Philosophic Issues in Cosmology 8: Foundational Propositions and Conclusions

“One question in science is not  ' is this hypothetical model true' but "is this model better than the alternatives'...If we believe dogmatically in a particular view, then no amount of contradictory data will convince us otherwise...” John Skilling, “Foundations and Algorithms” in Bayesian Methods in Cosmology

This is the eighth post summarizing Issues in the Philosophy of Cosmology by George F.R.  Ellis.   A complete list of the issues and theses he presents is given in the Appendix below*.    Before addressing the philosophic issues themselves, some preliminary remarks are in order.

•  First, because of space limitations, the summary has been selective; a number of technical issues have not been discussed; if a reader is interested in these, I'd recommend the original article, via the web link given above. 
• Second, contrary to some comments on these posts, neither Ellis nor I are making any arguments for theism or anti-atheism in the post proper; philosophic alternatives are presented, and if a reader draws theological conclusion from these alternatives, that's up to him/her.* 
• Third, no values for evidential probability (in the post on Anthropic Coincidences) have been presented; indeed, Ellis argues (and I agree) that inferring an evidential probability for one datum (our universe) is not a valid procedure. 
• Fourth, the general focus of the article, and my emphasis in these posts, is on what can science say about cosmology and what philosophic assumptions underlie such scientific conclusions.

SCIENTIFIC CRITERIA

Ellis gives as an important criteria for a scientific theory that it be empirically testable.  My position may be even stronger than that of Ellis: if a theory cannot be confirmed by quantitative measurements then it is not in my view (and that of Fr. Stanley Jaki), science, but something else—mathematical metaphysics?

• What can be confirmed by measurement is limited by the time, distance and physics horizons mentioned in the first post. 
• Using electromagnetic radiation we cannot see further back in time than when radiation decoupled from matter, about 380,000 years after the origin. 
• We cannot see further in space than given by the distance horizon, the distance at which space will be expanding at faster than the speed of light. 
• We cannot duplicate the tremendous energies present in the initial, quantum stages of the beginning of the universe (these energies are orders of magnitude greater than even the huge energies that will be available in the SLAC Hadron supper collider), so we cannot test projected theories of particle creation. 

What can be measured are inferred consequences of various theories: what the cosmic background radiation (CBR) shows about homogeneity, isotropy, fluctuations, the cosmological constant (lambda, representing expansion pressure), etc. Recent examples are the report of Gurzadyan and Penrose of rings in the CBR representing cataclysmic events pre-Big Bang  and B-mode measurements  of the CBR from which are inferred gravitational waves in the early universe and thus inflation.   One may disagree with the aspects of the theory, but the tie-in with measured data is commendable.

THESES FOR PHILOSOPHIC ISSUES 

Ellis gives a series of theses for his position on philosophic issues and these are presented as an appendix, to give a complete summary. The theses in Issue F, “The explicit philosophic basis”, will be presented in detail. As a preliminary and review, here are theses pertinent to the science of cosmology (NOTE: the theses are taken directly from the article even though no quotation marks are present):

• THESIS A1: The universe itself cannot be subjected to physical experimentation. We cannot re-run the universe with the same or altered conditions to see what would happen if they were different , so we cannot carry out scientific experiments on the universe itself.
• THESIS A2: The universe cannot be observationally compared with other universes.  We cannot compare the universe with any similar object, nor can we test our hypotheses about it by observations determining statistical properties of a known class of physically existing universes.
• THESIS B3: Establishing a Robertson-Walker geometry for the universe relies on plausible philosophic assumptions. The deduction of spatial homogeneity follows not directly from astronomical data but because we add to the observations a philosophical principle that is plausible but untestable.

(In Thesis B3, Ellis refers to the notion that the universe is isotropic and homogeneous (on a large scale). From our vantage point, we can see that the CBR (cosmic background radiation) yields this result; but to show that the inference is valid for the universe as a whole, we would need to make the same observation from at least two other (far removed) vantage points. However, if the Copernican Principle is invoked that we do not occupy a special place in the universe (this is the philosophic principle Ellis refers to in Thesis B3), then what see is equivalent to what would be seen from other positions, and the homogeneity and isotropy is demonstrated.)

• THESIS B6: Observational horizons limit our ability to observationally determine the very large scale geometry of the universe.  We can only see back to the time of decoupling of matter and radiation and so have no direct information about earlier times; and unless we live in a 'small universe', most of the matter in the universe is hidden behind the visual horizon. Conjectures as to its geometry on larger scales cannot be observationally tested. The situation is completely different in the small universe case: then we can see everything there is in the universe, including our own galaxy at earlier times! (emphasis and exclamation point added)
• THESIS C1: The Physics Horizon limits our knowledge of physics relevant to the very early universe. We cannot experimentally test much of the physics that is important in the very early universe because we cannot attain the required energies in accelerators on Earth. We have to extrapolate from known physics to the unknown and then test the implications; to do this, we assume some specific features of known lower energy physics are the true key to how things are at higher energies. We cannot experimentally test if we have got it right. 
• THESIS C2: The unknown nature of the inflation means inflationary universe proposals are incomplete. The promise of inflationary theory in terms of relating cosmology to particle physics has not been realized. This will only be the case when the nature of the inflaton (the particle representing the scalar force causing inflation)has been pinned down to a specific field that experiment confirms or particle physics requires to exist.
• THESIS D2: Testable physics cannot explain the initial state and hence specific nature of the universe. (emphasis added)

Ellis expands on Thesis D2 as follows:

"A choice between different contingent possibilities has somehow occurred; the fundamental issue is what underlies this choice. Why does the universe have one specific form rather than another, when other forms consistent with physical laws seem perfectly possible? The reason underlying the choice between different contingent possibilities for the universe (why one occurred rather than another) cannot be explained scientifically. It is an issue to be examined through philosophy or metaphysics." (emphasis added).

This last proposition is, I believe, the most important of those Ellis sets forth.

• THESIS E1: Physical laws may depend on the nature of the universe.

Ellis is saying here that the fundamental constants (e.g. the fine-structure constant, the gravitational constant may vary in time and space). It is a philosophical assumption that they remain constant. (Note: one recent finding, which is controversial, suggests that there is an asymmetric variation through space [and time] in the fine-structure constant.)

PHILOSOPHIC CRITERIA FOR SCIENTIFIC THEORIES

• THESIS F1: Philosophic choices necessarily underlie cosmological theory.Unavoidable metaphysical issues inevitably arise, in both observational and physical cosmology. Philosophical choices are needed in order to shape the theory.
•  THESIS F2: Criteria of satisfactoriness for theories cannot be scientifically chosen or validated. Criteria of satisfactoriness are necessary for choosing good cosmological theories; these criteria have to be chosen on the basis of philosophical considerations. They should include criteria for satisfactory structure of the theory, intrinsic explanatory power, and observational and experimental support.   These criteria are listed below:

1. Satisfactory structure:  a) internal consistency, b) simplicity (Ockham's razor), and c) aesthetic appeal ('beauty' or 'elegance')

2. Intrinsic explanatory power: a) logical tightness, b) scope of the theory—the ability to unify otherwise separate phenomena, and c) probability of the theory or model with respect to some well-defined measure.

3. Extrinsic explanatory power, or relatedness: a) connectedness to the rest of science, b) extendability providing a basis for further development;

4. Observational and experimental support, in terms of a) testability: the ability to make quantitative as well as qualitative predictions that can be tested; and b) confirmation: the extent to which the theory is supported by such tests as have been made.” (emphasis added)

The last criterion in my view (and that of many other scientists and philosophers of science) is critical. If a theory cannot in principle be confirmed quantitatively it is not science, but belongs to other disciplines.

• THESIS F3: Conflicts will inevitably arise in applying criteria for satisfactory cosmological theories. Philosophical criteria for satisfactory cosmological theories will in general come into conflict with each other, so that one will have to choose between them to some degree; this choice will shape the resulting theory.

Ellis elaborates on this last thesis:

“The thrust of much recent development has been away from observational tests towards strongly theoretical based proposals, indeed sometimes almost discounting observational tests. (emphasis added) At present this is being corrected by a healthy move to detailed observational analysis of the proposed theories, marking a maturity of the subject.”

• THESIS F4: The physical reason for believing in inflation is its explanatory power as regards structure growth in the universe. ... This theory has been vindicated spectacularly through observations of the CBR and matter power spectra. It is this explanatory power that makes it so acceptable to physicists, even though the underlying physics is neither well-defined nor tested, and its major large-scale observational predictions are untestable. (emphasis added).

Expanding on Thesis F4, Ellis adds:

“Inflation provides a causal model that brings a wider range of phenomena into what can be explained by cosmology (Criterion 2b), rather than just assuming the initial data had a specific restricted form. Explaining flatness (omega0 approximately 1, as predicted by inflation) and homogeneity reinforces the case, even though these are philosophical rather than physical problems (they [the initial restricted conditions] do not contradict any physical law; things could just have been that way). However claims on the basis of this model as to what happens very far outside the visual horizon (as in the chaotic inflationary theory) results from prioritizing theory over the possibility of observational and experimental testing. It will never be possible to prove these claims are correct.” (emphasis added)

Ellis asks, “how much should we try to explain” with cosmology? What should the scope of cosmology include?

• THESIS F5:Cosmological theory can have a wide or narrow scope of enquiry. The scope we envisage for our cosmological theory shapes the questions we seek to answer. The cosmological philosophical base becomes more or less dominant in shaping our theory according to the degree that we pursue a theory with more or less ambitious explanatory aims in terms of all of physics, geometry and underlying fundamental causation.

Elaborating on this point, Ellis says

“...The study of expansion of the universe and structure formation from nucleosynthesis to the present day is essential and well-informed. The philosophical stance adapted is minimal and highly plausible. The understanding of physical processes at earlier times, back to quantum gravity, is less well-founded. The philosophical stance is more significant and more debatable. Developments in the quantum gravity era are highly speculative, the philosophical position adapted is dominant because experimental and observational limits on the theory are lacking.” (emphasis added)....the basic underlying cosmological questions are

1. Why do the laws of physics have the form they do? Issues arise such as what makes particular laws work? for example, what governs the behaviour of a proton, the pull of gravity?...
2. Why do boundary conditions have the form they do?
3. Why do laws of physics at all exist? This relates to unsolved issues concerning the nature of the laws of physics: are they descriptive or prescriptive? ...Is the nature of matter really mathematically based in some sense, or does it just happen that its behaviour can be described in a mathematical way?
4. Why does anything exist? This profound existential question is a mystery whatever approach we take.
5. Why does the universe allow the existence of intelligent life? This of somewhat different character than the others and largely rests on them but is important enough to generate considerable debate in its own right. (Note: this question is that related to the Anthropic Principle--#6 in this series.)
 The status of all these questions is philosophical rather than scientific, for they cannot be resolved purely scientifically. How many of them—if any—should we consider in our construction of and assessments of cosmological theories?”

The next important question Ellis considers is how well does science, particularly cosmology, represent reality.

“It follows...that there are limits to what the scientific method can achieve in explanatory terms. We need to respect these limits and acknowledge clearly when arguments and conclusions are based on some philosophical stance rather than on purely testable scientific argument. If we acknowledge this and make that stance explicit , then the bases for different viewpoints are clear and alternatives can be argued rationally.”

• THESIS F6: Reality is not fully reflected in either observations or theoretical models. Problems arise from confusion of epistemology (the theory of knowledge) with ontology (the nature of existence) existence is not always manifest clearly in the available evidence. The theories and models of reality we use as our basis for understanding are necessarily partial and incomplete reflections of the true nature of reality, helpful in many ways but also inevitably misleading in others. They should not be confused with reality itself!”

“It may be suggested that arguments ignoring the need for experimental/observational verification of theories ultimately arise because these theories are being confused with reality, or at least are being taken as completely reliable total representation of reality. (emphasis added)   This occurs in

• "... confusing computer simulations of reality with reality itself, when they can in fact represent only a highly simplified and stylized version of what actually is."
• "...confusing the laws of physics themselves with their abstract mathematical representation (if indeed they [the laws] are ontologically real)
• ... confusing a construction of the human mind (“Laws of Physics”) with the reliable behaviour of ponderable matter...
• ...confusing theoretically based outcomes of models with proven observational results (e.g. claiming the universe necessarily has flat special sections (omega0 =1) and so this can be taken for granted, when the value of omega0 can and should be observationally determined precisely because this then tests that prediction.)”

Another  important question Ellis addresses is whether infinities are physically realizable or mathematical constructs. He agrees with the renowned 20th century mathematician David Hilbert that infinity is not a real quantity:

“Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea .. . which transcends all experience and which completes the concrete as a totality . . .” (quote is from Hilbert).

Since one can never count an infinite number of objects, the claim that the universe is infinite or that there are an infinite number of universes in a multiverse can never be tested or confirmed.

• THESIS I2: The often claimed physical existence of infinities is questionable. The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.

Ellis concludes that there is much uncertainty in what one can infer from cosmology, and those inferences one draws are based on the philosophical basis one uses. More importantly, the stance one takes should be related to the totality of man's existence in the universe.

“Firstly, even in order to understand just the material world, it can be claimed that one needs to consider forms of existence other than the material only — for example a Platonic world of mathematics and a mental world, both of which can be claimed to exist and be causally effective in terms of affecting the material world. Our understanding of local causation will be incomplete unless we take them into account.

 Secondly, in examining these issues one needs to take into account data about the natures of our existence that come from our daily lives and the broad historical experience of humanity (our experiences of ethics and aesthetics, for example), as well as those discoveries attained by the scientific method. Many writings claim there is no purpose in the universe: it is all just a conglomerate of particles proceeding at a fundamental level in a purposeless and meaningless algorithmic way. But I would reply, the very fact that those writers engage in such discourse undermines their own contention; they ignore the evidence provided by their own actions. There is certainly meaning in the universe to this degree: the fact they take the trouble to write such contentions is proof that they consider it meaningful to argue about such issues; and this quality of existence has emerged out of the nature of the physical universe.... Indeed the human mind is causally effective in the real physical world precisely through many activities motivated by meanings perceived by the human mind. Any attempt to relate physics and cosmology to ultimate issues must take such real world experience seriously, otherwise it will simply be ignoring a large body of undeniable data. This data does not resolve the ultimate issues, but does indicate dimensions of existence that indeed do occur.”

With respect to the significance of cosmology, Ellis concludes

• THESIS OF UNCERTAINTY: Ultimate uncertainty is a key aspect of cosmology.Scientific exploration can tell us much about the universe, but not about its ultimate nature, or even much about some if its major geometrical and physical characteristics. Some of this uncertainty may be resolved, but much will remain. Cosmological theory should acknowledge this uncertainty.

Some final thoughts of my own:

• First, Ellis's review of the philosophical issues underlying cosmology is a most useful antidote to more grandiose presentations that ignore considerations of epistemology and metaphysics. Although in this article he touches only lightly on the place of man in the cosmos, he has also written a short book, “Before the Beginning-Cosmology Explained”, that addresses this question and theological considerations more fully. The book also gives a much simpler (ground up from basic physics) summary of the science in cosmology than that in the article.
• Second, much of the reasoning used to justify various cosmological models and theories is abductive , that is, to say that theory/model is "true" because it is the best (most elegant) explanation for the phenomena.   That type of reasoning has been criticized by philosophers of science, e.g. Bas van Fraassen, William Stoeger, Nancy Cartwright.    There are historical examples to show that the best explanation (at the time) is not necessarily true--e.g. phlogiston, disproved by Count Rumford's cannon-boring experiments, the ether, disproved by the Michelson-Morley experiments.     Unfortunately (or maybe fortunately), as Ellis emphasizes, we can't experiment on the cosmos.

APPENDIX

SUMMARY TABLE OF ISSUES AND THESES
Issue A: The uniqueness of the universe

• Thesis A1: The universe itself cannot be subjected to physical experimentation
• Thesis A2: The universe cannot be observationally compared with other universes
• Thesis A3: The concept of ‘Laws of Physics’ that apply to only one object is questionable
• Thesis A4: The concept of probability is problematic in the context of existence of only one object

Issue B: The large scale of the Universe in space and time

• Thesis B1: Astronomical observations are confined to the past null cone, and fade with distance
• Thesis B2: ‘Geological’ type observations can probe the region near our past world line in the very distant past
• Thesis B3: Establishing a Robertson-Walker geometry relies on plausible philosophical assumptions
• Thesis B4: Interpreting cosmological observations depends on astrophysical understanding
• Thesis B5: A key test for cosmology is that the age of the universe must be greater than the ages of stars
• Thesis B6: Horizons limit our ability to observationally determine the very large scale geometry of the universe
• Thesis B7: We have made great progress towards observational completeness

Issue C: The unbound energies in the early universe

• Thesis C1: The Physics Horizon limits our knowledge of physics relevant to the very early universe
• Thesis C2: The unknown nature of the inflaton means inflationary universe proposals are incomplete

Issue D: Explaining the universe — the question of origins

• Thesis D1: An initial singularity may or may not have occurred
• Thesis D2: Testable physics cannot explain the initial state and hence specific nature of the universe
• Thesis D3: The initial state of the universe may have been special or general

Issue E: The Universe as the background for existence

• Thesis E1: Physical laws may depend on the nature of the universe
• Thesis E2: We cannot take the nature of the laws of physics for granted
• Thesis E3: Physical novelty emerges in the expanding universe

Issue F: The explicit philosophical basis

• Thesis F1: Philosophical choices necessarily underly cosmological theory
• Thesis F2: Criteria for choice between theories cannot be scientifically chosen or validated
• Thesis F3: Conflicts will inevitably arise in applying criteria for satisfactory theories
• Thesis F4: The physical reason for believing in inflation is its explanatory power re structure growth.
• Thesis F5: Cosmological theory can have a wide or narrow scope of enquiry
• Thesis F6: Reality is not fully reflected in either observations or theoretical models

Issue G: The Anthropic question: fine tuning for life

• Thesis G1: Life is possible because both the laws of physics and initial conditions have a very special nature
• Thesis G2: Metaphysical uncertainty remains about ultimate causation in cosmology

Issue H: The possible existence of multiverses

• Thesis H1: The Multiverse proposal is unprovable by observation or experiment
• Thesis H2: Probability-based arguments cannot demonstrate the existence of multiverses
• Thesis H3: Multiverses are a philosophical rather than scientific proposal
• Thesis H4: The underlying physics paradigm of cosmology could be extended to include biological insights

Issue I: The natures of existence

Thesis I1: We do not understand the dominant dynamical matter components of the universe at early or late times
Thesis I2: The often claimed physical existence of infinities is questionable
Thesis I3: A deep issue underlying the nature of cosmology is the nature of the laws of physics.

Thesis of Uncertainty: Ultimate uncertainty is one of the key aspects of cosmology.

Thaaaat's all folks.    Comments  welcomed.

*To forestall invidious comments, I'll have to modify this:  Post 4, "Creatio ex Nihilo...."had a theistic bias, and of course, the quotations above posts and my bio indicate my own theistic foundations.

Philosophic Issues in Cosmology 7: Is there a Multiverse?

Exploding Universes in a Multiverse Section
from Andrei Linde, Stanford University

“It’s hard to build models of inflation that don't lead to a multiverse. It’s not impossible, so I think there’s still certainly research that needs to be done. But most models of inflation do lead to a multiverse, and evidence for inflation will be pushing us in the direction of taking [the idea of a] multiverse seriously.” Alan Guth

 "Well, there is the hypothesis ... that all possible universes exist, and we find ourselves, not surprisingly, in one that contains life. But that is a cop-out, which dispenses with the attempt to explain anything. And without the hypothesis of multiple universes, the observation that if life hadn't come into existence we wouldn't be here has no significance. One doesn't show that something doesn't require explanation by pointing out that it is a condition of one's existence. If I ask for an explanation of the fact that the air pressure in the transcontinental jet is close to that at sea level, it is no answer to point out that if it weren't, I'd be dead.” Thomas Nagel, Mind and Cosmos.

This is the seventh in a series of posts summarizing Issues in the Philosophy of Cosmology  by George F.R. Ellis*.   Also, we'll discuss "inflation" below**, the extremely rapid expansion of the very early universe, since the existence of "bubble universes", a multiverse is predicated on inflation, and since this was not discussed extensively in previous posts.

The notion of an ensemble of many possible universes (small u), not causally connected, “a multiverse”, has been used to counter the unlikeliness of all the anthropic coincidences.  To quote Ellis*:

“If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist;  and this can help explain the fine-tuned nature of many parameters whose value values are otherwise unconstrained by physics... However there are a number of problems with this concept.  Besides, this proposal is observationally and experimentally untestable, thus its scientific status is debatable.” (emphasis added).

One  problem (other than the untestable aspect) is that the probabilistic character of the multiverse is never specified by authors who invoke it: 

“These three elements (the possibility space [the population description], the measure [the quantities  that describe the particular universe], and the distribution function [for the measure]) ,must all be clearly defined in order to give a proper specification of a multiverse.... This is almost never done.”

What is also not usually specified are the possible types of universes contained in a multiverse.  Which of the types below should be included?

• “Weak Variation: only the values of the constants of physics are allowed to vary?...
• Moderate Variation: different symmetry groups, or numbers of dimensions...
• Strong Variation: different numbers and kinds of forces, universes without quantum theory or in which relativity is untrue (e.g. there is an aether), some in which string theory is a good theory for quantum gravity and others where it is not, some with quite different bases for the laws of physics (e.g. no variational principles).
• Extreme Variation:  universes where physics is not well described by mathematics, with different logic; universes ruled by local deities; allowing magic... Without even mathematics or logic?

 Which is claimed to be the properties of the multiverse, and why?  We can express our dilemma here through the paradoxical question: Are the laws of logic necessary in all possible universes?”

Although the existence of multiverses cannot be justified by measurements, do they offer good explanations for the anthropic coincidences?  Ellis answers:

“It has been suggested that they (multiverses)  explain the parameters of physics and of cosmology and in particular the very problematic values of the cosmological constant (lambda, the constant for negative pressure)  The argument goes as follows:  assume a multiverse exists;  observers can only exist in one of the highly improbable biophilic outliers where the value of the cosmological constant is very small. ...If the multiverse has many varied locations with differing properties that may indeed help us understand the Anthropic issue:  some regions will allow life to exist, others will not.   This does provide a useful modicum of explanatory power.  However it is far from conclusive. (emphasis added) 

Firstly, it is unclear why the multiverse should have the restricted kinds of variations of the cosmological constant assumed in (these) analyses...If we assume 'all that can happen, happens' the variations will not be of that restricted kind;  those analyses will not apply.”

“Secondly, ultimate issues remain.  Why does the unique larger whole (the multiverse)have the properties it does? (emphasis added)  Why this multiverse rather than any other one?”

I will add to Ellis's comment that even though one universe in a multiverse has  an appropriate value for a particular constant (say, lambda), it will not necessarily be the case that other parameters will be appropriate.    There still has to be a conjunction of values for all the laws and constants, which requires either a Theory of Everything to give that (something to wonder about in itself) , or more amazing coincidences.

Ellis further argues that probability-based arguments cannot demonstrate the existence of a multiverse:

“Probability arguments cannot be used to prove the existence of a multiverse, for they are only applicable if a multiverse (that is to say, a population of multiverses) exists.   Furthermore probability arguments can never prove anything for certain, as it is not possible to violate any probability predictions, and this is a fortiori so when there is only one case to consider, so that no statistical observations  are possible. (emphasis in the original).  All one can say on the basis of probability arguments is that some specific state is very improbable.  But this does not prove it is impossible;  indeed if is stated to have a low probability, that is precisely a statement that it is possible... probability arguments ...(are) equivalent to the claim that the universe is generic rather than special, but whether this is so or not is precisely the issue under debate.”

The issue of whether a multiverse can contain an infinite number of universes (thus justifying the claim that “whatever can happen will happen”) is addressed by Ellis as part of the question whether an infinite number can be considered as real (rather than as a mathematical construct) in his analysis of the philosophic/ metaphysical questions involved in cosmology, and will be discussed in the last post of this summary.

In conclusion, Ellis argues  that Multiverses are a philosophical rather than scientific proposal. 

“The idea of a multiverse provides a possible route for the explanation of fine-tuning.  But it is not uniquely defined, is not scientifically testable ... and in the end simply postpones the ultimate metaphysical questions.”

These philosophic issues will be discussed in the final post of this series. 

*Quotations, unless otherwise specified, are from Issues in the Philosophy of Cosmology , George F.R. Ellis.

**All about Inflation.

One development of quantum cosmology that does have measurable consequences is the notion of inflation introduced by Guth (1981), here explained by Ellis:

“Particle physics processes dominated the very early eras, when exotic processes took place such as the condensation of a quark-gluon plasma to produce baryons. Quantum field theory effects were significant then, and this leads to an important possibility: scalar fields producing repulsive gravitational effects could have dominated the dynamics of the universe at those times. This leads to the theory of the inflationary universe, proposed by Alan Guth ...an extremely short period of accelerating expansion will precede the hot big bang era . This produces a very cold and smooth vacuum-dominated state, and ends in ‘reheating’: conversion of the scalar field to radiation, initiating the hot big bang epoch. This inflationary process is claimed to explain the puzzles mentioned above: why the universe is so special (with spatially homogeneous and isotropic geometry and a very uniform distribution of matter), and also why the space sections are so close to being flat at present (we still do not know the sign of the spatial curvature), which requires very fine tuning of initial conditions at very early times.   (emphasis added) Inflationary expansion explains these features because particle horizons in inflationary FL models will be much larger than in the standard models with ordinary matter, allowing causal connection of matter on scales larger than the visual horizon, and inflation also will sweep topological defects outside the visible domain.”

Inflation also explains the rarity (absence) of magnetic monopoles (predicted by the standard model of particle physics), the presence of stars/galaxies (from quantum fluctuations expanded by inflation) and several features of the observed CBR (Cosmic Background Radiation).    The projected time scale for the inflationary period is from about 10^-36s after the origin to about 10^-32s, during which period the volume increased by a factor of at least 10^78.   As pointed out above, the source of the inflationary increase is an assumed force, a scalar field or isotropic negative pressure, counteracting the force of gravity. Although the notion of inflation explains many puzzling features about our universe, not all physicists are satisfied with this explanation.   Other explanations have been offered, and as Ellis says:

“The promise of inflationary theory in terms of relating cosmology to particle physics has not been realized. This will only be the case when the nature of the inflaton (the hypothetical particle corresponding to the scalar inflationary field).  has been pinned down to a specific field that experiment confirms or particle physics requires to exist.outside the visible domain.” (emphasis in the original).

 Roger Penrose also has misgivings about inflationary theory, primarily due to what he thinks is a misplaced motivation for applying the theory to explain flatness and homogeneity:

“In the standard model these issues (the flatness, horizon and smoothness problems) are handled by the 'fine-tuning' of the initial Big Bang state, and this is regarded by inflationists as “ugly”.   The claim is that the need for such fine tuning is removed in the inflationary picture and this is regarded as a more aesthetically pleasing physical  picture.”  (Road to Reality, p.754)

 It should be understood that in this context, “aesthetically pleasing” corresponds to the absence of an intelligent designer to set the “fine-tuning”,  that is to say the absence of a creative God, or, alternatively, the absence of an as yet unknown “theory of everything” that would set the fine-tuning by some universal physical law (my take).

Recent B-mode measurements of the microwave background radiation are in agreement with inflation in that there is evidence of strong gravitational waves in the radiation.   Added 28/12/14:See the comment below for links that contradict this interpretation.

Taking inflation to be true because it is the "best" explanation for several cosmological features is an example of "abductive" reasoning, reasoning to the best explanation.    Such reasoning has been faulted by several  philosophers of science (Nancy Cartwright, Bas van Fraassen) with some cause.   Historically phlogiston was the best explanation for heat before Count Rumford's cannon-boring experiments;  ether was the best explanation for electromagnetic wave vibration before the Michelson-Morley experiments.

Philosophic Issues in Cosmology 6: Are we special?--the Anthropic Coincidences

“Scientists are slowly waking up to an inconvenient truth - the universe looks suspiciously like a fix. The issue concerns the very laws of nature themselves. For 40 years, physicists and cosmologists have been quietly collecting examples of all too convenient "coincidences" and special features in the underlying laws of the universe that seem to be necessary in order for life, and hence conscious beings, to exist."  Paul Davies.

" The argument (the Anthropic Principle) can be used to explain why the conditions happen to be just right for the existence of (intelligent) life on the earth at the present time. For if they were not just right, then we should not have found ourselves to be here now, but somewhere else, at some other appropriate time."  Roger Penrose.

"One doesn't show that something doesn't require explanation by pointing out that it is a condition of one's existence. If I ask for an explanation of the fact that the air pressure in the transcontinental jet is close to that at sea level, it is no answer to point out that if it weren't, I'd be dead.” Thomas Nagel, Mind and Cosmos.

 "A common sense interpretation of the facts suggests that a super-intellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature.   The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question."  Fred Hoyle

This is the 6th in a series of posts summarizing an article by George F.R. Ellis  on Philosophic Issues in Cosmology.

The 10,000 dials and 10,000 monkeys analogy
         The presence of organic life in the universe (namely us) requires a series of unlikely happenings and restricted values for physical laws and constants.   This “fine-tuning” (as it's been called) has been likened to a room full of 10,000 dials, each of which has to be set to a precise setting in order to achieve action; 10,000 monkeys are let into the room and each adjusts a dial and, lo, action occurs.   The set of coincidences was termed “The Anthropic Principle” by Brandon Carter in 1973, when he introduced it in a conference to oppose the “Copernican Principle”, that man has no special place in the universe.

References
The Anthropic Principle has been discussed extensively in books and articles.   There is a concise summary by Robert Koons in his philosophy lectures , giving various interpretations, with arguments for and against each.  (I'll summarize some of these below.) A good collection of articles with different (and opposing views) of the Anthropic Principle is given in God and Design  (ed. Neil Manson).   There are many versions of the Anthropic Principle ranging from the Weak Anthropic Principle, WAP, which tautologically observes that if the universe weren't fit for us to be here we would wouldn't be here discussing the principle  (see the Penrose quote above), through the Strong Anthropic Principle, SAP, that the universe has been fine-tuned for intelligent life (us), on up to the Completely Ridiculous Anthropic Principle (by Martin Gardner—you complete the acronym).

Can unlikelihood be quantified?
In assessing the improbable nature of the anthropic coincidences, some authors assign a specific  probability to the value of some particular physical constant.  Such assignment is not always justified,  because probability considerations are ill defined, in the usual sense of evidential probability.   For example, theoretical calculations have shown that if the strong nuclear force were 2 % higher or 2 % lower, then the elements as we know them would not have been formed.  This does not mean that the probability of having the strong nuclear force at an anthropic value is 4%.  In order to give a probability for this range, the population distribution of the parameters for the strong nuclear force would have to be known.  Moreover, there is a difficulty in using probability in an after-the-fact, rather than a predictive sense.  The way to use probabilities in assessing the anthropic coincidences is via Bayesian probability techniques, with well-defined prior assumptions, and to use the resulting Bayesian probability as a measure of belief.

Ellis's interpretation
Ellis, in his presentation of the anthropic coincidences, focuses on the special nature of physical laws that allow for the presence of life, rather than on their improbability:

“One of the most profound issues in cosmology is the Anthropic question...why does the Universe has the very special nature required in order that life can exist? The point is that a great deal of “fine tuning” is required in order that life be possible.  There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible;  in particular various fundamental constants are highly constrained in their values if life as we know it is to exist...What requires explanation is why the laws of physics are such as to allow this complex functionality (life) to work.  ...We can conceive of universes where the laws of physics (and so of chemistry) were different than in ours.  Almost any change in these laws will prevent life as we know it from functioning.”

Ellis posits as a first requirement for the laws of physics “the kind of regularities that can underlie the existence of life”:   laws that are not based on symmetry and variational principles are unlikely to produce the kind of complexity that would be required for life. He also sets up general conditions that allow for organic life and cosmological boundary/initial conditions.    In this respect he cites the following as necessary:

• “Quantization that stabilizes matter and allows chemistry to exist through the Pauli exclusion principle;

• The number D of large spatial dimensions must be just 3 for complexity to exist.

• The seeds in the early universe for fluctuations (quantum fluctuations) that will later grow into galaxies must be of the right size that structures form without collapsing into black holes...

• The size of the universe and its age must be large enough...we need a sufficiently old universe for second generation stars to come into existence and then for planets to have a stable life for long enough that evolution could lead to the emergence of intelligent life.  Thus the universe must be at about 15 billion years old for life to exist.

• There must be non-interference with local systems.  The concept of locality is fundamental, allowing local systems to function effectively independently of the detailed structure of the rest of the Universe.  We need the universe and the galaxies in it to be largely empty, and gravitational waves and tidal forces to be weak enough, so that local systems can function in a largely isolated way.

• The existence of the arrow of time, and of laws like the second law of thermodynamics, are probably necessary for evolution and for consciousness.  This depends on boundary conditions at the beginning and end of the Universe.

• Presumably the emergence of a classical era out of a quantum state is required.   The very early universe would be a domain where quantum physics would dominate leading to complete uncertainty and an inability to predict the consequence of any initial situation; we need this to evolve to a state where classical physics leads to the properties of regularity and predictability that allow order to emerge.

• The fact that the night sky is dark...is a consequence of the expansion of the universe together with the photon (light particle) to baryon (mass particle) ratio.  This feature is a necessary condition for the existence of life:  the biosphere on Earth functions by disposing of waste energy to the heat sink of the dark night sky.  Thus one way of explaining why the sky is observed to be dark at night is that if this were not so, we would not be here to observe it. 

• Physical conditions on planets must be a in a quasi-equilibrium state for long enough to allow the delicate balances that enable our existence, through the very slow process of evolution, to be fulfilled.” (see the Theology of Water.)

There are a number of other constraints, limited values for forces—gravity, electromagnetic, weak nuclear, strong nuclear—and fundamental constants, including that for particle masses and number of particles that are needed for life to evolve.  In summary, Ellis puts the Anthropic Principle as the following:

     “Life is possible because both the laws of physics and the boundary conditions for the universe have a very special nature.  only particular laws of physics, and particular initial conditions in the Universe, allow the existence of intelligent life of the kind we know.  No evolutionary process whatever is possible for any kind of life if these laws and conditions do not have this restricted form.”

Robert Koons summarizes some general objections to invoking the Anthropic Principle for carbon-based life "well isn't that special" (as the Church Lady might say):

1. The problem of "old evidence";
2. Laws of nature don't need to be explained;
3. We had to be here in any event (see Penrose's quote above);
4. Exotic life might exist;
5. The Copernican Principle--rejection of anthropocentricity is fundamental to science;
6. We're only one among many universes (see below).

Objection 1 can be countered by the argument that such evidence is used frequently in science when direct experiments can't be done--witness the General Relativity explanation of the advance in the perihelion of Mercury.
Objection 2 would do away with all interpretations of theory, quantum mechanics, and the philosophy of science.
Objection 3 is countered as in Thomas Nagel's quote above; as information seeking life form we need explanations.
Objection 4 is invalid--we're talking about conditions for carbon-based life; science-fiction can explore and has explored conditions for exotic life.
Objection 5--the Anthropic Principle was introduced to rebut the Copernican Principle.
Objection 6--the multiverse proposition is not itself proven.

The philosophic/metaphysical context for these Anthropic conditions that Ellis sets forth will be given in the final post for this summary.   It should be noted that one interpretation of the anthropic coincidences is the theory that infinitely many universes with potentially different physical laws and constants exist and so it is not unlikely that in all these one universe with appropriate conditions for life would be present.    The analogy is like that of having a lottery ticket with the numbers 1 1  1  1  1 be the winner.   That combination of numbers looks improbable, but since there are a whole host of numbers from 00000  to 99999, it is no less probable than any other number.    This brings up the notion of a multiverse, which will be discussed in the next post.

Philosophical Issues in Cosmology 5: What Measurements Tell Us

Astronomical Distances.  From telescopes.stargate.org

 “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science.” Lord Kelvin.

This, the fourth in a series summarizing George F.R. Ellis's article on Philosophical Issues in Cosmology, will deal will information provided by measurements.   In addition to Ellis's article, Ned Wright's Cosmology Tutorial web site gives a clear, accurate and detailed picture of how astronomical measurements give cosmological data:

The following types of data are primary:  positions and luminosities of stars and galaxies (including x-ray, UV, visible, IR, microwave  and radio-frequency radiation ); wavelengths of spectral lines from these objects; Doppler shifts of such wavelengths  (shifts in the wavelength that depend on the velocity of the object emitting the radiation);  frequencies, intensities and polarizations of the microwave  cosmic background radiation (CBR).  

The Cosmic Distance Ladder

Distance Ladder from Skynet University(UNC)

It's important to realize that there is, so to speak, a “ladder” of inferences of secondary data from these primary data.   For example, the distances of nearby stars (10-100 light years or so distant from us) can be estimated relatively accurately by parallax measurements.   From the intensity of light observed, one can then estimate accurately the intrinsic brightness of these stars.   One can then use other properties, at known distances, to set up what are called “standard candles”:  properties that relate to the intrinsic brightness, so that the intrinsic brightness can be inferred, to give from the observed intensity an inferred distance.

 Various standard candles are used at  various distances, including cepheid variables to supernovae and galactic lensing of quasars.   One of the first standard candles was the intrinsic brightness of the Cepheid variables.   Hubble used these to estimate the distance of stellar objects and to construct his plot of red shift versus distance, which was the basis for the expanding universe theory.   Since that time more accurate measures have given very good linear relation between red-shift (velocity moving away from us) and distance from us.

Mass Density and Curvature of Space

Space Curvature: top, omega 0 >1;
bottom, omega 0 <1
from Hendrix at University of Oregon

One can also count the number of objects within the field of view and from this make an estimate of the total number of objects to be seen, and thus infer the total (baryonic—ordinary) mass.  From this astronomical data one can infer the following: the actual ratio of matter to a critical value;  this ratio is designated “omega 0” (with uppercase Greek letter).   If omega 0 is >1, space-time is positively curved  (like a sphere) and the universe expansion will eventually turn into a collapse, for a “big crunch”;  if omega 0 is = 1  space-time is flat and the universe will expand in a uniform way;  for omega 0 <1, the universe is curved as in a saddle surface, and will expand indefinitely.

Dark Energy

Observations of red shifts from distant supernovae and from temperature anisotropies in the cosmic background radiation suggest that there is a “dark energy”, a pressure (as in the “lambda” constant in Einstein's original formulation)  that makes the  expansion of the universe accelerate.   (What this is saying is the expansion rate is slower for older, more distant objects, faster for more recent, closer objects, so there is an acceleration of the rate.)

 Evidence for an Expanding Universe

The following observations, in addition to the red shift, confirm the picture of a universe expanding from a hot big bang:  the cosmic background radiation, the relative abundance of hydrogen to helium in the universe (about 3/1) and the lack of heavy elements in far distant galaxies.     The cosmic background radiation is like the embers of a burnt-out fire, the embers of the hot “Big Bang” spread evenly throughout the universe.   The small irregularities in the cosmic background radiation indicate the fluctuations that grew into stars and then galaxies.  The relative abundance of hydrogen to helium is consistent with models of element formation that took place at an early, high temperature stage of the universe.    For far distant galaxies (10 billion years light distance, say), they are also at an early stage of development (remember, going in distance is also going back in time) and therefore heavy elements have not yet formed by the collapse of red giant stars.

Ellis lists  (among  others) the following common misconceptions about the expanding universe:

• Misconception 1: The universe is expanding into something. It is not, as it is all there is. It is just getting bigger, while always remaining all that is. .
• Misconception 2: The universe expands from a specific point, which is the centre of the expansion. All spatial points are equivalent in these universes, and the universe expands equally about all of them.  Every observer sees exactly the same thing in an exact RW geometry. There is no centre to a FL universe.
• Misconception 3: Matter cannot recede from us faster than light. It can, at an instant; two distantly separated fundamental observers in a surface {t = const} can have a relative velocity greater than c if their spatial separation is large enough. No violation of special relativity is implied, as this is not a local velocity  difference, and no information is transferred between distant galaxies moving apart at these speeds. For example, there is presently a sphere around us of matter receding from us at the speed of light; matter beyond this sphere  is moving away from us at a speed greater than the speed of light. The matter that emitted the CBR was moving away from us at a speed of about 61c when it did so.

The next in this series will deal with the Anthropic Principle.

Philosophic Issues in Cosmology 4: Creatio Ex Nihilo--Theology versus Physics*

Evolution of the Universe (Wikipedia)

"In the beginning God created the heavens and the earth. The earth was formless and void, and darkness was over the surface of the deep, and the Spirit of God was moving over the surface of the waters.…" Gen 1:1-2 (KJV).

Bible-Hub.com Lexicon

"The laws of nature themselves tells us that not only can the universe have popped into existence like a proton and have required nothing in terms of energy but also that it is possible that nothing caused the big bang," Professor Steven Hawking (Discovery Channel broadcast).

 “When men choose not to believe in God, they do not thereafter believe in nothing, they then become capable of believing in anything.” G.K. Chesterton"

"My reasons for presenting the ideas underlying a modern scientific theory stem rather from a belief that philosophy and theology are indeed the 'queen of sciences' (emphasis added) and, as such, are charged with the awe-inspiring task of overseeing all modes of enquiry and of cohering them in a unity of vision that is both emotionally and intellectually satisfying." Chris Isham, "Creation as a Quantum Process" in Physics, Philosphy and Theology.

"We believe that God needs no pre-existent thing or any help in order to create, nor is creation any sort of necessary emanation from the divine substance.  God creates freely "out of nothing":If God had drawn the world from pre-existent matter, what would be so extraordinary in that? A human artisan makes from a given material whatever he wants, while God shows his power by starting from nothing to make all he wants." Catholic Catechism 296. 

HISTORICAL

The Hebrew for "formless and void" in Gen 1:1 is "tohu-bohu" or "tohu va vo-hu).   A scholar in Hebrew (as a distinguished from a Hebrew scholar--this guy was a retired Irish physician) told me that the real translation of "Tohu Bohu"  was topsy-turvy, a mess, confusion. That would be more in accord with notion held by many physicists that Creation arose from quantum fluctuations, as indicated in Hawking's quote and the diagram above.

So, where did "ex nihilo" come from?   One citation from the Old Testament can be used to justify this:

"I beseech thee, my son, look upon the heaven and the earth, and all that is therein, and consider that God made them of things that were not; and so was mankind made likewise." (2 Maccabees 7:28, KJV)

And in the New Testament:

 "By faith we understand that the universe was created by the word of God, so that what is seen was not made out of things that are visible" Hebrews 11:3

The first Christian writer to promote the doctrine of "Creatio ex nihilo" was Theophilus of Antioch in the late 2nd Century, who wrote

 "but then they (the Platonists) maintain that matter as well as God is uncreated, and aver that it is coeval with God. But if God is uncreated and matter uncreated, God is no longer, according to the Platonists, the Creator of all things, nor, so far as their opinions hold, is the monarchy of God established. And further, as God, because He is uncreated, is also unalterable; so if matter, too, were uncreated, it also would be unalterable, and equal to God; for that which is created is mutable and alterable, but that which is uncreated is immutable and unalterable. And what great thing is it if God made the world out of existent materials? For even a human artist, when he gets material from some one, makes of it what he pleases. But the power of God is manifested in this, that out of things that are not He makes whatever He pleases;" Theophilus of Antioch, Letter to Autolycus

It's a long quote but well expressed (note the points taken up in The Catechism). Theophilus was contesting the view of Greek philosophers, Platonists, neo-Platonists, that the universe was eternal, that a demi-urge had created it from pre-existing stuff.   Theophilus's  theologic cudgel was wielded against the Gnostics by later Christian theologian/philosophers  and fully developed by St. Augustine.
It was St. Augustine who developed arguments about time, that time could have begun with creation, which is a view remarkably in accord with much of modern cosmology.

"...no time passed before the world, because no creature was made by whose course it might pass." St. Augustine, City of God bk 11, ch.4.

As Keith Ward puts it,

"For Augustine, God brought about time and space as well as all the things that  are in them.   Just as God did not create space at a certain place, but non-spatially caused all places to exist, so God did not create time at a certain moment, but non-temporally caused all time to exist." Keith Ward, Quantum Cosmology and the Laws of Nature.

Note that Ward's interpretation above does not require a first moment of time, a "t=0", although Augustine did accept, on the basis of Revelation, that the Universe (which to him was much smaller than our conception) had a definite beginning.

St. Thomas Aquinas also contended against the Greek philosophers' version of Creation.    He agreed with Aristotle  that creation required a First Cause, which Aristotle called the Prime Mover and which Aquinas called God.    However, he believed that only Revelation, not reason, could assert that Creation began at an instant in time:

"By faith alone do we hold, and by no demonstration can it be proved, that the world did not always exist ... it cannot be demonstrated that man, or heaven, or a stone were not always. Likewise neither can it be demonstrated on the part of the efficient cause, which acts by will. For the will of God cannot be investigated by reason, except as regards those things which God must will of necessity; and what He wills about creatures is not among these, as was said above."  St. Thomas Aquinas, Summa Theologica, Part I, Question 46.

Even though the world might be eternal, Aquinas maintained that God's creative agency would be and is continually active, as a creatio continua.

TIME ISSUES

Before discussing the positions on creatio ex nihilo taken by contemporary theologians, I should briefly comment about the forms "time" might take in a cosmological description of the evolution of the universe, and whether "creatio ex nihilo" requires a beginning, an instant in time about which we can say this is   t=0, and there is no t<0.***

Our ordinary understanding of a universal time is confounded by the prescriptions in special and general relativity.   Special relativity requires that the time of an event time depends on the frames of reference of the object and observer; thus,  an event A might be in the future for observer X in one frame of reference and in the past for observer Y in a different frame.  

A further complication is found in general relativity, gravitational time dilation.    To take these complications into account, spacetime is divided into space-like slices, for which some proper time, t,  is assumed to be the same everywhere in the slice.   This proper time  can be replaced by another parameter (varying with time) such as R (the radius of the universe) which is constant in a slice.  

The uncertainty principle of quantum mechanics introduces still another complication: uncertainty in time x uncertainty in energy > h/(2pi) .   This means that to specify t=0 exactly there would have to be an infinite uncertainty in the energy of the system.

CONTEMPORARY

Now to consider the positions taken by contemporary theologians (including physicists and philosophers who put forth theological arguments): for the most part these are reactive to various cosmological theories about the origin (or non-origin) of the universe.   I'll focus on the Big Bang (t=0) hypothesis and the Hartle-Hawking model (no beginning).  The list of theologians cited is not exhaustive but drawn mainly from various articles in Quantum Cosmology and the Laws of Nature. 

Also, if we ask  whether the universe had a beginning or existed eternally, and we believe in God as Creator, then there is another hidden question (which I'll not discuss).    If God is eternal and timeless, how does God act in a world that progresses in time;  in other words, what can we say about the temporality of God?   This question is addressed in Quantum Cosmology and the Laws of Nature by several of the authors.

THE OPINIONS OF THEOLOGIANS.

• The Big Bang hypothesis confirms creatio ex nihilo  by showing the Universe began at a definite time (t=0):  William L. Craig, Ted Peters**.  
• The Big Bang hypothesis might be true, but it is also possible that the Universe could be eternal, with creatio continua by God: George F.R. Ellis**, Richard Swinburne, Keith Ward**
• The Big Bang hypothesis and cosmology, for one reason or another, are not all that relevant to theological ideas about creation:  William Alston**, Ian Barbour** (in Robert John Russell's article),  Karl Barth, Wilhelm Drees**, Arthur Peacocke**(in Robert John Russell's article), William Stoeger**
• The Hartle-Hawking model offers theologic possibilities (see Summary below): Wilhelm Drees**, Chris Isham**, Robert John Russell**.

SUMMARY

The science/physics of creation is not all that settled with respect to creatio ex nihilo, either as a beginning in/of time or as a component of creatio continua.   In terms of treatments of General Relativity (GR), the FLRW model yield a singularity at R=0 (t=0),  the Penrose-Hawking singularity theorem showed that singularities are generally found as solutions of the GR field equations, and the Borde-Guth-Velenkin theorem demonstrates for classical relativity, if the Universe has an average positive expansion, it has to have a beginning.   But GR fails in the domain near R=0, t=0, such that quantum gravity theory would have to be invoked--but there is no theory of quantum gravity.

Now none of the theories which have a purported quantum mechanical base have any empirical support.    In the Hartle-Hawking model the introduction of the imaginary, it, to replace the time variable, t, in the general equation for the universe wave-function (if such were to exist) is arbitrary, done only for aesthetic reasons (to remove a singularity).    Robert J. Russell and Chris Isham claim that the Hartle-Hawking model is consistent with  creatio continua, with nothing at the boundary of the closed universe.    Robert J. Russell also argues that a finite universe is consistent with Creation theology, even if there is no definite beginning (as in Hawking's argument that the south (or north) pole is not the beginning of the earth.)  I don't understand that argument.    George F.R. Ellis points out that Hawking's argument that the universe is pre-existent, caused by nothing other than gravity, is not correct since the Hartle-Hawking model includes

"(pre-existent  Hilbert spaces, quantum operators, Hamiltonians,etc.) whose existence is if anything more mysterious than that of the universe itself."  quoted by Robert J. Russell**.

MY TAKE

It seems to me that the science/physics/cosmology of creation is not altogether settled, but does show empirical evidence for a creation event, a "Big Bang": the red shift showing a universe expansion; the COBE microwave background radiation showing the burnt embers of a very initial epoch; the hydrogen/helium ratio and lack of carbon-12 in ancient (far distant) stars; the more recent B-mode COBE results showing effects of early inflation.

Theologians seem to be wary about falling into a "God of the Gaps" pit, using the deity to explain what science cannot.    That fear I believe is unfounded.   At some point a God of the Gaps argument has to be introduced, as a prime mover, to explain why there is a science illumined by mathematical theory.    There are theological and philosophical issues that are not yet (and may never be) settled:  What is time?   Does God change with time, or is He eternally fixed and, if so, how does he act in time?

I'm not sure whether the theologians and scientists have improved very much, if at all, on the insights of Sts. Augustine and Aquinas.    Faith and revelation give insight.   The arguments of the Catechism are as forceful now as they were when first propounded by Theophilus of Antioch.   And finally, we should keep in mind the aphorism of St. Thomas Aquinas: "It is not that God is irrational but that our understanding is limited."

REFERENCES

*This piece was not taken from the article by Ellis, but has been scrounged from various sources (see below and links in the post).
**Quantum Cosmology and the Laws of Nature (click on the icon for the book and then on the right for chapters).
***Objections have been made to the use of t=0 as a "beginning" in that arbitrary mathematical mappings can change t=0 to t = - infinity (logarithmic transform) or t=+ infinity (inverse transform).   I don't consider such objections to be substantive, since they are artificial--we don't perceive the passage of time in a logarithmic or inverse transform way, although as any husband knows who has waited for his wife to finish shopping, the subjective passage of time is not necessarily linear with a clock.

Philosophic Issues in Cosmology 3: Mathematical Metaphysics--Quantum mechanical models for early stages of the universe.

"Perhaps the best argument in favour of the thesis that the Big Bang supports theism is the obvious unease with which it is greeted by some atheistic physicists.    At times this has led to scientific ideas, such as continuous creation or an oscillating universe, being advanced with a tenacity which so exceeds their intrinsic worth that one can only suspect the operation of psychological forces lying very much deeper than the usual desire of a theorist to support his/her theory (emphasis added).    Chris Isham*

This is the third of 8 articles on philosophical issues in cosmology. Most of the material has been drawn from George Ellis's article, previously referenced, and articles in Quantum Cosmology and the Laws of Nature--Scientific Perspectives on Divine Action (see Reference** below).
We concluded the second post in this series with the observation that General Relativity must break down at some point close to the extrapolated t=0, near the big bang, and that perforce, quantum mechanical models had to be used for  a theory of creation.    As Ellis, Isham and Grib point out, there are fundamental problems in doing so.

Schrodinger's Cat--simultaneously alive and dead
until the box is opened (from Wikipedia.Org)

A major one is the so-called measurement problem, which is at the heart of difficulties in the interpretation of quantum mechanics.    The quantum mechanical state function can be represented as a superposition of several possible states that could be measured—when the measurement is made and a particular state results, then the superposition “collapses” into the state that is measured (e.g. Schrodinger's cat paradox).  

An associated difficulty is the probability interpretation for measurement:  the universe  state function (wave function) gives probabilities that particular values of dynamical variables will be  measured—what does probability mean in this context; are there an infinite number of possible universes (corresponding to various possible measurements) and who does the measurement?   To quote Christopher Isham* (referring to the measurement problem):

 “This poses the obvious problems of (i) when is an interaction between two systems to count as a measurement by one system of a property of the other? and (ii) what happens if there is an attempt to restore a degree of unity by describing the measurement process in quantum mechanical terms rather than the language of classical physics which is normally used?   There is no universally accepted answer to either of these questions.” (emphasis added). Chris Isham*

That being said, the following quantum mechanical models have been proposed for the origin of the universe  (the list is not exhaustive, and only general comments on each will be given; for more information please see the cited articles):

1. Quantum fluctuations in the vacuum (Tryon, 1979).
2. Tunneling from “superspace” into “real” space-time (Vilenkin, 1983) 
3. The Hartle-Hawking Block Universe, replacement of t by ti (i=square root of -1) (Hartle, Hawking,  1981)
4. Chaotic Inflation  (Linde, 1986)***
5. The Participatory Universe (Wheeler, 1990)
6. Creation from non-Boolean logic to Boolean by an “observer” (Grib,1990)**

Note that in none of these (except possibly 3 or 5) was the creation “ex nihilo”; for 1, the vacuum pre-existed; for 2 the “superspace” (a hypothetical space of multi-dimensions); for 4, previous universes from which a “bubble” universe emerged via inflation; for 6, a hypothetical space of quantum universe states.

Model 1, Quantum fluctuations in the vacuum, is deficient in the following respect.     There is nothing in this model to specify a unique time at which the fluctuations to enable creation should occur.   Accordingly there might be creation of  many universes, interacting with each other, but such has not been observed.   And to emphasize again, a vacuum is not "nothing"...there is space, virtual particles, annhilation and creation operators, occupied zero-point energy levels from which the fluctuations occur.

For 3, the Hartle-Hawking model, the replacement of t by ti gives a term t^2 instead of -t^2  in the Schrodinger equation for the universe, which enables a solution without a singularity.    The variable t becomes space-like, rather than time-like at very early values, and the space-like ti gradually becomes a time-like variable (goes back to t) as the value of t increases.  An exact value for the time of origin becomes undefined (where does the earth start, at the South pole?).

Hartle-Hawking Model (from StrangeNotions.com)

 The diagram illustrates this (vertical axis is increasing “t”).   Note that there is no experimental justification for the replacement of t by ti;  the justification is “esthetic”, that is the substitution removes the singularity at t=0.   It is said that the coordinate ti "gradually changes" from space-like to t, time-like...how is the gradual change effected?  Is the universe a fraction f with ti and a fraction 1-f with t?   I have never seen this explained.

In order to understand the significance of models  5 (the Participatory Universe of John Wheeler) and 6 (the quantum logic model of Andrej Grib), a comment on an interpretation of quantum mechanics   that links quantum mechanics to consciousness will be helpful.    (See also references in my previous posts "Do quantum entities have free will.." and "Quantum Divine Action via God, the Berkeleyan Observer..".)

The Participatory Universe and Quantum Logic models stem from the interpretation, first set forth by Von Neumann, London and Wigner, that since measurement is done by an observer, the final step in the measurement process must be awareness of the measurement result by the consciousness of the observer.   Accordingly the conscious observer must be an intrinsic part of quantum mechanics.  

Wheeler's Participatory Universe Icon
From the University of Toronto site

 Wheeler construes this basic relation to consciousness  as implying a universe of  information ("It from Bits"), so that by looking back in time we create the past universe,  as symbolized in the famous icon shown  at the left.

Grib's quantum logic model invokes a reality of non-Boolean logic that we (as observers) convert to Boolean logic situations, which is the only type of logic that our minds can comprehend.  Grib speculates that perhaps it was God who made the initial observation to create a “real” universe (one perceived according to Boolean logic).   According to Grib, time is a framework (lattice) for arraying the non-Boolean events in a framework that can be scanned as Boolean, and quantum mechanics is the theory for converting the non-Boolean system to Boolean.

As far as bubble universes go, chaotic inflation is a hypothesis.  There are, however, some recent preliminary results from B-mode measurements of the Cosmic Background radiation that support the existence of inflation (not necessarily chaotic inflation).

Nevertheless it should be clear that none of these models can be confirmed or denied by measurements.  Thus they are outside the realm of science, but properly belong to the domain of mathematical metaphysics  (my take).   As in the Hartle-Hawking model, assumptions are made to remove the singularity  at t=0, R=0.    Such models without a singularity are to many physicists more aesthetically pleasing than those with, because to them the absence of a singularity is consistent with the absence of a Creator.

We'll explore some implications of these models for theology in the next post in this series, Creatio ex nihilo: Theology vs. Physics.

References
*Chris Isham, "Creation of the Universe as Quantum Process"in Physics, Philosophy and Theology--A Common Quest for Understanding.
**Chris Isham, "Quantum Theories of the Creation of the Universe"; Andrej Grib, "Quantum Cosmology, the Role of the Observer, Quantum Logic" in Quantum Cosmology and the Laws of Nature--Scientific Perspectives on Divine Action (click on the book icon, and then on the article listed on the right).

Philosophic Issues in Cosmology 2: Relativistic Theories for the Origin of the Universe

There was a young lady named Bright,Whose speed was far faster than light;She started one day In a relative way, And returned on the previous night. A.H.R. Buller, Punch 

This is the second of 7 (or maybe 9) posts, from articles on the Magis Facebook Site, 2010.   They attempt to summarize George Ellis's fine article, Issues in the Philosophy of Cosmology. 

The usual exposition of Einstein's General Relativity Field Equations is very forbidding, full of Greek subscripts and tensor notation;  a clear, simplified version has been given on the web by John Baez, and is appropriate for considering the Big Bang.  The standard general relativity model for cosmology is that given by Friedmann-LeMaitre-Robertson-Walker,  usually designated by  FLRW. The FLRW model proceeds from the following simplifying assumptions: a) the universe is isotropic (looks the same in every direction, from every point in space);  b) there is a constant amount of matter in the universe;  c) on a large scale (hundreds of times the distance between galaxies) the universe has a homogeneous matter density (matter is spread evenly throughout space);   d) the effects of “pressure” (from radiation or the vacuum) can be neglected.

With these simplifying assumptions, the equation for the “size” of the universe, its radius R, becomes simple, and looks just like the equation of motion for a particle traveling under an inverse square law, like that of gravity.  (Note:  this is not to say the size of the universe is really given by some value R;  the universe might possibly be infinite—more about that later—but to show how space is expanding.)    The universe might expand and then contract in a “Big Crunch” (like a ball falling back to earth), corresponding to positively curved spacetime (like a sphere); it might expand with a constant velocity of expansion (like a projectile going into orbit), corresponding to flat space-time (like a plane); or it might expand with an accelerating velocity of expansion (like a projectile achieving escape velocity), corresponding to a saddle-shaped curvature of space-time.     It should also be emphasized that the FLRW solution to the Einstein General Relativity equations is by no means unique, nor is it the only solution with a singularity.   It is a model, however, that is in accord with measured data (red shift, COBE microwave background radiation).

The assumptions stated above do not apply rigorously.   Observations have shown a filament or bubble-like structure to the universe with clusters and meta-clusters of galaxies. (A theoretical picture for this filament structure has been proposed.)  In the early stages of the universe radiation pressure was very likely significant.  More recently, measurements have shown that the expansion rate is increasing, which is presumed due to “dark energy”, possibly a pressure due to vacuum energy.    Moreover, at some point in the expansion the scale of the universe gets so small that classical physics does not apply and quantum mechanics has to be used for theory.   Unfortunately quantum mechanics and general relativity have not  yet been reconciled into one general theory, so there is a fundamental difficulty with this melding of the two theories.

The simple solution above for FLRW models gives an acceleration of R proportional to 1/R^2, which signifies that there is a singularity at R=0, that is to say, if you try to plug in R=0 you'll get infinity.   This would be the same as the infinity at the source for other forces proportional to 1/R^2, coulomb attraction or gravity.   Ellis has this to say about the significance and existence of the  FLRW singularity:

“the universe starts at a space-time singularity ...This is not merely a start to matter — it is a start to space, to time, to physics itself. It is the most dramatic event in the history of the universe: it is the start of existence of everything. The underlying physical feature is the non-linear nature of the EFE  (Einstein Field Equation): going back into the past, the more the universe contracts, the higher the active gravitational density, causing it to contract even more....a major conclusion is that a Hot Big Bang must have occurred; densities and temperatures must have risen at least to high enough energies that quantum fields were significant, at something like the GUT (Grand Unified Theory) energy. The universe must have reached those extreme temperatures and energies at which classical theory breaks down.”  (emphasis in original).

Ellis is saying that even though we can't observe the universe at that time when it was so small  and temperatures were so high that quantum properties would have been significant, we can infer that this was the case theoretically,  that is to say that there was a “Hot Big Bang” at  the beginning of the universe with extremely high temperatures (energies)and an extremely small volume.

Thus, given the contracting size of the universe as one goes back to the origin, there will be a time such that quantum effects must come into play.  However, there are some basic limitations to using quantum mechanics as a theory for the origin of the universe.  As Ellis points out:

“The attempt to develop a fully adequate quantum gravity approach to cosmology is of course hampered by the lack of a fully adequate theory of quantum gravity, as well as by the problems at the foundation of quantum theory (the measurement problem, collapse of the wave function, etc.)”

(Added later:  The Hawking-Penrose Theorems shows that a class of solutions to the General Relativity equations have a singularity in the solution.   Also, the Borde-Guth-Vilenkin Theorem shows that under conditions of universe average expansion,  there is a beginning point.    Since all such solutions are non-applicable at the singularity because quantum gravity enters the picture, the relevance of such theorems is perhaps questionable.)

See "Philosophic Issues in Cosmology 3: Mathematical Metaphysics--Quantum Mechanical Theories in Cosmology, for the ways physicists apply quantum mechanics to deal with theories of origin (or non-origin) of the universe.