivalent to the statement that the universe is homogeneous and isotropic.

The standard explanation of the Hubble diagrams given by general relativity is simple and elegant. What we measure is that the wavelength of light increases in proportion to the distance the light has traveled. There is no need to suppose that the galaxies are themselves mobile, because it is sufficient to assume that the space through which the light is travelling is growing. If I were to draw a waveform representing the light on a piece of rubber sheeting, grasp it by both ends, and pull it apart at a uniform rate, the distance between successive crests would steadily increase. The relativistic account, in essence, is that light from distant galaxies travels through space that becomes more and more extended as time goes on. The longer the light travels, the more its exposure to this expansion and the more red-shift it shows when we observe it.

It is important to remove a possible misconception. Not everything is growing in accordance with this so-called “Hubble flow.” All smaller scale cosmic structures, even clusters of galaxies, are bound together by mutual gravitation. These are often moving towards each other, counter to the Hubble flow. Moreover, very small objects such as astronomers and laboratory equipment are bound together by electromagnetic forces. To these, the cosmic expansion is at best an insignificant contribution to their relative positions. The modern conception of the expanding universe, then, will have it that the space between the material structures of the universe is expanding or in some way changing its scale.

The finite speed of light provides both an opportunity and a difficulty for cosmology. Because light is not instantaneous, we have to distinguish between our picture of the universe – what our instruments reveal – and what has been called a map[8] of the universe at a given time. This map is a mathematical representation of what we would see if we could take a simultaneous look at things. Moreover, we want to know how the map changes with time. This latter, the map as a function of time, is what cosmological models purport to describe. We can now see why the finite speed of light is advantageous for our knowledge. If we were not able to look back in time as we look outward in distance, we would have no way to know how the map is changing except by observing the universe over many millennia.

Let us examine in more detail this notion of a map. Like a road map, it locates key features of the landscape – I guess I should say, the skyscape – relative to each other and indicates how they are connected. Like a topographic map, it abstracts from most features of the landscape to give an overview of the terrain.  But unlike these familiar maps, it exists in algebraic form rather than as a picture. In this way, it is more like the GIS data that cartographers use to produce their maps.  

As used here, the word “map” calls to mind the word used by mathematicians for a generalized notion of a function. This they call a mapping.  Our cosmic map is a mapping from the four dimensional space-time of general relativity onto a three-dimensional cross-section of constant time.  It is important for us to understand what this means and what it implies, because this map is, I think, the formal object of modern cosmology.  But before we can unpack this sentence, we will need not only to consider what the modern cosmologists mean by space, time, and space-time, but also which version of the universe is being mapped.

There is a distinction in the meaning of “universe” that the cosmologists make in their own thought but which is usually not mentioned in the popular literature. They distinguish between the universe as considered under three aspects. First, there is the whole universe, the entirety of physical reality. Next, there is the “observable” universe. This is the universe as it is in principle observable by a given observer. This universe is a sphere centered on the observer having a radius equal to the speed of light times the age of the universe, as it would be measured by that observer. Finally, there is the actually visible universe – the universe insofar as we are able to observe it in fact with our instruments.  This universe may also be thought of as a sphere; much progress has been made lately to push our empirical knowledge out towards the edge of the observable universe, without, however, having reached it. Whatever we say about the observable universe is an extrapolation from what is known or conjectured about the visible universe. As to the whole universe, this is what the mathematical models deal with. The various cosmological models describe different possibilities for the whole universe. Any judgments between the possibilities have to be made on the basis of what is seen in the actually visible universe.  Thus we must always begin our considerations with the universe in this sense.

Now that we know what is being mapped, we must consider the elements of the map. First we must see what is meant by “space,” and then by “time.”  Finally, since the map is always changing, we must consider how we ought to understand the claim that the universe is expanding.

Space

It is a commonplace that the universe consists mostly of space. But what is space? I think we can distinguish three approaches to this question. The first is that of the common man, which is also that of the natural philosopher. The second is that of the pure mathematician. The third is that of the physicist, which is also that of the cosmologist, and this is a sort of mean between the other two. I will try briefly to describe them in this order.

The idea of space, as Einstein himself explains, arises from our experience of putting boxes inside of boxes.  From this it is clear that the concept of place precedes the notion of space.  But prior to the notion of place is the notion of being extended, that is, of having part outside of part. Experience shows us that there are three independent extensions, and that bodily substances must have all three of these, which are commonly called length, breadth and depth. Without body we would not have space; thus space considered naturally has three dimensions.  The common man, if he thinks of this space at all, imagines it as a sort of empty room in which things exist and move around. The natural philosopher, naturally enough, has some questions about this. Is space something really distinct from body? Does it have natural limits? Is it immobile? Why does body require three dimensions? Is it just a fact of experience that it is limited to three dimensions, or is it impossible that there should be more?

Rather than try to answer these questions, let’s return now to the idea of the big empty box. We can think about the dimensions of the box in abstraction from the box and so be led to the idea of a three dimensional coordinate system. To the pure mathematician, a space is an abstraction of this sort. But he does not stop at this abstraction; he goes on to construct more complicated objects using these abstractions. Through the setting aside of spatial images and the extension of the methods of algebra, it is easy to extend abstracted 3-D coordinate space to as many dimensions as we please.  Each of these dimensions is conceived in exactly the same way as a continuum of numbers. The numbers may either be real, complex, or whatever kind if number he wants or needs. The various dimensions are related to each other by rules which the mathematician stipulates. For example, one can stipulate that it is possible to take differentials of distance in each of the dimensions without involving any of the other dimensions. In this case, the coordinates are called orthogonal.  But this is not necessary, nor need the rules conform to the requirements of Euclidean geometry.

The physicist makes use of the mathematician’s algebraic constructs, but they are obviously not sufficient for his purposes. To make a space physical, its dimensions must be related at least in principle to real physical measurements.  They no longer need to be dimensions in an univocal sense, nor need they be restricted to three.  For example, classical mechanics uses configuration spaces in which some of the coordinates are measures of position and others are measures of momentum. The description of a body freely moving in space thus requires six dependent variables, with time as a parameter. The space of the physicist is like that of the common man in that he understands it in terms of physical realities, but he is like the mathematician in that he uses an artful algebraic structure to relate these real things to each other.

The space of the theory of relativity is what is known technically as a four dimensional pseudo-Riemannian manifold[9]. The four dimensions are, of course, three of space and one of time.[10]  The student of the theory of relativity likes to use the phrase “space-time” to describe the object of his study because he is more inclined to think about this very elegant four-dimensional description of the world. The cosmologist, on the other hand, is inclined to keep space and time separate in his thought if not always in his descriptions, perhaps because his scientific roots lie in astronomy.  From here on, we will follow the cosmologists, as well as common sense.

So once again: what is space? It is certain that space is not a mechanical ether; by this we mean that it is not a substance possessing the ordinary properties of matter – mass, temperature, inertial resistance, etc. Space must not have any properties of its own that would impede the action of bodies or of radiation. Yet it is not nothing[11], since it underlies many accidental properties.  Besides containing radiation and ordinary matter, various fields exist throughout. Besides the familiar gravitational and electromagnetic fields, we now have the Higgs field and no doubt other exotic ingredients. The primary field filling space is the gravitational field. This is a field sui generis. Others may be called fields of force, but this field is not like that. Other fields have quanta, and perhaps the gravitational field does too, but the truth about this is not known. The theory of relativity proposes that its very nature is to be a manifestation of the physical dimensionality of space and time.  

The conception of space as measured extension opens the door to geometries that are non-Euclidean in nature. The use of these geometries to describe motions in the presence of strong gravitational fields has been very successful, and so this approach is useful to astrophysicists and even to rocket scientists.  The cosmologist, however, is not interested in the universe on the small scale. One of his principal tasks is to determine the geometry of space as a whole, that is, to determine its global gravitational field.

In the standard cosmological model, space on the large scale is presumed to be homogeneous and isotropic. This is the cosmological principle. The background space might be compared to the smooth equilibrium surface of the ocean. The presence of other beings produce ever changing distortions in the field, just as winds and boats create ever changing ripples in the sea. But the level surface remains as a principle, and in fact it is only that which one will see from a great distance.[12] It is assumed that this space will be characterized at any given time by a simple and uniform geometry. The cosmological principle demands this simplicity.

The background geometry of the whole universe should in principle reveal itself in the visible universe, but what this data is telling us is not certain. Until recently, it seemed easy in principle to find out whether the universe has an overall curvature, though not so easy in practice. Since curvature is produced by mass-energy, the density of this in the universe should determine whether there is enough to make it closed (positive curvature); or if not enough, whether the density is just right to make it flat, or so low as to result in negative curvature.  Until recently, everyone assumed that the cosmic expansion must be slowing down. The rate of deceleration would have to be small, since the Hubble graph was so nearly linear. But it stood to reason that the mutual gravitational attraction between the galaxies would cause some deceleration. The only question was whether there is enough mass to bring the expansion to a halt asymptotically, to eventually reverse it into a collapse, or to be insufficient to prevent an unending expansion.  Now that it seems that the rate of expansion is increasing, the old formula used to analyze the situation is not going to be valid. There are still ways to examine the question[13], and all the evidence so far points to a flat, or very nearly flat, universe.  

The idea that space is flat, and therefore (on the average) Euclidean, is appealing, at least to many of us[14], but in view of the fact that the claim is usually understood to be about the actually existing universe and not merely about an abstract manifold, it does raise some questions.  If it is flat now, was it always flat? Does the flatness of the cosmos imply that it is infinite in extent? If not, what limits it? On the other hand, does it follow from having the universe begin with a Big Bang that it is finite, that it started out small or even point-like?  

The last question of these is the most easily answered, since it is just a matter of explaining the conception. All that is meant by the Big Bang is that if the cosmic expansion is traced back in time, one arrives at a beginning of motion and time as well as of the being of the universe. The Big Bang is a singularity, in the sense that time and space are not defined for anything prior to it. It is analogous to the point which terminates a line. Such a point is the beginning of a line but it is not itself a line.[15] The Big Bang is an event, not an extension. In fact, since points do not actually exist, the initial universe must have had extension in all three dimensions. The Big Bang as such is not inconsistent with an infinite universe, though that would imply that the universe has no size and cannot grow larger. Some possible interpretations of the cosmic expansion would be precluded.

But neither does a flat universe, having a Euclidean like metric, have to be infinite. There are very good reasons for holding that the universe must be finite. Aristotle and the medieval cosmologists saw no conflict between a finite universe and Euclidean geometry because the universe was thought to be contained by a natural substance, albeit one whose material was not like the material down here below the moon.

A universe that is both flat and finite does seem to conflict with the cosmological principle and the related claim that no observer is in a special or privileged position in it.[16] Unlike in the case of a positively curved finite manifold, which curves back in on itself like a sphere, a flat finite space must have a two dimensional surface, and so not all places within it are alike. As the ancients had a horror vacuui, so moderns seem to have a horror of being special. One wonders if our horror is just as questionable as theirs.  A balloon hovering above the ground, in the absence of wind, is pressed in all directions equally by the air. Yet the atmosphere is not really homogeneous and isotropic. It just looks like that as long as one is not very large stays well away from the edge. Our visible universe certainly looks homogeneous and isotropic on a sufficiently large scale, but we cannot really say what the whole universe is like. I do not think that reason requires one to suppose that the universe has throughout its extent a flat geometry, just because the visible universe seems to.[17]  If there really is something like an edge somewhere beyond our sight, it would be any observers near the edge that will be special. Our vantage point will be mediocre, so their fears should be allayed.

Another apparent difficulty for accepting a finite flat universe arises from a confusion between the mathematical and the physical.  We cannot infer from our inability to imagine Euclidean space going on forever that the world itself is like that. If matter and radiation are finite, so also is space, in the physical sense.  Cosmologists have no trouble agreeing with Aristotle that outside a finite universe there might be absolutely nothing at all.

Even mathematically, it is possible for a manifold to be flat and finite while not being the imaginable space of Euclid. Flat has a somewhat peculiar meaning to the mathematician nowadays.  A manifold is flat if it can be flattened without tearing or overlap. Imagine a piece of string laid out in a curve. Now straighten it out, ignoring its thickness. The string models a one dimensional flat manifold, however it is laid out. A piece of paper models a two dimensional flat manifold, however it may be bent or even crumpled up. It may even be rolled into a cylinder without ceasing to be flat in the sense we are using the term. An ant crawling along any direction except that parallel to the axis will by going straight ahead wander around without escaping from a closed loop. Since flatness is a manifestation of how infinitesimally small elements of a space are connected to each other and not a description of large scale structure, even in higher dimensions than two, the flatness of the space does not necessarily mean that it is unbounded. If, as I think, an actual infinity of space and matter makes no sense, I am not thereby required to reject the flatness of space and the validity of Euclidean geometry for measurement in appropriate circumstances and on appropriate scales.[18]

Time

Is it meaningful to assign an age to the universe? In the theory of relativity, measures of space and time are the relative things. Clocks run at different rates for different observers, either due to their relative motions or due to the presence of variable gravitational fields.  Does the idea of a cosmic time make sense in this context? Herman Bondi wrote: “Although the existence of such a time seems in some way to be opposed to the generality, which forms the very basis of the general theory of relativity, the development of relativistic cosmology is impossible without such an assumption.”[19]

In speaking of “such a time,” Bondi means not just a time that is an independent reality but also a preferred time that has real significance for the universe as a whole. To hold that there is such a time is to hold that there are preferred observers.  Since it is a leading idea of the general theory of relativity that all reference frames are equivalent for the formulations of the laws of physics, one might think that no reference frames can have priority over others. This is incorrect in the context of cosmology. Those observers who are at rest with respect to the universe as a whole will be able to give the simplest and truest possible description of it.[20]  Relativistic cosmology is consistent with the existence of such observers. They called “comoving observers,” for they move only with the Hubble flow. Imagine a grid painted on a balloon, and observers located at all the intersection points of the grid. If the balloon is inflated or deflated, these will keep their relative positions on the surface. This is the defining characteristic of comoving observers.  It is assumed in the theory that these observers will see the cosmos, on a sufficiently large scale, as isotropic and homogeneous.  Non-comoving observers will see a greater or lesser deviation from these symmetries according to how fast they are moving with respect to the comoving observers. Since it is posited as a first principle that the universe really has these symmetries, these observers may be regarded a privileged in compared to others, for they see the whole cosmos in this respect as it really is. Moreover, all observers in comoving reference frames who see identical physical conditions for a given event in the universe are said to share the same epoch and share a common universal time. This is the proper time of the cosmos as a whole, and the current epoch of the cosmos is its present age.

Physics gives indirect support to the idea that there is a preferred time that many if not all things participate in. To quote Malcolm Ludvigsen, “It is a remarkable feature of our universe that clocks reading electron, proton, and gravitational time appear to remain synchronous.”[21] These measures of time are based upon units determined by the electron mass, the proton mass, and the gravitational constant, respectively. The unit of time determined by G would be especially suitable for cosmology.

There is reason to think that we are approximately comoving observers. The fact that the cosmos looks nearly homogeneous to us is one sign. This has been verified by the recent observations made from space.  Also, our motion is very slow compared to the Hubble flow. This means that we can take the results of our measurements as representing pretty accurately the results that would be obtained by an observer at rest in the whole.  Using the best current value for Hubble’s constant, we can infer that the Big Bang occurred about 13.8 billion years ago. This is in reasonably good agreement with estimates made by other methods.

For the philosopher, the question of whether the unity of time can be grounded in the expansion of the cosmos is an interesting one. This is a good example of a question of interest to the natural philosopher but not to the physicist as such.  Yet it does touch upon matters that concern the cosmologist. If the universe, as one mobile being, were expanding in a uniform manner, it would seem to be a plausible suggestion. Assuming that natural units can be established without periodic returns, we would have all we need to update Aristotle’s account of time as a measure of the motion of the fixed stars. But there are some difficulties with this idea.

If the rate of expansion is increasing with time, as the recent data from red shifts indicate, there must be some prior time-keeper by which this motion is judged to be accelerating. This time-keeper is light. Some motion must be postulated to be uniform, and light seems a very suitable candidate. The idea that light is the primary timekeeper is intriguing, though it has the consequence that beings other than light, including the universe as a whole, do not participate perfectly in time, and it seems to imply that the primary timekeeper is many rather than one. Since light seems to have been the first thing to exist in the natural world, the primordial light, which still exists and moves, seems to me to be suitable. This light may even be one in some sense, perhaps by way of entanglement.

On the other hand, maybe the expansion is uniform and the apparent irregularity is explained by changes in our measuring tool. There may even be some evidence from astronomical observations that light does move faster as time goes on, though this is very controversial.  This would give rise to the appearance that the expansion of the universe is accelerating. Attributing the unity of time to the expansion of the universe rather than to the motion of light seems to have the advantage that the former posits a single, unified mobile whereas the latter posits many mobiles. But the comparison is not as obvious as it sounds. Even if the cosmos is a unified whole, it does not follow that its motion is one or that it is suitable to measure out time. It is not even clear that what is happening to it is motion, strictly speaking.

Expansion

I have already indicated that the cosmic expansion is not a local motion. Further arguments may be give to show that it cannot be. Local motion is change of place. There can be no local motion if there is no place not occupied by the mobile and which it is able to enter. There are no places outside the universe as a whole. It might even be argued that since the universe is not in a place (nor is it anywhere) it is not even the kind of thing that could be thought of as mobile, at least as a whole.

If the cosmos is moving with some other motion, the two possibilities would be that it is altering or that it is growing. It is hard to see what growth might mean in the absence of anything analogous to food to fuel the growth. Unless the visible universe is being fed by something outside, whether you want to call it another universe or an unseen part of our universe, growth does not seem to be the right way to characterize the expansion. There was an idea early in the history of modern cosmology that certain nebulae were spewing matter into the visible universe, but this proved to be untenable. Although there is no way to rule out an invisible pasture, there is no positive reason to think it exists.

On the other hand, current thought about the expansion does posit something that looks like growth. According to this opinion, new mass-energy is appearing in the universe, from nowhere, or from who knows where.  This energy manifests itself as space. The cause is given a name – dark energy – but not an explanation. That the universe expanding from within through the unexplained appearance of new matter and energy has received support from the evidence that the expansion rate is increasing. If the universe is not just coasting or better yet decelerating, some cause must be acting to speed it up. Thinking that the cause lies outside the visible universe, they name it only as something having the same nature as the effect.  Although some are so irrational as to claim that there is no cause[22], I think most would suppose that there is something out there that we just can’t detect.

The final possibility is that the expansion of the universe is some sort of alteration. This seems to fit with the way the expansion is described in the mathematics. A scale factor is posited to measure the ratio of the distance between galaxies to the wavelength of light used to measure the distance. This is analogous to the scale of an ordinary map, with the qualification that the scale changes with time.  Mathematical models of the cosmos are contrived to predict the scale factor function inferred from observations. Ratios are quantitative relations, but they may describe qualitative relations inasmuch as these are know to us through measurement. Perhaps that is what is involved here. Perhaps we are seeing the results of alteration either in the measured or in the measure.  If the universe, the measured, is altering, we are back to the same kind of difficulty we had with growth. If one is willing to give up the cosmological principle, one might posit that there is some qualitative dis-equilibrium in the whole universe which is being adjusted by an alteration of the visible universe, or perhaps by a rearranging of the mass-energy in it. We would then need to understand why the visible universe looks so homogeneous. If the measuring tool, light, is the thing that is changing in the requisite way, we have not explanation at hand why it should.

As you can see, I have a lot of questions but not many answers. It is not at all clear what is going on with the universe, but it is clear that cosmology is in a very preliminary and provisional state of development. Before certain fundamental issues in relativity and quantum mechanics are sorted out, the story told by the cosmologists should be held with considerable fear of error on those grounds alone.  I have in mind, for example, non-locality, an idea which has recently received compelling empirical support. Possible implications of non-locality for cosmology have not yet, to my knowledge, been seriously addressed. Why, then, should the natural philosopher be concerned with modern cosmological theories, except perhaps for polemical reasons? It seems to me that there are at least two good reasons to be involved in the discussion of these issues. First, because clearing away impossible ideas helps in an incidental way in the search for understanding. Second, because some of the ideas incorporated into the theory are most likely true, and a little truth about difficult matters is always worth having, even in the form of conjecture. We can learn from modern cosmology that some previous ideas about the universe are false, even if we do not have complete certainty about better ideas to replace them.

As far as theories within the specialized sciences go, there is no going back. When a new explanation replaces an old one, it is never just a recurrence of an abandoned one. Even if it incorporates something from an abandoned theory, the old is modified, no longer just what it was, as when in a Mozart symphony the thematic material is modulated to a new key.  Such, for example, is the appearance of something analogous to elastic waves in Maxwell’s theory of electromagnetic radiation. In other cases, the old is incorporated into the new as a limiting case, as Newton’s theory of gravity is into relativity. The old cosmologies, either those of the ancients or those of the Newtonians, will not recur in their original forms as the standard model is adapted to new research or perhaps completely abandoned. The case is different for the solid conclusions of natural philosophy, as these rest on common experience and not on ever expanding and improving empirical evidence.  Whatever the cosmologists bring forth, as new ideas emerge in the underlying physics or new phenomena come to light, the natural philosopher stands ready to examine the results in light of solid principles.


[1] St. Augustine, Confessions,  XI, 14.

[2] Relativity, The Special and the General Theory (1961), p.106. 

[3] The Big Bang and the Expanding Universe have become commonplace notions for readers of popular scientific literature, as well as for astronomers and physicists.  I will therefore give only a brief account of the origin and development of these ideas. For a good historical account of these developments, see The Day We Found the Universe, Marcia Bartusiak.

[4] Edwin Hubble, The Realm of the Nebulae, Dover Publications (New York, 1958), p. 168.  The photographs of spectra are taken from p. 118.

[5] The proper motion of the sun was estimated empirically by randomizing the proper motions of stars within our galaxy.  We see here the Copernican principle at work.  See The Realm of the Nebulae, p. 106.  He does not justify the assumption that the solar motion is effectively equal to the motion of our galaxy.  I am sure he did not think we were at rest in the Milky Way, but he thought it reasonable to assume that we were not moving very fast in it.  We now know that the sun partakes in a rotational motion of the galaxy, and presumably this is allowed for in modern calculations. 

[6] If the  a universe consisting of a gas-like collection of small particles, Newtonian dynamics give essentially the same results as relativistic dynamics for a homogeneous and isotropic expanding universe.  This model, now called “Newtonian Dust,” is treated in textbooks on general relativity such as Foster and Nightingale A Short Course in General Relativity, sect.6.5.  After showing the similarity of the results, they explain why, nevertheless, the Newtonian treatment is inadequate to the real universe, which after all has in it many other things that are not like dust.  In addition, the Newtonian treatment is a sort of hybrid, since it must assume things about light that were not originally part of classical dynamics.

[7] Cosmology (1960), Ch. IX, Sect. 1.

[8] According to Edward Harrison, Cosmology: The Science of the Universe  (Cambridge University Press, 2000),  p. 279, E. A. Milne introduced the term “world picture” to describe the universe as we perceive it.  As Harrison says, “the world picture is godlike, the world picture is wormlike.”

[9] Roughly speaking: a Riemannian manifold is a mathematical space that is flat (or Euclidean) in the neighborhood of every point in it.  It is pseudo-Riemannian if not all terms in its differential distance have the same sign.  The manifold of special relativity, for example, is pseudo-Riemannian because when the spatial components of ds2 are all positive, the dt2 term is negative.

[10] An equal number of orthogonal dimensions made of projections of these can also be used.

[11] This notion, that space is not nothing, is almost as far as Einstein would go.  He was willing to call it an ether, but he insisted that it was not a frame of reference, absolute or otherwise.  Quantum physicists characterize it as the quantum vacuum, the realm of virtual particles. From the Aristotelian perspective, one must say that the thing we are thinking about (which I like to call “the in-between”) is a body, a composite of matter and form, but thought of in abstraction from any accidental forms really existing in it other than its extension.  Since almost all mathematical (but not quantum) conceptions of particles treat them as points, the physicist doesn’t worry about questions such as whether space exists inside ordinary bodies. 

[12] The scale at which the lumpiness of the universe evens out is very large indeed.  It is estimated at 100 megaparsecs.  This is given the colorful name, “The End of Greatness”.

[13] See, for example, http://map.gsfc.nasa.gov/universe/uni_shape.html.  Data from the WMAP satellite strongly confirms the flatness of space. “We now know (as of 2013) that the universe is flat with only a 0.4% margin of error.”

[14] In his excellent book The Road to Reality, Roger Penrose expresses his aesthetic preference for a negatively curved universe.  He writes words of wisdom, however, about the reliance on such preferences, and to the hasty drawing of conclusions.  See Sect. 28.5.

[15] This does not imply that the Big Bang happened at some point within the cosmos.  There is no center from which the expansion happened. If there is reference to some center, such a point does not lie within the universe.  See Penrose, The Road to Reality, p.722.

[16] Note that this does not mean that there are no privileged observers.  This will be clarified later.

[17] This has caused some anguished soul-searching among those who think there should be nothing at all special about our world, and flatness seems to them to be a special case.  This is one of the so-called problems that is supposed to be solved by the inflation theory.  They say that it was not flat in the beginning, but because it got to be so big so fast, we can’t see the curvature of the initial universe.

[18] The qualification in necessary because distances as measured do not conform to Euclid in the presence of strong gravitational fields, as near the sun.

[19] Cosmology, Ch. VIII, sect. 8.

[20] General Relativity: A Geometrical Approach (Cambridge University Press, 1999), p. 7.

[21] Op. Cit., p. 11.

[22] See, for example, A Universe from Nothing, by Lawrence M. Krauss.