Contemporary astrophysics has opened the way for a remarkably deep insight into the creation and nature of the universe. The General Theory of Relativity, Hubble’s redshifts, Penzias’ and Wilson’s discovery of a universal background radiation, the discovery of black holes, Quantum Theory, and a host of other discoveries have led to a grand scheme of universal origins called "Big Bang cosmology." In the view of many physicists and philosophers, this remarkable cosmological theory points to a creation event as well as an ordered unfolding of the universe which is virtually inexplicable without a determinative ordering principle. In 1983, Paul Davies connected the evidence of physics to the finite age of the universe:

Today, most physicists would not make this kind of direct claim because of several recent additions to the classical Big Bang model. The four most influential changes are:

These developments have added considerable complexity to what is now known as the "contemporary Big Bang model" which makes the insight into a creation event less direct, but makes the insight into universal design more probative and beautiful.

Though the contemporary Big Bang model still indicates that the post-Big-Bang observable universe is finite in space and time, it does not account for what is termed "the universe as a whole" which considers two additional possibilities:

If the above two conjectures are not correct (and therefore, if the universe originated with the Big Bang and is limited in extent to the observable universe), physics would provide a strongly probative argument for a creation event through the finitude of universal past time. However, the possibility of a pre-Big-Bang era and space beyond the observable universe requires an investigation into domains about which physics can only speculate. Nevertheless, a philosophy of space and time can be applied to the notion of physical simplicity (i.e., a unified era), and to the conditions of spatiality to show that the finitude of the post-Big-Bang universe probably extends to a pre-Big-Bang universe (if, indeed, such a pre-Big-Bang universe existed). Thus, the combination of philosophical evidence (an ontology of space and time) and physical evidence (a notion of physical simplicity in a unified era) can provide considerable evidence for the finitude of universal past time, and therefore, for a creative event at the universe’s first moment.

If a pre-Big-Bang universe existed, then it would both enhance the probative force of arguments for universal design, and reveal the magnanimity and beauty of that universal design. This insight was quite poignant in the classical Big Bang model, as evidenced by two of the greatest contributors to that model – Roger Penrose and Arno Penzias:

If a pre-Big-Bang universe existed, it would have had to have done so through a unified field, the physics of which is radically different from the post-Big-Bang (General Theory of Relativity) field. This means that the initial conditions of a universe of gases and galaxies was not only intrinsic to the Big Bang, but also to an era whose physics was radically different from the one in which the gases and galaxies emerged. The unfolding of one kind of universe into another would seem to reveal even more poignantly and beautifully Penzias’ "underlying supernatural plan."

This investigation will be divided into the following sections:

The classical Big Bang model gives considerable evidence for the finitude of the post-Big-Bang universe through four methods:

As will be shown below, the first two methods are as valid today as they were in classical Big Bang cosmology. However, the second two methods were mitigated by the probability of an inflationary era (predicted by Andre Linde and others) which pointed to the presence of large quantities of vacuum energy in the universe.

Vacuum energy is evidenced in the "borrowing" of energy for virtual particle pair creation within a quantum system. It is different from mass energy in that it opposes gravity and actually increases in magnitude with distance. When Linde and others discovered the probability of an inflationary era, they also pointed to the probable existence of vacuum energy in the universe as a whole (i.e., in addition to the vacuum energy in quantum systems). This had the effect of undermining the calculation of an open (solely expanding) universe on the basis of mass energy’s effect on total universal gravity. However, the presence of such vacuum energy requires the universe to expand (and not to contract) from the moment of the Big Bang, onward. Thus, the undermining of one method of showing the finite age of the post-Big-Bang universe led to another more conclusive one.

The presence of vacuum energy also mitigated the fourth method for determining a finite age of the universe (the universal singularity hypothesis of Stephen Hawking and Roger Penrose). Prior to 1985, the Hawking-Penrose Singularity was considered to be one of the most probative pieces of physical evidence of a limit to past time in the universe. In 1980, Hawking wrote, "a curvature singularity that will intersect every world line…[makes] general relativity predict a beginning of time."

Quentin Smith, summarizing Hawking and Penrose, lists the five conditions necessitating a singularity according to standard GTR:

Prior to the discovery of evidence for an inflationary era (and its vacuum energy), all five of these conditions were thought to be met in the universe. Quentin Smith summarized the consequences of this by noting:

However, the increasing likelihood of an inflationary era (with the accompanying vacuum energy required to produce it) changed this reasoning, because it violates the third of the above conditions (the mass density and pressure of matter never become negative). If there was an inflationary period at the early phase of the universe, then there would exist a very strong pressure associated with the universe’s vacuum energy which is equal to minus the density. Recall that vacuum energy is different from mass energy in that it opposes gravity and increases in magnitude with distance. The presence of this energy would then exert a very strong negative pressure of matter, violating Hawking’s third condition. Though this result mitigates the prediction of a singularity in the GTR model, it does not rule out the occurrence of a singularity at the beginning of universal space-time asymmetry. In any event, a singularity is only one of a myriad of different ways in which an intrinsic limit to universal time might be manifest.

Inasmuch as universal inflation is unlikely to have occurred infinitely throughout the past, then the universe would seem to either:

The first option implies a beginning of universal time 13.7 billion years ago. The second option suggests a beginning of time at "13.7 billion years plus the time intrinsic to the Planck era." As will be discussed in Section II, physical evidence can show the likelihood of the finitude of such a pre-Big-Bang era. Philosophical evidence can also show this through the Hilbertian paradox.

In view of these changes to the Big Bang model, our consideration of the finitude of the post-Big-Bang universe will be divided into two parts:

Classical Big Bang cosmology is grounded in the General Theory of Relativity (hereafter "GTR") which shows the interaction of gravity with the other three fundamental forces (electromagnetic, strong nuclear force, and weak force) through a dynamic space-time field. Though many current discoveries and theories have raised doubts about the sufficiency of GTR to describe a pre-Big-Bang, non-observable universe (e.g., the temperature of the Planck era, the quantum vacuum fluctuation hypothesis, the quantum gravity hypothesis, unknown effects of electromagnetic forces at the earliest stage of the universe, superstring theory, Linde’s chaotic inflation theory, and the Hawking imaginary time conjecture), it is still considered valid for describing the post-Big-Bang, observable universe.

The Newtonian view of a universe of infinite space and time held sway for nearly 260 years. This assumption was dramatically changed when Einstein published his famous work on the General Theory of Relativity. One of the peculiar predictions of GTR (first made by Friedmann) was the finitude of the observable universe. This prediction was later confirmed by the discoveries of Hubble, Penzias and Wilson, and many others.

The General Theory of Relativity holds that space is neither nothingness nor an empty vacuum. It is a dynamic interrelational "field" through which mass-energy interacts. This dynamic field of interaction can vary in its metrical and geometrical configuration. When it does, it can become curved, and so curve the trajectory of mass-energy interacting through it. This would make the shortest distance between two points a curve! Perhaps stranger still, the metric of this field can vary so that the three-dimensional scale of an equal quantity of mass-energy could be different from place to place. The density of mass-energy manifest in deep space might be quite extensive compared to the density of mass-energy at the base of a black hole (where the relative scale of energy manifestation is considerably restricted). In essence, then, the General Theory of Relativity holds that where there is density of mass-energy, there is likely to be a shortening of the radius of curvature of space which implies a compression of the scale of space.

Gravity no longer needs to be viewed as a Newtonian force. All gravitational effects can be explained in terms of the curvature of space. If, for example, a large amount of mass-energy is concentrated in a particular region, the radius of curvature of space will shorten, compressing the scale of space. Now, if some moving body (a second manifestation of mass-energy) should approach the first body, it will be drawn toward the compressed region (i.e., towards the shortest distance between two points). It will even orbit around the curvature of the compressed region (because the shortest distance between two points is a curved line in curved space – a geodesic). This explains "attraction at a distance" without making recourse to Newton’s "force of attraction."

Another oddity of the General Theory of Relativity is that mass-energy takes on the curvature (compressed scale) of the space through which it interacts. Thus, if a manifestation of mass-energy inheres in a region of space with a compressed scale, it too will take on that compressed scale. This peculiar quality opens the way to a bizarre phenomenon predicted by the General Theory, namely, black holes.

As a star collapses, it also compresses the scale of space (shortens the radius of curvature) in that region. The mass-energy of the star takes on the compressed scale of space in that region, which, in turn, compresses the scale of space even more, which, in turn, makes the star conform to the more compressed scale of space, etc., until the entire mass-energy of the star is situated in a single coordinate approximately 10^-33 cm (the Planck minimum).

If a second manifestation of energy (say, a planet or a star) were in the region of the black hole, it would follow the spatial curvature of the black hole (towards the shortest distance between two points) until it could go no further (the base of the black hole). As it was moving toward the base, the front end of the star would take on a more compressed spatial scale than the back end of the star, making the star into a kind of spaghetti trailing around the curvature of the black hole. In ordinary circumstances, the star would not be able to reverse its direction and go in the direction of the greater distance between two points. Its fate, as it were, is sealed.

The General Theory of Relativity can be and has been applied to the universe as a whole. It has been used to show the finitude of space in the observable universe, the finitude of time in the post-Big-Bang universe, the succession of events which are likely to occur in a universal collapse, and even the dynamics of universal expansion in inflationary and non-inflationary scenarios. Unfortunately, this grand theory does not extend to the pre-Big-Bang, non-observable universe.

In 1929, the famous American astronomer Edwin Hubble made the remarkable discovery that the greater the distance a light source (such as a galaxy) is from the Earth, the more its spectral lines are displaced (shifted) toward the red (low frequency) end of the spectrum. A brief explanation of this will reveal how Hubble was able to calculate the size, density, and age of the observable universe. Three aspects of elementary physics are needed to understand Hubble’s discovery:

Hubble first discovered that galactic motion relative to our galaxy is dominated by redshifts. This means that the universe, as a whole, is expanding. Now, if the universe as a whole is expanding, then all galaxies are moving away from all other galaxies, implying that the universe has no center.

We are now prepared to interpret a second feature of Hubble’s finding: the redshift increases in proportion to the distance from the Earth (i.e., the greater the distance from the Earth, the greater the redshift). Let us break this proposition down into two parts and translate them. Recall that "greater redshift" means "moving away from an observer faster," and "greater distance" means "a longer time ago."

If things are moving away from me faster longer ago, they must be moving away from me slower today. In short, the observable universe was not only expanding, it was slowing down in its expansion. This allowed Hubble and his followers to make a series of remarkable deductions which ran contrary to the hypothesis of an infinite universe. The following conclusions update those of Hubble and his followers to account for elements of the contemporary Big Bang model (particularly the inflationary era and a pre-Big-Bang unified era).

1) Gravity (what Newton described as the force of attraction between bodies, and what General Theory of Relativity calls the curved or compressed scale of space) is the cause of the slowing down of the universe’s expansion in the past. By knowing the rate of deceleration, we can determine the strength of universal gravitation.

2) The density of mass-energy is what causes gravity to increase. The greater the density of mass-energy, the greater the gravity. If mass-energy were infinitely dense, so also would be gravity. If there is infinite attraction in the universe, the universe could never have expanded. Indeed, if it were already expanded, it would inexorably implode until it became similar to a black hole.

3) If the universe has experienced inflationary periods, it has probably only been in a state of expansion (see below, Section II). If one assumes that the unified era and the inflationary period immediately succeeding it were relatively short in duration, and the current inflationary period has been occurring only since the time of a redshift of .5, then the age of the universe can be calculated by using Hubble’s constant which was applicable during the lengthy non-accelerating period (between the first and current inflationary periods). From these data, it seems that the observable universe is approximately 13.7 billion years old.

4) In view of the above, the total mass of the observable universe must be finite (currently estimated at 10⁵³ kg). Using this as a base, we can also calculate the approximate number of particles which do not have rest mass (e.g., photons) and derive reasonable estimates for the amount of energy in the observable universe. Though these numbers are quite large, they are nevertheless quite finite.

5) There is evidence to suggest that the early inflationary period of the universe was preceded by a superunified period (see below, Section II.C). In this super-unified period, what was to become the observable universe had a very small radius (approximately 10^-33 cm) and a temperature above 10³²K, which would make the General Theory of Relativity inapplicable. This period (which I have termed the "unified era," also called the "Planck era") has been variously described through quantum cosmology and superstring theory (see below, Section II.C). Parts of these theories may have validity in the description of this extreme phase of the universe.

6) After the unified era, the universe seems to have moved through several phases to arrive at nucleosynthesis (the generation of atomic nuclei):

Each of these eras represents its own branch of physics moving from the very elementary generation of particles (such as quarks and supposed gravitons) to protoparticles which have passed away, leaving "massless" remnants (such as photons) to short-lived interdeterminately existing particles (such as pi-mesons) to the particles which still exist in abundance today and constitute both simple and complex atomic nuclei (protons, electrons, and neutrons).

Hubble’s theories were quite remarkably confirmed through the discovery of an independent form of evidence: a universal isotropic microwave background radiation.

In 1965, two scientists from Bell laboratories, Arno Penzias and Robert Wilson, discovered a 2.76° K isotropic radiation almost perfectly uniformly distributed throughout the universe. The red-shifting of this very low level radiation indicated that it originated approximately 13.7 billion years ago. The universality of the radiation indicated that it originated at a very early stage of the universe. The uniform distribution of the radiation indicated that the universe expanded (in large scale) isotropically. If it had not, then the radiation would be distributed anisotropically.

A universal distribution of radiation is quite anomalous, for it cannot arise under ordinary circumstances. If an explosion happens in a particular region of space, the radiation (shock wave) from the explosion rushes out from the epicenter but is not present at all places from the epicenter. Furthermore, it is certainly not of the same intensity at each place from the epicenter, because it grows weaker as it moves away. What peculiar conditions, then, would give rise to a shock wave which is everywhere and uniform?

First, the radiation would have had to have been omnipresent at some primary stage of the universe. If it were not, the places where the radiation was not would simply become greater and greater as the universe expanded. Thus, if we are not going to postulate the deus ex machina of a radiation of 2.76° K spontaneously appearing with an accompanying redshift (indicating a 13.7 billion year old age), it would be reasonable to admit that the radiation was omnipresent at some primary stage of the expansion.

Omnipresence does not necessarily entail uniform distribution (the same temperature at all places). So, how can the universe’s uniform distribution of the red-shifted radiation be explained? If we look at the stages of nucleosynthesis, the most likely explanation seems to be that the universe emerged out of a primary moment with an ordered expansion. There are many reasons for suspecting this besides the uniform distribution of the universal radiation. For the moment, suffice it to say that the datum of the uniform radiation coincides almost perfectly with a variety of other independent data (including the General Theory of Relativity and Hubble’s redshifts). This suggests that the universe moved out of its first moment in such a well-ordered way that it preserved the uniformity of the background radiation through all subsequent eras.

The view of the observable universe as a finite, ordered, large-scale homogeneous, isotropically expanding whole is a far cry from Newton’s infinite space with its aggregating mass points in a Euclidean vacuum. As will be explained below, when this standard Big Bang view is modified to account for past and present inflationary eras, it reveals a finite age of the post-Big Bang universe and the possibility of a pre-Big-Bang (unified) era. Though physical evidence can show the finite age of the post-Big-Bang universe, it can only show a likelihood of a finite age of the pre-Big-Bang universe (see Section II.D). Given this probabilistic caveat, it seems likely that the universe began in a super-small, super-unified state, and emerged through a highly ordered process into a large-scale, well-ordered complexity.

By the end of this paper, I will show the likelihood of a finite age of the universe on the basis of physical evidence. This will be adduced in the following three steps throughout Sections I and II:

If the unified era is the universe’s first era, and if that era was finite in duration (as the physical evidence seems to suggest), the beginning of the unified era would seem to represent a moment of universal creation. If time in this era (which is quite distinct from "time" in the GTR era) is asymmetrical (which will be shown below – Section II.B), and this asymmetrical time is finite, then the unified era would have to have an intrinsic temporal limit. There cannot be any "prior" to this limit, for there would be no time and no condition in which this "prior" would be manifest. If something is not to come from nothing, this condition would imply a causative force transcending space-time asymmetry.

Physics has provided three kinds of evidence for the finite age of the post-Big-Bang universe:

2) the unlikelihood of indefinite oscillation, and

The second law of thermodynamics postulates that every instance of work (a use of free energy in a system) gives rise to an overall increase in entropy within a total system (a state of energy which can no longer be used for work). If the universe as a whole were considered a system, then its expansion and all the work within it would be continually increasing its entropy. Since work would occur within a universal collapse and even a universal black hole, entropy is inescapable in virtually every universal condition. Therefore, if the universe had existed for an infinite amount of time, but only had a finite amount of work energy, it would have reached a state of maximum entropy (thermodynamic equilibrium). However, in fact, the entropy in the universe is quite low, indicating that it has not existed for an infinite amount of time.

If the universe has only been expanding and its volume is finite, then the universe has existed for only a finite amount of time. As will be shown below, this is very probably the case. However, if the universe has not been "solely expanding," then it must have been oscillating (expanding, then contracting, then re-expanding, etc.), for it is expanding at the present time. Therefore, if it can be shown that an infinite number of oscillations is highly improbable, then the universe’s past time would have to be finite. There are two indications of the improbability of indefinite universal oscillation:

2) an increase in cyclic expansion

1) The Radiation Paradox. Every expansion (i.e., explosion of the universe) would produce an immense amount of radiation. Since this radiation is approaching thermodynamic equilibrium, it can be expected to remain throughout each contraction and re-expansion. Therefore, if the universe has oscillated an infinite number of times, there should be an infinite amount of residual radiation in the universe. This is clearly not the case. Even the naturalist, Quentin Smith admits:

2) Increase in Cyclic Expansion. The second piece of evidence militating against an indefinitely oscillating universe is related to the first. If each cycle inevitably leads to increased radiation, then that radiation will cause increased pressure. This increased pressure, in turn, will make each cycle longer, giving rise to more cubic volume of the universe before a collapse. If the universe has existed through an infinite number of oscillations, then there should be an infinite amount of radiation leading to an infinite amount of pressure, leading to an infinitely long cycle producing an infinitely large universe. This is clearly not the case. The observable universe, though very large, has a very finite volume, indicating a very finite age of approximately 13.7 billion years.

Quentin Smith looks at the problem from the opposite direction, but arrives (even as a naturalist) at the same conclusion:

If one excludes the possibility of a deus ex machina (God surreptitiously removing all of the radiation from previous cycles, or the universe violating the first law of thermodynamics and allowing for the complete annihilation – nothingness – of previously existing matter), an infinitely oscillating universe seems to contradict the current condition of the observable universe.

As noted above, both contemporary and classical Big Bang cosmology invariably entail a "solely expanding" universe. The difference between the two versions of Big Bang cosmology arises out of the currently recognized probability of dominant vacuum energy causing universal acceleration or inflation. Classical treatments of Big Bang cosmology usually include only matter and radiation. As will be shown below, if vacuum energy is not included, then there is not enough baryonic and non-baryonic matter to close the universe. If vacuum energy is included, then the very large pressure accompanying it will require that the universe be "solely expanding," even if it is in a closed configuration.

Since the existence of this vacuum energy is contested by some, I will present the argument for a solely expanding universe from both:

1) the classical model (accounting only for baryonic and non-baryonic matter),

Gott, Gunn, Schramm, Tinsley, Sandage, and Tammann have compiled striking evidence between 1970 to 1980 for a solely expanding observable universe. Their calculation is based on the following line of thought. According to the classical Big Bang model, the total mass-energy density of the observable universe will determine whether the universe is open (will continue to expand unendingly) or closed (will implode very probably into something like a black hole). If the average mass per unit volume, or mass density, is currently large enough (5x10^-30 grams per cubic cm – the so-called "critical density"), then the universe will be closed and will likely collapse. But if the average mass density is less then the critical density, the expansion of the universe will be able to run away from gravitational attraction. As the universe continues to expand, gravitational attraction becomes weaker and it can never slow the universe down to a halt. The universe will, therefore, continue to expand forever. Gott et. al. show (through the assumptions of the classical Big Bang model) from three distinct tests that the universe is most probably open.

(1) One can try to determine the deceleration parameter of the universe (q₀). Estimates of this can be made by comparing the redshifts of remote galaxies. This deceleration parameter gives an indication of the mass density of the observable universe which can then be compared to the critical density to determine whether the universe is open or closed. Current measurements suggest that the universe’s actual average density is less than the critical density, meaning that the universe is likely to be open.

(2) Estimates can be made about the average density of the observable universe from the mass density of all its galaxies. If we assume that the entire mass of the universe is contained within its galaxies, then the mass density of the universe is far too small to be closed. As Craig notes, there are two methods for determining this. First,

Secondly, as Craig notes,

(3) Assuming that the vast majority of deuterium arose out of cosmogenesis, then one could determine the average mass density of the universe by examining the ratio of deuterium to helium.

Deuterium manifests an incomplete fusion process (since it takes longer to fuse helium with its extra proton and neutron). If the universe were expanding rapidly, many such incomplete fusion processes could be expected to occur. Thus, the ratio of deuterium and helium-3 to helium-4 should indicate the velocity of the expansion, which, in turn, would reveal the amount of gravity present during the expansion, which would, in turn, reveal the mass-energy density in the universe. Current measurements of this ratio indicate a mass-energy density considerably less than that required to close the universe.

These three pieces of independent evidence indicate an average mass density of the universe (according to the classical Big Bang model) well below what would be required to cause a universal collapse. Therefore, according to these assumptions, the universe would appear to be open, the oscillating universe hypothesis invalid, and the age of the observable universe to be approximately 13.7 billion years old.

As noted in the introduction to this paper, several recent developments in astrophysics have made the contemporary Big Bang model more complex. Four of the more important developments are:

These developments have added considerable complexity to what is now known as the "contemporary Big Bang model" which makes the insight into a creation event less direct, but makes the insight into universal design more probative and beautiful.

The contemporary Big Bang model may be discussed in four parts: 1) the evidence for an inflationary era, 2) the effects of vacuum energy (required to produce an inflationary period) on a solely expanding universe, 3) the potentiality for a pre-Big-Bang universe as suggested by the presence of vacuum energy, and 4) the possibility of a pre-inflationary universe.

1) The evidence for an inflationary period. Contemporary astrophysicists have gathered significant evidence for an inflationary period at the inception of the universe. In brief, evidence from the Hubble telescope, the COBE satellite, and consequent computer modeling of the universe seems to indicate that the universe would have had to have gone through an inflationary or super-accelerating period (caused by the presence of vacuum energy) in order to arrive at its current state.

Andrei Linde details four pieces of physical evidence in favor of an inflationary period near the origin of the universe:

Some physicists believe that an inflationary condition exists even today. This current mild inflationary period followed a period of deceleration which occurred until the era marked by a redshift of approximately 0.5.

2) Vacuum energy and a solely expanding universe. The occurrence of this inflationary (accelerating) universe is attributable to the effects of vacuum energy which negatively interacts with density and has a strong pressure associated with it. Current evidence suggests that this pressure exceeds the gravitational attraction induced by the vacuum energy, causing an overall acceleration in the expansion of the universe.

Recall that vacuum energy is evidenced in the "borrowing" of energy for virtual particle pair creation within a quantum system. It is different from mass energy in that it opposes gravity and actually increases in magnitude with distance. When Linde and others discovered the probability of an inflationary era, they also pointed to the probable existence of vacuum energy in the universe as a whole (in addition to the vacuum energy in quantum systems) to induce this inflation.

Alan Guth has elucidated some of the stages which are likely to have occurred at the inception of inflation:

If this is correct, then the universe would be solely expanding (in either a flat or open configuration) and the calculations showing an open universe (according to the assumptions of the classical Big Bang model) would be unnecessary. This abandonment of classical calculations, however, does not affect the fact that the universe has been "solely expanding," because the outward pressure produced by the vacuum energy would prevent such an accelerating universe from collapsing in upon itself even if it were in a flat (just between open and closed), or even in a barely closed, configuration. Therefore, the assumption of vacuum energy in the contemporary Big Bang model requires that the universe be "solely expanding."

3) Linde and Guth on regional inflation. Andre Linde has proposed a model to explain the transition from the universe’s initial state to its inflationary era. He gives a chaotic, fractal-like twist to traditional inflationary theory. The theory is premised on the notion of scalar fields which mediate the interaction between electromagnetic and weak forces:

Linde adapts this notion of scalar fields to the universe as a whole and shows how it could explain inflationary regions by various scalar fields having arbitrarily different values in different regions ("chaotic" – "fractal-like" inflation). This obviates the need for phase transitions, super-cooling, or even the standard assumption that the universe originally was hot, which complicated earlier models of inflationary theory. For Linde, scalar fields can take on arbitrary values in the early universe. Some of these values will result in the universe expanding quite rapidly while others result in very little expansion.

Using chaotic inflation as a base (where different regions can have incredibly different volumes), he conjectures that each inflationary region can produce new regions (like the multiplication of a fractal):

He then makes recourse to multiple singularities expressing temporal beginnings and ends of specific regions of the universe:

Alan Guth and others have explored Linde’s conjecture and have concluded to the possibility of eternal inflation into the future, but not into the past. Notice that this does not conflict with Hilbert’s prohibition of an infinite past because future eternity is merely a potential infinity (in Hilbert’s parlance) which can keep on going into the future, but is only finite at any given present moment. Thus, "eternal inflation" does not imply an achieved infinite series, but only a potentially infinite – indefinite – series. Though Guth does not make recourse to Hilbert’s prohibition or ontological analysis, he indicates skepticism about inflation proceeding infinitely back in the past on the basis of physics (the inevitability of a singularity in any known model):

How, then, did inflation begin? This question is likewise unresolved, but is open to String Theory and quantum cosmological inceptions of inflation:

Though Linde’s and Guth’s theories do not explain the inception of inflation, they indicate the likelihood of a beginning of inflation and are open to quantum cosmological and String Theory as possible explanatory models.

If Guth’s suspicions are correct, then the inflationary universe (having either multiple regions or only our own) could have begun with either (1) an initial inflationary moment, or (2) a pre-inflationary unified state (perhaps describable by quantum cosmology and/or String Theory). If the first option is true, then the beginning of inflation is the beginning of the universe (approximately 13.7 billion years ago). If the second option is true, then the likely beginning of the pre-inflationary Planck era would constitute the beginning of the universe. The following will clarify this.

4) The possibility of a pre-inflationary universe (a Planck era). Recall that in the standard GTR model, electromagnetic, strong nuclear, and weak forces interact with gravity through the curvature of a dynamical space-time field. But this cannot be the case in a Planck era because the units of space are too small (less than or equal to the Planck minimum of 10^-33 cm). Nevertheless, gravity is dominant in this era in a quantized form. (At low energies, it must be consistent with GTR). This unification of gravity entails a form of time considerably different from the one described in the standard GTR model. The extreme and unusual conditions which might have constituted such an era are briefly (and speculatively) described in Section II.C through quantum cosmology and String Theory. This era could have had a long duration and could have been conditioned by a highly irregular quantum cosmological temporality. As will be shown below (II.B.), this highly unusual form of time would still entail an asymmetrical relation of events, and would not permit backward causation or time reversal.

In sum, if option #1 were true (post-Big-Bang universe only), and Guth’s conjecture that inflation must begin with a singularity is also true, then physics will have already demonstrated that the universe is finite in age (approximately 13.7 billion years old). Option #2 (pre-Big-Bang unified era), though more speculative, allows physical evidence to show a likelihood of finite age. If both options require (at least probabilistically) a finite age of the universe, they will also require a causative power transcending space-time asymmetry.

Before investigating quantum cosmological and String Theory conceptions of a totally unified era, it may prove helpful to give a brief ontological explanation of proto-time. The physics of time in a totally unified era is very incomplete, which has led many to speculate about imaginary time, symmetrical time, backward causation, and other unusual variations of event asymmetry. Thus, it seemed appropriate to present an ontological explanation of time which shows the natural asymmetry of events wherever there is change or changability (including unified fields, string conditions, quantum cosmological conditions. and other variants of the GTR model).

Ontological method may seem quite foreign to physicists and other non-philosophers. Though ontology does not derive its data directly from the empirical world, it does try to establish the necessary conditions and parameters of contingent existence (i.e., changeable existence, which includes physical existence). As such, it could reveal some necessary properties even of an unknown totally unified era. It must be stressed that the ontological time discussed below is not absolute. Its conditions and parameters allow for tremendous quantitative and qualitative variance. It is therefore compatible with any cosmological model of time which admits its broad ontological parameters. One of these parameters, as will be seen, is the asymmetry of transitions that occur through it.

Brevity constrains me to summarize my much more extensive investigations of this matter. Interested readers may wish to make recourse to them.

Ontological explanations are different from descriptions and scientific explanations. Descriptions relate data to an observer (e.g., the sun is rising). Scientific explanations relate data to other data through qualitative and quantitative apparatuses (e.g., the earth is rotating on its axis and is orbiting around the sun). Obviously, true descriptions can be false explanations. Ontological explanation is distinct from scientific explanation because it relates data to necessary conditions rather than relating data to data. Thus, the question for ontology is, "What are the conditions necessary for the possibility of…?"

When Aristotle and Zeno were asked to define motion, they did it in terms of its two necessary conditions, namely space and time. When they were asked to define space and time they did it in the same way, which involved magnitudes (divisible unities). Divisibility evidently entails separation; not complete separation, but rather intrinsically unified separation (in contrast to, say, two discrete points).

Let us begin with "space." This ontological discussion is important to astrophysics because some physicists and astronomers have theorized about the possibility of an infinite amount of space in a hypothetical non-observable universe. Inasmuch as the "non-observable universe" is non-observable, physics cannot empirically prove or disprove this conjecture. Hence, I must make recourse to ontological methodology to determine whether such conjectures are intrinsically contradictory.

Physicists have also theorized about the possibility of a really infinitely divisible spatial continuum. Again, such a conjecture could not be empirically verified without an empirical test of infinite division. Such a test is probably a long way off! Hence, I am again constrained to use ontological method to test for intrinsic contradictions.

The ontological response to the above two conjectures can help astrophysicists (non-empirical, non-mathematical way) to formulate notions of "pre-space," "proto-space," and "spatiality" which seem to be abundant in many contemporary cosmological theories.

First, space is not nothing. There cannot be "more or less" of nothing as there can be "more or less" of space. Nothing is simply nothing. As will be seen below, nothing is not continuous, dimensional, connectable, or orientable. Yet space in the observable universe has all four of these characteristics.

If space is not nothing, then what is it? Let us begin with locomotion. Locomotion entails displacement (i.e., a change in place). Displacement, in turn, entails distinct yet unified places. "Distinct yet unified places" entails: 1) contemporaneous separation of those places, and 2) intrinsic unity of those contemporaneously separated places. Were there no unity between contemporaneously separated places, there would be no possibility of moving from one to the other. Completely disunified places preclude motion.

This intrinsic unity of contemporaneously separated places constitutes the most fundamental quality of space, namely, continuity. Continuity, in turn, is the condition necessary for the possibility of the other three characteristics of space in our observable universe, namely dimensionality, connectivity, and orientability.

Perhaps the most well-known proposal comes from Stephen Hawking in his popular work, Brief History of Time. It is commonly referred to as the "no boundary condition" ("edgeless") universe. Since the time of Richard Feynman, mathematical integration of the electromagnetic, weak, and strong forces has been accomplished through the so-called "sum-over-histories" approach to path integrals.

In order to accomplish this, it is necessary to take the three spatial dimensions and one temporal dimension and convert them into four spatial dimensions. This, of course, only has a mathematical reality, for there are only three spatial dimensions, and reducing the time dimension to a spatial dimension requires the use of imaginary numbers.

The difficulty with this technique, as Hawking himself admits, is that:

The theoretical difficulties involved in integrating imaginary numbers into a real time scheme provoked researchers to propose another scheme of quantum cosmological integration giving priority to real path integrals (as distinct from imaginary ones). The theory of "instantons" (the rare geometries that give particularly large contributions to real as distinct from imaginary path integrals) could be a partial solution to the problem of ontologizing imaginary numbers.

One such proposal was formulated by Steven Coleman and Frank De Luccia based on their research into the possibility of false vacuums, which are quantum-mechanically unstable, though classically stable, excited states. Hertog points to several difficulties in using this conception of instantons. Stephen Hawking and Neil Turok attempted to resolve some of these problems with a class of instantons that did not require the existence of "false vacuums" and tunneling, but this gave rise to other problems (such as multiple singularities).

Three conclusions may be drawn at this juncture:

Another approach to the unified era (which does not exclude a quantum cosmological approach) may be found in superstring theory which integrates gravity with the other three forces of nature without implying infinities in algorithmically finite structures.

String theory is a derivative of elementary particle theory. It views particles as extended one-dimensional, massless, "string-like" objects 10^-33 cm long. These strings (whether open or closed) vibrate, and each kind of vibration corresponds to a particle type. Strings may interact with one another, giving rise to a wide variety of particle-like and energetic expressions. Superstring theory not only attempts to integrate the four forces, but also all the spins of all possible elementary particles. Hence, it finds symmetries between fermions (half integer spins) and bosons (full integer spins).

Though string theory holds out a possibility for theoretical explanation of total unification in the universe’s initial state, it faces two major difficulties. First, it requires ten (and in M-theory, even eleven) dimensions for complete symmetrical integration. Secondly, five possible super / heterotic symmetries of strings instead of one seem to suggest a kind of arbitrariness in the whole theoretical apparatus. Thus, superstring theory faces the same three challenges as the Hawking or instanton quantum cosmological theories:

The following five physical-ontological factors would seem to have been present in any model of a pre-Big-Bang unified era (quantum cosmological, string theory, or other) which transformed itself from a unified field to a GTR field (and an open inflationary state):

Even though the above reasoning process contains ontological analyses (such as the assumption of event asymmetry through proto-time and the unlikelihood of an extra-universal deus ex machinas which begs the question of the existence of God anyway) it is not devoid of physical evidence and physical reasoning. If there really was a pre-Big-Bang unified state within our universe, then that universe would have to have undergone a radical transition to a GTR, open inflationary state, which transition implies both changeability and a finite amount of disunification. Though this transition cannot be considered direct physical evidence of an intrinsic temporal boundary to a hypothetical pre-Big-Bang universe, it does, with the help of two ontological analyses, imply such an intrinsic temporal boundary. Though this approach will never be completely satisfactory to a physicist, it does present a probative clue to the probable conclusion of future physical investigations. Unfortunately, the current lack of physical evidence does not allow us greater certitude.

If the above analysis is correct, and there really was a pre-Big-Bang unified era, then the following five conditions would have likely been intrinsic to it:

Two ideas should be borne in mind as we proceed to draw conclusions from the above physical evidence. First, metaphysical conclusions cannot be deduced from the evidence of physics unless all natural processes are completely known. If all physical processes are completely known, then the inherent limits of physical causation would also be known, and if these completely known physical processes could not explain the existence of time and the universe, then a metaphysical cause (such as a causative force transcending universal space-time asymmetry) could be legitimately deduced.

However, the current state of physical knowledge is incomplete (as is amply shown in the speculations about quantum cosmology, string theory, and regional inflations). Therefore, we are left with adducing (instead of deducing) metaphysical causes of our universe. Adduction brings out as much evidence as possible in both the physical and ontological domains to substantiate reasonable and responsible beliefs. Such conclusions do not follow necessarily from their premises, but they are substantiated (and therefore not arbitrary). One cannot arbitrarily deny them unless new evidence is uncovered which mitigates previous evidence or previous models based on that evidence.

Secondly, Hilbert’s proscription does constitute a deductive process demonstrating the inherently contradictory nature (and therefore the impossibility) of infinite past time. As such, it stands on its own. However, it is interesting to note that current astrophysics (in combination with two ontological analyses) points adductively to an intrinsic temporal limit to universal past time. This forms a complementarity between adductive and deductive (physical and ontological) evidence which has two important effects:

Bearing these two ideas in mind, we may now draw a fourfold conclusion about the finitude of past-time in the universe (without making recourse to the Hilbertian proscription). Why a fourfold conclusion? Because each conclusion is based upon a different allowable interpretation of current evidence from physics. It is important to note here that each of these four allowable conclusions adductively substantiates the finitude of universal past time (universal space-time asymmetry). Each of these conclusions has been explained above, and so they will only be reiterated here with references to the appropriate sections in which they are explained.

These four conclusions represent current interpretations about the Big Bang, regional inflation, and pre-Big-Bang scenarios. Some are more speculative than others, but all adductively indicate an intrinsic temporal limit to the universe, which implies a creative force transcending space-time asymmetry.

The above physical evidence points beyond the creation event to the mentative qualities of the "creative force transcending space-time asymmetry." As noted above, Paul Davies believes that:

These odds are beyond astronomical, and they are relatively unaltered by inflationary theory and other contemporary astrophysical developments. One may want to say that the cosmological constant (giving rise to inflation) in its relation to other fundamental constants explains why the universe avoided the far more probable catastrophic black hole scenarios predicted by Penrose. However, it does not explain why the value of the cosmological constant fits so "coincidentally" with other fundamental constants to avoid such catastrophic scenarios. In light of this, Penrose’s and Davies’ conclusion about a "very special choice of initial conditions" is as valid today as it was in 1979. The probative value of this reasoning opens the possibility of significant mentative capacity within the "creative force transcending space-time asymmetry."

This idea is further enhanced by the contemporary Big Bang model. If one looks at the general propensity of the universe from the time of the Big Bang, one cannot help but conclude to the general, irreversible tendency toward greater disparity and dispersion. This is manifest not only in universal entropy, but also in the inflationary conditions which dominated the very early universe and may be effective even now (after a redshift of .5). This same propensity would be further verified if there had been a pre-Big-Bang unified era, for the breakdown of the unified field into a GTR field adds one more instance of radical disunification to the ones known to have occurred in the post-Big-Bang universe (i.e., inflation, the breakdown of the universal plasma into particles, the continuous expansion of those particles, etc.).

Yet, in the midst of this general universal tendency toward disunification (disparity and dispersion), the universal constants have subtle interrelationships which allow for the unfolding of systemic instances of greater unification (i.e., in galactic clusters and the eventual emergence of complex schemes of recurrence in carbon bonding, cellular metabolism, and other manifestations of genetic, metabolic, sensate, and conscious activity). One might want to be impressed by the counter-disunifying tendency written into the universe’s initial set of conditions which were to become manifest 13 billion years later. The subtlety, intricacy, and seeming "long term planning" which imperceptibly weaves itself into the vastly dominant tendency toward disunity, disparity, and dispersion, gives one pause to recall the words of Arno Penzias:

Though contemporary Big Bang cosmology requires more varied, complex, and even ontological analysis to establish the finitude of past time, it adds a depth, breadth, complexity, beauty, and probity to Penrose’s and Penzias’ contention about an "underlying supernatural plan." One might derive from this a sense, a kind of probative intuition, about a remarkably deep and comprehensive Intelligence and Beauty.

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