Did the Universe Begin? X: Recapitulation

from http://www.xkcd.com/1352/.

We have now come to the end of my series about whether or not the universe had a beginning.  This is part of a longer series dissecting the debate between St. William Lane Craig and Sean Carroll.  I started out with some general reflections on the debate:

Thoughts on the Carroll-Craig Debate
God of the Gaps
  (see also: Gaps at the Dinner Table)

Then I started talking specifically about possible evidence from physics for and against the universe having a beginning.  For ease of understanding I'm going to label each main new argument with FOR or AGAINST to define its main orientation, but the posts also deal with the various counterarguments (that's the tire swing going back and forth above...). I've provided an executive summary of each of these posts, so that you can easily see the main thrust of what I said.  Minus all the caveats, hedging, and detailed explanations my scientific training tends to encourage.

(I've heard that politicians hate talking to scientists because, like the Elves in Tolkien, we seldom give a straight answer to a question.  In scientific cultures, we show "sincerity" by discussing all the problems and caveats with our ideas, whereas in political circles this sounds like insincere waffling designed to please too many people...)

Did the Universe Begin? I: Big Bang Cosmology (FOR, as far as it goes...)
- the classical Big Bang Model predicts an initial singularity where time began
- tentative because quantum effects were important and invalidate our usual geometrical notions
- also tentative because we don't really know how inflation began

Did the Universe Begin? II: Singularity Theorems (FOR)
- classical General Relativity theorems by Hawking and Penrose
- assumptions of Hawking theorem invalid during inflationary epoch
- Penrose theorem says that if space is infinite, there was a beginning
- Penrose theorem invalid in quantum situations, but my work suggests that it might be extendable to quantum gravity, if horizons always obey the 2nd law of thermodynamics.

Did the Universe Begin? III: BGV Theorem (FOR)
- if the universe has a positive average expansion, then "nearly all" geodesics cannot be extended infinitely to the past
- implies that inflation had to have a beginning in time, at least in some places
- can evade theorem by a "bouncing" cosmology where the universe contracts and then expands

Did the Universe Begin? IV: Quantum Eternity Theorem (AGAINST)
- if the usual rules of QM hold at all times, you can calculate what the state would be at any time to the past or future.
- in realistic cosmologies the energy is probably either zero or undefined, making the theorem inapplicable.

Did the Universe Begin? V: The Ordinary Second Law (FOR)
- given reasonable assumptions, 2nd law of thermodynamics requires a beginning
- most plausible way to evade this is to postulate that the "arrow of time" reverses
- such models would have a "thermodynamic beginning" but no "geometrical beginning"

Did the Universe Begin? VI: The Generalized Second Law (FOR)
- second law of thermodynamics also seems to apply to cosmological horizons
- can be used like ordinary 2nd law to argue for beginning
- can also be used as singularity theorem (see II above)
- this closes certain loopholes, but if the universe is finite and the arrow of time reverses, a bounce may still be possible.

Did the Universe Begin? VII: More about Zero Energy
- a more technical explanation of why the energy of the universe can be zero

Did the Universe Begin? VIII: The No Boundary Proposal (AGAINST/FOR)
- a beautiful set of speculative ideas which unify the "laws of physics" with the "initial conditions", by providing a rule for what the state of the universe is.
- contrary to popular conceptions, the Hartle-Hawking proposal has no beginning in time
- the Vilenkin tunnelling proposal is similar in spirit but does have a beginning.
- unclear whether these proposals are well defined, and Hartle-Hawking appears to give wrong predictions.

Did the Universe Begin? IX: More about Imaginary Time
- a more technical explanation about the notion of imaginary time used by Hartle-Hawking

If you put all of the physics information together, the conclusion I would draw is that: We don't know for sure whether the Universe began, but to the extent that our present-day knowledge is an indicator, it probably did.  However, as Carroll correctly says, we can also construct models where it doesn't have a beginning.  Taking into account known results from geometry and thermodynamics, the most plausible such models are 1) spatially finite, and 2) have a reversal of the arrow of time (e.g. the Aguirre-Gratton model).

I also noted that models like AG still have a low entropy "initial condition" somewhere in the middle of time.  One might think that this type of "thermodynamic beginning" still calls out for some type of explanation.

Then I wrote a more theologically-oriented post about whether the Hartle-Hawking no boundary proposal leaves any room for God to have created the universe:
Fuzzing into Existence
- short answer: yes, if you think of God as a storyteller, not a mechanic.

I also discussed the possibility of Reparameterizing Time; is it even meaningful to ask whether time is infinite or finite when you can change coordinate systems?  In this post I also argued that the main theological question of whether the universe needs an explanation seems to me much the same whether the universe has finite or infinite time.

Now, let me make another observation about the tire swing.  Although the weight of the evidence is that the universe probably had some sort of beginning—and even more likely that there was some sort of low entropy "initial condition" even if geometrically time stretches past before that—this cannot be said to be certain.  There is always the possibility that new scientific data or methods could radically change our picture of the very, very early universe.  Similarly, while a finite past seems more in accordance with traditional Christian theology than an infinite past, there appears to be no strictly logical connection between the two ideas, once the act of Creation is viewed in a more timeless, "authorial" way.  Thus one might conceivably have a theist who thinks time is infinite, or an atheist who thinks time was finite.

Should the argument for God's existence really rest on such a slender foundation as the ultimate decision of physicists about Big Bang Cosmology?  Well, one thing is clear.  In ages past it didn't depend on it.  Obviously, Sts. Abraham and Sarah, David and Solomon, the prophets and apostles, and all the men and women who followed in their footsteps up through the 19th century, including eminent scientists such as St. Faraday and St. Maxwell: these cannot have believed in God because of the Big Bang Theory, because—guess what?—nobody knew about it yet!  What does the Bible say about these people?

Now faith is confidence in what we hope for and assurance about what we do not see.  This is what the ancients were commended for.  By faith we understand that the universe was formed at the word of God, so that what is seen was not made out of what was visible.  (Hebrews 11:1-3)

Our belief that God is the Creator does not depend on the vicissitudes of scientific progress, the swinging back and forth of the tire swing (or is it accelerating?)  It doesn't matter, because in this case we have a more certain source of knowledge than Science.

By faith!  The skeptic may scoff here, and say that faith is belief without evidence, but that is not the definition used in the passage above.  It says that faith is confidence about what we hope for, but do not see.  Unless we identify sight (conceived broadly as anything which can be directly experienced in terms of our 5+ senses) with evidence (things which allow us to conclude something about the world)—an identification which would incidentally also make Science impossible—the passage does not say that the ancients were commended for believing without evidence.  But the example of the biblical heroes does give some pointers about what type of evidence was relevant to them.

The ancients did not believe that God was the Creator because they had a detailed scientific theory about where it comes from.  (Indeed, if we take our minds off Genesis for a moment and read the Wisdom literature of the Bible: Job and Psalms and Ecclesiastes and Proverbs, the Scriptures seem to emphasize more our lack of knowledge about the details of creation, then any detailed programme of events...)  On the contrary, the ancient Jews and Christians knew God, by personal acquaintance as it were, and therefore knew him to be creative and powerful, mighty in word and deed.  Thus they could take him at his word that he is the Creator of all that we see.

The glory of Creation does indeed point to the glory of the Creator, so that it is possible for ordinary human reasoners to come to know that there is a Creator intellectually.  But this sort of Theism, by itself, isn't what Christians mean by faith.  Once we come to know God personally, we learn the more important fact that we can trust him, and know with confidence that there is nothing in existence which does not depend on him.

And therefore, although we see in this world visible things emerging from other visible, material things, we know that ultimately their origin comes from "God’s invisible qualities—his eternal power and divine nature" (Rom 1:20).  He created everything through his Word, Jesus Christ, from whom we have come to know what God is like.  This way of knowing does not seem to depend very strongly on the details of past, present, or future scientific knowledge.

One could definitely argue that the Bible teaches that there was a Beginning (whatever this means from God's perspective).  For example, the quotation above from Hebrews speaks of the formation of the visible universe.  But whether or not this fact has been revealed by God, it is not obvious to me that the most important theological aspects of Creation really depend essentially on time being finite, or even well-defined.  (Admittedly, if you believe that time is infinite, it might be easier to slip into a false notion whereby matter exists independently of God, who is merely the Chief Organizer of the cosmos.  That would be a heresy—a false belief which may seriously obstruct your ability to relate to God or others properly—but it does not follow necessarily from time being infinite.)

The main point of the doctrine of Creation, I think, is that God is real, and that everything else is derived from his power and will.  We know this doctrine is true because we know God.  Not because of the Big Bang, as natural as it is to connect the two ideas.

About Aron Wall

I am a postdoctoral researcher studying quantum gravity and black hole thermodynamics at the Institute for Advanced Study in Princeton. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my first postdoc at UC Santa Barbara.
This entry was posted in Physics, Reviews, Theological Method, Theology. Bookmark the permalink.

27 Responses to Did the Universe Begin? X: Recapitulation

  1. Jack Spell says:

    Heck of a series, Aron; really enjoyed it.

  2. Felipe says:

    Carrol-Craig Debate*
    You put Carrol-Chen =P

    [Oops. Fixed. My neural network comes with an autocomplete feature, and I can't figure out how to turn it off!---AW]

  3. TY says:

    Prof. Aron:
    Thanks again and, Jack, that makes two of us regarding the series. I said back in August 24, 2104 in Slightly Less Random Links, I looked forward to seeing this series in book form, and I will add here, complete with the technical details. Understandably, that couldn't be packed in a blog for general readership..

    TY

  4. Aron Wall says:

    Jack, TY, thanks so much for your compliments.

    But what makes you think I'm done with the series? :-) This was only a miniseries that has come to an end. I still need to say what I think of the Cosmological Argument, address fine tuning, and Carroll's specific arguments against theism! So save your book orders for later...

    [Added later: Never mind the fact that I myself called it the "end of the series" at the beginning of the post itself...]

  5. Andrew says:

    Regardless of any future blog posts, I too would LOVE to read a book authored by you that addresses scientific arguments against/for theism.

  6. Aron, your summary of BGV above is badly misleading. There is nothing in BGV that says all past-directed geodesics have to end on the SAME singularity. And BGV allows comoving geodesics to be past-infinite. So we could have a situation where different past-directed geodesics end on different singularities, and the set of singularities marches backward infinitely in time.

    So it's just false to claim BGV requires that "if the universe has a positive average expansion, it had to have a beginning."

  7. TY says:

    Aron:
    The Book would make a huge contribution to science and theology. I can wait.

    (A) It would dispel a lot of common myths about these two approaches to understanding how did things begin and the way thing are. If would show the two are not undivided but complementary.

    (B) The finely tuned and intelligent character of the world we live it opens up many interesting questions and people want both well-reasoned and reasonable expositions.. Science can only go so far in providing a narrative but then we need additional insights from theology and religion. But we need to see the science and to be convinced of the limitations.

    (C) And it would be a natural extension to include in the Book a few chapters on quantum theory, the notion of indeterminacy versus determinacy, the fact that the quantum world seems to obey a logic of its own, and how the mind enters our understanding of this "weird" world (as some describe it). A discussion of quantum theory necessarily would include the Many World Interpretation of Quantum Mechanics . And all of this takes us to the question of whether the human mind transcends the physical universe and, if that is true or plausible, then an an ultimate mind, which is God, is that more convincing. So we are back to where we started on the question of creation and the beginning of time.

    TY

  8. Aron Wall says:

    Welcome to my blog, Robert.

    Of course the details you're looking for are in the post I linked to, but you're right I could have done better on the summary. I meant that there has to be a beginning somewhere. I've adjusted the summary. For the record, the original summary Robert was responding to read like this:
    - if the universe has a positive average expansion, it had to have a beginning
    - implies that inflation had to have a beginning in time
    - can evade theorem by a "bouncing" cosmology where the universe contracts and then expands

    and I have modified it to read:
    - if the universe has a positive average expansion, then "nearly all" geodesics cannot be extended infinitely to the past
    - implies that inflation had to have a beginning in time, at least in some places
    - can evade theorem by a "bouncing" cosmology where the universe contracts and then expands

  9. Jack Spell says:

    Aron,

    I have a question that I had meant to ask you a while back concerning the AG model's avoidance of the BGV theorem. It seems to me that there are two possible ways to interpret an AG-like bouncing spacetime:

    (1) Do so with a monotonic arrow of time running from -\infty \to +\infty and the "bounce" occurring on a null hypersurface. If this option is preferred, then wouldn't that mean that the Second Law of Thermodynamics would be violated for an infinite temporal duration from -\infty \to t_{0} as entropy decreases consistently during the contracting epoch?

    (2) Do so with dual AoTs, both of which running away from a spacelike hypersurface at t_{0} where the "bounce" occurs. If this option is preferred, then wouldn't this amount to the spacetime not in fact evading BGV because then what we would have is two different spacetimes, each of which always being in an expansion phase—and thus each of them satisfying the condition H_{av} \gt 0?

    As always, thanks in advance for your time.

  10. Jack Spell says:

    Please feel free to correct my LaTeX coding with the correct start/stop indicators.

    [Done!--AW]

  11. Aron Wall says:

    Jack,

    As you say, there exist two different types of AG models, one where the arrow of time reverses on a null hypersurface, and the other where it reverses on a spacelike hypersurface. These correspond to two different ways of slicing de Sitter space, and they would lead to physically distinct spacetimes once you include non de Sitter phenomena such as vacuum decay, matter and/or black holes. There is a diagram of these two choices in Fig. 1 of this paper.

    In either case, the Second Law is "violated" in the contracting phase, in the sense that entropy decreases with time. But that's just another way of saying the arrow of time is reversed during the contracting phase. We could redefine the Second Law to say that entropy always increases away from the special slice.

    In case (1), I'm not sure what you mean by t_0. What time coordinate are you using? In case (2), the spacetime has just one connected component, so that is why we call it a single spacetime instead of two different spacetimes.

  12. Jack Spell says:

    Aron,

    I apologize for my mental lapse in my description of case (1); I did not mean to attribute the time coordinate t_{0} to this case.

    Just to make sure we are on the same page with our terms, would you mind answering the following questions:

    1. Do either of the physical interpretations of the AG model presuppose any particular philosophical theory of time? More specifically, must one ascribe to the B-Theory in order to properly interpret the AoT reversal?

    2. When you speak of the "arrow of time [being] reversed during the contracting phase," are you saying nothing more than just that entropy is decreasing during this phase? What I mean is, you don't in any way mean to imply that there is a reversal of ontological time, right? In other words, even though the AoT reverses in the sense that entropy is decreasing, do you still hold that the time coordinate varies monotonically from -\infty \to +\infty and that there is a non-reductionistic arrow of time that goes from past to future and is not determined by entropy increase?

    There is one final issue that I would like to raise. I warn you, even though it will at first appear to be the same argument that I made in our previous, lengthy discussion—the one in which you had 47 final comments :-) —, I assure you it is not. I will lay it out formally so that you can easily spot any false premises or invalid reasoning on my part.

    First, let me state that the type of spacetime of which we will be discussing is one that obeys the condition H_{av} \lt 0. For simplicity's sake, let us also assume that the rate of contraction is constant; that way I don't have to keep writing "on average."

    1. If we trace the worldline of a non-comoving geodesic observer \mathcal{O}, we will find that her motion relative to comoving test particles \mathcal{CTP} in a contracting congruence will be processionary.

    2. If (1), then the measure of relative velocity v_{rel} between \mathcal{O} and each \mathcal{CTP} will increase successively by some nonzero value.

    3. If \mathcal{O} and \mathcal{CTP} are in processionary motion for an infinite temporal duration, then \mathcal{O} will eventually observe an infinite number of \mathcal{CTP}.

    4. If (2) and (3), then there will be an infinite number of increases in the value of v_{rel}.

    5. If (4), then v_{rel} will eventually reach an infinite value.

    Thus, if the argument is sound, then it leads to absurdity: relative velocities cannot reach infinite values. But it would also therefore follow that an infinite interval of prior contraction is impossible.

    Please don't yell at me for yet another lengthy post :-) It's just something that I've been thinking about and I was wondering what you thought. Thanks.

  13. Aron Wall says:

    Jack asks:

    1. Do either of the physical interpretations of the AG model presuppose any particular philosophical theory of time? More specifically, must one ascribe to the B-Theory in order to properly interpret the AoT reversal?

    I don't think there's a strict logical contradiction with the A-theory, since the A-theorist could just say that entropy happens to be decreasing relative to the "true" direction of time flow.

    However, it might be possible to make the A-theorist feel a bit uncomfortable by asking what happens if there are conscious beings who live "backwards in time" in the period where entropy is decreasing? Would they feel anything different than we do? If they do feel something different, how is this possible given that the laws of physics are (almost) the same in the backwards direction? If they don't feel anything different, how do we know we aren't living backwards in time ourselves? What reason do we have to believe in A-theory if it is disconnected from our actual experience of time?

    2. When you speak of the "arrow of time [being] reversed during the contracting phase," are you saying nothing more than just that entropy is decreasing during this phase?

    I'm talking about the "thermodynamic arrow of time", so yes I just mean that entropy is decreasing during this phase (due to there existing special low entropy final boundary conditions, but no special initial boundary condition).

    What I mean is, you don't in any way mean to imply that there is a reversal of ontological time, right? In other words, even though the AoT reverses in the sense that entropy is decreasing, do you still hold that the time coordinate varies monotonically from −∞→+∞ and that there is a non-reductionistic arrow of time that goes from past to future and is not determined by entropy increase?

    As a B-theorist, I'm not sure that I believe in any such thing as "ontological time", apart from whatever structures are defined using geometry, thermodynamics, and the laws of physics.

    A time coordinate is just an arbitrary label. You could make a time coordinate which goes from -\infty \to +\infty, or a time coordinate which goes from +\infty \to -\infty, or one which goes from 0 \to 7, and they could all be describing the exact same universe. It's just an arbitrary labelling scheme for spacetime points.

    One game we can play which does not depend on coordinates is this. Suppose we have a Lorentzian spacetime manifold; this is the type of geometry used in GR, where each point has two lightcones coming out of it. But at any given point x, we don't know which one to call the "past" or the "future" lightcone. Let's says we arbitrarily decide which one is which at the point x. Then we can extend this to the rest of the spacetime by the following technique: for any other point y, connect the two points x and y by some curve. Then by "parallel transporting" the lightcone from x to y, we can figure out which cone is past/future at the point y. Thus we have labelled the entire spacetime with a notion of past vs. future, up to a single arbitrary 2-way choice.

    (There are a couple ways in which this construction might go wrong. First, if the spacetime has 2 or more disconnected components, then there is no way to connect points on different components and therefore we have to choose the "bit" of information separately for each component. But you might want to call this several spacetimes, rather than a single spacetime. Secondly, on some exotic manifolds, if you go around a closed curve you might end up flipped in time. On "non-time-orientable" spacetimes like these, there is no way to define past vs. future. But these are typically regarded as physically unrealistic solutions to General Relativity and ignored.)

    Regarding your new argument, I'm not sure what you mean by "processionary". I'm not sure I've ever heard this word before. Also, I don't think your argument is valid when you proceed from (4) to (5). A quantity can increase an infinite number of times without ever reaching infinity, if it doesn't increase by the same amount each time. That is, the sum of an infinite series of positive numbers can be finite.

  14. Jack Spell says:

    Regarding your new argument, I'm not sure what you mean by "processionary". I'm not sure I've ever heard this word before.

    http://dictionary.reference.com/browse/processionary

    Also, I don't think your argument is valid when you proceed from (4) to (5). A quantity can increase an infinite number of times without ever reaching infinity, if it doesn't increase by the same amount each time. That is, the sum of an infinite series of positive numbers can be finite.

    I said "For simplicity's sake, let us also assume that the rate of contraction is constant; that way I don't have to keep writing 'on average.'" Therefore, it will increase by the same amount each time, right?

  15. Aron Wall says:

    Jack,
    I was indeed able to find the disctionary.com definition of "processionary", but it is just "of, related to, or moving in a procession". That doesn't tell me what is processing from what, or along what. (That's the hazard of turning verbs into nouns in technical writing---one loses all sense of who is doing what to whom). And what do you mean by procession? Do you mean that some quantity is monotonically increasing or decreasing? If so, you should just say that.

    I said "For simplicity's sake, let us also assume that the rate of contraction is constant; that way I don't have to keep writing 'on average." Therefore, it will increase by the same amount each time, right?

    No. The "rate of contraction" is the rate at which space is contracting. (I assume you meant constant decrease of spatial length per unit length per unit time, which would correspond to an exponential decrease of the scale factor of the universe with time, since that's the relevant definition of uniform contraction for the BGV theorem.) But for step 4 of your argument, you need for v_{rel} to be increasing by a uniform amount. Since v_{rel} is a different quantity from the expansion of the universe, it does not increase uniformly, just because the expansion increases uniformly. The amount by which v_{rel} increases depends not only on the current expansion of the universe, but also its current value.

  16. Dennis Jensen says:

    I so happy to have found your blog page. I’ve wanted to pose some cosmological questions to someone who has a thorough understanding in this field of study. After going through a number of your blogs I have to admit that I greatly appreciate the scientific acumen and expertise you’ve demonstrated.

    I’ve been going though a number of your old post, mainly since the Carroll/Craig debate, in the hopes of seeing whether you may have responded already to a question I have. You mention in your Comment Policy that it’s okay to place new comments in old blogs which correspond somewhat to the comments/questions raised. I haven’t seen my question raised elsewhere as of yet, so I’ll pose it here.

    It seems to me that there is a very simple thought experiment, maybe it’s too simple to call even that, which shows that an on average expanding universe cannot be past eternal. But I haven’t noticed others presenting this as evidence. Could you suggest any deficiencies for the following argument?

    With an expanding universe, as one looks back in time, the universe will become continually smaller. It will eventually reach a point at which it cannot become any smaller. We cannot conceive that it can become continually smaller and never cease to do so. Physical processes will eventually alter this contraction into the past. If this shows an expanding universe must have a beginning, I can only think of the following as a serious defeater.

    As we go back in time, the universe should eventually enter a quantum gravity regime (I hope I’m using the correct terminology). Now is it that something simply cannot become smaller than a Planck scale or is it that we just do not know what will happen at this size? If the former, then clearly there must be an origin to an expanding universe. If the latter, then we are cast into the unknown and this thought experiment fails to demonstrate an absolute origin.

    If it is merely a problem of entering a quantum era that makes this scenario powerless to prove an origin to the universe, I wonder why this has not been offered as an argument when quantum issues were not being considered. The BGV theorem, for example, supposedly shows that an on average expanding universe must have a beginning so long as quantum mechanics does not apply. Well, if we preclude quantum mechanics from consideration, wouldn’t it be simpler to appeal to this thought experiment rather than to the BGV to show that the universe is not past eternal?

  17. Aron Wall says:

    Welcome to my blog, Dennis.

    So one crucial thing the BGV theorem does is to provide a mathematically precise definition of "expanding on average" even in spacetimes which aren't homogeneous and isotropic at one moment of time, in order to prove the result in such cases. Whereas your argument, being cast in the form of words, isn't really precise on what the meaning of "size" is. Since concepts of space and time are very tricky in general relativity, one wants to be careful here.

    But suppose for simplicity we restrict to the case of a homogeneous and isotropic universe. If we also suppose that space is infinite and "flat" at one moment of time (meaning that it has the geometry of a Euclidean space, then the most general metric we can write down is:

    ds^2 = dt^2 + a(t)^2 (dx^2 + dy^2 + dz^2).

    This is just like the metric of Minkowski spacetime, except that distances at a given time are made bigger or smaller by the "scale factor" a(t).

    In a classic FRW big bang model, a(t) \to 0 at a finite time in the past, and it doesn't make sense to talk about times before that. But suppose that instead we set a(t) = e^{\kappa t} to be an exponentially increasing function of time, \kappa being a constant. This would correspond to a scenario of "eternal inflation", but in which the inflation goes back infinitely far to the past as well as to the future (normally that term "eternal inflation" only refers to inflation lasting forever to the future...). This spacetime would go back forever to the past. In such a universe, the average expansion, in the sense of rate of expansion per unit length, defined as

    \frac{1}{a}\frac{da}{dt} = \frac{d\,\ln(a)}{dt},

    would be constant, and thus the universe would be the same at all moments of time, despite the fact that it is always expanding (this is possible because the universe is infinite).

    The universe described by this metric appears to evade your argument, since its "size" is infinite at all times. Yet it still in a sense has a beginning, even though it also goes back infinitely in time. How is this possible? The answer is that some timelike goedesics (those which are at rest relative to the expansion of the universe, that have constant x, y, z) go back infinitely far in time, but all the rest of the timelike geodesics end up exiting the spacetime geometry I wrote down in a finite amount of proper time to the past. The BGV theorem says that this conclusion continues to hold even if we drop the assumptions of homogeneity and isotropy, so long as the "average expansion" (in a new sense defined in their paper) is positive.

    As we go back in time, the universe should eventually enter a quantum gravity regime (I hope I’m using the correct terminology). Now is it that something simply cannot become smaller than a Planck scale or is it that we just do not know what will happen at this size? If the former, then clearly there must be an origin to an expanding universe. If the latter, then we are cast into the unknown and this thought experiment fails to demonstrate an absolute origin.

    The latter. Some people have indeed suggested that distances shorter than a Planck distance wouldn't make sense in a theory of quantum gravity, but such statements are speculative until we have a confirmed theory of quantum gravity.

    And yes, "quantum gravity regime" is correct terminology.

  18. Dennis Jensen says:

    Wow. I never imagined the issue was so complicated. Thanks Aron.

  19. Dennis Jensen says:

    On second thought, I suppose I should have imagined that the issue is this complicated since it took an entire theorem and many years to verify it. Or is "verify" the correct word in this case? The BGV is not empirically verified, that is, verified by observation, but I don't think cosmologists consider it in any way questionable, do they?

  20. Aron Wall says:

    Dennis,
    A theorem is, by definition, something that has been proven mathematically. Thus a theorem itself does not require empirical verification; however, whether a theorem applies to a given situation does have empirical elements. If a theorem takes the form "if x then y", or "all x's are y's", then just because the theorem is true does not mean that x is in fact the case in a physical situation.

    The BGV theorem applies to any classical, Lorentzian metric which has the property of having positive "average expansion" as defined in their paper. The theorem is a purely "geometrical" fact in the sense that it doesn't require the Einstein equation or anything like that to hold. On the other hand, if the universe is sufficiently quantum that we can't write down a definite spacetime metric, then the BGV theorem is inapplicable to the situation.

    (An analogous statement might be true in quantum gravity, but we couldn't possibly prove that in our current state of understanding.)

  21. Andrew says:

    Are you done with the series? (It's been epic), but there's, a second argument for an eternal universe in the Carroll-Craig debate by Carroll. Which I think you might have addressed in the arXiv paper Craig referenced. But it concerns entropy, that the best models for solving it are eternal with only a thermodynamic beginning. (Like how you describes the Hartle-Hawking model). Yeah, I pay attention and learn from your posts! :D

    I looked it up and all I could find was this short comment on the argument by Guth: https://edge.org/response-detail/25538

  22. Aron Wall says:

    Andrew,
    Yes, the series on "Did the Universe Begin?" is over. I'm not sure what "second argument for an eternal universe" you are referring to. I discussed eternal models with low entropy in the middle in part V.

  23. Aron, would you mind if I stated the following on my web page and then reference this page?

    “Cosmologist Aron Wall, after assessing the various lines of evidence, also concludes that the universe more probably had a beginning than not.”

    I’m fully aware that you think this is a very weak conclusion since you mention that it seems that the evidence can so easily swing from one conclusion to another and that our faith should be based on something stronger. I agree, but I also think that there is some evidence here, some probability claim can be made, and so this would have power for a cumulative case argument. This statement seems to me to be your opinion from what you’ve concluded above. But if you think I am misstating your view or that it needs more qualification, or if you think I should not say this at all, please tell me. I’m aware that in his debate with Carroll, Craig cited you’re opinion on some point and with his quotation or summary statement it sounded as though you were making a claim that was stronger than you intended. So I’d like to ask you first rather than make the same mistake.

  24. Aron Wall says:

    Dennis,
    The statement is fine, except that I think it would be more accurate to refer to me as a physicist rather than a cosmologist, since unlike e.g. Alex Vilenkin or Alan Guth, most of my actual research is not in cosmology.

  25. Pingback: Cosmology, philosophy and theology – what more could you ask for? | the Way?

  26. Ronald Cram says:

    Aron, since the completion of this mini-series a new paper was published and I would love for you to comment on it. Or, if you have commented and I've missed it - let me know.

    The paper is "Cosmology from quantum potential" by Ali and Das.
    http://arxiv.org/pdf/1404.3093v3.pdf

  27. Pingback: Christianity and Science | Evangelicals in the Episcopal Church

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