Christian historian Dr. Wallace Marshall and I are debating whether or not enough evidence points to the existence of a god. For background and format, and Dr. Wallace’s opening statement, see entry one. For other entries, see index.
Up to now we’ve been focusing on the Kalam Cosmological Argument, and again in answer to Dr. Marshall’s latest response, due to limitations of space, I will here summarize only the essential points I think should put a close to that subject.
Even if that means we are agreeing to disagree, readers can now assess on their own whether those disagreements are reasonable, by reading through our previous exchanges in this subject. Our next entries in this debate shall address another argument we raised in our opening exchange.
That the Evidence Points to Atheism (V)
by Richard Carrier, Ph.D.
Dr. Marshall has established two common patterns: he ignores my arguments rather than actually responding to them; or he ignores expert testimony to assert probabilties contrary to it. Which defects prove his argument meritless.
Ignoring Arguments
To avoid my argument that causal laws cannot predate causal laws, Dr. Marshall falsely claims I said “causal laws cannot exist in the absence of a physical cause of such laws.” My actual words were exactly the opposite: “it does not matter whether physical things need exist or not to do that.” Marshall thus avoids addressing the actual point: that it’s logically impossible that “everything must have a cause” before causal laws exist. Therefore it cannot be the case that existence requires a cause. This is not begging any question. Marshall is begging the question when assuming causal laws exist before anything has caused them to exist.
To avoid my argument that “never exists” means doesn’t exist (and “nowhere exists,” likewise), Marshall falsely implies that modern Platonists say abstract objects both never exist and always exist; and both nowhere exist and exist in a Platonic realm. False. My argument is that there must first be somewhere for a thing to exist before it can exist. Thus a causal agent cannot create a place for itself to exist before that place already exists. And therefore “someplace” to exist can never be caused by things that nowhere and never exist.
Existing in a Platonic realm is existing somewhere. [1] If the Platonic realm did not exist, neither could its contents. But nothing can exist nowhere and still exist to cause a place for itself to then exist. Likewise Platonists argue abstract objects always exist and thus exist (changelessly) in time. They cannot exist before time any more than I can exist north of the North Pole. Things cannot predate their own existence.
Marshall has never actually responded to either argument. Yet they entail any first cause of existence won’t have a cause and cannot have pre-dated a place and time to exist.
Ignoring Expert Physicists
Once we admit spacetime must exist uncaused, we need nothing else to explain the rest of the universe—even if all existence began, and no one knows it did; but if it did, an uncaused singularity or quantum of spacetime with no properties or contents is far simpler than any god hypothesis and yet can explain all observed existence. Not only can this be shown logically, but also from known physics.
I’ve shown by logical argument that an empty point of spacetime governed by no laws will evolve randomly, and that a random selection among all possible outcomes will inevitably include a universe like ours (to a probability infinitesimally close to 1). As this is far simpler than a god and requires no further explanation, it’s a more probable uncaused cause of existence than a god. Marshall repeatedly refused to address this argument. He still never has.
Meanwhile, all actual experts in cosmological science agree that an empty singularity or quantum of spacetime can have caused all observed existence, with far fewer assumptions about that initial empty-state than are required for the far more fantastical hypothesis of a god. Including literally every expert Dr. Marshall has himself cited. There is a reason no cosmologist on the planet agrees with him.
These experts also agree we don’t know if “all existence” began. Marshall even quotes Vilenkin admitting this! Marshall doesn’t respond to my noting that even Vilenkin’s arguments for “past geodesic incompleteness” are for our timeline going back to a quantum state beyond which we cannot say what may or may not have gone before, because we have no physics with which to answer that question. And I’ve quoted numerous cosmologists being very clear about this. Whereas Marshall has quoted none saying we know existence must have had a beginning; not even Vilenkin has said that.
Ignoring Expert Mathematicians
Similarly, all actual experts in transfinite mathematics agree actual infinities are possible, including past infinite timelines. I’ve not only cited countless authorities on this, but have shown even Dr. Marshall’s own sources say this. He’s found no living expert who agrees with him.
Even when he is repeatedly told by Herb Silverman himself that Silverman didn’t mean what Marshall claims, Marshall continues to deny it, without reason. I’ve noted Marshall is confusing “not a number” with “not a quantity” and “not a real number” with “not real” and “needn’t” with “doesn’t.” [2] But Marshall refuses to accept even Silverman’s own clarifications and continues to insist Silverman believes things he’s clearly denied. We cannot warrant a belief built on such a denialist methodology.
Marshall also continues to misquote Oppy (who in fact concludes the opposite of what Marshall claims) even after I pointed this out! [3] Marshall doesn’t even understand the point when he claims “The truism, ‘If there’s no beginning, then no one started adding’, does nothing to advance an answer but merely restates the problem,” as if Marshall didn’t even read Oppy, who concludes otherwise. [4] No one needs to count an infinity for it to exist. And when there is no beginning, there is no “first count” so there is no “time” we are looking for to place it at. Thus an inability to find one is irrelevant.
Proposing “an infinite series exists” cannot be rebutted by saying “that set is empty.” Otherwise we’d have to conclude numbers don’t exist! Whether an infinite set contains points in time or anything else, an infinite set is by definition not an empty set. If there are infinitely many places to be, it simply does not follow that there are no places to be. Hence Marshall’s argument that “nowhere to be” follows from “everywhere to be” (‘if no one can count time, there is no time we could exist at’) is simply incoherent. And as best I can tell, all living experts on this subject concur.
Ignoring Experts as a Christian Methodology?
In all these cases, Marshall simply ignores all the opinions of experts when they do not agree with him, which is an invalid way to warrant a conclusion. On science and mathematics, I actually listen to scientists and mathematicians. I don’t ignore them.
Conclusion
The Kalam Cosmological Argument rests on no premises that can be established as probable. Actual experts in transfinite mathematics agree an infinite past is possible; actual cosmological scientists agree we don’t know for sure if existence ultimately began, and agree that if it did, its uncaused first cause was not probably a god. Many first causes are not only possible but more probable and supported by current science.
-:-
Such is my closing statement on the cosmological argument.
Continue now to read my next entry at Marshall’s request
-:-
Endnotes
[1] To be clear, I am not a Platonist. I’m arguing ex hypothesi. I am actually an Aristotelian with respect to abstract objects (they are all the inalienable properties of spacetime itself): see discussion in Richard Carrier, “How Can Morals Be Both Invented and True” (21 August 2017), “All Godless Universes are Mathematical” (23 May 2017), and “Defining Naturalism II” (31 March 2010). See also Richard Carrier, Sense and Goodness without God (2005), index “numbers” and “abstraction.”
[2] To follow what has happened here: Marshall takes his latest quote from an article by Adam Kirsch, and Kirsch is quoting Silverman’s 2012 book Candidate without a Prayer (p. 26), which I showed Silverman corrected in the 2018 letter to the editor of Free Inquiry that I quoted, showing Silverman’s corrected words were “Infinity is a useful construct created by humans and need not exist in reality,” not “does not” exist in reality; I even asked Silverman himself to clarify what he meant to be sure; and when Marshall still didn’t believe him, I asked for and received an even clearer clarification.
[3] My words, from my last entry: “Oppy’s saying these absurdities are only alleged is not conceding Marshall’s argument. To the contrary, Oppy extensively refutes it.” And again in endnote 3 there: “Even in the very book Marshall quotes, Oppy goes on to challenge that these are absurdities, not agree they are.”
[4] Graham Oppy, Philosophical Perspectives on Infinity (2009), pp. 59-63, 116-22, 223-30, 285-89.
So, we have two experts debating. One says
“Dr. Carrier continues to blatantly beg the question in a manner I’ve never seen in debates with fellow academics.” (Marshall)
The other says
“Dr. Marshall has established two common patterns: he ignores my arguments rather than actually responding to them; or he ignores expert testimony to assert probabilties contrary to it.” (Carrier)
What we need is a moderator to help interested laypeople to decide which expert to trust., lol
Ignoring Expert Mathematicians, paragraph 3, line 1, “marshall” should be “Marshall.”
Also fixed. Thanks again.
It seems to me we may be reasoning backwards. We know so much about the universe now, principally how vast it is, that it is perhaps conceptually required that a super powerful, limitless being have created it. Only such a being could hold and preserve souls in the universe for eternity, which is the point of theistic religion, I think, although souls have only been mentioned in the comments so far. Some apparently are to be stored in heaven and some in hell, but all will be stored somewhere. It would require a super strong being to counteract max entropy in that way. I know this wasn’t a consideration when the argument was first created, or at least far less of a consideration, but it is definitely a consideration now that we know so much about the universe and its forces, particles, etc..
Dr. Marshall has added another qualification to this being, namely, it is “plausibly personal”, which reduces even further the probability of its existence.
Anyway, thanks for the discussion. It remains civil in here, quite a feat in itself!
The problem, of course, is the same it always is: where did this super powerful being get the energy to do that? At the absolute best, you’re adding a powerless entity that contained just enough energy to make the universe; at worst, you’re explaining a seemingly impossible amount of stuff by invoking a source of yet more stuff. Most God arguments look at some problem, however real, and then just sort of handwave “Something somewhere fixed it”. For a God argument to be valid, there’d have to be some kind of independent evidence. Imagine if we found some huge rift to another universe that was constantly pouring out matter and energy. Suddenly we would need to explain that.
The only argument I’ve ever seen make any sense is the idea that a God had to be the one to organize the stuff in the universe. If there were some huge barrier in science right now to us explaining how the universe was assembled, then God would make some sense. Think about it: is intelligence really that amazingly defined by making big things, or rather well-organized things? But instead, science has pretty scrupulously explained that you get pretty much everything we see from the emergent properties of a few forces.
“To avoid my argument that “never exists” means doesn’t exist (and “nowhere exists, likewise)”
wher is the argumunt? I mean beyond ur mere assurting it.
God that is within a time and place – within a wher and when can nevr be god cus he’d be within creation and therfor a creature.
God ixistid befor creating whens and whers and hows.
He didn’t create a where so he could occupy it and ixist. that’s totally daft.
Ur trying t ‘locate’ god in the univurs in ordr t grant ixistuns is BROBDINGNAGIAN folly it must be statid.
“My argument is that there must first be somewhere for a thing to exist before it can exist. ”
That’s only tru’v the univurs and its contents.
God is not part’v the univurs therefor I dersay u’v been trying t put the sadl on the rong caml from the first.
It’s a tautology. “Never exists” means doesn’t exist. It cannot mean “at some point exists”! That would be a logical contradiction. Likewise “nowhere exists” cannot mean “somewhere exists.”
To be nowhere is to not be. That’s what nonbeing means.
Anyone who thinks otherwise is either not being rational or hasn’t really thought this through.
If I might be so bold,
‘to never exist’ means not to ixist at any time or at any point in time.
God’s ixistunt is not cuntinjunt upon time so it is tru he ‘nevr’ exists as time cannot apply tu him – He’s its Creator.
Similarly, ‘to be nowhere’ means not t be at any place in space.
God dus not and cannot hav a location or a place nor ‘need’ a place, He’s the creator’v where.
He ixists without being anywhere.
To be God is t be nowhere nesasrily. – where and when can’t apply. That’s whot being God means. If such things did apply then he wudn’t be god but a creatid entity.
I no it’s very difficult t fathum.U’r applying inappropriat univursal standards tu the Creator, wher u’l always create strawmen t nock down.
Imam Abu Yusuf al-QâDî and Imam MuHammad Ibn al-Hasan ash-Shaybaniyy and others:
تَعَالى عن الحُدُودِ والغَاياتِ والأَركانِ والأَعضَاء والأَدَوَاتِ لا تَحوِيهِ الجِهَاتُ السّتُّ كَسَائِرِ المُبْتَدَعَاتِ
“Allâh is supremely clear of all boundaries, extremes, sides, organs, and instruments. The six directions do not contain Him, for these are attributes of created things”
Such is the saying of Imam Abu Ja
far who is among the heads of pious predecessors. Abu Jafar explicitly states that Allâh is clear of being contained by the six directions ie above, below, ahead, behind, right, and left.I’m sorry but you are just talking nonsense.
You want to believe directly contradictory things: God never exists and God sometimes exists.
That’s simply irrational.
No there is no contradiction –
wher’v I sed God ixists ‘sometimes’
God is not subjict t time at all.
sometimes/nevr/always ar wurds t du withTIME.
God creatid time.He creatid place.
it’s like assurting: man creatid pillow
therefor man must be ‘pillowy’ – if man isn’t pillowy, it’s nonsense.
whot a daft argumunt.
I think Dr Carrier This is your fundamental flaw – ur urijinal sin- tu think that God is subjict t a time or a place – that he resembls his creation….
and if He isn’t he can’t ixist. wasting milliuns’v wurds attacking a strawman.
God ixists sans time / sans place. That’s theism 101.
So, God does not exist now?
If he exists now, he exists sometimes. Ergo, you are saying he sometimes exists.
If he dopesn’t exist now, he doesn’t exist. By definition. That’s what the verb “does not” means.
And as this is true now, it’s true at all times past as well: if at any past time it was true up to that point that “God never exists,” he didn’t then exist.
He cannot exist “before” time either; as that is also a contradiction in terms.
Likewise, to not exist anywhere is what the words “does not exist” mean. So either God does not exist here or anywhere else and thus God does not exist; or there is some place God exists. Nothing else entails any meaningful proposition. And declaring meaningless statements true is irrational.
I think u’r being trifl unfair.
God ixists at no time; he ixists without time. no sometimes, no ofn, no rerly.
we du use wurds like ‘always’, ‘now’, in turms’v our perspectiv t indicate God’s ixistuns at iturnity.
ur ‘ergos’ are well off the mark. Is the delibrate obfuscation?
Prhaps
this is beter put:
The claim that God is timeless is a denial of the claim that God is temporal. First, God exists, but does not exist at any temporal location. Rather than holding that God is everlastingly eternal, and, therefore, he exists at each time, this position is that God exists but he does not exist at any time at all. God is beyond time altogether. It could be said that although God does not exist at any time God exists at eternity. That is, eternity can be seen as a non-temporal location as any point within time is a temporal location.
https://www.iep.utm.edu/god-time/
That’s linguistic mush.
Existing everywhere is a location in space. Thus existing always is a location in time. God exists at every moment of time. There is no moment of time at which he does not exist. Thus it is illogical to say he exists at every location in time and exists at no locations in time.
No amount of playing games with words can escape this fact.
To be entirely honest, this feels little a tiresome by now. Dr. Marshall began his defense with a brute fact, which is not an argument at all. His three “extra” justifications for premise 1 fall almost immediately. Indeed, 2/3rds of them would support Dr. Carrier’s points BETTER than his own. The last is either a non-sequitor or doesn’t even make sense (wouldn’t follow even if the concepts were true). With premise 1 left undemonstrated, we can logically say there is no reason to accept Dr. Marshall’s conclusion (even if it happens to be correct).
Dr. Marshall quote mines many experts in support of premise 2, but Dr. Carrier has done a rather irrefutable job of showing just that. The scientists do not agree with what Marshall is proposing (at the very least not in the sense that is required to support premise 2). Marshall seems stuck on infinity being a number (it’s not) and on his personal interpretation of high level cosmological models (of which he is not an expert and where the experts that created the model disagree with him).
There’s no need to even address the way Dr. Marshall jumps from the actual conclusion (the universe had a cause) to a number of claims about that cause. I would have issues with that as well, but it’s moot. Neither premise of the Kalam stands (again, in the sense that they MUST for the conclusion to logically follow). Even if a God exists, the Kalam is not a rational argument for his existence.
Perhaps science will learn more in the coming years. Perhaps we will be able to pierce the veil of ignorance covering the ultimate origins of our universe (and maybe existence from there).Maybe a god will be there waiting for us. Maybe not. But lets go with what we have for now, instead of jumping ahead to things we can’t know.
Could you explain the distinction–if there is one–between existing “in space” and existing “at a location”? I think the miscommunications about god “existing nowhere” might hinge on what each of you means by “somewhere”: Marshall’s position–I assume–is that “outside of space” is not necessarily synonymous with “no location.”
Indeed. I’ve been clear several times the location need not be spacetime.
The argument does not depend on that, but on the simple logic: God cannot create a place or time to be. Because he has to already be somewhere at some time to even exist, much less do anything.
One cannot avoid this argument by saying God was somewhere else, and then created space; because that concedes we do not need god to explain the existence of places. Ergo, it no longer follows that we need God to explain space. If a place has to exist uncaused (as this argument entails it does), then Occham’s Razor leaves us with the only place we’ve observed exists: space.
In other words, the issue is not that God cannot exist unless we posit a place for him to exist (that’s also true; but Marshall can easily just concede there is a special place for God to exist, like heaven or something). The issue is that once we admit that places must exist uncaused (and Marshall logically would have to, to admit God exists in some extra place somwehere), it can no longer be argued that places require a cause. Ergo it can no longer be argued space required a cause.
It could yet still be true that space had a cause (albeit a cause located in some other, perhaps even supernatural place); but we have no evidence that’s likely and no need of that hypothesis at all, so we can’t leverage that possibility into a probability as Marshall requires.
“Marshall thus avoids addressing the actual point: that it’s logically impossible that “everything must have a cause” before causal laws exist. Therefore it cannot be the case that existence requires a cause. This is not begging any question. Marshall is begging the question when assuming causal laws exist before anything has caused them to exist.”
Dr Carrier, please help me understand this. The statement “everything must have a cause” before causal laws exist, is an obvious, logical impossibility. There’s no confusion here.
But why does it follow that existence does not require a cause? (are you referring to physical existence?)
What is wrong with saying that an infinite, spiritual being created the causal (physical) laws, which govern the physical existence that began after those laws were created?
When existence doesn’t exist, nothing exists.
A causal law is something.
Ergo, when existence doesn’t exist, causal laws don’t exist.
Ergo, existence cannot “require” a cause.
It could “incidentally” have a cause (like a god or anything else). But it cannot require a cause. Because that would entail a causal law. But causal laws cannot precede the existence of laws.
Since the requirement of a cause does not exist before anything exists, it cannot be argued that existence required a cause. It could have arisen uncaused precisely because at that moment no causal laws existed. After that moment they do.
We also covered earlier in the exchange the peculiar dodge of not talking about “causal laws” but “simultaneous causation,” but there is no known causal law there. We have no evidence it’s true even now that “everything has a simultaneous cause,” and such would be unlikely anyway, as we could not then explain why such a law existed (“why” does there “need” to be an infinite stack of simultaneous causes for every single event and thing?). So it cannot likely be true that there is such a causal law. On whether anything (even if not all things) could be subject to such a causal law, and what would not be by that same reasoning, see my extensive series on Edward Feser.
Thank you for the clarification.
That’s why I asked whether you were referring to “physical existence”, specifically.
So the statement “physical existence requires a cause”, is not an logical impossibility, but it may lack the evidence to render it probable.
I will check out the link you suggested.
Analytically, yes. For example, if prior to the physical there was some other kind of existence that mandated that law, i.e. preventing spontaneous creation of the physical. But that other existence could then not have required a cause, because prior to that other existence there by definition were no laws, thus there cannot have been causal laws. And so on.
However, there is no empirical or logical basis for believing such a prior world existed. We have no need of it to explain the present world. Since we know something must have started uncaused, we no longer have any reason to believe it wasn’t this world (if existence started at all, which we have not even verified as probable either).
Although I’m also not even sure “other kinds” of worlds can be coherent. As I’ve said before, I suspect it’s logically impossible for anything to exist that isn’t reductively physical, as in, “shaped stuff” in “spacetime,” since once you define “stuff” and “spacetime” so broadly as to include all logically possible things and places to be, you by definition have defined every logically possible thing as physical.
I just found this Q&A (“How Can the Universe Not Have a Beginning?”) with the famed physicist Roger Penrose arguing for a past eternal multiverse.
I then checked around and sure enough he makes a good case for it similar to the one I’ve noted many other cosmologists do, e.g. see this interview with Penrose, which explains how his model, Conformal Cyclic Cosmology, the BGV theorem is bypassed because entropy is reset.
For more on this see “New Evidence for Cyclic Universe Claimed by Roger Penrose and Colleagues” (2018) and the Wikipedia article on Conformal Cyclic Cosmology.
I personally don’t think his model is as likely as several other past-eternal models that likewise bypass the consequences of the BGV theorem. So we don’t really need this proposal. But we still don’t have any evidence proving his model false, much less impossible. So it’s one more example of how we don’t know the universe wasn’t past eternal, and the BGV theorem doesn’t apply to many plausible models still being considered.
Dr. Carrier, recently a new paper has been written, where the author assured us that the BGV applies even when taking quantum gravity into account. Here’s what he stated:
“It is, of course, interesting to probe deeper the fate of geodesic incompleteness, as described by BGV theorem, in a complete theory that incorporates quantum fluctuations of matter fields as well as spacetime. In Sec. II, while discussing the issue of geodesic incompleteness of the congruence u, the effects of quantum fluctuations were incorporated through the (covariantly defined) lower bound `0 on distances. The existence of a lower bound on geodesic intervals seems to a be a generic consequence of combining principles of GR and quantum mechanics, and expected to be independent of any specific model/framework of quantum gravity.”
Source: BGV theorem, Geodesic deviation, and Singularities in spacetime
I sent this to Dr. Carroll, but he didn’t respond to my email yet. So, I don’t know.
That isn’t saying what you describe (did some Christian claim it did?). It’s simply stating the obvious: classical geodesics always end at spacetimes collapsed to quantum scales (a “quantum” rather than classical singularity), because we have no theory to model what happens after that. Unless this paper is claiming to have discovered the correct theory of quantum gravity (in which case it will win a Nobel Prize in short order), it cannot be claiming to know what resides on the other side of a quantum singularity. And true enough, I read that paper, and it never makes any claims whatever as to what is or is not on the other side of that quantum state.
I should also note, that paper (which isn’t even about whether the past is finite or eternal) does not address Penrose’s conformal geometry model, which also eliminates the BGV—by eliminating the scaling assumptions required by it. On the Penrose model, there is no measurable relation between entropy today and entropy in previous epochs. Whereas the BGV requires (i.e. assumes) conservation of entropy.
Thank you for responding. So, it’s hard to see how I did not describe it correctly. In fact, I just restated what is written in page 4 (‘Some Remarks’).
He is saying here that the incompleteness of the geodesics is a generic consequence of “combining principles of GR and QM” and its results are “expected to be independent of any specific model/framework of quantum gravity.”
So, this paper seems to be responding to people like Sean Carroll who claims the theorem is entirely classical. And so, it would not say anything about the real universe, since it is quantum.
For example, in the paper entitled “Current observations with a decaying cosmological constant allow for chaotic cyclic cosmology”, (p. 24) physicists George Ellis and Emma Plattsa stated:
“Singularity Theorems: Borde et al. have given claims that the universe must have been singular (BGV), but these are based on restrictive assumptions that need not hold in the real universe. In particular, the BGV theorem relies on two assumptions; either there is only expansion, or the average expansion is positive Hav > 0 along a specific geodesic, and the second is that the behaviour can be modelled entirely classically. For any of our inflating systems, during inflation there is a period in quantum fluctuations of the inflaton field are assumed to be converted into classical perturbations of the fields. The quantum fluctuations are assumed to arise from the vacuum spontaneously, a behaviour not modelled by classical dynamics… It is therefore not correct to invoke the BGV theorem in this context as the behaviour of a classical geodesic during this phase is not well established. We therefore evade this theorem simply by not satisfying the required axioms for the theorem to hold true in either instance.”
So, that’s what the author of the new paper is trying to eliminate, namely, the second assumption the theorem makes. So, it would apply independently of quantum gravity and fluctuations.
But I agree a past-eternal model like the CCC of Penrose, or a contracting phase from the infinite past would also eliminate the theorem, since they wouldn’t violate one of the assumptions.
“did some Christian claim it did?”
No, but I’m sure they would if they had read the paper. It seems nobody noticed it. Since it is relatively recent and nobody cited it. I found it myself.
Finally, I agree that it doesn’t explicitly say anything about the universe being eternal or not. However, it does eliminate one assumption that has been advocated by Sean Carroll many times in debates (including the famous Craig vs Carroll). In fact, even Vilenkin seemed to concede that his theorem didn’t take QM into account.
Yes. That means, quantum mechanics doesn’t prevent the collapse to a quantum singularity. That doesn’t mean anything about what precedes that singularity.
If it were, it would mention scientists who say that and address what they said. It doesn’t. It’s simply saying that quantum mechanics doesn’t prevent the geodesic’s interruption by a quantum singularity. Which Carroll didn’t challenge (so it isn’t addressing anything Carroll has said). Penrose, meanwhile, has challenged that, but by pointing out an assumption in the BGV about scale conformality that this paper doesn’t even address (so it clearly isn’t responding to him either).
Ellis and Plattsa are talking about what Carroll was: when they say “during this phase” they mean: during the phase when spacetime is contracted to or erupts from below a quantum threshhold. Ellis and Plattsa would agree all universes start at a quantum singularity even in eternal inflation; what they are disagreeing with is that this means nothing can precede those singularities, i.e. that time is past finite. The BGV cannot say that it is. Because though the BGV can establish there must be a quantum singularity in the past, it has nothing to say regarding what precedes that quantum singularity, because we have no model of how anything operates at that scale (no working theory of quantum gravity etc.). Thus eternal inflation can be past eternal, exactly as Ellis, Carroll, et al. describe. This paper you are referring to says nothing against them on this point and isn’t even about that issue.
By contrast, and perhaps making clearer what I just said, note “or a contracting phase from the infinite past” technically is addressed by the BGV, in that if we assume classical laws only, previous contractions would have to be finite in number owing to the second law of thermodynamics (the presumption of non-entropy reversal). However, this assumption collapses when we reintroduce quantum mechanics, which gives all entropy reversals a nonzero probability, and on an infinite timeline all nonzero probabilities approach 100%, so the BGV can no longer hold, and we no longer have an entropy argument against a past infinity of collapses.
But collapses aren’t required. As Susskind shows in his analysis of the BGV, even the BGV entails absurdly vast numbers of previous universes (that they are a finite number is thus not even relevant anymore), and B, G, and V have all conceded his point. None require a collapse. They only require spontaneous inflation from a quantum-scale starting point (which looks like a quantum singularity, and thus an incomplete geodesic, to anyone on the other side of it). Thus the universe can just keep inflating forever, continually producing Big Bangs all over the place. And even the BGV entails our Big Bang is statistically almost certainly a very late comer in this process, being at the end of an unimaginably long string of previous Big Bang events. When we add the fact that quantum mechanics eliminates the entropy argument, there remains no further argument against this “unimaginably long string of previous Big Bang events” being in fact infinitely long. That’s what Carroll et al. mean by the BGV failing to account for quantum mechanics.
Okay, Dr. Carrier. So, I agree with most points, however, I’ll make some comments regarding the points I disagree with.
“note “or a contracting phase from the infinite past” technically is addressed by the BGV”
So, what the BGV addressed is the cyclic model (ekpyrotic). But I talked about the single bounce universe. In this case, there wouldn’t be infinite contractions and expansions. Rather, it’s just a universe that is contracting from the infinite past that has a bounce and expand to the infinite future (it goes from minus infinity to infinity to plus infinity; -3, -2, -1, 0, 1…). The entropy is then reset at the bounce because of the repulsive effects of LQG.
I think this is the best model we have now. It’s very simple, it doesn’t require any strange quantum state (which may require indeterminism to decay). It satisfies the BGV, since the geodesics (the geometry as well as the particles) converge in a point, but continue on the other side of the bounce (the contracting phase – so, it is geodesically complete).
Now, Vilenkin has an argument against this. He says the contracting phase would be unstable because of perturbations and singularities, so it would not make the expanding phase. However, other physicists disagree.
I’ll give you an example. In the paper “Fully stable cosmological solutions with a non-singular classical bounce”, physicists Ijjasa and Steinhardt wrote:
“We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.”
Vilenkin is clearly biased against an infinite past. Perhaps that’s because he wants to promote his “Tunneling from nothing” model. You could point out that what matters is the argument and not the biases, but I disagree. I came to the sad realization that the bias will blind the person, and she will ignore the evidence against her, and cherry pick the science that seems to offer support. So, we should be very skeptical of Vilenkin.
Now, regarding the entropy and the contracting phases: Vilenkin analyzed it in his article “Did the universe have a beginning?” Vilenkin wrote:
“Another possibility could be a universe which cycles through an infinite series of big bang followed by expansion, contraction into a crunch that transitions into the next big bang. A potential problem with such a cyclic universe is that the entropy must continue to increase through each cycle, leading to a “thermal death” of the universe. This can be avoided if the volume of the universe increases through each cycle as well, allowing the ratio S/V to remain finite. But if the volume continues to increase over each cycle, [then] the universe [must be] past-incomplete.”
However, I sent the exact part to physicist Steinhardt, and luckily he responded to my email. A very nice guy indeed. It was a honor to talk to him (since he is one of the fathers of inflation).
He responded the following:
“(1) It has been a long time since we have invoked extra dimensions and branes in designing cyclic models. Those notions turned out not to be essential so we abandoned them a dozen years ago. Think about just the usual 3 space dimensions and one time; we can use a scalar field plus potential similar to inflation but the potential has different properties. (2) The Vilenkin argument does not apply. We have to assume that space is infinite throughout and that during each cycle space stretches by a constant factor. Multiplying an infinite space by a constant factor still produces an infinite space. But, if the space has a density of matter, multiplying by a constant factor decreases the density by a constant factor. (3) So, going forward in time, each cycle begins with the creation of a certain density of matter and radiation being created by the scalar field; by the end of that cycle, that density is exponentially diluted by all the expansion; it is negligible compared to new matter and radiation created after the bounce by the scalar field once again; the older stuff dilute and negligible; the next cycle occurs and the process repeats; all the older matter and radiation is superdiluted and only the new matter and radiation counts. (4) How is it possible for this to continue? Gravity can produce unbounded amounts of energy – during each cycle, gravitational energy is converted to scalar field energy, which is converted then to matter and radiation. And nothing we know stops this from happening forever going forward. (5) Running backwards in time is a little more subtle to describe because you have to imagine that (going backwards) most of the matter disappears (into scalar field energy). (6) So, what Vilenkin missed is that the universe is not uniformly shrinking. This is a self-similar process that can repeat for ever back in time. An observer cannot tell one cycle from another — they see the exact same thing – from cycle to cycle.”
You can read his paper titled: “A new kind of cyclic model” where he also explains that there is no need to use the branes…
So, it seems Vilenkin is really biased against an eternal past. Nevertheless, real experts disagree with his conclusions.
A last point I want to make refers to your term “quantum singularity”. It seems wrong to me. In the article “In What Sense Is the Early Universe Fine-Tuned?” (p. 13) Sean Carroll stated: ‘”The Borde-Guth-Vilenkin (BGV) theorem [33] demonstrates that spacetimes with an average expansion rate greater than zero must be geodesically incomplete in the past (which is almost, but not quite, equivalent to saying there are singularities).”
So, perhaps your use of the term “quantum singularity” is incorrect. To say something is geodesically incomplete, is to say that the worldlines/ trajectories/geodesics converge (end) in some point.
Cheers, Dr. Carrier.
…what the BGV addressed is the cyclic model (ekpyrotic)…
Actually, no. The ekpyrotic model isn’t an eternal inflationary model. It also bypasses the BGV, because that says nothing about other universes already existing that continually collide with each other, since that’s not a temporal model (the number of universes that exist in that model is not predicated on time, so there can just be an infinite number of simultaneous universes, continually colliding into each other).
BGV only addresses eternal inflationary models. And all it can prove is that they all must start at some quantum singularity; not what can or cannot precede that singularity.
…the single bounce universe…
Also not an eternal inflationary model. Thus also not addressed by the BGV.
…An observer cannot tell one cycle from another…
That’s the Penrose model.
…it seems Vilenkin is really biased against an eternal past.
IMO probably true. But he remains honest. Which is why one has to read his words carefully (Craig tends not to do so).
And yes, “quantum singularity” is just a shorthand I made up. There is no word for it in physics. The “singularities” Carroll is talking about are true singularities: points at which dimensions become infinitely small (and thus equations explode with infinite numbers). Which we now know cannot exist, owing to quantum mechanics (e.g. gravity stops working below a certain quantum scale, so collapses cannot continue—this means even black holes today do not contain actual singularities, they cannot; what they do contain is unknown, because we have no theory of quantum gravity yet).
A “quantum” singularity is a non-infinitesimal singularity: it is what happens when gravity breaks down below a certain scale. It’s what is in black holes. And what the Big Bang will have started with. Exactly what happens at that scale is unknown. No classical physics can describe it. And no quantum physics fully describes it. Hence I use the term “quantum singularity” to distinguish that state from just “singularities.” In a quantum singularity, dimensions do not drop to zero (they are not infinitely small), but have a minimum positive diameter and circumference, both in time and space (hence Hawking’s “nutshell” theory is based on the fact that below a certain scale, time has an undefined value: there is never an infinitesimal amount of time). The size we know is the Planck length, which is roughly 1 x 10^-35 meters. Which is far from infinitesimal.
To say something is geodesically incomplete, is to say that the worldlines/ trajectories/geodesics converge (end) in some point.
Correct. But we know “that point” can never be an infinitesimal point. Quantum Mechanics entails that’s impossible. So the farthest the BGV can get to is a quantum point: a Planck-radius. The geodesic must end there. Because, as Vilenkin himself has admitted, we have no physics to predict what will happen or exist below that scale. And therefore we have no physics to tell us what does or does not or can or cannot precede that state.
This is what Carroll et al. mean by the BGV only presuming classical physics and thus being unusable for predicting what predates the end of the geodesic. The BGV literally says nothing about that. Because it cannot. To say something about what precedes that Planck radius requires a working theory of quantum gravity. Which we don’t have, and the BGV makes no attempt to propose.
Thank you for your clarification regarding the “quantum” singularity and geodesics. I was a little confused about that.
“Actually, no. The ekpyrotic model isn’t an eternal inflationary model. It also bypasses the BGV,”
I’m sorry, but the BGV does address the cyclic model. Have you read the paper (p.4)? It says:
“We finally comment on the cyclic universe model in which a bulk of 4 spatial dimensions is sandwiched between two 3-dimensional branes. The effective (3 + 1)- dimensional geometry describes a periodically expanding and recollapsing universe… There are brief periods of contraction, but the net result of each cycle is an expansion. For null geodesics each cycle is identical to the others, except for the overall normalization of the affine parameter. Thus, as long as Hav > 0 for a null geodesic when averaged over one cycle, then Hav > 0 for any number of cycles, and our theorem would imply that the geodesic is incomplete.”
The problem, however, is that the BGV was published in 2003. The ekpyrotic model was still in its infancy. Many other versions and variations of this model have been developed since then.
For example, in the article titled “Geodesically Complete Analytic Solutions for a Cyclic Universe” (2011), Neil Turok and Shih-Hung Chen stated:
“Using models and methods inspired by 2T-physics, we show how analytic solutions can be obtained in flat/open/closed Friedmann-Robertson-Walker universes. Among the analytic solutions, there are many interesting geodesically complete cyclic solutions in which the universe bounces at either zero or finite sizes. When geodesic completeness is imposed, it restricts models and their parameters to a certain parameter subspace, including some quantization conditions on initial conditions in the case of zero-size bounces, but no conditions on initial conditions for the case of finite-size bounces. We will explain the theoretical origin of our model from the point of view of 2T-gravity as well as from the point of view of the colliding branes scenario in the context of M-theory.”
In the book “Endless Universe” (2008), Neil Turok stated: “In the cyclic universe model described thus far, the cycles continue regularly forever into the past and future. At present, there is no known theorem or principle that prevents this from occurring.” (p.83)
So, again, it seems Vilenkin was wrong. He tried hard to refute an eternal past. More recently he also wrote a paper trying to refute the Aguirre-Gratton model, as well as the Carroll-Chen… He claimed the Carroll model would be unstable because of singularities (ignoring the possible effects of gravity).
Furthermore, Quantum gravity may not be necessary after all. For example, in a very recent paper (2019) titled Theoretical Cosmology (p. 14), physicists George Ellis and A. A. Coley stated:
“We should [also] note that there are generic spacetimes which do not have singularities. In particular, the proof of the Penrose singularity theorem does not guarantee that a trapped surface will occur in the evolution. It was proven that for vacuum spacetimes a trapped surface can, indeed, form dynamically from regular initial data free of any trapped surfaces.”
He also stated in page 45 (I think) that GR has a deficiency (as you stated), namely, it doesn’t take Quantum Gravity into account.
The ekpyriotic model is not cyclic. You are confusing it with the “ekpyrotic cyclic universe,” a variant. The original ekpyriotic model just has infinite universes constantly crashing into each other. There are no cycles.
But yes, past eternal cyclic models also have post-BGV defenses. They rely on quantum mechanics breaking the assumptions of the BGV at small scales, e.g. showing that a temporal-spatial geodesic ending in a quantum state does not entail no prior temporal-spatial geodesic, but only that if there is one, its presence requires a nonclassical theory (e.g. a theory of quantum gravity) to explain, which is what everyone has been pointing out for over a decade now. Note that Vilenkin himself has admitted this. He just couches it in language obscure to non-physicists.
This is not a valid response to the BGV, however. One has to quantize gravity to prevent a singularity forming. The whole point of the BGV is the argument that if nothing stops gravity, all of existence must begin with a singularity.
The only valid response is that something does stop gravity: quantum mechanics—there is a scale below which gravity can no longer operate; so there can never be a singularity. Note this could be what one might mean by “generic spacetimes which do not have singularities.” The Ellis-Coley paper is vague as to what they mean by that however. As far as I can fathom the only classical solution they could be referring to would mean statistically anomalous collapses that avoid singularities, but that could only refer to bounce-states after an initial singularity; because the BGV proves that if you walk back through a zillion bounced singularities, the sequence has to stop (and thus has to have started) with a final (an initial) singularity. It’s statistically inevitable, because all nonzero probabilities approach 100% on an infinite timeline, thus all timelines are finite. It’s just that the BGV only proves this by assuming quantum mechanics doesn’t prevent singularity formation, which assumption is well known to be false on present physics.
Update: I sent the new theorem to Sean Carroll and he responded:
“I don’t understand that quote, sorry. The BGV theorem does not apply in quantum gravity, it’s a statement about classical spacetimes.”
I also sent to George Ellis, and he responded the following:
“Hi
I have not examined that paper in detail but the basic issue remains: the BGV theorem is a result of a geometric assumption that is untrue for example in k = 0 de Sitter universes (a(t) = exp H t) as well as k=+1 de Sitter universes (where a(t) = cosh H t) hence it works by simply omitting the solutions that are non-singular by excluding the conditions that allow them to exist. The essence is that if you demand that df/dx > epsilon > 0 then f(x) necessarily goes through zero. If you allow df/dx =0 (as in the case of the k = +1 de Sitter universe) you can get a bounce. This is true irrespective of whether you have quantum theory involved or not.
George Ellis”
So, I responded: “Thank you for your detailed response regarding the de Sitter space. But it seems to me QM is not a problem to the theorem anymore.”
And he replied: “No, the problem runs deeper than that.”
Correct. Quantum theory is a reason for “simply omitting the solutions that are non-singular by excluding the conditions that allow them to exist,” and the only reason known so far to always apply (and thus this is as near to 100% certain to be true as makes all odds, and therefore the BGV is essentially 100% certain to not apply to the real world). There are other ways a classical spacetime can avoid “solutions that are non-singular by excluding the conditions that allow them to exist,” which is what Ellis means by the “broader” problem; but you should note, none of those classical scenarios have a high probability.
In fact they usually require coincidences, and thus could not actually survive an iteration into an infinite past, because the probability of an infinite string of random coincidences is infinity to one against. There are, however, alternate versions of classical spacetime, e.g. that propose “something happens” at near-singularities to prevent a proper singularity from forming, and they can be iterated to past infinity, but as these are speculations (we have no evidence any of them are true), they bear insufficient probability in themselves to challenge the BGV (which would remain true “so far as we know,” until some such special exception actually is found to be true).
So really, the only reason to reject BGV right now is quantum mechanics. It’s the only thing known to be true that entails the BGV is false (or rather, in formal terms, unsound; it could be true by accident, but we shouldn’t believe things that are only accidentally true, unknown to us). This doesn’t mean cosmologists can’t keep proposing classical models that also overcome the BGV; but that they can come up with them is not a refutation of the BGV, but merely a competing hypothesis as much in need of evidence as the BGV.
Prof. Ellis did not dismiss the paper. He simply stated he didn’t examime it in detail. However, he did read it. And didn’t present any objection to the paper. He simply explained that a bounce would eliminate the geodesic-incompleteness. Furthermore, whether that bounce is classical or not is irrelevant to the point. So, a quantum theory would have some implication for a bounce; nothing more than that.
Now I’m sure this paper eliminates the ‘quantum gravity’ objection, as the author suggested. If I had misrepresented the paper, Prof. Ellis would have corrected my mistake.
Regarding the fact that we have no proof of a bounce just like there is proof the BGV is true, is not an argument against the bounce.
There are three options here:
The BGV is proof the universe began.
There are viable alternatives to the BGV.
A bounce is proof the BGV is wrong, since we have evidence a bounce did happen.
We only need option 2 to be true. Nothing more. If there are viable alternatives (with equal evidence), then the necessity of the BGV is undermined.
Sheers.
As I already told you, that paper never mentions the quantum gravity objection to the BGV. Go back and read what I said on that point. You confused what it said about something else.
No, the BGV proves that if spacetime is classical, there must be a finite number of previous universes. So you’d have to say the BGV is a proof that, on classical gravity, all of existence began, but did not necessarily start with this universe. Susskind showed even on the BGV’s own assumptions, the number of previous universes there could have been is so large as to be practically indistinguishable from infinite.
Not only that, but the BGV doesn’t even apply to the observable universe, which we now know makes singularities impossible, and the BGV depends on singularities being possible. Ellis himself just told you this.
That’s incorrect. The BGV is entirely compatible with bounces. The BGV does not say there have not been previous bounces (the BGV paper even explicitly mentions bounce models as compatible with their theorem). The BGV says that if there were previous bounces, they cannot continue infinitely into the past, i.e. there can only be a finite past number of them. But to get this result, it has to assume singularities are possible. And we know they aren’t. Even before we get to alternative models of cosmology.
Ellis is telling you that only bounce models that ensure no singularities ever occur will negate the BGV. The most well known reason is quantum gravity. But there are other reasons that could be the case too. He isn’t telling you anything different than that. Read his words carefully.
Update: I sent an email to Vilenkin and fortunately he responded to my email.
I asked him: “Hi, Prof. Vilenkin… I’ve recently read about the BGV and its potential implications for the beginning of the universe and found it very interesting. However, there is a possible problem with it (or so I think).
In an email to William Lane Craig you stated: “The BGV theorem uses a classical picture of spacetime. In the regime where gravity becomes essentially quantum, we may not even know the right questions to ask… The question of whether or not the universe had a beginning assumes a classical spacetime, in which the notions of time and causality can be defined. On very small time and length scales, quantum fluctuations in the structure of spacetime could be so large that these classical concepts become totally inapplicable.”
However, recently a new paper has been written where the author assured us that the BGV applies even when taking quantum mechanics into account…”
So, I sent Vilenkin the same quote from the paper I presented to you, Dr. Carrier, in the beginning of our discussion and asked:
“So, my question to you is this: does this paper show quantum mechanics is irrelevant to the BGV? Does it contradict what you stated in your email to Dr. Craig?”
His response was the following:
“I am familiar with Dr. Kothawala’s paper. In the acknowledgement to that paper he thanks me for pointing out potential issues with his approach, but he does not respond to my points.
Without getting into technicalities, Dr. Kothawala makes some guesses about how the classical BGV theorem will be modified if quantum gravity effects are taken into account. However, we do not have a quantum
theory of gravity and I have no way of telling whether his guesses are right or wrong. So I stand by my statement in email to Dr. Craig.
Best wishes for the holidays!
Alex V”
So, it is the end of our discussion here.
Yeah. Vilenkin just told you the BGV does not apply to quantum mechanical universes because we don’t have a working theory of quantum gravity.
Thus, he is admitting to everything I just said.