This is a blog about my thoughts on a paper by Daniel Linford called Neo-Lorentzian Relativity and the Beginning of the Universe. It's not a final draft, of course, and I'll update it with future edits when I deem it necessary.
Linford's paper involves two overall sections, with little mini-sections (never boring) in between. I am more interested in the first half of Linford's paper, which has to do with Linford's general point that William Lane Craig's so-called Neo-Lorentzianism is incompatible with using Relativistic Cosmology to demonstrate the second premiss of the Kalam Cosmological Argument, namely, that the universe began to exist (Linford calls this position ANL, which couples Neo-Lorentzianism with an A-theory of Time).
We'll get to more details below, but one of the reasons Linford has for rejecting ANL is that it doesn't solve what Linford calls the "Omphalos Objection", which is the idea that all the empirical evidence we have for the past-finitude of the universe is consistent with the universe being, say, five minutes old or even infinitely old. I'll get to my comments on this below. There are also other objections Linford raises, objections against Craig's instrumentalism about how space-time is modeled mathematically, objections against Craig's candidate for identifying the "preferred foliations" (the hypersurfaces of Constant Mean (extrinsic) Curvature picked out by Cosmic Time), forays into York Time (I looked into this for the first time, so my thanks to Linford for bringing this to everyone's attention), and concerns about the requirement that ANL needs to be a robust, competing theory (pitted against Relativity): Linford argues that Craig's ANL is not robust or detailed or complete enough. More of this will inevitably come up. I've found that I have strong issues with much of the discussion in Linford's footnotes. It might come down to interpretative issues.
Let me quickly note what motivated my writing this blog in the first place. A while ago, I met Linford on social media and he expressed the view that no one who had not understood the mathematics of relativity had any right to speak on it, to which I responded by arguing that if you understood the relevant concepts, then you could still have an intelligible discussion on the competing physical interpretations. This led to my being surprised to find out (from Linford) that there just aren't any competing interpretations of the mathematics, that Lorentz, Einstein (1905), and Einstein/Minkowski all had theories with different mathematics, and that it is those differences in the mathematics that account for why they have different physical interpretations. Now, in a sense, Linford is correct; each of these gentlemen, along with any contemporary theoretical physicist propounding a variation on these theories, will be describing a theory whose mathematical content will be different relative to that theory. What Linford was saying sounded rational, so I lowered my credence level in what I had thought I read (that there are competing physical interpretations of an identical mathematical formalism) and gave Linford a promissory note that I would read his paper, more literature on relativity, and get back with him on whatever I found out (mistaken or not), if the opportunity arose. What I did find out ended up confirming what I had initially said. Linford is correct that, taken as a whole, Lorentz and Einstein described theories whose overall content involves different differential equations. Correct. But that's not what was being argued. What was being argued was that the mathematical core of the Special Theory of Relativity was the Lorentz Transformation Equations, and that it is those equations that Lorentz and Einstein had different, competing, physical interpretations about. As far as I am able to tell, after reading a variety of different, authoritative sources on relativity, Craig is absolutely correct and vindicated on this. If I communicated this clumsily in my social media interaction, my apologies to Linford, but this is what I had intended to say.
Enough preface. Let's dive in. This will be organized topically.
A. Brief Glance at the Abstract
Here's a quote. It'll be helpful to pay attention to this for a bird's-eye-view.
Many physicists have thought that absolute time became otiose with the introduction of Special Relativity. William Lane Craig disagrees. Craig argues that although relativity is empirically adequate within a domain of application, relativity is literally false and should be supplanted by a Neo-Lorentzian alternative that allows for absolute time. Meanwhile, Craig and co-author James Sinclair have argued that physical cosmology supports the conclusion that physical reality began to exist at a finite time in the past. However, on their view, the beginning of physical reality requires the objective passage of absolute time, so that the beginning of physical reality stands or falls with Craig’s Neo-Lorentzian metaphysics. Here, I raise doubts about whether, given Craig’s NeoLorentzian metaphysics, physical cosmology could adequately support a beginning of physical reality within the finite past. Craig and Sinclair’s conception of the beginning of the universe requires a past boundary to the universe. A past boundary to the universe cannot be directly observed and so must be inferred from the observed matter-energy distribution in conjunction with auxilary hypotheses drawn from a substantive physical theory. Craig’s brand of Neo Lorentzianism has not been sufficiently well specified so as to infer either that there is a past boundary or that the boundary is located in the finite past. Consequently, Neo Lorentzianism implicitly introduces a form of skepticism that removes the ability that we might have otherwise had to infer a beginning of the universe. Furthermore, in analyzing traditional big bang models, I develop criteria that Neo-Lorentzians should deploy in thinking about the direction and duration of time in cosmological models generally. For my last task, I apply the same criteria to bounce cosmologies and show that Craig and Sinclair have been wrong to interpret bounce cosmologies as including a beginning of physical reality.
A couple things jump out at me as I read this.
First, it's hard to know what Linford means by relativity being 'literally false' for the Neo-Lorentzian. Is a literally true relativity theory the one espoused by Einstein before Minkowski? But then isn't the paradigmatic way relativity theory is taught in universities the geometric approach of Minkowski? So, is Minkowski's version literally true? If the case is made that Minkowski's space-time realism is implicit in 'early-Einstein' (1905), I don't find that case compelling, for reasons I can't get into here. (More than one historian of science and/or philosopher has defended the view that Minkowski's geometrical project was latent in 'early-Einstein'. I have read their defenses and I come away unpersuaded.)
Suffice it to say, the effects of Lorentzian relativity are just as real: if your inertial frame is not in uniform motion relative to the privileged frame of reference, relativistic effects ensue: clocks really slow down; measuring rods really shrink and distort. Thus, it strikes me, as it might other Neo-Lorentzians, that Linford is doing a pinch of 'gate-keeping' when labeling Neo-Lorentzian relativity as not 'literal' relativity. Why couldn't the Lorentzians say the same thing about early-Einstein, that his formalism had a physical interpretation that wasn't literal relativity?
It seems to me that all three versions of relativity have a kind of literal relativity and that the kind of relativity involved is determined by considerations of the physical interpretation involved. Didn't Lorentz lecture on Relativity Theory until his death? And lest it be said that Craig's interpretive trichotomy is a historical anachronism, I personally can't make sense of why it would be based upon the voluminous amount of quotations from the relevant authorities that corroborate Craig's assessment. I'm not able to retrieve all the sources appealed to by Craig, but every single one of the sources I have been able to retrieve don't show any evidence at all of Craig taking anything out of context or cherry-picking favorable data to serve some metaphysical bias. For example, Karl Popper's way of framing the interpretations is literally indistinguishable from Craig's in Quantum Theory and the Schism in Physics: From The Postscript to the Logic of Scientific Discovery.
Second, I will end up disagreeing with Linford's argument that the Neo-Lorentzian can't infer a 'past boundary' from the matter-energy distribution of the universe. I'll explain more below, but for now, it seems like Linford's argument is that if there isn't a realistic connection between this distribution and the universe's chronogeometric structure, there's no way for Neo-Lorentzians to infer a past boundary to the universe. I will find this flawed on a couple different levels (realistically connecting these two is what makes for space-time realism, which is sufficient for a B-theory of time).
Third, I will address Linford's argument that Craig's Neo-Lorentzianism is not 'well specified' enough to make the inference that there's a boundary in the finite past. This will have to do with Linford's skepticism in the form of the so-called Omphalos Objection, which I find wholly unpersuasive in this particular context.
And, lastly, I want to touch on the issue of Cosmic vs. York Time.
B. Comments on Linford's Introduction
I won't say much here other than to note some housekeeping issues. A note on footnote 1:
The case that relativity and the A-theory of time are not compatible has been presented in various places, but see Putnam (1967); Rietdijk (1966); (Penrose, 1989, 201, 303-304); Petkov (2006); Romero and Perez (2014). For work by physicists discussing Neo-Lorentzian theories, see Bell (1976); Builder (1958); Maciel and Tiomnio (1985, 1989a,b); Prokhovnik (1963, 1964a,b, 1973, 1986). Balashov and Janssen (2003) have offered a masterful reply to Craig’s Neo-Lorentzianism, to which Craig replies in his Unpublished-a. For a recent critical discussion of the view that absolute time is better accommodated by General Relativity than by Special Relativity because absolute time can be associated with cosmic time, as maintained by Craig and certain other A-theorists, see Read and Qureshi-Hurst (2020).
This is a nice spread, but for readers like me, this will be needing some fleshing out. I'll mention quickly that Craig has responded to Putnam's argument almost immediately in The Tenseless Theory of Time. I can't say too much about that here or it'll make the blog needlessly complex. As far as Rietdijk is concerned, I couldn't discern a 'case' that the A-theory and SR are incompatible; all Rietdijk seems to be doing is showing that SR, when B-theoretically understood, implies determinism. Maybe I'm missing something? The Penrose citations were even more confusing to me as I couldn't find a 'case' against the A-theory at all. Page 201 is a discussion of USEFUL, TENTATIVE, and SUPERB theories, and on pages 303-304, there is a discussion of the double-slit experiment (?). I checked to see if I had the right edition and, sure enough, it was the 1989 edition. I'm positive I'm missing something here so I withhold judgment on this.
Vesselin Petkov's Is There an Alternative to the Block Universe View? is ultimately unpersuasive to me, though it's a valiant attempt. It amazes me how much thinkers like Petkov are so enamored of graphs and how every aspect of the graph needs to correlate with an actually existent object/event in the world for it to mean anything. The three-dimensionalist can, so far as I can see, make perfect sense of the Minkowski space-time diagrams. These diagrams aren't meant to function like a literal picture or an image of reality. It's perfectly sensible to understand these graphs as having points that stand for different events in space and time, even if the geometrical constructions on the graph are four-dimensional. All the three-dimensionalist does is take these geometrical constructions as symbols that represent and illuminate an event in three-dimensional reality, say, a Lorentz contraction or some other kinematic effect.
There are numerous examples that can serve to illustrate this. Represent my existence on a space-time diagram so that, on the graph, there is a series of points that serve to stand for different temporal slices of my four-dimensional worm as depicted on the graph. Even if presentism were true, the presentist has no problem using this graph. She can say, "Right! The back edge of the worm, on the graph, represents my 'coming into being' in 1983." No problem at all! It wouldn't make sense to say that the graph itself is meaningless if all the points of the geometrical construction don't correlate with actually existing parts of reality! The three-dimensionalist simply takes the part of the construction on the graph that begins with the year, 1983, and makes it symbolize/represent/stand-for an event that used to exist, doesn't now exist. Seeing it graphed a certain way may serve heuristic and/or pedagogic purposes, but those purposes hardly depend on the graph having to image actually existing objects/events in the world. It's so obvious it hardly needs pointing out, so, once again, I may be missing something.
Of course, this paper goes into painstaking detail to make its points with more rigor than I can show here, and what I said above hardly touches on every aspect of Petkov's argument, but maybe I could mention a couple more things in the paper that might give a clue as to where I'm generally coming from.
First, I got the impression that Petkov was just assuming that if it weren't for Minkowski's four-dimensionalism, we'd be stuck with a multiplicity of 'spaces', which just seems to be Einstein's 'early' interpretation of SR, and Craig takes cognizance of this in his writings, of course. But Petkov makes the point that Einstein's 'early' interpretation was already four-dimensional. He argues that a 3-d ontology automatically commits you to absolute simultaneity. I'm just not seeing this. First, there's a big difference between a theory being four-dimensional with metrical entanglement (with two continua) and a theory being four-dimensional with space-time being one continuum. 1905 SR is not the latter at all, so far as I'm able to discern. Second, the 1905 SR 3-d ontology would just commit you to a vast array of relative simultaneities, one for every inertial frame an observer occupies, not an absolute simultaneity! So, I don't follow Petkov here at all. Early-Einstein did have a 3-d ontology, but it's a fractured ontology, as Craig puts it. There is a different world, a different three-dimensional space enduring through time, for every inertial frame. I see no justification for Petkov's claim that subscribing to a 3-d ontology necessarily commits you to absolute simultaneity.
Second, Petkov has this curious quotation on pg. 21 from Lorentz that has him admitting the 'failure' of his approach to SR, making it look like he gave up his ontology in the face of SR. This is from The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat, note 72*, commenting on pg. 197.
If I had to write the last chapter now, I should certainly have given a more prominent place to Einstein's theory of relativity ( 189) by which the theory of electromagnetic phenomena in moving systems gains a simplicity that I had not been able to attain. The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time and that my local time f must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the if we want to describe phenomena in terms of x', y', z, t' we must work with these variables exactly as we could do with x, y, z, t.
While the book was published in 1909, it says the note was added, in the 2nd edition, in 1915. The problem is that Petkov cites Lorentz here in the context of supporting the flawed point noted above: that subscribing to a 3-d ontology commits you to absolute simultaneity. That just isn't true.
And, more importantly here, whatever Lorentz's thoughts were in 1915, he evidently thought differently in 1927. Craig quotes Lorentz as saying,
The experimental results could be accounted for by transforming the co-ordinates in a certain manner from one system of co-ordinates to another. A transformation of the time was also necessary. So I introduced the conception of a local time which is different for different systems of reference which are in motion relative to each other. But I never thought that this had anything to do with the real time. The real time for me was still represented by the old classical notion of an absolute time, which is independent of any reference to special frames of co-ordinates. There existed for me only this one true time. I considered my time transformation only as a heuristic working hypothesis.
Why doesn't Petkov mention this? It makes Lorentz's 1915 comments bewildering, to say the least. But academics can change their mind, especially when in constant engagement with an evidence-base over the years. So, Lorentz (1927) seems to be telling us that Lorentz (1915) had only temporarily believed that 'local time' is not a mere mathematical artifice (had temporarily believed that t wasn't true time and that t' wasn't merely a local time).
For a response to Gustavo Romero and Daniela Perez's Presentism meets black holes, see Presentism and black holes by Geurt Sengers.
A quick comment on Yuri Balashov & Michel Janssen's Presentism and relativity, which critiques Craig's argument for the compatibility of Relativity Theory and Presentism - Linford calls their review 'masterful'. Why 'masterful'? Why isn't Craig's response 'masterful'? Why does Linford call their review masterful, and describes Craig's response as just a 'reply'? The editorializing, while mildly annoying, is okay, I suppose, but you begin to notice which side has Linford's sympathies.
Getting tense about relativity, by James Read & Emily Qureshi-Hurst, is a very interesting paper, with some good arguments against A-theorists using GR to get a Cosmic Time. Again, though, I can't go through my issues with those arguments here, without this blog morphing into a "large, loose, baggy monster". Suffice it to say, I disagree with almost everything they have to say. I find it amusing that William Lane Craig is called 'Lane Craig', and we're told that 'Lane Craig' 'augmented SR' to make it compatible with an absolute frame of reference ("amusing", because that is literally the first time I've ever seen Craig cited like this, which tells me that it's probably the case that Read/Qureshi-Hurst had only wrestled with Craig's arguments over a short period of time, if they had ever even heard of him before their paper, and probably for one time only - so, I'm not entirely confident that their comments on Craig's views are sufficiently scrupulous). Yet I find this language highly subjective. Recall Craig's theological perspective: given that God exists and is in time, how should we understand relativistic effects, how should SR and GR be understood, given God's reference frame? Not many theoretical physicists, astrophysicists, or cosmologists (if any) are going to be engaging in this kind of research program. So, without that metaphysical perspective, there won't be a way to get to where Craig is coming from when we're told that he supposedly 'augments' SR. But I digress.
In what follows, I'll follow Linford's structure, where he gives us three claims that are necessary (but which may or may not be sufficient) for 'establishing' that the universe began to exist a finite time ago: (1) the A-theory of time is true, (2) we can 'identify' a(n) open/closed past boundary where the universe doesn't exist before that boundary, and (3) show how the 'span' of Absolute Time between that boundary and today is finite.
C. A-Theory and Neo-Lorentzianism
(You could probably have an endless debate about the meaning of the relevant concepts, so all I'm going to do is provide extremely terse definitions and leave it at that. Let the reader be aware that I know they are terse and we could nuance all these definitions, but for the sake of simplicity and efficiency, it'll be better to be terse here.)
I'll make the A-theory of time committed to the idea of temporal becoming. Presentism is the idea that only the tensed present exists (but not necessarily the idea that only the tensed present has always existed - I like Crisp's quantificational way of putting it: that our most inclusive quantifiers only range over present objects/events/states of affairs, or something like that). Neo-Lorentzianism has to commit itself to some absolute (or privileged) frame of reference and, for my purposes, has to commit itself to an Absolute Time, Space, and Motion, of some sort (I'm taking into account the different ways this can be understood: I think Quentin Smith has a different take on whether this frame of reference is necessary, but it's okay for my purposes here that I leave it as being merely sufficient). Linford discusses a minimalist analysis of Neo-Lorentzianism that Craig gives, so I'll make it explicit when that comes up. These positions don't have to go together. Einstein (1905) was an A-theorist, but neither a Presentist nor a Lorentzian. You can be a Lorentzian and be a B-theorist.
I'll follow Linford and make ANL stand for A-theory + Neo-Lorentzianism. Linford mentions one of two (at least) reasons for opting for an A-theory, that it's a properly basic belief.
(Another reason is the ineradicability of tense from language, and so the reason why tensed propositions are true is that the reality of tense makes them true. It's implausible to think that the potentially infinite number of tensed propositions we use to govern our lives and make timely decisions are all false propositions. More can be said here, but I have to be terse. Linford doesn't mention this reason, but he let me know in a personal communication that he doesn't find it persuasive at all. I completely disagree, but that'll be a discussion for another time.)
Linford then relates ANL to SR. I agree with most of this section, but I find myself quibbling with minor details. First, Linford mentions Maciel and Tiomnio (1985, 1989a,b) and Petkov (2006) as counterexamples of the oft-repeated claim that the different physical interpretations of relativistic effects are empirically indistinguishable. This is nice to know and when I get the time I'll read them; suffice it to say, since this is a minority position, I'll stick with the idea of empirical indistinguishability as a working hypothesis until I see good reasons to give it up.
Second, it is amusing that, when Linford is rightly pointing out the possibility of being an A-theorist without being a Neo-Lorentzian, it is never mentioned that this is precisely Craig's stance on Einstein's 1905 position on SR before going the geometrical route of Minkowski! And even if, as Linford points out, Craig argues that the only plausible way to be an A-theorist in a special relativistic context is to be a Neo-Lorentzian, I'm not sure what the issue is supposed to be. That a philosopher stands with their convictions and gives arguments in their favor is, and should be, a virtue of the entire academic community. If that is Craig's position, then so be it. I happen to agree.
Third, the way Linford sets up the dialectic is different than the way I'd set it up. Linford appears to be setting up the dialectic by having Lorentz react to Einstein. But to me, this gets things exactly backward when it comes to the metaphysics. It is the Newtonians, and so the Lorentzians, with their belief in Absolute Time and Space, justified by metaphysical arguments, that are just fine and dandy with everything Einstein presented to them, except that their conception of physical time needed some tweaking; but exactly nothing from Einstein's interpretation of the relativistic effects (that I can see) in any way provided a defeater to the Newtonian or the Lorentzian in terms of giving up Absolute Time and Space. From the latter's standpoint, there are hardly any reactions or stitching required at all. Their theory, on the metaphysical level, is left standing there, waiting in Right Field for the opening pitch to even be made. If this isn't historically accurate, then at least this is the feeling I get.
Thus, thought experiments like Poincare's creatures don't look to me like reactions against the geometrical interpretation; they look more like illustrations of why proposing a geometrical approach to space-time doesn't pose any kind of non-question-begging metaphysical threat. The geometrical interpretation proposes an empirically equivalent interpretation (excepting one of Linford's footnotes, I think) to those who already hold the position of Absolute Time and Space for metaphysical reasons. The latter has no need for that geometrical hypothesis. The metaphysical reasons justify staying with Absolute Time and Space, and to explain the relativistic effects involved with Time's measures, or physical time, they postulate a set of forces that are causally responsible for those effects.
Fourth, Linford brings up Lorentz's "conspiring forces", Simon Prokovnik's alteration of Newtonian gravity, Universal Forces with "exotic properties", and "teleparallel gravity". I think Linford's larger point here is that he indicts (or mildly scolds or will indict or mildly scold) Craig for not coming up with a full-throated version of ANL, like Prokovnik has done. Instead, Craig provides a set of conditions that are sufficient for a view to being neo-Lorentzian for his purposes: (1) you have 3-d objects that endure through one dimension of time, (2) the speed of light is constant and independent of the speed of its source only in the absolute, preferred reference frame, and (3) you get your relativistic effects only when inertial frames are in motion relative to the absolute, preferred reference frame.
Personally, I see nothing wrong with Craig's approach here. It would be like indicting Craig for not bolstering a full-throated theory of causation or a full-throated theory of the metaphysics of causation when Craig affirms that whatever begins to exist has a cause (one of Fodor's misplaced objections). Like Craig said in his debate with Sean Carroll, "There is no analysis given of what it means to be a cause in this first premise. You can adopt your favorite theory of causation or take causation to be a conceptual primitive." So, the fact that Craig enumerates a set of sufficient conditions for a theory to be neo-Lorentzian I think is a feature, not a bug. It provides a degree of theoretical latitude while you continue to research your main argument. So, whether the relativistic effects are described by a more precise, full-throated neo-Lorentzian theory or not, there are theoretical parameters we can use to sufficiently explain why the relativistic effects don't have to be conceptualized geometrically.
A comment on exotic properties - it seems to me that exotic is being used here as a mild kind of pejorative and may even be closely synonymous with just metaphysical, so that metaphysically-oriented physicists, like Newton or Lorentz, or physics-oriented metaphysicians, like Zimmerman, Crisp, or Craig, might just think that what is being labeled as exotic is, relative to their background beliefs, as humdrum as anything else they're ontologically committed to on the basis of metaphysical reasons and/or arguments.
I also didn't see (or haven't yet seen) Linford's interaction with the response of Neo-Lorentzians to the cavil that there's something amiss with the postulation of said universal forces as conspiring, which is made to sound sinister, strange, exotic, ad hoc, or whatever. First, I'm not sure that the sentiment itself is entirely without precedent in the history of natural philosophy. For example, wasn't it Heraclitus who said that Φύσις κρύπτεσθαι φιλεῖ, that Nature loves to hide, or conceal itself?
I'd like to focus some attention on footnote 10 as well:
"There are some additional nuances in Craig’s view, since Craig denies the existence of instants. We might have expected Craig to endorse the existence of instants given his presentism, but Craig has long maintained that instants do not exist. For example, Craig argues that “only intervals of time are real or present and that the present interval (of arbitrarily designated length) may be such that there is no such time as ‘the present’ simpliciter; it is always ‘the present hour’, ‘the present second’, etc. The process of division is potentially infinite and never arrives at instants” (Craig, 1993a, 260); also see (Craig, 2000b, 179-180). Craig maintains that time is gunky, i.e., that every interval of time has proper sub-intervals, and he maintains that time cannot be decomposed into instants one of which is the present. I confess that I find the conjunction of presentism and gunky time difficult to understand. For example, if presentism is the thesis that the only things that exist simpliciter are present and that there is no present simpliciter – as Craig’s gunky time seems to entail – does nothing exist simpliciter?"
I find Craig's view on the so-called "extent of the present" to be misunderstood by almost every critic I've come across. Having already responded to misconceptions in James Fodor's critique, let me use this footnote as another opportunity to make Craig's view clear. I will be extremely brief because of the scope of this blog, but here goes.
It's correct that Craig does not believe in the existence of instants. But the quotation that Linford lifts from Craig (1993 and 2000b, as cited in Linford's paper) is completely out of context. Craig does not believe that the present, metaphysically speaking, should be conceptualized in terms of metrics of any physical measure (though it has its own intrinsic metric). He goes along with something extremely close to Bergon's idea of pure duration. However, Craig does say that if you were to conceptualize the present metrically, as an interval in terms of a physical measure, then there would be no such thing as the present simpliciter. It's only after one conceptualizes 'the present' metrically, as an interval in terms of a physical measure, that the 'process of division is potentially infinite'.
Therefore, it's incorrect to infer from this metrical point that Craig subscribes to time being gunky, in the metaphysical sense. You must make a distinction between the metrical gunkiness of time construed in terms of the intervals of a physical measure and pure duration, which would be the metaphysics of the existent present (yes, metaphysical time - or pure duration - does have, as Craig has often pointed out, its own intrinsic metric, but this metric has nothing to do with those metrics involved in physical measures, like seconds, minutes, years, etc - those physical measures are only useful insofar as they approximate the intrinsic, non-physical metric of pure duration).
Making this distinction completely answers the final question: of course, it doesn't entail that nothing exists! It would be like saying that time ceased to exist in my kitchen if my kitchen clock stopped ticking. The operativeness of metric-involving, measuring devices doesn't determine the ontology of the thing measured, where the thing being physically measured, whatever it happens to be, has an intrinsic metric independent of such physical measures.
D. Identifying the Universe’s Past Boundary
This is the point that you can't use pre-relativistic physics and appeal to the universe's matter-energy content to infer a past boundary to the universe, which is what Linford calls the Omphalos Objection, the objection that the procedures of empiricism are insufficient to show when or if the universe or time began to exist since it's possible that God made the universe or time with all the matter-energy content it has that makes it empirically appear as if the universe or time began to exist billions of years ago, when God really made them 5 minutes ago. If God made Adam from the dust of the ground in a second about 5 minutes ago, and Adam appears to be about 30 years old, with empirically confirmed metabolic processes that can be dated back to around 30 years ago, then obviously these empirical procedures are worthless for determining when and/or if Adam began to exist.
I read this section with patience because I find this excessive skepticism preposterous. I attribute this to my temperament, I guess, because Linford does cite papers that take this idea seriously. I still haven't read them so I can't tell if the papers actually endorse this skeptical thesis or whether they are entertaining it for the sake of exploring its consequences for those who do endorse it. The first problem I have is seeing how this is even an objection for minds whose mold is the same as, or similar to, my own. As someone who takes empirical procedures seriously, I'm not the kind of theoretician that tosses out what those procedures tell me because they conflict with a prior belief I have about when or if the universe began. I would think, "Yes, if I keep my belief that God made the world 6,000 years ago, and empirical procedures show that it's 4.5 billion years old, then the Omphalos Objection would be really cool to use if I want to continue to believe that the world is young. But I can't believe this. I'm giving up my belief that the world is young. Now, all I have left are the results that those empirical procedures gave me. Now, all I have reason to believe is that the world is 4.5 billion years old. The objection becomes irrelevant." So, there may be other reasons why pre-relativistic physics can't reveal when and/or if the universe began, but the Omphalos Objection, at least in this context, isn't necessary here, or at least it isn't for me.
What would make it necessary is if, somehow, Neo-Lorentzianism itself prevented you from inferring a past boundary from the universe's matter-energy content, and that this is due to the fact that there's no literal connection between that content and the chronogeometric structure revealed by the connection. The idea is that if there is this literal connection, then the universe actually has a chronogeometric structure, vindicating Minkowski's physical interpretation of the Lorentz transformation equations, vindicating space-time, vindicating space-time realism, the B-theory of time, the tenseless theory of time, and invalidating Craig's appeal to A-theoretic versions of Neo-Lorentzianism to salvage his contention that the universe began to exist, which undercuts the Kalam. So, if relativistic physics empirically demonstrates that space-time is maximally extended (not possibly truncated), then we don't end up in the epistemic predicament of skeptical catastrophe.
What we have next in Linford's paper is a series of fanciful, yet interesting, ruminations on globally hyperbolic, Misner, and maximally extended space-times. Linford seems to assume, without argument, that A-theories of time are committed to the idea that all, and only, physically reasonable space-times are those that are globally hyperbolic in a realistic sense. However, Linford points out, if Misner space-time is not globally hyperbolic (Manchak), and Misner space-time is also physically reasonable, and if globally hyperbolic space-times can be regions of Misner space-time, then there's no way to empirically detect whether or not globally hyperbolic space-times are maximally extended or perhaps just isolated regions of Misner space-time. And, therefore, to skip a couple steps in the argument, you have this epistemological problem that Linford calls super weak observational indistinguishability, the idea that, from "within our cosmological horizon and within some reasonable proper time", a variety of different space-times can't be distinguished by the mere empirical detection of its global properties. And so-called FLRW space-times, those that describe our space-time, presumably, are those that are physically reasonable, and so, for the A-theorist, FLRW space-times have to be globally hyperbolic. This means that, according to super weak observational indistinguishability, a FLRW space-time with a singularity, one that is maximally extended, can't be empirically discerned and distinguished from globally hyperbolic, maximally extended space-times that are, or could be, regions of Misner space-time, which means that our empirical tools can't settle whether the maximal extensionality of the global hyperbolicity of our FLRW space-time marks the beginning of that space-time itself, or whether such a 'beginning' is just the front-edge of a space-time embedded within a wider Misner space-time. Thus, due to these possibilities, empirically discerning the global hyperbolicity of our FLRW space-time doesn't settle its overall, maximal extensionality, and so it doesn't solve the so-called Omphalos Objection.
I find this whole line of argumentation unpersuasive, excessively skeptical, and easily dismissed if its structure were superimposed in other epistemological contexts. I'll provide more detail on some of this below, but for now here are some cursory comments.
First, is anyone a realist about Misner space-time? I've only ever read it used instrumentally to illustrate different features of GR. Maybe the ones that are realists about the universe's chronogeometric properties construe Misner space-time realistically?
Second, all this seems to me to be saying is that we can transplant all the evidence that relativistic cosmology seems to suggest onto space-times that totally contradict what that evidence seems to suggest. In other words, it's totally possible that all the empirical evidence you have for your belief in the properties of the external world you think you inhabit, along with your memories, can all be transplanted into an empirically indistinguishable world where you're just a brain in a vat, or where you're plugged into The Matrix, or where you're being perpetually deceived by an Evil Demon bent on giving you false beliefs. It seems to me that Linford's line of argumentation, this Omphalos Objection, is basically a gigantic, cosmological application of an age-old, skeptical possibility that epistemologists have addressed for centuries, so far as I can see.
So, if you just reject the underlying premise, that epistemic justification requires the neutralization of far-fetched, speculative, observationally indistinguishable realities, the overall sting of the argument is taken away for me. It seems to be just assuming that the use of empirical evidence to 'establish' empirical claims about reality requires infallibilism when it comes to that kind of epistemic justification. Well, this is preposterous to me, and the philosopher who opts for fallibilism when it comes to using empirical evidence to 'establish' empirical claims about reality, where 'establish' does not mean 'infallibly and certainly support the idea to such an extent that it rules out other observationally indistinguishable realities', is perfectly within her rights to use the resources of relativistic cosmology to render the second premiss of the Kalam, not infallibly established, but just more plausible than its denial, which is, or should be, the standard of success for a premiss in a philosophical argument.
D.1. Sidebar on the BGV-Theorem
I do not accuse Linford of this, but there seems to be a rampant, unjustified kind of panic attack every time Craig uses the Borde-Guth-Vilenkin (BGV) theorem as evidence that renders the second premiss more plausible than its denial, from absurd claims that he doesn't understand it (despite Vilenkin saying explicitly that he does understand it), to straining at the gnat of whatever they think 'begins to exist' has to mean to make Craig look as silly as possible (despite Vilenkin contributing a chapter called 'The Beginning of the Universe' in a book called The Kalam Cosmological Argument, Volume 2: Scientific Evidence for the Beginning of the Universe, wherein Vilenkin says explicitly,
". . . The obstruction may be found in the Borde-Guth-Vilenkin (BGV) theorem.8 Loosely speaking, our theorem states that if the universe is, on average, expanding, then its history cannot be indefinitely continued into the past. More precisely, if the average expansion rate is positive along a given world line, or geodesic, then this geodesic must terminate after a finite amount of time. Different geodesics, different times. The important point is that the past history of the universe cannot be complete.", pg. 152.)
As exhibit A for why the BGV theorem is so confusing to people who come at it from the perspective of, and in the context of, Natural Theology is when they read criticisms of how this theorem is allegedly misrepresented in that context. I've seen this numerous times throughout my life in similar contexts and it really is baffling every time I run into it.
Quick segue - (In the context of soteriology, I've seen someone like Leighton Flowers quote a Calvinist to define the concept of compatibilism, use that definition in the context of an anti-Calvinist argument, and when the Calvinist critic didn't know that Flowers quoted that reputed Calvinist (that the critic actually followed, respected, and agreed with!), would accuse Flowers of misrepresenting compatibilism, or not understanding compatibilism. It's as if the mere transplantation of an accurately defined concept into a dialectical context that argues against the truth of a proposition that partisans of that proposition are passionately committed to magically transforms that accurate definition into a misrepresentation.
I had something similar happen to me in the context of music appreciation. One of my friends was a die-hard Radiohead fan and swore up and down that every song they did was genius. But my friend also detested the Grunge music of the late 80's and early 90's. While driving with him one day, I popped in Pablo Honey (1993), Radiohead's debut album, and he hadn't heard it before. But because of how old it was, and how it was their first album emerging from that early 90's, atmospheric murkiness, their sound was undeniably 'grungy', even if not completely. He expressed his distaste for it immediately. But when I told him that this was actually Radiohead's debut album, the band he worshipped, then immediately he began to look past the 'grungy' sound and started to actually like it! Something psychologically jarring happens, an aporia of sorts, when something you're committed to shows up, justifiably, in a context you are not fond of, and that if you meet it in that latter context first, then, because you're not fond of it, its appearance there will be almost unrecognizable to you. But when you're told that this is indeed the thing you like, hiding behind a mask, it's only after you're told this that you have any hope of becoming fond of the context that you hitherto were not fond of.)
In the spirit of these, I hope not entirely wasteful, anecdotes, I submit Linford's representation of the BGV theorem and why I find it almost entirely irrelevant and misapplied:
"For example, the Borde-Guth-Vilenkin (BVG) theorem (Borde et al. (2003)) has sometimes been interpreted to show that the universe has a past singular boundary. However, the BVG theorem actually shows that if the average value of a specific generalization of the Hubble parameter along a time-like or null geodesic congruence is positive, then that congruence must be incomplete to the past. The resulting congruence can be isometrically embedded either into a space-time with or without a global past boundary. That is, supposing that we inhabited such a congruence, we might see a boundary to our past, even though other observers in the same space-time would have an infinite and unbounded past."
First, it is BGV, not BVG, but no biggie.
Second, what this has to do with rendering the second premiss of the Kalam more plausible than not is not only lost on me, but I'm also left wondering why the observers Linford is talking about here, the ones that see an infinite and unbounded past, couldn't be in our space-time, one with a singular, closed boundary, but with different sort of cosmological phenomenology. The space-time where we see the relevant 'congruence' is the space-time we have every reason to believe we exist in. The fact that you can 'isometrically embed' this congruence into another space-time we have no reason to think is actually the case doesn't matter to me at all.
This leads to the next worry, which is just the aforementioned, excessive skepticism I addressed above (or, at least, what I think is excessive). Again, as for my own approach with how I epistemologically appropriate cosmological, empirical evidence, I believe whatever the evidence seems to suggest, and the epistemic justification I gain from such evidence isn't compromised at all by considerations of empirically, or observationally, indistinguishable realities that are theoretically possible, but for which we don't have any positive evidence. In light of this, I'm convinced that the more conservative epistemologist can side with the phenomenal indications of such empirical evidence, always open to potential defeaters down the road, but not allowing potential defeaters to be mere, theoretical possibilities involving the aforementioned, indistinguishable realities. (I address Linford's issues with this phenomenalism below.)
D.2. Realism vs. Instrumentalism about the GEOMETRY of Space-Time
The only alleged obstacle left for Linford to throw in my way here is this odd restriction that I can't use relativistic cosmology to support the idea that the universe began to exist if I don't also believe that relativistic cosmology has to do with realistically conceptualizing the universe's matter-energy content in terms of the universe's chronogeometric structure (real space-time curvature). Linford's reasons for my having to do this are not persuasive at all, to me. Linford opposes a realistically construed chronogeometric structure with Craig/Sinclair's decision to "endorse the existence of non-zero universal forces whose effect is to make our world appear as though relativity were true."
Linford's language, again, is mystifying to me. As though what kind of relativity were true? As though the kind of relativity that is due to space-time curvature were true? So, as if Minkowski's physical interpretation of the Lorentz transformation equations were true? So, not as though Einstein's first physical interpretation of such equations were true, the interpretation he had prior to being convinced by Minkowski's geometrical approach? Linford's collapsing all of this into the neat and tidy "as though relativity were true" is just overly simplistic editorializing to me.
Apart from the language used here, I think Linford's reasoning here mandates that we precisely understand what's going on when Instrumentalists infer chronogeometric structure from the distribution of the universe's matter-energy content. There is something going on here that requires us to look 'under the hood' a little more here.
I recently had another extremely helpful conversation with Linford who helped me understand that one of the key dialectical contexts within which to understand Craig's space-time instrumentalism is noticing another debate wherein the disputants are in disagreement with Craig. On the one hand, we have those who disagree with Craig's space-time anti-realism and think that space-time is fundamental, and so not reducible to the laws of nature; on the other hand, we have those who disagree with Craig's space-time anti-realism and think that space-time is not fundamental, and so is reducible to, or explained by, the laws of nature. Call the former set of disputants A and the latter, disputants B. Neither A nor B is a neo-Lorentzian, like Craig, and so they disagree with Craig for different reasons, since both A and B are space-time realists for non-overlapping reasons (since those reasons involve reasons as to why space-time should or shouldn't be fundamental) and Craig is a space-time anti-realist. But, it seems to me, there is also an overlapping aspect to A/B's reasons for disagreeing with Craig's space-time anti-realism, namely, that without a tight, realistic connection between the universe's matter-energy content and the universe's chronogeometric structure, there would be no way to accurately and reliably infer the structure from that content.
There seems to me to be an eerie similarity between this line of argument and that between realists and anti-realists about the existence of abstract objects like numbers when it comes to Quine's customary criterion of ontological commitment, and the indispensability argument based upon it. What appears to be going on in Linford's argument against Craig's space-time anti-realism is very, very similar to how realists about abstract objects might pressure anti-realists about those objects to ontologically commit themselves to those objects by virtue of the fact that such anti-realists accept the truth of mathematical statements like 1+1=2. The tacit reasoning here is that merely accepting the truth of such statements ontologically commits the anti-realists to the existence of numbers as abstract, mind-independent entities.
Notice how similar the reasoning is. Craig accepts the truth of statements like Relativity involves space-time curvature but does not ontologically commit himself to the entity space-time or its curvature. Thus, he is a space-time anti-realist because he is an instrumentalist about space-time curvature. So, Linford's broaching of the debate between the space-time fundamentalists and the space-time non-fundamentalists doesn't settle anything at all for me with regard to why their underlying assumption (the assumption regarding the indispensability of the above-mentioned realistic connection between distribution and structure) should be believed. Of course, Craig could enter into the space-time fundamentalism debate counterfactually if he wanted, and he touches on it in certain places (Linford will briefly mention one of these places later and I'll comment on it below when it comes up).
Another point that Linford makes argues that Instrumentalism means we're basically in the dark about the universe's chronogeometric structure: "On the resulting instrumentalist interpretation of length contraction, time dilation, and the relativity of simultaneity, rulers and clocks provide systematically spurious results due to the influence of universal forces. For that reason, rulers and clocks are no help in determining our world’s true chronogeometry."
No help? Over and over again, I read in Craig, and the numerous authorities that Craig cites in this regard, that rulers and clocks are extremely helpful in determining the world's true chronogeometry because rulers and clocks (paradigmatic examples of Newton's measured time and space) are, more or less accurate, approximations of and to the absolute properties of that structure. We will get to Constant-Mean-Curvature is a moment (along with Linford's problems with it), but insofar as we can calibrate and set our measuring instruments in synch with the privileged frame of reference, the CMC properties of the expanding cosmological fluid, we can know that the readings of rulers and clocks that are measuring that frame of reference are approximations of and to that frame. How this leads to the conclusion that rulers and clocks leave us 'in the dark' about the universe's chronogeometric structure is lost on me.
Also this from Linford: "If length contraction, time dilation, the relativity of simultaneity, and other relativistic effects are to be treated instrumentally because they are subject to the influence of universal forces, we should say that gμν is merely an apparent metric that affords empirically adequate predictions and so does not reflect the true metric of the underlying chronogeometry. That is, gμν is afforded an instrumental interpretation in Special Relativity. But if gμν is afforded an instrumental interpretation in Special Relativity, gμν should equally be afforded an instrumental interpretation in General Relativity."
It's hard to know where to begin here. First, just because these relativistic effects are instrumental if they're conceptualized in terms of gμν doesn't mean that these effects are instrumental in every sense. The effects are real. Clocks really retard and measuring rods really distort. But ANL-instrumentalists will conceptualize that retardation and that distortion differently from the Minkowskian due to the different metaphysics of the two views. Second, just because the ANL-instrumentalist conceptualizes gμν instrumentally doesn't mean that gμν doesn't tell the ANL-instrumentalist anything at all about geometry-independent realities. Like I said above, the kind of instrumentalism I adhere to (and that I think Craig might endorse) is the idea that gμν graphically represents something geometrically and that those geometrical properties stand for or symbolize properties of things and events in a completely three-dimensional world, an Absolute Space, in Absolute Motion (persisting) through one dimension of Absolute Time. The properties of the graphical representation and the metaphysics of ANL are completely consistent and once some set of translational procedures are agreed upon, philosophers and physicists could, if they chose, use the geometric properties of the graphical representation to actually tell them something about tensed reality, about true chronogeometric structure, even if we agree with Newton's absolute/measured distinction, making the measurements more or less accurate approximations of absolute time/space/motion after such measurements 'ride along' with the chosen, privileged frame. The next, more interesting (to me), part of the dialectic is to determine whether the potential candidates for such a frame are available, and it seems to me (and Craig and others) that they are.
Thus, no one (that I know of) denies that "... test masses couple to space-time" and that such coupling is necessary "for inferring chronogeometry from observational data"; what I have trouble seeing is that the way this coupling 'couples' has to be realistic in the relevant sense, the sense in which such a coupling implies that extra-representational reality itself is geometrical. I'm not seeing how Instrumentalists might not see the coupling in the Instrumental sense.
For instance, I think there's a realistic connection between the geometrical way in which such coupling is represented graphically and the way in which those representations stand for and symbolize extra-representational properties of ways measured spaces and times approximate Space and Time. Nothing about this point regarding realistic coupling is, in any way, some kind of experimentum crucis, once and for all putting the Instrumentalists to a non-plus. The realists need to interact with how the instrumentalists are conceptualizing the coupling and show them how such a conceptualization is utterly incompatible with our ability to let static, four-dimensional representations stand for three-dimensional phenomena, and that once the translation rules are fixed and in place, why the inference from three-dimensional matter-energy distribution to four-dimensional chronogeometric structure can't be made. Personally, this seems to be such an obvious thing we can do that I'm at a loss as to how to make this any clearer. A graph's properties can stand for real things and for things that were or will be real, and if the geometry on a graph can stand for real things, things that will be real, or things that were real, then I see no reason why the instrumentalist can't use such graphs for pedagogical purposes, to graphically depict what the ANL-instrumentalist is trying to say about the metaphysics of relativity. Like I said above, endurantists can make pedagogical use of how my space-time worm is depicted on a graph or diagram, and while she isn't a realist about the existence of the point representing my birth and the point representing my death, these points can stand for events or things that were existent or will be existent. And insofar as the graph illuminates these points, instrumentalists about the static existence of the things/events depicted by those points can still make pedagogical use of them depending on what their teaching purposes are.
While going line by line might strike the reader as an exercise in banal drudgery, I can't help but quote Linford's quotation of Misner, Thorne, and Wheeler: “Space tells matter how to move. Matter tells space how to curve”, from their monumental Gravitation. But the Instrumentalist (or, at least, me) is stuck staring wide-eyed at this quotation as if it were some kind of refutation or aporia. "Right", responds the Instrumentalist, "We agree with the truth of that statement. But we also believe - and it hasn't been addressed, so far as we can see - that agreeing with the truth of that statement doesn't automatically, ontologically commit you to the existence of space-time, just as agreeing with the Mathematical Platonist that it's true that 2+2=4 doesn't automatically, ontologically commit you to the existence of '2' and '4'." The Instrumentalist is well aware that the Realist believes that the graphs and diagrams are accurate because they successfully represent the universe's matter-energy content; but the Instrumentalist can also interpret those graphs and diagrams to successfully represent the universe's matter-energy content.
The instrumentalist and the realist are perhaps agreeing with the utility of the graphical representations. They just seem to differ on how to interpret them. In other words, the instrumentalist reacts to Linford's quote from MTW with the same kind of incredulousness that an Arminian might have when a Calvinist quotes from Romans 9 to support Calvinism. Arminians fully endorse Romans 9, so just quoting it at them won't make a dent. They interpret the Scriptural data completely differently than the Calvinist, just as the instrumentalist interprets the graphs/diagrams depicting chronogeometric structure differently - and it's because of these disparate interpretations that there is a divergence in the metaphysics endorsed. And it's due to this divergence on the metaphysics endorsed that there is a divergence in what it is these graphs/diagrams are telling us about the universe's matter/energy distribution. But nothing that I can see in this latter divergence would take away from the fact that in both interpretations of the chronogeometric structure, the distribution of the universe's matter-energy content indicates the universe's past-finitude.
Let me try to give another analogy. In NFL instant replays, sometimes the commentators, when discussing a particular play, will represent the entire arc of a pass with an entire, drawn, marked-out line. There's nothing about that line that the "line-anti-realist" would disagree with in terms of what it is in reality that the line is supposed to stand for or symbolize. It's supposed to stand for how the entire arc of a pass began and ended in dynamic reality. In reality, we didn't observe the arc all at once or the commentator's line tracing it out. We saw the pass leave the quarterback's hand, fly up into the air, begin its descent, and then ultimately its arrival in the hands of a receiver. Let that dynamic reality be analogous to the universe's matter-energy content. Let the line tracing out the entire arc of the pass be analogous to the universe's chronogeometric structure. And suppose for the sake of argument that we don't have direct access to the commentators and that we only have direct observational access to the footfall as it is already flying through the air. Could we infer how the commentators would draw the line from the way the football is whistling through the air? The realist-analog will say that you can and that the moral you should draw from this is that reality itself has the same properties as the commentator's static line; otherwise, we couldn't make sense of the aforesaid 'coupling'. The instrumentalist-analog will say that you can and that the moral you should draw is that reality itself doesn't have to have the properties that the commentator's static line has. The reality could be a dynamically-becoming-pass with a beginning that will end and an end that had a beginning, and it's completely copasetic to make the commentator's static line stand for different tensed stages of the dynamic pass. It's also completely possible to infer identical chronogeometric structure from a dynamic or a static pass in reality. The so-called 'coupling' could still be made; it would be made on the basis of connecting properties either to existent things/events or to things/events that are, were, or will be, existent.
Thus, consider Linford's statement here: "An instrumental interpretation accepts the observable matter-energy distribution and accepts the Einstein Field Equation and geodesic equation, but only as useful calculational devices. Instrumentalists deny that the Einstein Field Equation and geodesic equation have ontological import for inferring unobservable chronogeometric structure. Thereby, instrumentalists sever the inference from the matter-energy distribution to the real chronogeometry."
As you might suspect, I find this too ambiguous. Of course, I'm still wondering if Linford is speaking for all Instrumentalists here. Is Instrumentalism a wide enough umbrella that we could place instrumentalists of differing stripes depending on the degreed/varied way they conceptualize 'ontological import'. But yes. The do deny that the said equations have ontological import in a sense, or the denial could take on more than one sense. And if they can affirm ontological import in some other sense, it just won't follow, so far as I can see, that the 'inference' spoken of here is severed, in every relevant sense. As I mentioned above, I can't see how one variety of instrumentalism can't salvage that inference by making the chronogeometry inferred from the kind of matter-energy distribution that was, is, and will be existent. Those can be objective states of affairs that had obtained, are obtaining, or will obtain. I'm not following at all why, for the inference to be a successful inference, for there to be no 'severing', the inferred chronogeometric structure needs to be inferred from the kind of matter-energy distribution that is a statically existing, tenseless, four-dimensional structure. And what about the adjective 'real' in real chronogeometry? The ANL-instrumentalist can simply conceptualize 'real' in terms of those properties of the chronogeometry that can be mapped onto those properties of the mass-energy distribution that had been, are now, and will be existent. I see no issue with this whatsoever.
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D.3. Rambling Segue - THE NOTORIOUS STEVEN WEINBERG QUOTATIONS
In this section, I want to settle, once and for all (or, at least, for myself) how it is that Craig misappropriated Weinberg's alleged thoughts about why we shouldn't seek to conceptualize gravity geometrically, that is, we shouldn't go the other way and infer that the universe's matter-energy distribution is nothing but a geometrical object just because it's possible to infer from it the universe's chronogeometry, that is, just because we're able to infer chronogeometric properties from a non-geometrical object or collection of objects/events. If the allegation goes through, Weinberg is basically saying that the entire project, prevalent in universities today, ubiquitous in the syllabuses of students at Ivy League schools bespeckled across the Anglophone world, is giving people the wrong idea, the idea that you can infer any kind of metaphysics at all about the universe on the basis of Einstein's Relativity Theories. Allegedly, Weinberg thinks this for reasons that generally support the overall anti-metaphysical stance he takes across the board, making him part company with both Minkovskians and Lorentzians.
In order to properly represent what's going on here, I'm going to quote Weinberg first, then Craig, and then Linford. We'll see what it seems like they're all saying and then, hopefully, you can see how what Linford says about how Craig misappropriates or misapplies Weinberg is completely bewildering to me.
Let's look at Weinberg first. The relevant quotes here come from the first couple pages of the book, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, 1972.
On the very first page of the Preface, pg. vii, Weinberg says the following:
Let me make explicit the following points here:
1. Weinberg is dissatisfied with the usual approach to GR. What approach? Well, the approach in most textbooks on GR, the ones that give geometric ideas a starring role, the ones that lead students to believe that space-time is a Riemannian manifold. Weinberg is explicit here, so far as I can tell. When students ask "why the gravitational field is represented by a metric tensor" or "why the field equations are generally covariant", it's salient that Weinberg is NOT wanting to answer these students by giving any indication that space-time is an actually existing Riemannian manifold! I'm not sure how much more clear Weinberg can get, even in this first paragraph. Let's call this point the DISSATISFACTION THESIS. This thesis blindingly makes it the case that Weinberg is not keen on the very approach to GR that Linford finds plausible.
2. The geometrical approach to GR has driven a wedge between GR and the theory of Elementary Particles. If matter can't be understood in terms of geometry, then we shouldn't expect Riemannian geometry to realistically describe gravitation. "The passage of time has taught us not to expect" the other fundamental forces of nature to be understood geometrically, and so too much geometry only 'obscures' "the deep connection between gravitation and the rest of physics". Right. Even by the third paragraph here, I'm not sure how much more clear Weinberg can be here. The Dissatisfaction Thesis makes it extremely clear that Weinberg personally doesn't believe geometry should realistically describe gravitation, but now we have another thesis, call it the INCOMPATIBLE WITH OTHER FUNDAMENTAL FORCES THESIS, which is more than Weinberg's personal belief, but a solid reason for why Weinberg holds the belief he does, namely, that if geometry were to realistically describe gravitation, it would incompatible with the other fundamental forces of nature, getting in the way of a grand unified theory.
Let's move on to pg. viii:
3. Here we see Weinberg replacing Riemannian geometry with the mentioned 'principles'. When geometric objects events 'find their way into a theory of gravitation' based on the 'principles', Weinberg makes it clear that when they do 'find their way', the geometrical concepts, those concepts are only a "mathematical tool" for the 'exploitation' of the aforesaid principles, not a fundamental (one wants to say 'realistic') 'basis' of 'theory of gravitation'. Call this the MATHEMATICAL TOOL THESIS.
4. Weinberg also explicitly says that his book is a "nongeometrical approach":
Call this the NONGEOMETRY THESIS.
5. And just because it's relevant (Linford quotes from it without leaving a pg. number in the footnote), I'll quote from pg. 147 as well:
Let's call this the ANALOGY THESIS. Basically, Weinberg is saying that it's not surprising that Einstein and company thought that the effects of gravitational fields were due to space-time curvature, the geometry of space-time. The Riemannian tensor, which generalized the Gaussian curvature, gave every indication that this was the way to go. But Weinberg reiterates the DISSATISFACTION THESIS here again, and says explicitly that space-time curvature 'is an analogy', that it's not even very useful. Weinberg ultimately opts for predictive, over explanatory, success. Weinberg admits that his view here is 'heterodox', but that is beside the point for my purposes here.
In sum, we have 5 theses, which probably overlap a little, but they serve to bring out an aspect that's worth emphasizing:
1. Dissatisfaction Thesis
2. Incompatible with Other Fundamental Forces Thesis
3. Mathematical Tool Thesis
4. Nongeometry Thesis
5. Analogy Thesis
With all of this in mind so far, let's turn to Craig's quotations of Weinberg and determine what Craig is trying to do in quoting him.
I first find Weinberg embedded in footnote 53, on pg. 121, the footnote itself initially connected to another quote from Arthur Fine's book, The Shaky Game: Einstein, Realism, and the Quantum Theory.
First, let me quote Craig's quote of Fine and get to Weinberg that way:
"According to Arthur Fine, few working, knowledgeable scientists give credence to the realist existence claims for entities like the four-dimensional manifold and associated tensor fields in GR; rather GR is seen as "a magnificent organizing tool" for dealing with certain gravitational problems in astrophysics and cosmology: "most who actually use it think of the theory as a powerful instrument, rather than as expressing a 'big truth'."
Fine seems to be corroborating the Mathematical Tool Thesis here. This quote, then, is given a footnote, and in that footnote we see Craig citing Weinberg above, from pg. 147. Craig even includes the part of the quote that mentions "photographic plates, frequencies of spectral lines" (etc . . .) and didn't seem to discern a problem at all for why he was giving the quote. From Craig's perspective, it looks like Craig was citing Weinberg to give further support to what he already quoted Fine as saying, that if it is 'a magnificent organizing tool', then it's sensible to think that the geometric interpretation of gravity would "dwindle to a mere analogy". The only tension I can find in the two quotes is that Fine seems to think of this idea as held by the majority of knowledgable scientists (or, at least, this is how Craig represents him), but Weinberg was saying that his views are heterodox. I'm not sure what's going on there, but it's possible things had changed from 1972 to 1988, but, again, these side points are important for my purposes.
On pg. 122 of Craig's Tenseless Theory of Time, Craig cites Weinberg again, his pg. vii that we already commented on above. In footnote 56, we have Craig citing pg. 251 in Weinberg, something we haven't look at yet, in reference to the 'graviton'. Pg. 251 is the beginning page of chapter 10, "Gravitational Radiation", where Weinberg makes his case for the graviton, since, as Craig tells (122), "the theory of gravitational radiation provides "a crucial link" between GR and the microscopic frontier of physics, since radiative solutions of Einstein's equations lead to the notion of a particle of gravitational radiation...", the graviton. So, nothing so far, and so far as I can see, regarding Craig misappropriating Weinberg.
In Time and the Metaphysics of Relativity, in the chapter "Absolute Time and Relativistic Time", pg. 189, we have the same quote from Fine we already discussed above, with footnote 64 going over it again, Weinberg 147, already discussed above. I don't think there's anything nefarious going on in footnote 64. If you look at Craig's quote of Weinberg 147, Craig leaves out the last line, the line where Weinberg is up front about the fact that his views here are heterodox and would be objected to by "many general relativists". Craig is just citing Weinberg to show that an authority in the field agrees with him about the point he is presently trying to make. (I already pointed out the possibility above that things might have changed sociologically from 1972 to 1988, but even if we settled that point, it would be more interesting to know what the state of play is in 2023. But even if we found that out, it seems to me that would be irrelevant for figuring out whether Craig misappropriated Weinberg somehow).
On pg. 90, Craig quotes Weinberg, pg. vii, already discussed above. Footnote 66 adds an additional thought from Carlo Rovelli's "Halfway through the Woods: Contemporary Research on Space and Time". This further corroborates what Craig, Fine, and Weinberg are saying. He says that understanding "the gravitational field" as being "nothing but a local distortion of spacetime geometry" "tends to obscure, rather than enlighten, the profound shift in the view of spacetime produced by general relativity", and prefers the view that "spacetime geometry is nothing but a manifestation of a particular physical field, the gravitational field."
All these quotations are repeated by Craig in God, Time, and Eternity, chapter 9, "God's Time and Relativistic Time", pg. 191-192, and also in Craig's Time and Eternity, in "The Static Conception of Time", pg. 179, with a little less detail, of course.
In summary, I've shown the relevant pages of Weinberg (pgs., vii-viii, in the preface; and, pg. 147) and all the relevant pages in Craig's popular and scholarly work where he cites Weinberg, along with some other quotations from Rovelli and Fine. We're now in a position to examine Linford's footnote 19. Here is the second paragraph of the footnote quoted in full:
"I’m not sure what sort of forces Craig and Sinclair would put in place of space-time curvature; they never offer a fully worked out and mathematically precise alternative to General Relativity. (Craig, 2001a, 189) cites (Weinberg, 1972, vii), but Weinberg alternately states that his focus on geometry is a pedagogical strategy instead of a denial that gravity is the curvature of space-time (1972, viii) and that he is otherwise ambivalent concerning the metaphysical upshot of General Relativity: “The important thing is to be able to make predictions on the astronomers’ photographic plates, frequencies of spectral lines, and so on, and it simply doesn’t matter whether we ascribe these predictions to the effects of gravitational fields on the motion of planets and photons or to a curvature of space and time.” In other words, Weinberg’s attitude – at least as of 1972 – was that, instead of trying to determine the metaphysics of space-time, we should “shut up and calculate”. This is obviously not an attitude that friends of ANL can adopt. Moreover, Weinberg is no friend of Craig’s approach to relativity. Weinberg’s anti-metaphysical interpretation of relativity is likely the result of a wholesale anti-metaphysical attitude that would reject appeals to absolute time and absolute space. Elsewhere, Weinberg has argued that we should “score” physical theories against whether they satisfy Lorentz invariance (2003, 85) – whereas ANL only appears, but does not actually, satisfy Lorentz invariance – and that we should think Einstein was rightly victorious in his debate with Lorentz (2003, 68, 85)."
Set aside the requirement that Craig and Sinclair would need to specify the sort of forces required for a full-throated neo-Lorentzian theory to be constructed. I've touched on this above with the point that I'm not seeing anything wrong with Craig's providing sufficient conditions for a theory to be Lorentzian and specifying phenomena that would satisfy that desiderata.
Further, notice the editorializing again. GR is just identified with space-time curvature. That just doesn't seem to be necessary. Consider that Rovelli quote above and consider what Weinberg's overall project is in the book, gravitational radiation, the graviton, how all this stuff is related to successfully motivating a quantum theory of gravity, how the spacetime geometry is a manifestation of the gravitational field, etc. These don't seem to be alternatives to GR, but different physical interpretations of GR with the goal of assimilating it into a larger grand unified theory, a goal that might be, in principle, stifled if the other three fundamental forces can't be understood geometrically or ontologically identified as geometric objects. I like the quote from Rovelli because it's in line with not tossing out spacetime geometry entirely (and so you can still learn about GR in terms of that spacetime geometry and what it seems to suggest about spacetime curvature), but physically interpreting that geometry in the terms that Rovelli has a preference for.
I find this whole attitude appropriate and in line with the way methodological dispositions function from within the parameters of particular research programs. Linford entreats the neo-Lorentzian to provide the full-throated, mathematical theory that 'replaces' GR understood in terms of real spacetime curvature, but not only may this not be feasible without the GUT required to confirm it (an ongoing research program, as far as I am aware), it may not even be necessary if the case is made that the decision to understand GR in terms of real spacetime curvature is underdetermined by the data, by what all sides agree is empirically the case.
But set all of that aside. Look at what Linford says about Craig's appropriation of Weinberg. This is bewildering to me, especially considering everything we discussed up to this point. First, Linford says Weinberg focuses on geometry as a pedagogical device and that he is otherwise 'ambivalent' concerning the metaphysics of GR. Pause. Consider the first part. Yes, the focus on geometry is a pedagogical device. More specifically, from a pedagogical point of view, Weinberg is saying, at the top of pg. viii, that he wants to introduce geometry as a means to 'exploit' The Principle of Equivalence, so as not to make the geometry a 'fundamental basis' for GR (or, theory of gravitation). That's the context for Weinberg. But Linford makes this in reply to Craig, pg. 189 (Time and the Metaphysics of Relativity), discussed above. This is indicated by Linford saying: "... but Weinberg alternately states" (emphasis mine) that his view is pedagogical. Why does Linford say 'alternately'? Nothing about Craig (189) is inconsistent with Weinberg's decision to make the geometry of GR a pedagogical device. Craig would wholeheartedly agree with making the geometry of GR a pedagogical device, as long as that pedagogical device doesn't involve realistically construing that geometry so as to make gravity literal spacetime curvature. So, this piece of it is bewildering to me.
But consider the second part, the part where Weinberg is 'ambivalent' about the metaphysical upshot of GR (quoting Weinberg, pg. 147, discussed above). And keep in mind this is supposed to be in response to Craig (189). What is Linford's point here supposed to be and how is it inconsistent with what Craig (189) is trying to argue for? His point is that there is something illicit with citing Weinberg since Weinberg is unsympathetic with the 'metaphysical upshot' that is ANL. In fact, he is anti-metaphysics across the board.
I find this a completely underwhelming and unpersuasive point to make. I've seen people make this kind of argument all the time. Craig can't cite Vilenkin on whether his theorem suggests that the universe began to exist because Vilenkin doesn't believe in God. Or, I can't cite any of Leibniz's criticisms of Spinoza because Leibniz believes in monads (and I don't). I can't cite any of Hume's criticisms of causation in terms of 'necessary connection' because Hume based our belief in the uniformity of nature on custom (I don't). I can't cite Huemer's Moral Intuitionism because of Huemer's criticisms of Divine Command Theory are bogus. I can't cite Bart Ehrman's reasons for believing that Jesus was a historical figure because Ehrman wasn't a Christian. I can't cite John Earman in support of the idea that Newton's views are dismissed too quickly because Earman was a spacetime realist. I could go on and on but you see the point.
Weinberg's reasons for being anti-metaphysical or for denying any metaphysical upshot to relativity theories are completely unrelated to the idea that these reasons are perfectly consistent with someone who is not anti-metaphysical, and who may or may not be a neo-Lorentzian. Weinberg being anti-metaphysical is partly responsible for being contingently related to his being an anti-realist about the geometry of space-time curvature, but it's evident from the quotations above that that isn't the whole story at all. Weinberg specifically discusses the reasons above: understanding gravity geometrically impeded the progress of physics because it gets in the way of unifying the other fundamental forces, which have been seen to not be geometrical, demoting geometry as being, not fundamental to GR, but in service of exploiting the Principle of Equivalence. These particular reasons could be endorsed by metaphysician and anti-metaphysican alike! To all appearances, Craig is citing Weinberg to support those reasons for dismissing the idea that gravity shouldn't be realistically understood in terms of the geometry of spacetime curvature. Craig agrees with those reasons. He thinks that those reasons are true. And they both agree that those reasons undermine realistically interpreting gravity in terms of geometric, spacetime curvature. Both agree that those reasons support the same conclusion. Dialectically, it is just irrelevant if Weinberg is anti-metaphysical and Craig is a neo-Lorentzian. Consider the debate about the existence of universals, for example. Perhaps a Platonist and a nominalist could unite on a particular reason for thinking the Aristotelian is mistaken. But it would be perverse if the Aristotelian were to object to the Platonist citing the nominalist's support for that reason (a reason the Platonist also thinks is true) on the basis of the fact that the nominalist and the Platonist disagree metaphysically on pretty much everything else.
So, when Linford says that, "Weinberg’s anti-metaphysical interpretation of relativity is likely the result of a wholesale anti-metaphysical attitude", I might say that, sure, but that attitude is like a distal cause, lying way back in Weinberg's motivational structure. The more proximate causes are the reasons Craid and Weinberg (and Fine) are all in agreement about (summarized by the five theses I enumerated above).
Linford's final point is that "Weinberg has argued that we should “score” physical theories against whether they satisfy Lorentz invariance (2003, 85) – whereas ANL only appears, but does not actually, satisfy Lorentz invariance – and that we should think Einstein was rightly victorious in his debate with Lorentz (2003, 68, 85)."
I have two responses to this. First, by Linford's own logic, shouldn't he be barred from citing Weinberg for supporting the idea that Einstein is to be preferred to Lorentz since, as far as I'm aware, Linford isn't anti-metaphysical? Second, this point is just an application of Linford's flawed point already discussed, that you can't cite anyone for any reasons they endorse (and that you agree with) if you can find other beliefs your citation has that disagree with your own. Two things can be true at once. Craig agrees with Weinberg that understanding gravity realistically in terms of geometric spacetime curvature is stalling scientific progress, that it should be a pedagogical device or mathematical tool, that it should be used, not as the foundation of GR, but in service of exploiting the Principle of Equivalence, and all of that! Craig agrees with all of it, thinks all of it is true, and so there's no citational impropriety in Craig citing Weinberg's authority in these particular domains. But Craig can also disagree with Weinberg's anti-metaphysical attitude and that one criterion Weinberg endorses (whether a theory satisfies Lorentz invariance is the key factor in determining which theory to prefer).
With Linford taken care of here, perhaps the reader can at least sympathize with how they could be utterly in the dark as to the alleged impropriety of citing Weinberg based on what Linford has given us here.
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D.4. Three Criticisms of Instrumentalism
Linford has three criticisms of Instrumentalism. First, Instrumentalists are unable to infer chronogeometric structure from the universe's matter-energy content using the geodesic equation, the equation determining the geodesic incompleteness of the universe, which is the typical way physicists confirm whether our spacetime is singular.
Second, Instrumentalists can't use the divergent Ricci scalar curvature, used to determine parts of spacetime that are infinitely large, indicating a singularity. This is because Instrumentalists won't ontologically commit themselves to the reality of any aspect of whatever chronogeometry such equations allow you to infer.
Third, Linford draws attention to an analogy between ANL and another theory from "Feynman, Pitts, and Schieve" that makes Einstein's tensor describe, not space-time, but a "gravitational field" "defined on a background Minkowski (flat) space-time equipped with a metric ημν."
The analogy is that both theories make gμν (Einstein's tensor) describe, not space-time, but some "physical field" "defined on a background space-time." Pitts and Schieve's way of laying gμν on top of Minkowski space-time makes the cosmological singularity infinitely far away. This is because you can't lay gμν on top of a singularity, since there are no space-time points at the singularity, and so if you don't put the cosmological singularity infinitely far away, gμν will end up being laid upon an undefined field.
Let me respond to these in order.
1. Keeping in mind that geodesics are a part of chronogeometry, I'm still not understanding why the instrumentalist can't make use of the inferred chronogeometric structure in the same way I used it above: not to ontologically commit herself to such structure literally, but to make the structure stand for events/things that don't exist, hyperplanes of simultaneity that did or will exist, and also for the hyperplanes that now exist.
One way the instrumentalist can make use of chronogeometric structure (along with the metric tensor, for example) is to make predictions about the universe's cosmic expansion. Then just compare these predictions with various observations about the cosmic background radiation or the age of the oldest stars. If the predictions agree with the observations, the instrumentalist is justified in inferring the past-finitude of the universe, and date it to be around 13.8 billion years old. You don't have to think that the universe is, in fact, chronogeometric to make use of that chronogeometry to tell you things about the real, tensed universe.
2. The same can be said for the divergent Ricci scalar curvature, which is more chronogeometry. Yes, if the universe isn't literally a chronogeometric object, I can't use this curvature parameter to say that the chronogeometric object that is our universe had literal, arbitrarily large curvature pathologies.
But again, Linford isn't doing much here to steel-man the instrumentalist here. There's no reason that I can see why the instrumentalist can't use this bit of chronogeometry, as it is defined in terms of the Ricci tensor, which is then related to the energy-momentum tensor, which provides a description of the matter-energy content of the universe. This chronogeometric description can then be made to signify a structure that stands for events/states/things in the universe that have existed, now exist, or will exist; and among the events/states/things that have existed are events/states/things that are signified by whatever it is the divergent Ricci scalar curvature seems to be indicating.
Keep in mind that this is what I'd do with the chronogeometric structure as everyone can see it. But let's see what this starts to look like when you lay this structure on space-times or fields.
3. We saw what happens when gμν was laid on top of Minkowski space-time. What happens when gμν is laid on top of a gravitational field? (assuming I'm correctly understanding the view, of course) According to Linford, the same thing will have to happen: the singularity will become infinitely far away for the same reason it became infinitely far away when laid on top of Minkowski space-time. If the singularity is only finitely far away, gμν will be laid on top of that singularity, which is a problem, because anything laid on top of a singularity becomes undefined.
Linford says: "Craig and Sinclair might reply that the gravitational field has a well-defined value at every point of the underlying space-time if the underlying space-time is truncated where the gravitational field becomes undefined; in that case, Craig and Sinclair would have reason to think that the underlying absolute time has a boundary."
I didn't find this particularly helpful. Linford is speculating about what kind of reply Craig/Sinclair might give. But I'm again wondering why truncating space-time in this context should invite the skeptical worries redolent of the Omphalos Objection.
Let me explain a step at a time here. I understand Linford's Omphalos Objection; I'm just having trouble understanding why the sting of it, in this context, is supposed to be as potent as advertised. The worry is supposed to be that truncated space-times are necessarily subject to the Omphalos Objection. I get that, but the reason why they're truncated is that they bump up against a cosmological singularity. And this gets to the point for me. The truncation is not arbitrary, as Linford had stipulated it would need to be for the Omphalos Objection to derive its sting.
It's not arbitrary because we have independent reasons for placing that singularity 13.8 billion years ago other than the naked appeal to chronogeometric structure. So, I can appeal to that structure, note the truncation, note that space-time as revealed by that structure is not maximally extended, but also note the independent reasons we have for not having to put the singularity infinitely far into the past, so we're not necessarily lost in a sea of ignorance and skepticism, and so the Omphalos Objection seems defanged in this context, for we can appeal to more than just chronogeometric structure when determining the duration of the universe's matter-energy content and how it terminates in a singularity a finite time ago.
I have to be brief regarding these 'independent reasons', but it would go a little like this. Infer the cosmological singularity on the basis of the expansion rate of the universe, measuring the red shift of distant galaxies or the cosmic microwave background radiation or the distribution/movement of galaxy clusters: an instrumentalist about chronogeometric structure can appeal to all these independent reasons to place the singularity about 13.8 billion years ago. Thus, if Craig/Sinclair were to say "the gravitational field has a well-defined value at every point of the underlying space-time if the underlying space-time is truncated where the gravitational field becomes undefined; in that case, Craig and Sinclair would have reason to think that the underlying absolute time has a boundary.", I find this perfectly permissible and the Omphalos Objection doesn't rear its head for me.
E. THE QUESTION OF A METRIC
The only problem left is this problem of a metric. Linford writes: "Craig and Sinclair would still need a principled reason for choosing a specific metric for absolute time." This was first mentioned at the beginning of Linford's "The Beginning of the Universe, the Omphalos Objection, and ABIDO" when he talked about the "metrical conception of the beginning of the universe" (he quotes Pitts). I skipped this to touch on other issues, but now I find it unavoidable.
Linford quotes Craig/Sinclair as saying: "we can say plausibly that time begins to exist if for any arbitrarily designated, non-zero, finite interval of time, there are only a finite number of isochronous intervals earlier than it; or, alternatively, time begins to exist if for some non-zero, finite temporal interval there is no isochronous interval earlier than it (Craig and Sinclair, 2012, 99)."
Both of these analyses strike me as plausible, so what's Linford's issue here? Near the beginning of the paper, Linford says:
"Craig and Sinclair have failed to adequately justify the adoption of a specific metric of absolute time. I offer an alternative metric for the duration of absolute time that is at least as good as (and possibly superior to) the one Craig and Sinclair favor. On the alternative metric, past time is infinite. For Craig and Sinclair, that the universe began to exist requires that past absolute time is finite. Without a way to adjudicate which of the two metrics – if either – corresponds to absolute time, we cannot infer whether past absolute time is finite."
It's evident from this quotation that Linford wants Craig/Sinclair to have a principled reason for choosing a specific metric for Absolute Time.
Linford is referring to Craig's decision to identify that metric with cosmic time (a concept used in the FLRW models of cosmology to describe the evolution of the universe; it's also defined as the time-coordinate in the metric of the space-time, and it is related to the expansion of the universe), and make the metric of cosmic time the time that "corresponds to the absolute time at which the events on that hypersurface [I'll get to this below] take place" (Linford, 35-36).
Linford will oppose this identification by proposing York Time, as propounded by Philipp Roser in his Gravitation and cosmology with York time (of course, Linford also cites 'York Time' as being the idea of James W. York Jr. in a paper called Role of Conformal 3-Geometry in the Dynamics of Gravitation [1970] - it is a novel method for defining the time coordinate in GR as evidenced by considerations of the 'conformal' structure of space-time: York Time is the method.)
Ultimately, Linford will contend that "We do not know whether the absolute duration between the absolute present and the past boundary is infinite.", and that Craig/Sinclair's decision to use the metric of Cosmic Time to identify the hypersurfaces of Constant Mean (extrinsic) Curvature (CMC), as the preferred foliation, fails to correspond to Absolute Time (or, is such that such a correspondence can't be known). This is because identifying the preferred foliation, the hypersurfaces of CMC, as Cosmic Time isn't principled enough to distinguish Cosmic Time from York Time, since they both identify the preferred foliation as the hypersurfaces of CMC.
Since Linford doesn't see a way to adjudicate between the two, he opts for agnosticism, and so he thinks we don't know right now whether the gap between the absolute present and the past boundary is infinite or finite.
This is all argued in Linford's section 2.3, Identifying the Span of Past Absolute Time. Linford calls this entire challenge ABIDO (Absolute Infinite Duration Objection) and says that there are four steps ANLs need to take to overcome ABIDO:
1. "identify the requisite preferred foliation."
2. "determine a way to order the hypersurfaces in that foliation from the objective past to the objective future."
3. "identify a labeling of the hypersurfaces in the preferred foliation that corresponds to absolute time."
4. "show that the total past duration of absolute time – as measured by differences in the labeling of the hypersurfaces – is finite."
Linford thinks ANLs have met the burden of 1 and 2, but not 3, and therefore not 4.
Let's go through these one step at a time:
Step 1 - Linford says, "when Craig and Sinclair look for a preferred foliation of our space-time, they are right to pick out the CMC foliation as a suitable candidate."
Step 2 - Linford concludes, "The arguments from empirical adequacy and from IMPAPT [Immediate Phenomenological Access to the Passage of Time] allow one to identify an objective ordering for the hypersurfaces in the CMC foliation of an FLRW space-time."
Step 3 - This is where Linford begins to lose me. Let's start with this quote:
"Craig frequently moves back and forth between the CMC foliation and cosmic time as if the cosmic time labeling and the CMC foliation were equivalent.28 They are not. Foliations do not uniquely determine a labeling of the hypersurfaces that they pick out. Unfortunately, Craig’s arguments for identifying the cosmic time as the objectively correct labeling of the preferred CMC hypersurfaces either do not uniquely pick out the cosmic time or else are not obviously stronger than arguments for other possible labelings."
First, in my reading of Craig, there is absolutely no evidence that Craig moves back and forth between CMC foliation and cosmic time as if they were equivalent.
I have no idea where Linford is getting this idea other than the weak example we find in footnote 28: "For example, on page 220 of Craig’s 2001b [God, Time, and Eternity], Craig cites Qadir and Wheeler (1985) in support of Craig’s comments on cosmic time. While Qadir and Wheeler use the phrase ‘cosmic time’ in their paper, Qadir and Wheeler’s ‘cosmic time’ is York time. Despite Qadir and Wheeler’s placement of the Big Bang at past time-like infinity, Craig states – on the same page! – that cosmic time places the Big Bang at approximately fifteen billion years ago."
I find this footnote nearly incomprehensible (and I don't mean this in a pejorative way).
I want to make two overall points here.
1. First, I don't have access to Qadir and Wheeler's book so I can't investigate the context of the quote for myself. I'll just assume that this part of their book is as Linford represents it. Second, maybe I'm a poor reader, but I have no idea where Linford gets the idea that Craig cites Qadir/Wheeler in support of Craig's comments on cosmic time. To let the reader know where I'm coming from, let me go through the full context of where this "footnote 51", in God, Time, and Eternity, comes from. It appears in chapter 7, "God, Time, and Relativity", in the third section, 'Cosmic Time as a Measure for God's Time', where Craig is responding to the worry that "the identification of our cosmic time as the sensible measure of God's time is wholly conventional." Craig responds with this:
"It is true that the General Theory itself does not mandate a specific foliation of spacetime; but this is only to consider the theory, as Kroes puts it, in abstracto, apart from any de facto boundary conditions arising from the nature of material reality. The answer explicitly ignores ''the notion of the evolution of the universe" and considers just a manifold of points. Once we introduce, however, considerations concerning the de facto distribution of matter and energy in the universe, then certain natural symmetries emerge which disclose to us the preferential foliation of spacetime and the real cosmic time in distinction from artificial foliations and contrived times."
Craig supports this point with a quotation from Michael Shallis,
"It is also possible, however, to take a single clock as standard, taking it to define a universal time coordinate, and to relativize everything to it.... Of course, the choice of a coordinate time is, to a certain considerable extent, arbitrary-in principle one could take any clock as one's standard. But in a cosmological context, it is natural to take as standard a clock whose motion is typical or representative of the motion of matter in general---One which simply 'rides along', so to speak, with the overall expansion of the universe. 51"
And now we find Qadir and Wheeler in Footnote 51, after this quotation,
"Michael Shallis, "Time and Cosmology," in The Nature ofTime, ed. Raymond Flood and Michael Lockwood (Oxford: Basil Blackwell, 1986), pp. 68-69. Cf. Asghar Qadir and John Archibald Wheeler, "York's Cosmic Time Versus Proper Time as Relevant to Changes in the Dimensionless 'Constants,' K- Meson Decay, and the Unity of Black Hole and Big Crunch," in From SU(3) /0 Gravity, ed. Errol Gotsman and Gerald Tauber (Cambridge: Cambridge University Press, 1985), pp. 383-394."
There are a couple things to note about this footnote and the way it relates to the Shallis quote. First, the cosmological context Shallis is talking about is Proper Time for particular comoving observers, and, as Linford pointed out earlier, when a(t) is a monotonic function, then the cosmic time t can be used as a parameter to label the different hypersurfaces in the CMC foliation; in this particular case, the cosmic time t would correspond to the proper time for the comoving observers that Shallis is referring to.
Second, and I can't say this with my preferred degree of confidence, since I don't exactly know what pgs. 383 to 394 say, but if I could make an educated guess from the title of their contribution to From SU(3) /0 Gravity, York's Cosmic Time is being contrasted with Proper Time, and since Proper Time in the title here is being related to the way Proper Time is being used in the Shallis quotation, then Craig is referring the reader to the way York's Cosmic Time is distinct from the Proper Time it's being contrasted to by Qadir and Wheeler.
Third, there are a variety of ways to interpret 'Cf.' here. I mentioned this in a tweet that Linford has responded to already, but I think it's worth mentioning again here (so the reader can make up their own mind). The Latin abbreviation "cf." is short for the phrase "conferre" which means "compare." It is used in academic and other formal writing to indicate that the reader should compare the information in the current text to a different source. When used in this context, it is often followed by a reference to the text against which the reader should compare. Now, this is compatible with Craig referring the reader to a source that may or may not fully support what it is that it is being compared to, in this case, the quote from Shallis about Proper Time. By using "cf.", Craig may be directing readers to other parts of the text, or, in this case, another text altogether, that may be relevant and complementary to his argument. But it is also used (and I think it's plausible to think that Craig is using it like this here) to call attention to similarities or differences between two pieces of evidence. Therefore, it would be far too quick for Linford to assume that Craig is using the citation from Qadir and Wheeler to call attention to a supportive similarity between York's Cosmic Time and the kind of Cosmic Time that Craig endorses, the latter of which is perhaps consistent with the way Proper Time is being used in Qadir/Wheeler (since it's being contrasted with York's Cosmic Time in the title itself as indicated by the word 'versus' in "York's Cosmic Time versus Proper Time"). Moreover, since this is the only place in the entire manuscript that York's Cosmic Time is even mentioned, it's far more likely that Craig cited Qadir/Wheeler to draw attention to the way Proper Time was functioning in the way Craig was understanding Cosmic Time and contrasting that with the way that particular kind of Proper Time relates to another sort of Cosmic Time, namely, York's Cosmic Time.
And, therefore, Linford's decision to mention Craig's citation of Qadir/Wheeler as an example of Craig's inadvertent waffling between cosmic time labeling and the CMC foliation (giving the impression that he thinks they're equivalent) seems maladroit.
So, let's jump into the meat of the issue and discuss Cosmic Time, York Time, and the Constant Mean (extrinsic) Curvature as our 'preferred foliation'.
E.1. CMC Foliation and the Decision between Cosmic and York Time
I confess that this was the most exciting part of Linford's paper, mainly because I hadn't studied York Time in any kind of depth or entertained this idea with any kind of due consideration in the context of Craig's cosmological case for premiss 2 of the Kalam (this has been largely responsible for this blog taking over six months to complete). So, it was a sheer pleasure to wrestle with this option as a challenger to Cosmic Time as the preferred identification of the foliation of the hypersurfaces of Constant Mean (extrinsic) Curvature (CMC).
Because of the density of this section, I may have to quote Linford a lot here and respond in kind. Let me actually begin here, in Linford's 'Step 1' to set up some concepts: "Consider a monotonically expanding FLRW space-time. Proper time, as recorded by observers who are co-moving with the universe’s expansion, can be used to label the CMC hypersurfaces. This labeling is called the cosmic time. (However, the labeling is not unique; for example, the CMC hypersurfaces could instead be labeled with the scale factor.)"
A monotonic expansion is one that is always expanding, where there is never a non-zero expansion rate, but it doesn't necessarily mean that that rate is constant. Proper Time measures an observer's elapsed time as it moves along with a particular worldline in space-time. And since the CMC hypersurfaces are space-like hypersurfaces, and such hypersurfaces have constant mean curvature, and such curvature is a scalar measure of average extrinsic curvature, it makes sense that in a monotonically expanding FLRW space-time, the CMC hypersurfaces can be labeled by Cosmic Time, which would be the Proper Time recorded by observers co-moving with the expansion of the universe. And since Cosmic Time acts as a scalar field on such hypersurfaces, that field can correspond to a time coordinate of the FLRW metric. Thus, the consideration of scalar fields describes the behavior of fields; it's a mathematical function that gives you a value for all space-time points. And, so, when you have a constant mean curvature of space-like hypersurfaces (or, CMC hypersurfaces), that itself is a scalar measure of the average of that curvature. And Cosmic Time is the scalar field on those hypersurfaces that is corresponding to the time coordinate of the noted metric.
Now, in making the correct point that the labeling of the CMC foliation as Cosmic Time (where cosmic time is a scalar field) is not unique, Linford expresses this by comparing a Cosmic Time labeling with a labeling of the CMC foliation in terms of Scale Factor, which is just a particular kind of Scalar Field, one that provides a description of the evolution of the universe's size in the relevant space-time. So, the scale factor gives you the size of the universe in an FLRW space-time by being a function of time that provides a description of how that size changes with time. It's used to give us the universe's rate of expansion and its space-time curvature.
Now, while I agree that Cosmic Time and the universe's Scale Factor are distinct concepts that don't necessarily pick out the same CMC foliation, I don't see why they can't contingently overlap. After all, both Cosmic Time and the Scale Factor of the universe are scalar fields, so why can't the Proper Time of observers co-moving with the expansion of the universe (corresponding to the time coordinate of the FLRW metric), granting that it increases monotonically with such an expansion, contingently overlap with the way the universe's Scale Factor (as a function of time describing how the universe's size changes over time) picks out its own monotonically increasing time coordinate? In other words, have the Scale Factor's monotonically increasing time coordinate correlate with the monotonically increasing time coordinate picked out by Cosmic Time (in other words, make the labeling correlate with each other, even if the labels are conceptually unique, and so don't necessarily have to pick out the same, or similar, CMC hypersurfaces).
It just seems to me wholly plausible that the Proper Time of those co-moving observers, co-moving with respect to the universe's expansion, would pick a labeling of the CMC hypersurfaces that was pretty damn close to the labeling given to us by the Scalar Factor, since the Scalar Factor labels the CMC hypersurfaces by also considering the universe's expansion, even if it's only in terms of such hypersurfaces monotonically increasing size over time, rather than the proper time of co-moving observers relative to that same expansion. That just tells me about their conceptual distinctness accounting for not necessarily picking out overlapping CMC foliation, but it's perfectly compatible with their conceptual distinctness accounting for, or being consistent with, labeling different aspects or properties of an ontologically unique CMC foliation.
Linford proceeds: "In passing, I note that the CMC foliation is unique only for closed universes. In the case of an open universe, there are an infinite collection of distinct foliations (Lockwood, 2007, 120). Moreover, Michael Lockwood has argued that evidence for black hole decay is evidence that the actual universe has no CMC foliation (Lockwood, 2007, 152). Here, I set these objections to one side in order to examine the case for accepting one of the CMC foliations as the preferred foliation."
Here I mainly have another editorial comment. Right. The foliation is unique in a closed, but not in an open or flat universe. Right. Lockwood gives evidence that black hole decay indicates that our universe has no such foliation. I find this comment "in passing" to be rhetorically irritating because it sows in the mind of the reader seeds of doubt about the 'entire case' about to be considered about accepting a preferred foliation! Though there's still no overwhelming consensus about whether the universe is closed, open, or flat, one wonders why this stipulation is just thrown in here without even a footnote from the physicists working in the area that make particular cases for and against the relevant options.
In the case of Lockwood, nothing of detail is discussed; it's just the name of a credentialed expert, a mention of his published work, and the rhetorical aura of Linford having all this additional ammunition against Craig's case 'waiting in the wings': there being such an abundance of this 'additional ammunition' that he can't even fit it in the already dense and detailed paper we're reading.
In my opinion, either throw it in a footnote or don't mention it at all. After all, Linford doesn't mention any physicists or philosophers of physics that disagree with Lockwood at all! Why is that, I wonder? Why isn't there even a footnote about how some critics have disagreed with Lockwood about the entropy of black holes not being a counterexample to the Bousso-Gibbons-Hawking-York (BGHY) entropy bound, or that such an entropy bound isn't fundamental and so can be modified to account for black hole entropy, or that there is still debate ongoing in this particular research program? I'll let the reader come to their own conclusions. Again, it's not the inaccuracy of what's relayed to us by Linford, it's this rhetorically charged editorializing I find jarring at times.
With these considerations out of the way, let's proceed to Linford's 'Step 3', Identify a labeling of the preferred foliation.
This brings me face to face with this thing called York Time
E.1.1. York Time vs. Cosmic Time
So, this is how Linford introduces York Time: "... contemporary physicists have suggested labeling the CMC hypersurfaces with a quantity termed the York time (York (1972); (Roser, 2016, 49)). The York time is the trace of the extrinsic curvature K of each CMC hypersurface. In the case of a model satisfying the FLRW ansatz, the York time is proportional to the negative Hubble parameter, i.e., TrK ∝ −H. Consequently, in FLRW models, there is an order preserving bijection between the York time and the cosmic time."
Let me begin with some introductory remarks (for my sake, mostly). Evidently, York Time gives you a time coordinate that's based on space-time's conformal structure, independent of its metrical structure. I'm keeping in mind here, at least, six points about York Time: (1) it is the integral of the negative reciprocal of the Hubble parameter over cosmic time; (2) it has been used for labeling the CMC hypersurfaces; (3) it is supposed to be a more precise and consistent description of the early universe; (4) it gives a better understanding of the universe's behavior at high energies; (5) it gives a physical interpretation that is connected with the universe's rate of expansion; (6) it's related to cosmic time, which means it bridges a connection between space-time's conformal properties and the universe's global properties.
If York Time gets us the universe's global properties, among which are the universe's CMC hypersurfaces, without the universe's metrical properties, Cosmic Time is supposed to get us the metrical properties based on space-time's conformal properties and the scalar field discussed above. From what I can gather, both the conformal and metrical properties have to do with the ways that angles and distances in spacetime's geometry are related, but with the metrical properties, such angles/distances are based on all the properties of the metric tensor, whereas with York Time, considering only the conformal properties, such angles/distances are based on only a specific aspect of the metric tensor, the conformal structure of that tensor: it analyzes spacetime geometry without considerations of scale factors or scalar fields.
And now it becomes clear why York Time might be considered a strong competitor with Cosmic Time, since, when you analyze the universe's spacetime geometry without considering issues of scale, you can analyze the dynamics of the early universe when there were extremely high energies. And if you can more accurately label the CMC hypersurfaces in the early universe without considerations of scale, since, as Linford points out, each hypersurface is a Cauchy surface, "...the full state of the world on one CMC hypersurface suffices for determining the state of the world on any other CMC hypersurface in the same foliation." So, if York Time wins out over Cosmic Time as the correct labeling of the CMC hypersurfaces, then the universe is past-eternal.
And this is the part I have the hardest time understanding. In what sense does York Time imply a past eternal universe? Linford: "each of the CMC hypersurfaces in the preferred foliation can be labeled with t, a(t), or with any bijective and order-preserving function of t, for example, inverse powers of a(t), i.e., τ = −a(t)−n. (The mapping must be order-preserving in order to be consistent with the results of step 2.) Note that τ labels the cosmological singularity with −∞ and the present with τ = 0. Hans Halvorson and Helge Kragh argue that this raises doubts about whether the past finitude of the universe has “intrinsic physical or theological significance” (Halvorson and Kragh (2019)).
My interest is piqued by −∞. After dismissing "Misner's cosmological model", Linford mentions what we said above about York Time being proportional to the negative Hubble parameter (TrK ∝ −H), giving us an "order preserving bijection between York time and the cosmic time". I found this puzzling since it makes it sound like York time and Cosmic time aren't competitors. But from what I came to understand, they are and they aren't. (Reminder: this contrasts with Cosmic Time, which primarily considers, not the Hubble parameter, let alone the negative of that parameter, but the scale factor, which is an observable quantity - the Hubble parameter is derived from Cosmic Time, rendering Cosmic Time the more fundamental of the two times).
They are in the sense that they lead to two different time coordinates that label the CMC hypersurfaces differently, one based on the proper time of observers comoving with the universe's expansion, the other based on space-time's conformal properties. But what's relevant here is that Cosmic Time and York Time relate to the Hubble Parameter differently. For Cosmic Time, the Hubble Parameter is a measure of the expansion rate of the universe, and it is inversely proportional to the scale factor of the universe. For York Time, the Hubble Parameter is defined in terms of the integral of its negative reciprocal over cosmic time. Thus, York Time is proportional to the negative of the Hubble parameter, which means that as the Hubble parameter (H) decreases, York Time increases, and as the Hubble parameter increases, York time decreases. As far as I can make out, since the Hubble Parameter is a measure of the expansion of the universe, it's physically equivalent to the Scale Factor (even though, above, I thought it was decided that Cosmic Time and the Scale Factor were distinct labelings of the CMC hypersurfaces, but I'll leave that to the side for now). Nevertheless, even if they're physically equivalent, that doesn't mean that the Hubble Parameter isn't less fundamental than the scale factor, leaving the door open for Craig to be an instrumentalist about what York Time is doing to the Hubble parameter, compared to how such a parameter is understood using Cosmic Time alone (in terms of the Friedmann equations).
With this in mind, consider what Linford says here: "... in FLRW space-times, York time varies inversely with a(t) and, like τ, the York time labels the cosmological singularity with negative infinity. As Roser describes, “[...] just as in the case of Misner’s parameter [...] the ‘beginning’ lies in the infinite past [...] The York-time approach to quantum gravity gives no explanation of a beginning because the universe simply has none. It is infinitely old” ((Roser, 2016, 58–61); also see Roser and Valentini (2017))."
I do not, by any means, claim to have greater expertise than either Linford or Roser. I can only speak for myself. In my admittedly brief foray into studying this material, I find all of this hullabaloo about York Time, and what 'negative infinity' and 'infinite past' means, in the context of the Kalam, to be a prime example of mathematical implications that have absolutely no real-world consequences at all, ontological consequences that would actually imply a past-eternal universe. I understand that both York Time and Cosmic Time are mathematical constructs, York Time being the integral of the negative reciprocal of the Hubble parameter over cosmic time, Cosmic Time being the integral of the inverse of the scale factor over time. Nevertheless, if there were ever a time to be an Instrumentalist about York Time, this is it. The option should be especially open to an Aristotelian like Craig when it comes to the question of whether or not time is discrete, continuous, or neither, for an Aristotelian like Craig will opt for 'neither' and construe time as a whole that is prior to any metrical parts we happen to carve into it. But this brings to my mind a glaring objection that Craig can adduce regarding what seems to be something that would be a consequence of endorsing York Time.
[Before I get there, let me clear up possible confusion. I do believe, in a relevant sense, that York and Cosmic Time are both mathematical constructs (I'll mention this in the next paragraph), but I don't think that determines one to be an Instrumentalist regarding the reference of the particular CMC foliations either one identifies. The way the instrumentalism would play out here is that, regarding York Time, there never actually were, are, or will be real-world counterparts of the CMC foliations that it purportedly identifies, but with a caveat I'll mention in a moment. Now, with Cosmic Time, I believe this to be a mathematical construct as well. So, why am I not an Instrumentalist about the CMC foliations that it purportedly identifies? The short answer is that I think that instrumentalism comes in degrees and/or it can apply to local parts of a mathematical description without having to be a complete amputation of description and reality in all aspects. For example, I'd be a Realist about the way Cosmic Time identifies the present CMC hypersurface, but also qualify this to apply to all the CMC hypersurfaces that have or will be present, and so use Cosmic Time's static way of representing these hypersurfaces as an ontological guide as to the hyperbolic typology the universe has, has had, and will have, and so without a realist, ontological commitment to all the hypersurfaces identified by Cosmic Time's mathematical description. Now, insofar as the mathematical description of York Time's identification of the CMC hypersurfaces contingently overlaps with the CMC hypersurfaces that Cosmic Time indicates, then we'll have good reason about when to be a realist about those hypersurfaces, namely, whether they have had, have, or will have present existence. But insofar as the CMC hypersurfaces identified by York Time deviate from the hypersurfaces indicated by Cosmic Time, I'll have reason to be an instrumentalist about the hypersurfaces that 'approach negative infinity', a result of using the integral of the negative reciprocal of the Hubble parameter over cosmic time. I would make almost the same exact move if Hartle-Hawking's Quantum Gravity Model proposes to 'round off' space-time by introducing imaginary numbers in Einstein's equations, getting rid of the singularity. If I were to even entertain this, I'd treat the introduction of imaginary numbers in this context completely instrumentally.]
To see what I'm talking about, consider that because York Time, mathematically expressed, is, once again, the integral of the negative reciprocal of the Hubble parameter over cosmic time, and it varies inversely with the scale factor of the universe, so that when the universe expands, York Time gets smaller and smaller, approaching zero as the universe becomes infinitely large, it seems we have to specify how York Time approaches negative infinity. York Time's intervals approach negative infinity.
Now, my concerns, at this point, are whether or not these intervals are equal or unequal (whether the intervals are equal or not depends on the value of the Hubble parameter and the form of the integral) and in what sense these intervals are approaching negative infinity. I get that the approaching of such intervals toward negative infinity is a consequence of the mathematics, but assuming a realist construal of such a consequence, are these intervals equal or unequal?
If they're equal (if time were discrete), when the scale factor of the universe approaches 'zero' as York Time approaches 'negative infinity', this would place 'zero' somewhere in the past, our past, infinitely distant from us, specified by an actually infinite series of equal intervals. If this is what a realist construal of York Time would imply, then there's no, in principle, reason why Craig can't have an instrumentalist take on these aspects of York Time.
But if the intervals are unequal (if time were continuous), Linford is trading on an ambiguity here. In this innocuous sense, my birth is infinitely distant from me today, that is, I can endlessly halve intervals separating my present existence from the date of my birth. But this doesn't avert the reality that I began to exist a finite time ago in the sense of the metric that Linford quoted Craig/Sinclair has using near the beginning of this blog:
"we can say plausibly that time begins to exist if for any arbitrarily designated, non-zero, finite interval of time, there are only a finite number of isochronous intervals earlier than it; or, alternatively, time begins to exist if for some non-zero, finite temporal interval there is no isochronous interval earlier than it (Craig and Sinclair, 2012, 99)."
If the intervals are unequal, then they're not isochronous. Making the universe's scale factor approach infinity in the past in this sense (where the universe's density and curvature are infinite) doesn't imply that the universe is infinitely old. At this point, Linford may bring up the debate discussed above regarding space-time fundamentalism, since York Time's approach to Quantum Gravity makes the conformal structure of space-time more fundamental than the universe's metrical structure, so you can describe all the dynamics of the universe with such a conformal structure.
This means that the universe would be in a state of quantum gravity from eternity past and various quantum fluctuations would account for the structure and characteristics of such a past-eternal universe. But I doubt that this would give Craig pause at all considering that this research program is still in its infancy and hasn't convinced a substantial consensus, unlike the majority persuaded by the metric of Cosmic Time and its present implications.
Even if partisans of York Time agree with Craig's Aristotelian account of time (the whole is prior to the measurable parts that we might denominate in it), unequal denominations would still violate the conceptual parameters. The only option available to such partisans are those Aristotelians that conceptualize the discrete, equal intervals as denominated onto a whole that is prior to those denominations, but which extends the 'cosmological singularity' to 'negative infinity' (assuming that York Time deals with singularities at all) or gets rid of the singularity altogether, both options of which Craig could take an Instrumental interpretation.
Thus, whether the 'approach' of these intervals toward 'negative infinity' involves equal or unequal intervals, whether or not these people are Aristotelians about the metaphysics of time, Craig has plausible ways of negotiating these options.
Linford continues: "The point for our purposes is two-fold. First, as physicist Philipp Roser notes, “even if there are other options [for a labeling that coincides with absolute time], York time must be considered a favourite among them based only on a few theoretical principles” (Roser, 2016, 52).
Linford cites Roser, which is a conclusion of some thoughts that came before. On the previous page (51), Roser mentions that (1) York Time allows us to identify a physical time based on 'geometric degrees of freedom' (what was called 'conformal structure', above), (2) that such a time only depends on 'local degrees of freedom', (3) that the time parameter is identified as isotropic (implying 'shape' of degrees of freedom aren't used, leaving the 'metric determinant' and the 'momentum trace', both of which are isotropic quantities), (4) requiring monotonicity (discussed above, and so local scales like √g are excluded for identifying the physical time parameter), (5) that requiring monotonicity is "less restrictive" than not allowing spacetimes that can't be foliated in terms of constant mean curvature, (6) that Roser is "unaware of any other, non-equivalent foliation of the sort" where "constant mean curvature slicing guarantees monotonicity" (in other words, Roser isn't aware of any other option that guarantees monotonicity other than CMC slicing, and he relates this to the York parameter and the role it plays in the Hamilton-Jacobi formulation of Einstein's equations of GR).
So, Roser closes the section by pointing out that Roser cites the simplicity and elegance of the York Time interpretation to properly identify physical time.
I can imagine an adherent of Cosmic Time responding to these principles very easily, and I don't say this to be glib. I only wish Linford would at least give the other side a general idea of where the opposition might come from. For example, a partisan of Cosmic Time might disagree and think that while York Time could be instrumentally applied and defined on local levels, a cosmic time parameter must be defined globally, so any and all potential observers that are privy to the CMC slicing that Cosmic Time identifies will agree on what the time is. Secondly, the isotropy shouldn't only imply that cosmic time is the same in all directions, but that it is the same for all observers. Third, partisans of Cosmic Time agree about monotonicity, but that it should be in terms of global, rather than local, properties of the globally expanding universe, which would then imply the indispensability of considering those parts of the universe that are distant.
And, therefore, if the "order preserving bijection between the York time and the cosmic time" renders Cosmic Time differently as compared to Cosmic Time by itself, then, barring any reasons why Craig can't be an Instrumentalist about York Time, all that's left are the compelling reasons for preferring Cosmic Time as the preferred labeling of the CMC hypersurfaces (this decision receives extra credibility from the fact that Cosmic Time is the time adhered to by most physicists and that Roser himself says,
While it is true that York’s solution to the initial value problem gives reasons to take the proposal of York time as physical time seriously, it is unproven that the initial-value problem can indeed not be solved in another manner, in particular with another foliation. It is the case that no other solutions are known, but at least the possibility of other solutions has not been ruled out. (50-51).
Nothing Roser says here rules out physically interpreting York's solution instrumentally.)
Second, in FLRW space-times, York time varies inversely with a(t) and, like τ, the York time labels the cosmological singularity with negative infinity. As Roser describes, “[...] just as in the case of Misner’s parameter [...] the ‘beginning’ lies in the infinite past [...] The York-time approach to quantum gravity gives no explanation of a beginning because the universe simply has none. It is infinitely old” ((Roser, 2016, 58–61); also see Roser and Valentini (2017)). Importantly, if York time is at least as good a choice for absolute time as cosmic time, then we have reason to endorse the second premise in ABIDO, i.e., we cannot know whether the absolute duration between the present and the past boundary is infinite."
I defer to Linford's expertise here, but I was under the impression that York Time, as it functions in the Hamilton-Jacobi formulations of Einstein's equations, gets rid of the singularity altogether, not that it puts it at 'negative infinity'. I'd like corrections here if needed. I think the singularity stays in certain contexts, like if we're dealing with Schwarzschild space-time, but that wasn't mentioned.
From what I've already said above, rather than repeat it, I direct the reader to the places where I've already shown, by my lights, why York Time won't be as good a choice for absolute time as Cosmic Time, and so we can know whether the absolute duration between the present and the past boundary is infinite.
Linford continues: "Craig does try to articulate some advantages of identifying absolute time with cosmic time. However, each of the supposed advantages of cosmic time that Craig recounts fail to uniquely pick out cosmic time. In part, this is because, as mentioned earlier, Craig does not consistently distinguish the preferred foliation from his labeling of the preferred foliation with cosmic time. For example, Craig tells us that observers whose clocks measure the cosmic time will record the CMB as isotropic. Nonetheless, the CMB is also isotropic according to, e.g., York time or with respect to any other labeling of the CMC hypersurfaces."
I find this passage peculiar. Linford doesn't provide a citation here so I'm not exactly sure where he's getting this. I'm going to guess God, Time, and Eternity, pg. 223, where Craig is talking about how "modern equivalents of the aether serve to establish a preferred reference frame" (222). These points arrive in a section called "Cosmic Time as a Measure of God's time", starting on pg. 218.
But why does Linford assume that preferred foliations are synonymous with preferred reference frames? And if the context in which Craig discusses the isotropy of CMB is one in which Craig is talking about modern equivalents for establishing a preferred reference frame, I'm not seeing the relevance of Linford's points here.
We all agree that a preferred foliation has to do with the choice of a time parameter that labels the CMC hypersurfaces, but privileged reference frames have to do with the choice of a set of coordinates, in this case, the coordinates would be comoving, and so, as Craig says, "The radiation background will be anisotropic for any observer in motion with respect to an observer whose spatial coordinates remain fixed" (223).
But the conclusion here isn't: therefore, Cosmic Time identifies the requisite preferred CMC foliation. Craig actually concludes: "It is therefore a sort of ether, serving to distinguish physically a fundamental universal reference frame" (223-224).
Kanitscheider is then quoted as confirming that the CMB "furnishes a reference frame, relative to which it is meaningful to speak of absolute motion" (224). It is called an "empirically distinguished frame of reference, in Stapp's words, 'define an absolute order of coming into existence.'" (224).
Craig wonders (rightly, in my opinion), whether Einstein, if he had known about the CMB, "would have claimed that no fundamental frame exists relative to which all local inertial frames are in motion" (224). Craig quotes Arthur Miller (who is corroborating something Dirac is in agreement with) that, "...in a way Einstein was wrong, because the Lorentz transformation does not apply to everything. There is the microwave radiation, which does provide an absolute velocity. It provides an ether, but the real importance of Einstein's word was to show how Lorentz transformations dominate physics" (footnote 68, 224).
So, this discussion of the CMB is 'connected' to Cosmic Time by Craig's supplying "two supporting arguments" to "underscore" "the importance" of an "answer to our first question" (221). What "first question"?
These questions are on pg. 218. There, Craig asks, "(i) Does cosmic time provide a sensible measure of God's metaphysical time? (ii) Is cosmic time in some sense absolute?" (218).
Craig's discussion of CMB should be understood as part of underscoring the importance of answering the question of whether Cosmic Time provides a sensible measure of God's metaphysical time, not what Linford seems to be indicating, that the CMB is being used by Craig to "uniquely pick out a cosmic time"! I can see Craig fully admitting that the CMB isn't a symmetry breaker for choosing Cosmic over York Time for identifying the preferred CMC foliation. But that wasn't what Craig was trying to indicate in discussing the CMB at all.
In the relevant section, "Cosmic Time as a Measure of God's Time", Craig talks about (1) whether the choice of Cosmic Time 'as a sensible measure of God's time' is, pace Kroes, an 'arbitrary inertial frame' that we wouldn't be warranted as being identified as 'privileged', and (2) whether a consideration of GR in light of further considerations of "the de facto distribution of matter and energy in the universe" leads to "natural symmetries" that "disclose" a "preferential foliation of spacetime and the real cosmic time in distinction from artificial foliations and contrived times" (219).
It seems that Linford is focusing on this second point since it's speaking of Cosmic Time being the time parameter that identifies the preferential CMC foliation. But I think that Linford is missing a subtle point that Craig is making that undercuts the notion that, at this juncture, Craig is just conflating privileged CMC foliations with the time used to identify such foliations. This point can then be used to demonstrate that Linford's citation of Craig's discussion of the isotropy of the CMB isn't relevantly connected to the idea of identifying the preferential CMC foliation at all.
Here I quote Craig in full on pg. 220 (I underline the relevant subtleties below):
"Kroes himself admits that when we turn from the theory considered in abstracto to describing the actual evolution of the universe, "certain 'natural' cosmic time functions force themselves upon us",52 In universes with fundamental observers one may introduce a special co-ordinate system which "distinguishes itself from all the other coordinate systems by the fact that the spacelike hyperplanes of constant t coincide with the hyperplanes of homogeneity;" relative to this group of observers, we can "speak properly of 'the' evolution of the universe."53 To return to Eddington's analogy of the paper block, suppose that only by foliating the block into a stack of sheets do we discover that on each sheet is a drawing of a cartoon figure and that by flipping through the sheets successively, we can see this figure, thus animated, proceed to pursue some action. Any other slicing of the block would result merely in a scrambled series of ink marks. In such a case, it would be silly to insist that any arbitrary foliation is just as good as the foliation which regards the block as a stack of sheets. But analogously, the Robertson-Walker metric discloses to us the natural foliation of spacetime for our universe. It would, indeed, be disingenuous to insist that the universe is not really expanding homogeneously and isotropically in approximation of the Friedmann model, that it does not really have a certain spacetime curvature, density, and pressure, that it has not really been about 15 billion years since the singularity, but that any arbitrary foliation and contrived time will yield equally appropriate descriptions of the way the universe actually is and evolves.54 Eddington realized this, of course, and we have seen that he recognized the privileged status of our cosmic time, though he emphasized that no experimental knowledge of it was as yet available."
Also here on pg. 221:
"Thus, it is possible to single out on physical grounds-not from the theory alone, but from de facto material conditions in the universe---a special group of preferred observers, the fundamental observers, that serve to define a privileged cosmic time, which deserves to be called the real cosmic time in counterdistinction to other mathematically possible functions. Nor does this conclusion in any way clash with GR. That theory does not, pace Kroes, succeed in establishing the equivalence of all observers from a physical point of view, as we have seen, and there simply is no General Principle of Relativity that requires that no privileged time exists from the cosmological point of view."
All of this is leading up to Craig's underscoring the answer to his "first question" (whether cosmic time is a sensible measure for God's metaphysical time).
What can we glean from these two block quotations? Let me clarify six key concepts from the above quotes to explain why I don't think Linford is correct to charge Craig with conflating a preferred foliation with our means of labeling that foliation.
1. Natural cosmic time functions - Here, a natural cosmic time function is one that comes from physically observable properties of the universe. As the integral of the inverse of the scale factor over time, and you can observe this scale factor through the CMB (among other things), of course.
2. Special coordinate system of fundamental observers (also called a special group of preferred observers that serve to define a privileged cosmic time) - Like I said above, as soon as you're talking about coordinate systems, special or arbitrary, privileged or not, we're primarily referring to reference frames, not foliations. Though reference frames and foliations are often used together, they don't have to go together. In GR, the metric tensor can be used to describe the position of objects and the motion of those objects. In this case, a foliation wouldn't be necessary to have a coordinate system (reference frame). And a fundamental observer is just one that is at rest in such a privileged, reference frame, comoving with it like, for example, me, at rest, in the reference frame of my car going 65 mph.
If we're talking about the CMB here, the CMB could be such a privileged reference frame, as Craig argues in the part where he says it could be considered a modern ether. Of course, CMC foliations can be used as a privilege reference frame. So, the CMC foliation slices spacetime into the relevant hypersurfaces and then you can use those hypersurfaces to describe the global structure of the universe, but then you might use the CMB as the preferred reference frame to measure the properties of those particular hypersurfaces. Since, as Linford would agree, the CMB is isotropic and homogenous (for both Cosmic and York Time), fundamental observers at rest in the privileged reference frame of the CMB will be able to measure the properties of those hypersurfaces of the CMC foliation that Cosmic Time is purporting to identify.
3. Spacelike hyperplanes of constant t - These hyperplanes are meant to coincide with the hyperplanes of homogeneity (4, below) so that the spacelike hyperplane of constant t 'slices' space at a particular time. From what I understand, that particular kind of 'slicing' is why some call this a 'hypersurface', even if, mathematically speaking, it's a hyperplane. And perhaps this is where it's appropriate to perhaps bring up the 'preferred CMC foliation'. But as yet, I haven't seen an example of the alleged conflation.
4. Hyperplanes of homogeneity - a hyperplane in spacetime that's the same at all points in space on the hyperplane, all the same properties at all the points in space.
5. Robertson-Walker metric - this is just one of the solutions to Einstein's field equations that gets at the homogeneous/isotropic properties we've already talked about: ds^2 = -dt^2 + a^2(t) (dr^2 + S_k^2(r)dΩ^2)
But it seems that Craig is correct here, that this metric gives you a natural foliation of spacetime, and that such a foliation is given to us by the spacelike hyperplanes of constant t, which are supposedly orthogonal to something called the time-like four-velocity field. And yet this metric does give a way to describe the global properties/structure of the universe in terms of Cosmic Time. You still need Cosmic Time to identify the CMC foliations because the natural foliations of the spacelike hyperplanes of constant t of the Robertson-Walker metric don't on their own identify the preferred CMC foliation.
Thus, Cosmic Time still needs to label the CMC foliations; all the metric does is give us a natural foliation of spacetime by slicing it up into slices of space at different times (the spacelike hyperplanes of constant t). But Craig's main point is that "relative to this group of observers, we can 'speak properly of 'the' evolution of the universe'". And so this group of observers can have a privileged frame of reference, 'a special coordinate system of fundamental observers'.
It's all indirect, as far as I can see. The metric describes a natural foliation, but that natural foliation (the constant time surfaces) can then be used to describe the universe in terms of Cosmic Time, and then Cosmic Time can then be used to label the CMC foliation.
6. Privileged status of Cosmic Time (deserves to be called real cosmic time) - From the previous concept, it's really easy to see how Craig can arrive at the privileged status of Cosmic Time using the natural foliation given to us by the spacelike hyperplanes of constant t. The special group of 'preferred observers', the fundamental observers, clearly define a privileged cosmic time, a 'real cosmic time'.
I've seen nothing so far to indicate that Craig has conflated a preferred foliation with the Cosmic Time used to label it. All Craig does after this when he mentions the CMB is cite examples of preferred reference frames to lend plausibility to the idea of a preferred reference frame in the context of GR. Craig says, "...there simply is no General Principle of Relativity that requires that no privileged time exists from the cosmological point of view." Then, Craig provides examples.
So, I have no idea where Linford is getting this idea that Craig is guilty of the alleged conflation. And the only time the CMB is mentioned, it's not meant to be a preferred foliation or a way for that foliation to be labeled at all; it's meant to be an example of the privileged frame of reference, a modern ether.
The additional question of whether measuring the CMB as isotropic settles the question of whether that isotropy is being recorded by Cosmic or York Time isn't something that Craig was even addressing. Craig has already made his case for the Cosmic Time you can obtain through the natural foliation of spacetime provided by the discussed metric, so he's free to talk about how such a Cosmic Time would record the CMB as isotropic and how the CMB is an option for a preferred reference frame.
As for whether one should go with Cosmic or York Time, Craig didn't explicitly discuss this, but I think (from what I argued in earlier parts of this blog) that there's more reason to opt for Cosmic Time and to appropriate whatever insights York Time provides instrumentally. Of course, these reasons need to be developed much, much more, but that is the general blueprint for a paper that can dive into these reasons with more detail than I can here.
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Let me conclude this section by mentioning the places where Craig mentions the CMC foliation specifically and then show how the CMB can define Cosmic Time to give us a reliably consistent time scale for the universe.
First, there's mention of "constant curvature" pg. 208 in the context of the Robertson-Walker metric we discussed already, but we saw that this gave a 'natural foliation' of the spacelike hyperplanes of constant t. The only explicit mention of the CMC foliation I can find in God, Time and Eternity is on pg. 240 and 241. At the bottom of pg. 240, Craig concurs with Evamlro Agazzi that "cosmic time...is essentially an equivalent of the old absolute time..." The very next quotation at the top of pg. 241, from Frank Tipler, begins with "...this unique foliation of spacetime by constant mean extrinsic curvature hypersurfaces defines absolute space and time in general relativity: the hypersurfaces are absolute space, and the timelike trajectories which are everywhere normal to the hypersurfaces are absolute time" (241).
This comes the closest to Linford's criticism that Craig is conflating Cosmic Time with the preferred foliation that such a time is used to identify. It looks as if Craig is using the Tipler quote to corroborate the Agazzi quote, which seems to imply that Tipler's "unique foliation of spacetime by constant mean extrinsic curvature" just is Agazzi's "cosmic time", which is claimed to be "an equivalent of the old absolute time".
But I think there's a perfectly charitable explanation for this. If cosmic time refers to a time coordinate that describes the universe's expansion, or if it's a time parameter that's determined by the proper time of the clocks of fundamental observers co-moving with the expansion of the universe, then cosmic time can be used as a foliation, a way of dividing spacetime into a set of spacelike hypersurfaces. If cosmic time is used as a foliation in this sense, in a sense directly linked to the expansion of the universe, then this foliation is bound to perfectly overlap with the CMC foliation due to the homogenous/isotropic constraints on that expansion. So, you can understand the jump from Agazzi to Tipler in this way and there's no need to for the criticism.
There's a convenient segue into CMB (just so there's no confusion, I'm using CMB to stand for Cosmic Microwave Background-radiation) because later in the same paragraph, on pg. 241, Craig has Tipler providing three reasons "...we should exalt this foliation of spacetime above all others..." (the CMC foliation, that is), and Tipler's third reason is that "In a universe which is very close to the Friedmann case of homogeneity and isotropy (as our universe is) the rest frames of the foliation will coincide with the rest frames of the Cosmic Background Radiation." The reader will begin to notice the extent of how things coincide regarding the Cosmic Time, Cosmic Time as a foliation, the CMC foliation that Cosmic Time identifies, the contingent overlapping of the foliations of Cosmic Time and CMC, and now the contingent, approximate overlapping of the CMC foliation, the foliation of Cosmic Time, Cosmic Time, and the CMB, such that, because our expanding universe approximates the homogeneity/isotropy conditions, all of these things roughly coincide, and approximate to, the expansion of the universe. The CMB is a natural, privileged frame of reference for describing the universe's expansion, and so it only makes sense that, for example, the frames of reference of the fundamental observers co-moving with the universe's expansion would be extremely close to overlapping CMB's frame of reference.
It goes without saying that none of the foregoing goes any distance toward deciding between Cosmic and York Time; all it does is show that the charge of Craig's alleged conflation is too quick and excessively uncharitable.
Linford continues: "One might think that cosmic time has the advantage that physically embodied observers whose clocks measure cosmic time are easier to come by than physically embodied observers whose clocks measure York time. True enough, but this cannot be an advantage for friends of absolute time. On their view, absolute time is independent of the time recorded by any local (or even physically constituted) clock. As Craig, channeling Newton, would tell us, local clocks need not record God’s absolute time."
I find this response underwhelming. Yes, absolute time and its measures are distinct, but, as Craig has said over and over, the proper time of the local clocks of fundamental observers co-moving with the universe's expansion will very nearly approximate Absolute Time or function as a "measure of God's Time, and such an approximation should be sufficiently close so as to foreclose any kind of substantial gap redolent of Linford's Omphalos Paradox. Craig says in a couple of different places that "the earth is approximately at rest with respect to the galactic fundamental particle" and so "we also have a fair idea of what time it is" (221).
E.1.2. Phenomenal Conservatism Defended
Here, Linford presents some reasons against an appeal to the "phenomenological access to the passage of time" that I find hard to understand, but I'll do my best to respond to it.
Here's Linford's first reason: "To start, note that although Craig thinks we have phenomenological access to the passage of time, there is a distinction between time’s passage and the rate at which time passes. Local clocks do not actually measure cosmic time; instead, only the local clocks of observers who are co-moving with the universe’s expansion approximate cosmic time. Supposing that absolute time should be identified with cosmic time, the rate of temporal passage experienced by any observer moving with respect to the universe’s expansion is illusory. In fact, Craig argues that we are moving with respect to the universe’s expansion (Craig, 2001c, 56-57), so that Craig implicitly admits that, if cosmic time is absolute time, the rate at which we experience the passage of time is illusory. If the rate at which most observers experience the passage of time turns out to be a widespread illusion, then we have reason not to trust the rate at which time seems to pass."
I found this passage to be perplexing, not to mention, unfortunately, inscrutable. Agreed: there is a conceptual distinction between time's passage and the rate of time's passage. But to say that local clocks don't actually measure cosmic time is ambiguous to me. Yes, local clocks would experience time dilation if they aren't co-moving with the expansion of the universe. They would, therefore, 'not actually measure cosmic time'. But didn't we just get done going over Craig's reasons for thinking that we are extremely close to the cosmic frame of the expanding universe, and so the local clocks on Earth do an amazing job at approximating cosmic time.
(If the idea of 'approximation' is throwing off the reader, this shouldn't be understood in terms of a completely dissimilar, unfamiliar presentation of something that melts away once approximation becomes identification. For instance, consider any spherical object in the world. If it's in our world, we can only experience 'approximately' spherical objects because nothing in the empirical world will have a one-to-one correspondence between it's spatiotemporal properties and the spaceless, timeless mathematical properties of geometrical objects. But that won't mean that, because is an 'approximately spherical object', we can't know, or can't have excellent reason to believe, that the shape before us is approximating is a sphere, and not some other object, like a dodecahedron!)
But then Linford grants us this and asks us to suppose that absolute time is to be identified with cosmic time, which I can't find Craig even doing. Craig will say things like: cosmic time is comparable to absolute time, or that it's equivalent to absolute time, or that it coincides with God's metaphysical time and records Newton's absolute time. 'Comparable', 'equivalent', 'coincide', and 'records' are weaker than 'identity'. Notwithstanding this, though, Linford goes on to say that even supposing that Cosmic and Absolute Time were identical, then "the rate of temporal passage experienced by any observer moving with respect to the universe's expansion is illusory." This is utterly opaque to me. Linford cites Craig's popular book, God and Eternity, though I'm not exactly sure where Linford is looking at here. I think it's this, on pg. 57 (not seeing anything on pg. 56), where Craig says, "Recent tests have even detected the earth's motion relative to this background radiation, thus fulfilling the dream of nineteenth-century physics of measuring the aether wind!" But, from this, I'm supposed to conclude with Linford that Craig 'implicitly admits' that "...if cosmic time is absolute time, the rate at which we experience the passage of time is illusory."?
This makes absolutely no cosmic sense to me. Linford's reason is that "If the rate at which most observers experience the passage of time turns out to be a widespread illusion, then we have no reason not to trust the rate at which time seems to pass." But this is just multiply confused to me. It's not a widespread illusion at all and it seems to me that Linford's reason for calling it an illusion is extremely weak. He seems to be presupposing that if I have phenomenological access to X, and X approximates Y to a very high degree, and X isn't identical to Y, then whatever I say about Y, on the basis of my phenomenological access to X, is an illusion. Again, the degree of skepticism Linford has is enormous and implausible. On principle, Linford would have to be skeptical about Plato's Forms only on the basis that the concrete particulars that exemplify the Forms approximate those Forms. To me, this would be a woefully inadequate reply to Plato.
Linford moves on to an additional reason (this is long, so what I want to focus on particularly is in bold): "the phenomenal conservative strategy suggests that, in our ordinary experience, clocks that can be physically constructed seem to measure time, so that perhaps we should think our local clocks measure absolute time. The suggestion followed that this gives us some reason to favor cosmic time as the measure of absolute time. However, we also have some seemings from attempts to construct quantum gravity theories or from attempts to construct an ontology for quantum theory that have elsewhere been argued to count in favor of York time as a candidate for absolute time. (Roser goes so far as to note that cosmic time is a “highly unnatural choice of time parameter when discussing the very early universe”, (Roser, 2016, 58).) Why should a metaphysics of absolute time favor the former seemings over the latter seemings? I don’t see a clear way to settle the dispute between the two conflicting sets of seemings in favor of one set of seemings and that would be considered widely attractive to all disputants. And without a way to settle the dispute, all else being equal and provided absolute time exists, I am inclined to agnosticism concerning the finitude of the duration of past absolute time. And that agnosticism provides sufficient justification for endorsing ABIDO."
I think Linford is all too quick here to surrender to agnosticism.
(i) The seemings here can be 'nested' and prioritized and tethered to a precification of the relevant concepts involved in the dynamic activity of reflective equilibrium, a process whereby you bring your seemings, judgments, concepts, and principles into coherence and balance. Now, Linford's deference to agnosticism is the end result of a particular instance of reflective equilibrium tethered to the way he's precisified the situation. Linford has lent to Cosmic and York Time a realist construal, and so the instantiation of the content of the relevant concepts are metaphysically incompatible, providing Linford with two incompatible sets of seemings, upon which Linford utilizes the principle that when confronted with two incompatible sets of seemings, then, in the absence of some relevant symmetry breaker, one ought to suspend belief to remain rational.
That relevant symmetry breaker, for me, is the way an instrumentalist construal of York Time relates conceptually to a realist construal of Cosmic Time (keep in mind the distinction between Cosmic Time* and Cosmic Time, where Cosmic Time* is what is related to York Time realistically construed: recall when I said, above, that for York Time, 'the Hubble Parameter is defined in terms of the integral of its negative reciprocal over cosmic time. Thus, York Time is proportional to the negative of the Hubble parameter, which means that as the Hubble parameter (H) decreases, York Time increases, and as the Hubble parameter increases, York time decreases' - the 'cosmic time' mentioned here is Cosmic Time*, not Cosmic Time). If Linford's noetic structure imports a realist construal of both times, the resultant aporia rationally compels him to an agnostic suspension of belief in what the covarying seemings are indicating.
This is further buttressed by Linford's disinclination to consider instrumentalist construals due to the way he conceptualizes the relationship between such construals and the relevant aspects of the world that they symbolically depict. (This was already gone over above in the context of instrumentalist construals of the geometric properties of a metaphysical entity called 'spacetime'.) This disinclination then perhaps motivates Linford to forego such construals as obviously in error. But it is precisely Linford's narrow conceptualization that is doing most of the heavy lifting here. If it's broadened to include symbolic depictions (e.g. the back edge of the tenseless, graphic representation of my space-time worm as plotted on a Minkowski diagram symbolically depicting my tensed birth, a metaphysical, diagram-independent reality), then the instrumental utility of York Time for accurately describing properties of the early universe will be where it's the most help.
Here's how it might look. Consider the Craig/Sinclair (2012, 106) quote that Linford doesn't find convincing and let me put this side-by-side with a section in some Lecture Notes that Craig personally handed the students in a class on the Kalam in the Fall of 2019. First, from Linford's paper:
As they write, “There may be no such things as singularities per se in a future quantum gravity formalism, but the phenomena that [General Relativity] incompletely strives to describe must nonetheless be handled by the refined formalism, if that formalism has the ambition of describing our universe” (Craig and Sinclair, 2012, 106). I don’t find this reply convincing. However, whether or not we should look upon divergences in physical theories as suspicious has been discussed at length elsewhere and I set the issue aside for the purposes of this paper.
But I don't think this can be set aside for the following reason. If York Time is construed instrumentally, then the relevant part of the 'cosmological timeline' it gives us, that aspect of the cosmological history that is prior to inflation (T = -∞ → T = 10^−5 - the Planck era), where a singularity is either extinguished or pushed back to infinity-past, isn't meant to tell us about real properties of singularities or real singularities in infinity-past at all.
(In passing, let me just get it out of the way that I know that singularities are mathematical constructs, but this just illustrates, as another example, the way instrumentalism about x can still relate to properties in reality that the different properties of x symbolically depict: in this case, singularities, as solutions to Einstein's field equations, are mathematical constructs that symbolically depict that divergence in GR where spacetime's curvature/density is infinite, regions wherein the known laws of physics don't apply.)
Here's the rub. I don't mind York Time being handled instrumentally in the context of a Quantum Theory of Gravity, but I don't have the same worries Linford has about why a realist construal of York Time (and its consequent connection with Cosmic Time*) is preferable to Cosmic Time, namely, that we can't have spacetimes that aren't maximally extended without the Omphalos Objection. Recall, I argued that when 
is laid on top of a gravitational field, rather than a Minkowski spacetime, it will be laid on top of the singularity, become prematurely truncated, and thus not maximally extended, and therefore subject to the Omphalos Objection. But I argued above that the sting of this objection is taken away in this case because the truncation isn't arbitrary; and it isn't arbitrary because have independent reasons, apart from conformal considerations of chronogeometric structure, to date the singularity to about 13.8 billion years ago (discussed briefly above).
Since it can be argued that these independent reasons authorize a spacetime truncation, it makes sense for Craig/Sinclair to say that the refined formalism of a future Quantum Theory of Gravity won't extinguish what GR had incompletely attempted to describe, partly due to GR being one of the most confirmed and tested theories ever.
What might this look like? A clue comes from the Lecture Notes on the Kalam I noticed. There, we read:
"If there is such a non-classical region, then it is not past eternal in the classical sense. But neither does it seem to exist literally timelessly, akin to the way in which philosophers consider abstract objects to be timeless or theologians take God to be timeless. For it is supposed to have existed before the classical era, and the classical era is supposed to have emerged from it, which seems to posit a temporal relation between the quantum gravity era and the classical era."
Now, assuming that York Time is construed instrumentally, and so we don't have to put the 'quantum gravity era' in eternity past, or singularities in eternity past, or extinguish singularities altogether, you keep Cosmic Time, lay on top of the gravitational field, and so on top of the singularity, truncate it, admit it's not maximally extended, admit that the gravitational field 'has a well-defined value at every point of the underlying space-time', and that it is undefined at the singularity, but dissolve the Omphalos Objection by providing the independent reasons (independent from a mere consideration of the conformal chronogeometry) that place the singularity 13.8 billion years ago. In this way, you have a principled reason for truncating spacetime the way you did because you can only extend it so far before it's truncated at a singularity that independent reasons suggest is around 13.8 billion years into the past.
Now, in the Lecture Notes, in footnote 23, in the context of "a synchronic emergence of time as a supervenient reality in the context of cosmogony", Craig says:
"The best sense I can make of it is to say that the Euclidian description is a lower-level description of classical spacetime prior to the Planck time. (One recalls Hawking’s remark that when we go back to the real time in which we live, there still would be singularities.) So the same reality is being described at two levels. That implies that if the classical spacetime has a beginning, then so does the quantum gravity regime. For they are descriptions of the same reality. In the one a singularity is part of the description; in the other it is not. So what is prior to the Planck time is not the quantum gravity era as such; rather what is prior is the classical period of which the quantum gravity description is the more fundamental description. If this is correct, then, given the beginning of the classically described universe, it is impossible for the universe as quantum gravitationally described to be without a beginning. For they just are the same universe at different levels of description."
This approach fits very nicely in the context of truncated spacetimes, GR, quantum gravity, singularities, Cosmic Time, and York Time. Of course, if York Time is construed realistically, then the quantum gravity regime will extend back to past infinity, and a successful theory of quantum gravity will have a refined formalism that won't have to do with singularities at all or will push them back to past-infinity. But if we're instrumentalists about York Time, things get a lot simpler. We can keep Cosmic Time and its description of classical spacetime, use it to label the CMC foliation, extend that spacetime back to the singularity 13.8 billion years ago, truncate it at the singularity since there it is undefined, admit to there being a quantum gravity regime, but also import the idea that the quantum gravity description and the classical (Euclidian) description are descriptions of the same reality at two different levels. Prior to Planck time, there is no actual quantum gravity era, but a classically described spacetime of which the quantum gravity description is the more fundamental, higher-level description. If this is right, and we can justifiably truncate spacetime with the independent reasons already discussed, keeping Cosmic Time and its labeling of the CMC foliation, being instrumentalists about York Time, then we might able to include York Time descriptions of spacetime prior to the Planck era as an additional higher-level description of a classically described universe with a beginning. So, if we have the same universe at different levels of description, then we keep Cosmic Time and instrumentalize York Time, and the utility of York Time lies in its contributing helpful higher-level descriptions of the very early universe, prior to Planck time, but with a singularity about 13.8 billion years ago.
With all this in mind, the rest of Linford's quotation is easily dispatched.
(ii) Roser is correct that Cosmic Time would be 'a highly unnatural choice of time parameter when discussing the very early universe'. That's why we can use higher-level, quantum gravity and York Time descriptions of that very early universe, prior to Planck time, but keeping in mind that if the classically described spacetime has a singularity dating the universe to be around 13.8 billion years old, and there are independent reasons, independent of mere conformal considerations of chronogeometry, to think this, then we keep the utility and empirical adequacy of higher-level descriptions of the early universe, and take an instrumentalist posture toward any ontological implications of the theoretical terms and concepts of such descriptions.
Linford continues: "York time may have some advantages over cosmic time as a candidate for absolute time. Cosmic time can be used to label a CMC foliation of our universe provided our universe satisfies the FLRW ansatz, that is, if our universe is exactly homogeneous and isotropic. Our universe is not homogeneous and isotropic; instead, our universe only appears to be homogenous and isotropic when one averages the mass-energy content over sufficiently long spatio-temporal scales. As Gerald Whitrow writes, “cosmic time is essentially a statistical concept, like the temperature of a gas” (1961, 246; also see (Lockwood, 2007, 117-118)). As Daniel Saudek notes, this leads to the consequence that cosmic time is defined only in a coarse grained way – that is, for what Saudek calls “stages” of cosmological evolution – and is inadequate for defining a total ordering over space-like separated localized events (2020, 56), as should be expected from a good candidate for absolute time. Thus, cosmic time can only be used as an approximate label of a CMC foliation of our universe. York time does not require homogeneity or isotropy; in fact, York time plausibly requires no averaging at all and so can be used as an exact label."
I'm not sure it's correct to say that the universe is not homogeneous and isotropic; I think it's better to say that our universe is approximately homogeneous and isotropic. So, for example, the distance between two points on a geographical area may not be exactly a mile due to the curvature of the Earth, the presence of obstacles, or other factors. However, if the distance is measured using a standard unit of measurement such as a mile, it can be considered an approximation of the actual distance. In a mathematical space-time, where the universe is homogeneous and isotropic, the distance between two points can be exactly a mile, but in the actual universe, the distance can only be approximately a mile. Thus, the mathematics of space-time will describe a universe that is homogeneous and isotropic, but the actual universe will be so only approximately. It just doesn't follow from this approximation relationship that we'd be correct in saying that the universe only seems or appears to be homogeneous and isotropic, but that it actually isn't. That it approximates homogeneity and isotropy makes the RW metric extremely useful.
And Linford admits that cosmic time is an approximate label of the CMC foliation of our universe. That York Time doesn't need homogeneity and isotropy is an advantage that realists about Cosmic Time can enjoy. At the very early stages of the universe, there was no homogeneity or isotropy. So, York Time can come in handy in describing the properties of the universe at this stage. But remember that this doesn't mean that the CMC foliation that York Time labels actually exists, that we're ontologically committed to the existence of that foliation because of the utility of the descriptions that York Time affords us. So, for example, just as Darwin was more or less correct in his original theory, despite 'black boxes', cosmic time is a more or less correct way to label the CMC foliation, despite the ordering of events at small scales or particular moments or localized events.
Again, Linford calls Cosmic Time Absolute Time, again. It's not. They're not the same. Cosmic Time approximates Absolute Time. These are not the same relationships.
Linford concludes with speculations about the inflationary multiverse, the cosmological horizon, but I'm not sure I can add anything here that I haven't said already.
I would like to make a quick comment on footnotes 30 and 31.
Footnote 30: "George Ellis and Rituparno Goswami have promoted a generalization of the cosmic time – the proper time co-moving gauge – as a candidate for the absolute time (2014, 250). Ellis and Goswami’s proposal would apply to inhomogenous or anisotropic space-times. However, Ellis and Goswami’s proposal labels a distinct foliation from the CMC foliation. Moreover, while one might have expected that any surface in the foliation labeled by absolute time is a space-like surface, Ellis’s proposal has the bizarre consequence that, in inhomogenous space-times, some surfaces in the foliation Ellis’s proposal picks out may be time-like surfaces. Therefore, if the proper time co-moving gaugage corresponds to absolute time, some moments of time are time-like surfaces, which is implausible. For this reason, the York time parametrization of the CMC foliation is arguably superior or at least not inferior."
As discussed above, Craig went over something extremely close to this by mentioning the clocks of fundamental observers co-moving with the universe's expansion, which just would be those observers' proper time. Moreover, all that follows from the fact that some of the surfaces that the proper time co-moving gauge correspond to are time-like is that there isn't exact correspondence going on here at all. The proper time co-moving gauge would, in these cases, be an approximate time parameter when such space-times are inhomogeneous. It's doesn't have to be an exact parameter to be effective for analyzing large scale properties of the universe, even with the presence of deviations from homogeneity. So, considering everything we discussed above, the York Time parametrization isn't obviously superior at all. Moreover, this move from correspondence to approximation Linford actually agrees with in footnote 31.
Footnote 31: "Craig Callendar and Casey McCoy object that in the de Sitter phase of an inflationary multiverse, all CMC surfaces have the same value of the York time (Callender and McCoy (2021)). If all of the CMC surfaces in the de Sitter phase have the same value of the York time, and the York time is identified with absolute time, then the awkward consequence follows that all of the CMC surfaces in the de Sitter phase are (somehow) simultaneous with one another. Nonetheless, Roser points out that an actual inflationary phase is only approximately de Sitter and that the York time really is “increasing during this cosmological period”".
This is ironic because Linford's reply here to Callendar/McCoy appeals to the same idea of approximation I've been making the entire time in response to his criticisms of Cosmic Time. Of course, if it's permissible to instrumentalize York Time, we can just reapply this point about approximation to the neo-Lorentzian appropriation of Cosmic Time. It all has to do with the simple point that approximations are great indications about what they approximate, and so it's somewhat of a failure of epistemic nerve to think that approximations pose any sort of skeptical threat worth us worrying about.
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CONCLUSION
I'll abruptly conclude here since this blog is already needlessly meandering and long (as I didn't have the time to make it shorter). I submit all of this as a testament as to where I am, completely open minded for any corrections, since the topics discussed here are extremely complex and I'm neither vain nor delusional enough to think I have everything figured out. In summary, I disagree with what I've called Linford's seeming editorializing when it comes to conflating descriptions of relativity with the metaphysical interpretations of those descriptions, I do think you can infer a past boundary from the matter-energy distribution of the universe, that you can infer chronogeometric structure from this matter-energy distribution, that there doesn't have to be a realistic connection between the structure and that distribution, that you can be an anti-realist about the geometry of that structure, that you can therefore solve the Omphalos Objection as a potent skeptical threat, that there's no reason to think that Steven Weinberg doesn't support Craig in the context that Craig cites him in, that there's good reason to prefer Cosmic Time over York Time for realistically identifying the CMC foliation, and that I wasn't convinced that Craig waffles back and forth between the preferred foliation and the means by which we identify it.
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