Cosmology and Cosmologists with the “Does God Exist” Problem

A Consideration of Kalam’s Second Premise

James D. Sinclair

I am a modeler by trade, employed by the United States Navy. My field is Artificial Intelligence, and the creation, maintenance, and analysis of results from sophisticated models of air combat. I work with teams of subject matter experts (hereafter, SMEs), each an individual expert in their field, much as Dr. Carroll is an SME in cosmology. So, I do not stand in relation to our area of interest in the same way that Sean Carroll does. I stand in relation to this problem in my accustomed role as a knowledge integrator.

The “model builder,” or knowledge integrator has to know the inherent limitations that come from the answers provided by the SMEs. To answer a question requires a context, a world of its own that intersects with the real one, but only imperfectly. Our models may reach for a conclusion that is a mere artifact or limitation of the toolset. Or, the conclusion may be sound. The problem of the artifact applies to cosmology specifically in the role of the prediction of a singular beginning to the universe from Einstein’s relativity

I’m going to focus on one narrow topic: the second premise of the Kalām argument. Does the universe begin-to-exist? As you learned in the Carroll–Craig debate, the premise has two components:

a) Does the universe have a beginning?

b) What is the nature of time?

The first of these two questions will be at issue for this chapter. The second is significant enough that it should be the topic of a second debate between Carroll and Craig.

Now, models may intentionally avoid having internal entities that correspond to structures within the real world. There may not even be an internal structure. Models of this type are called “instrumental.” For example, suppose in my field, I wish to build a model that determines if a missile impact destroys an aircraft. Such a model may be a sophisticated physical model of the missile fuzing and impacting an aircraft with lethal projectiles. A vulnerability model is built for the aircraft that specifies the location of critical systems. Against this is applied the physical prediction of the impact pattern of the warhead fragments. From this comes a prediction of the probability of lethal damage.

On the contrary, I could just take some dice and roll them. Certain numbers represent a kill; others, survival. This second model is purely instrumental. Not only does it not purport to have internal entities that are representative of reality, it has no internal entities at all. The first model, though, is an attempt at a realist model. In between, one may have “effects” level models that don’t strive to model all physical processes explicitly. Model toolsets are elastic, have high and low fidelity parts, and can be “telescoped” to focus just on the particular question one has in mind. We must interpret every result for its true significance (or lack thereof) in this light.

In the world of cosmology, there are many toolsets. Let me suggest three categories. There are Einstein’s equations within the General Theory of Relativity (GTR). There is a set of more speculative and competing toolsets within the rubric of Quantum Gravity (QG). And there is something that I’ll call GTR+, which are Einstein’s equations with corrections informed by considerations from QG.

GTR and the Singularity Theorems

This section will deal with global temporal boundaries within General Relativity and why they matter as well as the increasingly constricted boundaries of a beginningless cosmos.

Over the course of the last ten years, I’ve approached many cosmologists (via email) for the purpose of interviewing them on the models they’ve built. Most will indeed talk with you, which is remarkable, considering how busy they must be and the fact that the only thing in it for them is the joy of teaching. When we approach our SME, and ask her to school us on cosmology, she may first speak to us about GTR. Imagine GTR like a set of Legos. The possibilities for building worlds are endless, but there are some rules. There can be time machines in GTR, universes that lack a global definition of time, and universes that expand in one direction while simultaneously contracting in another. Our SMEs usually restrict themselves to something called Friedmann-LeMaître-Robertson-Walker (FLRW) space-times because such space-times closely match our empirical observations of the universe we actually live in. Such space-times are nearly homogeneous, isotropic, have a global definition of time, and aren’t time machines.

One of the interesting things about GTR is that there are some natural stopping points for the worlds one creates. Within GTR is the concept of worldline. A worldline, also called a geodesic, is the path through which an observer, such as yourself, passes through space and time. Even if just sitting in a chair, one is still tracing out such a path. Normally, these worldlines are said to apply to freely falling particles under the influence of gravity. When cosmologists speak at the public level, they might talk of an astronaut in a spaceship with the engine turned off. Imagine a universe filled with astronauts. We should like to know their past and future. In GTR, these paths may trace to past or future infinity. Or. they may wrap around in such a way that a time machine is created. Or, the past or future may be truncated. It is this last possibility in which we are interested. A worldline that stops short of infinity is an indicator of a pathological condition within a GTR space-time.

These “singular” pathologies can exist in the past or the future. They may be local anomalies, such as a black hole, or a global temporal feature that signifies a “Big Bang” origin or “Big Crunch” future fate. It is the curiosity of an observer literally “ending existence” when one reaches the end of a worldline, or “beginning to exist” as a worldline’s origin that initially interests us. Our toolset also allows us to freely reverse the arrow of time. From the 1960s to the present, GTR theorists have been probing these space-time pathologies with the use of mathematics. Does the universe, for example, have a beginning?

The 2003 Theorem of Borde, Guth, and Vilenkin (B-G-V)

Many theorems have been developed that have increasingly constrained the possibility of a beginningless GTR model. Theorists considered the issue of energy conditions within these singularity/incompleteness theorems and this led to a further development among Alexander Vilenkin and Arvind Borde (who fathered many theorems in the 1990s), along with one of the fathers of the inflationary theory, Alan Guth. They derived a novel result that suggests the past of an expanding universe likely has a global temporal boundary.^[1] What they did was start with the fact that observers sprinkled throughout an expanding universe are always flying further and further apart. Now, take a light beam and consider its future as it is observed by subsequent observers. The fact of the expansion has the effect of the observers seeing the light “red-shifted” at later and later times. B-G-V considered what would happen if you looked to the past and what spectators in the early universe would see. They were able to show that the worldline of light was inextendible to an infinite past because the light would then be “blue-shifted” to a degree that violated the conditions of relativity. Similarly, they considered what would happen if these same set of observers saw a drifting spaceship. Later and later in the history of the universe, the observers would observe the relative speed of the drifting ship at smaller and smaller velocity. But as one looked to the past, the spaceship would appear to be faster and faster to these earlier and earlier observers until the novel effects of approaching the speed of light were encountered. B-G-V took this to mean that there was a past boundary to an expanding cosmos. A conservative way of stating this would be to say that there is either a beginning, or some completely different type of physics must take over. There is a suggestion in their original paper that there is a quantum-based beginning of the nature of Vilenkin’s own “tunneling from nothing” proposal from 1982.

Now, I want to take a step back for a moment and talk about a problem called “rhetorical gloss” in public speaking. Consider philosopher Paul Valery, who suggested that “The simple is wrong, but the complex cannot be understood.” There is a temptation, especially in public speaking, to guard against the latter threat, and thus, risk the opposite horn of the dilemma. Oversimplification can also come in by not explicitly speaking to all caveats and underlying assumptions. Thus, the speaker oversimplifies, and the later critic of the speaker errs by claiming the speaker was unaware of this or that caveat. I don’t know how to solve this problem. But I do know discussions of the B-G-V theorem are particularly vulnerable. B-G-V is an important result. But it’s not a silver bullet or a sound-bite. Understanding its significance requires a context. In fact, the whole subsequent discussion of B-G-Vs “new physics at the boundary” leads to a whole different layer of complexity.

Diachronic Emergence, GTR+, and Treatment of Time

in Quantum Gravity

Our SMEs tell us that the past temporal boundary predicted by many GTR models could be representative of the breakdown of the toolset. As such, one wonders whether the prediction is just an artifact, or is still a pointer toward a genuine beginning for the universe. A good article to read about this type of problem in physics was penned by Isaac Azimov some years ago and is entitled The Relativity of Wrong^[2] Azimov warns against the fallacy of rejecting a model result merely because one may expect that eventually, a model paradigm will be replaced by a different one. Azimov tells us that paradigms do get replaced, but the replacement is usually just an incremental improvement in accuracy over the older one, even if the nature of the physics is completely different. Thus, while Newton gave way to Einstein, and Einstein will give way to Quantum Gravity, it’s a terrible error to throw away Newton and claim that he was just “wrong.” Newton was not far wrong, Einstein was “less wrong” than Newton, and Quantum Gravity is promised to be “less wrong” than Einstein. If wrong is just wrong, then we should not even trust Quantum Gravity or anything one might come up with. Can we learn nothing about the cosmos? There is clearly something wrong with throwing away the predictions of a theory just because another paradigm is on its way.

What we wonder, then, is whether the Big Bang singularity is just an artifact of GTR, or whether it is a true indicator of a beginning that will be better described in Quantum Gravity. Just because Einstein will be “overcome” does not mean he should be “thrown away.”

Now, our SMEs tell us the concept of time is well-known to be problematic within Quantum Gravity. Some theorists even believe that time does not really exist. We’ll have to confront this problem in two stages. Staying relentlessly within the rubric of our cosmological argument (kalām), for now, we will assume that time (and temporal becoming) do exist at the fundamental level. The philosophy of time problem deserves its own separate treatment.

Space permitting, we’ll examine some of the approaches being taken when talking of time within quantum gravity.

1) A generic “Quantum Foam”

2) Euclidean Geometry (“imaginary” time)

3) Use of a physical degree of freedom to play the role of time

Quantum Foam

So. what happens “at the singularity?” Here are two popular level descriptions, one strictly from GTR, and the other taking a step forward into the realm of quantum gravity. Yes, they are popular accounts, but they will help us think. Now, one must be careful of the aforementioned problem of “rhetorical gloss” in considering a popular account. Some things may not be meant literally. But while talking for the public’s sake, the theorist is forced to think in the terms of literal cosmic evolution. There literally is matter in motion. The universe is a thing that endures and undergoes real, literal change.

In both of these accounts, the author is speaking of an astronaut falling into a black hole. What happens to the astronaut? We shall start with these descriptions, and then, extend them into a discussion of a past temporal singularity.

In GTR world, Robert Geroch tells us:

Recall there is no event available to [an astronaut] on the singularity itself. In particular, there is no possibility for a further extension of [the astronaut’s] world-line after [he] hits the singularity. What, then, does “the world-line of [an astronaut] hits the singularity” mean physically? Mathematically, what happens is that this world-line just stops. Physically, this would mean that [the astronaut] is “snuffed out of existence”; after some finite time according to himself, he ceases to exist in space-time.^[3]

In an evolutionary view of reality, where matter really is in motion, an astronaut would literally cease to exist. Remarkably, there is not even a final moment of existence. The singularity is a boundary to space-time, but is not within space-time.

Now, let’s take this one step further. Here is a description I find illuminating of the approach to a “quantum foam.” The description (from 1993, but still relevant) again relates to an astronaut falling into a black hole. Physicist Kip Thorne tells us:

Einstein’s equation predicts that, as the astronaut reaches the singularity, the tidal forces grow infinitely strong, and their chaotic oscillations become infinitely rapid. The astronaut dies and the atoms from which his body is made become infinitely and chaotically distorted and mixed—and then, at the moment when everything becomes infinite (the tidal strengths, the oscillation frequencies, the distortions, and the mixing), space-time ceases to exist.

The astronaut is already dead, his body parts are already thoroughly mixed, and the atoms of which he was made are already distorted beyond recognition when quantum gravity takes over. But nothing is infinite. The “game” goes on.

Just when does quantum gravity take over, and what does it do? As best we understand it in 1993 (and our understanding is rather poor), quantum gravity takes over when the oscillating tidal gravity (space-time curvature) becomes so large that it completely deforms all objects in about 10^-43 second or less. Quantum gravity then radically changes the character of spacetime. It unglues space and time from each other, and then destroys time as a concept and destroys the definiteness of space. Time ceases to exist; no longer can we say that “this thing happens before that one,” because without time, there is no concept of “before” or “after”. Space, the sole remaining remnant of what was once a unified spacetime, becomes a random, probabilistic froth, like soapsuds. . . .

This random, probabilistic froth is the thing of which the singularity is made, and the froth is governed by the laws of quantum gravity. . . To recapitulate, at the center of a black hole, in the spacetime region where the oscillating BKL tidal forces reach their peak, there resides a singularity: a region where time no longer exists, and space has given way to quantum foam.^[4]

Thorne gives us a lot of rich detail that supplements Geroch’s GTR account. What is of interest to us is this prediction of the destruction of time and indeterminacy of space. In order to bound our problem, we’re going to imagine this is literally true. We’re going to put a stake in the ground to help us think.

Let’s turn the clock around and imagine emerging from the “singularity.” In GTR-world, we can tell from Geroch that there is actually no first moment. Yet, one nonetheless “begins-to-exist.” That’s bizarre, but that’s the physics.

Looking at the problem from Thorne’s quantum point of view, there would literally be no time associated with a quantum foam. In the foam, time is destroyed and space is indeterminate. So, what could it mean to say that a quantum foam precedes the process of “beginning-to-exist?”

Let’s think now about the whole universe and a possible quantum gravity temporal origin. One of the right questions to raise relates to Thorne’s correct observation that “without time, there is no concept of ‘before’ or ‘after.’” Many quantum gravity approaches suggest that the space-time background ceases to exist at the fundamental level.^[5]

But if the quantum gravity era has no time, then it is impossible for it to be a primordial era, earlier than the “classical” universe.^[6] This is the logic problem of diachronic emergence. What might this mean? The implication is that “quantum foam” serves as a past boundary to the universe, but is not actually a state of the universe. In this manner, it functions similar to a singularity in GTR. One might expect that the best physical model would be what I have described as GTR+; there are quantum-gravity inspired corrections to Einstein’s equations. There may be an era earlier than GTR itself may predict. But there seems to be a beginning, just the same. Much contemporary development in cosmological models takes place under this paradigm.

But if one doesn’t allow that space-time is destroyed in a quantum gravity approach, then something like B-G-V probably could still apply. Alexander Vilenkin tells us about these GTR+ models:

The question of whether or not the universe had a beginning assumes a classical spacetime, in which the notions of time and causality can be defined. On very small time and length scales, quantum fluctuations in the structure of spacetime could be so large that these classical concepts become totally inapplicable. Then we do not really have a language to describe what is happening, because all our physics concepts are deeply rooted in the concepts of space and time. This is what I mean when I say that we do not even know what the right questions are.

But if the fluctuations are not so wild as to invalidate classical spacetime, the BGV theorem is immune to any possible modifications of Einstein’s equations which may be caused by quantum effects.^[7]

So if space-time is “destroyed” by QG, there is a beginning. But if space-time isn’t destroyed, there may yet be a beginning if an incompleteness theorem such as B-G-V still points to a temporal boundary.

Imaginary Time

This problem took a serious turn into the philosophical realm in 1993, when philosopher Quentin Smith observed a related problem with a prominent attempt at quantum gravity: the Hartle-Hawking no-boundary model. In this model, Hawking & Hartle appear to suggest there is a primordial era for the universe, which features “imaginary time.” In this “era,” time acts exactly like a spatial dimension. It is supposed that there eventually is a “classical” era with ordinary (Lorentzian) time. The actual mathematics, however, includes a mathematical technique called the Feynman “sum-over-histories.” In quantum terms, there is a superposed wave function that generates a probability of the ultimate emergent universe being of a particular form. This model (and a related one from Alexander Vilenkin, called the “tunneling from nothing” model) is also sometimes presented as a topological transformation from “nothing” (a dimensionless point) to a 4D space-time.

But is imaginary time a primordial era? Smith takes Hawking to task as follows:

Clearly Hawking is offering a physical interpretation of four-dimensional space, i. e., Euclidean spacetime. But such an interpretation is implicitly logically self-contradictory. The problem appears in the statement that the four-dimensional space joins on to the real (Lorentzian) spacetime “once” (i. e., after) the quantum smearing effects subside: “The question then arises as to the geometry of the four-dimensional space which has to somehow smoothly join onto the more familiar spacetime once the quantum smearing effects subside”. If the four dimensional space does not possess a real time value, how can it stand in relation to the four-dimensional spacetime of being earlier than it? If the four-dimensional space is not in real (Lorentzian) time, then it is not really earlier than, later than, or simultaneous with the four-dimensional spacetime manifold. Accordingly, it is false that the 4-sphere joins on to the familiar spacetime once (i. e., after in real time) the quantum effects dissipate. Nor can this “once” refer to imaginary time, which would imply that the real spacetime is later in imaginary time than the 4-spere, which it is not. There is no imaginary time in real spacetime and real spacetime is not located in imaginary time. (To be so, its temporal dimension would have to be a fourth spatial dimension, which it is not) Indeed, “later” is not an appropriate expression to use of imaginary time, since the earlier-later direction is a feature only of real time. (Imaginary time is instead like a spatial dimension, in which there is no direction.) It is false, then, that “in the very early universe” there is a quantum phase in which the universe is a 4-sphere. “The very early universe” can refer only to the very earliest times, i. e., the lowest values of the real time coordinate.^[8]

Is Hawking’s use of the term “once” just rhetorical gloss? In 1996, philosophers Reed Guy and Robert Deltete formally followed up on Smith’s suggestion and reached a similar conclusion regarding both Hawking & Hartle’s “no boundary” quantum origin model and Alexander Vilenkin’s “tunneling from nothing” model. They analyzed the apparent temporal claims made in the H-H model in premise form and found the premises not compatible. Guy & Deltete’s conclusion was that “emerging from imaginary time is incoherent.”^[9]

In 1999, Jeremy Butterfield & Christopher Isham clarified the issue for many by establishing emergence in a synchronic, rather than diachronic, sense. They end up agreeing with Smith, Guy & Deltete, yet take them all to task as follows:

A considerable philosophical, as well as popular scientific, literature about the emergence of time has grown up around this [Hawking & Hartle’s] proposal. But we believe that much of that literature is marred by not taking sufficient cognizance of the problem of time, which besets the Euclidean program as much as quantum geometrodynamics. In a nutshell: by ignoring the problem of time, much of the literature makes it look as if the no-boundary proposal treats the emergence of time as a process in time, i. e., according to the temporal sense of “emergence” noted above. And then, unsurprisingly, the no-boundary proposal seems to face conundrums or even contradictions. But these are an artefact of ignoring the problem of time. In other words: we agree that the no-boundary proposal is very problematic: but this is because it must confront the problem of time (to whose solution it makes no contribution), not because of such conundrums.^[10]

Butterfield & Isham argue that the typical diagram used to describe the H-H universe, where the bottom of a cone is rounded off, showing an apparent join between and imaginary time era and a classical time era, is misleading. This, even though Hawking uses the diagram himself! Yet, Butterfield & Isham seem correct. There doesn’t seem to be a temporal relation between the H-H imaginary time mathematical structure, and the “classical” Lorentzian universe when you evaluate Euclidean models in detail. They say:

But this “emergence” is not a process in time: Hartle and Hawking’s proposed “framework,” and others such as Vilenkin’s, stands in no temporal relation to classical spacetime, or any of its parts (regions or points), even very early ones. This point is worth stressing, since three separate factors tend to obscure it. First, the word “emergence” suggests a process in time; in which case the framework (or perhaps better: its parts) would presumably be earlier than classical spacetime (or its parts). Second, the fact that quantum cosmology focuses on the early universe makes it very tempting to think of its proposals as concerning what temporally precedes the epoch which our present theories successfully describe. Third, many popular expositions of some of the specific proposals, including the Hartle-Hawking proposal, suggest the same (wrong!) idea. Thus one often sees a picture in which a cone-like spacetime structure (representing a cosmological solution of classical general relativity) is attached to a spherical shape that represents a Euclidean 4-manifold. This erroneously suggests that the bottom sphere is straightforwardly earlier than the classical cosmology represented by the open cone in the top half of the figure.

But the 4-manifold is not earlier: there is no temporal relation between the two halves represented in the figure (or their parts)! . . . In effect, they fall into two groups: the first group specifically concerns the no-boundary proposal; the second group returns us to the interpretative difficulties in common between the Euclidean program and . . . quantum geometrodynamics . . .—in particular, the cluster of problems called “the problem of time.” So first, recall that the no boundary proposal involves a sum over different manifolds M. So there is in any case no single bottom half-sphere, as the figure suggests—just as there is no single trajectory followed in a functional integral approach to elementary wave mechanics.

Second, the fact that a quantum tunneling amplitude can be given to a good approximation by e^−I/h where I is the value of the action of a solution of the classical dynamical equations with an imaginary time, does not mean that this solution has any ontological status in the quantum theory. The analogue of this point in the Hartle-Hawking proposal is, of course, the facts that the proposed 4-manifold has a Euclidean, not Lorentzian metric—and that in general relativity, a Euclidean spacetime has no more physical meaning than does an imaginary-time trajectory in normal physics. In fact, the interpretative difficulties become, if anything, even more obscure if we use (as we must) a complex metric.^[11]

Butterfield & Isham’s remarks seem to lead one toward embrace of an instrumental interpretation of the Euclidean “imaginary time” geometry. By this means one avoids the difficulties advanced by Smith, Guy, and Deltete. Or, perhaps, one could embrace a realist interpretation of the topological transformation picture (“nothing” transitions to a 3D space+1D time) as I am tempted to do. In such a view, physics and mathematics have difficulty modeling the concept of “creation ex nihilo.” So, when the universe emerges from “nothing,” “nothing” is actually modeled as a transition from “something” to “something.” A dimensionless point plays the role of “nothing.” I believe this is merely an interpretive difficulty that could point to an actual ex-nihilo origin for a universe.

Treating the non-classical physics instrumentally, or embracing the topological transition picture, still seems to bring us back to where we were with the “quantum foam” picture. The earliest era of the universe treated in a realist ontology is something like a GTR+ space-time. We still have a beginning.

Use of a Separate Degree of Freedom to Play the Role of Time

Some years ago, I queried cosmologist Martin Bojowald on this issue, an expert and proponent of loop quantum gravity. He indicated the following:

It seems to me that the conclusions you sketch are based on a severe truncation of the cosmological model, as it is commonly used in quantum cosmology. One analyzes the simplest case where it is essentially only the spatial volume which is left as the lone degree of freedom. This is what Hartle-Hawking and Vilenkin did, and also what is referred to in the article.

I suspect that this truncation is the reason for the conclusions of timelessness. In general relativistic systems one cannot formulate evolution with respect to an absolute time, but one can do so relationally. This requires the presence of suitable degrees of freedom (such as matter fields) which allow one to map different points in space-time to different values of the degree of freedom. In this case, the matter field can serve as a measure for time, which is pretty much what we actually do when we measure time with a clock or by looking at the planets or stars. Many quantum cosmological considerations, however, are based on truncations where such degrees of freedom are simply removed by hand. This simplifies some technical calculations, but makes the interpretation of results more complicated.

Matter fields in a bounce phase can certainly show a strong quantum behavior, in which case also the notion of time they provide may differ strongly from what we usually think of as time. But I do not think that this justifies the statement of timelessness. One can still decide what happened before and what happens after the bounce because there are some degrees of freedom which differ on both sides. And if gravity is quantized correctly, there is still a sense of causality.^[12]

Bojowald suggests that the Hawking-Hartle and Vilenkin methods are primitive, and the approximations used in building them may indicate that the truncation of time indicating a beginning may indeed be an artifact of failure to consider a more realistic condition with more physical degrees of freedom. In the specific case of Loop quantum gravity, the method “resolves” the GTR singularity by discretizing space in a complicated way and its mathematical forms are difference equations. Many LQG attempts at cosmological models suggest a “before the Big Bang” era. Studies usually pick something such as a scalar field to play the role of time, and map the volume of the universe on either side of the “Big Bounce.” This use of a physical degree of freedom to play the role of time in the theory is generic to many proposed quantum gravity toolsets. This can lead, though, to interpretive difficulties of its own.

For example, Martin Bojowald has recently argued that the bounce events of a cyclic model could represent a scenario similar to the arrow-of-time reversal models. He suggests that measurements of a state of the universe “after” a bounce might be unusable to derive knowledge of the state of the universe “before” the bounce. Information is lost through the bounce. Thus, the model contains “cosmic forgetfulness” as a salient feature. Similarly, an observer just “before” a bounce would find that attempts at predicting the post-bounce future suffer from cosmic forgetfulness as well. Bojowald interprets the situation as follows:

The kind of cosmic forgetfulness realized in this model provides an orientation of time, telling us not only which of the properties before the big bang can be forgotten, but also what direction “before the big bang” is. An observer after the bounce would be unable to reconstruct the full state before the bounce, but could easily predict the future development toward larger volume. This arrow agrees with the standard notion. Now asking how an observer before the big bang would experience the same situation, the answer is also clear: such an observer would be unable to determine the precise state at larger values of ϕ beyond the bounce, but could easily extrapolate the state to smaller values of ϕ. The state at smaller values of ϕ can be predicted, while the state at large values of ϕ is forgotten once the bounce is penetrated. Since one cannot forget the future, such an observer must be attributed a reversed arrow of time, pointing toward smaller ϕ. At the bounce, two arrows would emerge pointing in opposite directions as far as ϕ is concerned. In this sense, the model resembles [Carroll-Chen, Aguirre-Gratton and similar suggestions from other modeling teams using different methods].^[13]

Being careful to remember that authors sometimes employ rhetorical gloss, we see that Bojowald continues thus:

Taking the simplest models of loop quantum cosmology at face value is often seen as suggesting the big bang transition to be viewed as a smooth bounce, as one further element not just in a long history of the universe itself but also in a long history of bouncing cosmological models. Some indications, however, suggest otherwise. The bloomy scenario of loop quantum cosmology may well be this: a universe whose time-reversed pre-history we cannot access but which we grasp in the form of initial conditions it provides for our accessible part; a pseudo-beginning; an orphan universe, shown the rear-end by whatever preceded (and possibly created) it.^[14]

Would a quantum gravity resolution of the GTR singularity produce past eternality? Bojowald suggests it might produce a reversed arrow of time on the other side of the boundary. But, as the moments on one side of the boundary are in no sense earlier than the moments on the other side, there would be no infinite past (in a view of time that includes temporal becoming).

In fact, Heinz Dieter Zeh objects to the interpretation of the loop quantum gravity models as having a unidirectional arrow of time:

According to arguments used in loop quantum cosmology, the Wheeler–DeWitt equation (in this theory replaced by a difference equation with respect to a) can be continued through a = 0 to negative values of a. The configuration space of three-geometries is in this way duplicated by letting the volume measure assume negative values (turning space “inside out” while going through a = 0). Since the Hamiltonian does not depend on the newly invented sign of a, however, the Wheeler–DeWitt wave function must be expected to be symmetric under this parity transformation, too, in the absence of any artificial boundary condition. Its continuation would then have to be interpreted as an enlarged superposition of components that are all individually experienced as expanding universes. Since their WKB times, which represent classical times, can not be continued through a = 0, where the WKB approximation breaks down, the interpretation of negative values of a as representing pre-big-bang times is highly questionable. The fundamental arrow, including its consequence of decoherence with respect to a even outside the validity of a WKB approximation, must depend on some low entropy (no entanglement) “initial” condition in this time-like variable for all other (“spacelike”) degrees of freedom that occur as physical arguments of the Wheeler–DeWitt wave function. It would be hard to understand how the low entropy state at a = 0 could have been “preceded” by an even lower entropy at a < 0 in order to avoid a reversal of the thermodynamical arrow in the classical picture of an oscillating universe.^[15]

Suppose, though, that the arrow of time is unidirectional; what does the pre-Big Bang universe look like? If the universe away from the bounce is “classical,” one wonders whether the temporal coordinate in and near the bounce region is commensurable with the temporal coordinate in the “classical” regions said to be before and after the bounce. Why should one assume that? If there is a time, but it is incommensurable, then one still doesn’t have a primordial era. Why do we believe that if we pick some extra degree of freedom and assign it the role of time near and at the “bounce,” that this “‘clock” actually does tick off time on the same commensurable timeline as Lorentzian metric time in the classical eras? If the eras have incommensurable timelines, then what we appear to have is a causally disconnected multiverse rather than a cyclic model.

Recently, Bojowald (as part of a team) highlighted a related problem:

. . . the problem of time remains unsolved, affecting the right choice of dynamics. The problem is usually evaded (but not solved) by using specific choices of global internal times which tend to be unrealistic near the big bang, such as a free massless scalar or dust. As part of the problem of time, it is not known how to transform quantum wave functions or entire Hilbert spaces between different internal times, and therefore results found with one choice of global internal time do not necessarily hold for other choices. But if they depend on what time is used, they cannot be considered physical.^[16]

Different choices of the degree of freedom that represents the temporal dimension can yield different physical predictions for the universe. This seems especially problematic. What are the “real” physics? The problem seems to be generic in nature; i. e., not native to the specific paradigm of LQG. Perhaps the problem can be solved, as Bojowald et al. believe. But this method of bringing time to “full” quantum gravity states still seems problematic.

We should like to believe that time is grounded by some underlying reality, perhaps metaphysical, that is independent of physical measures such as clocks or arbitrary choices of physical degrees of freedom to “be” time. The origin of clocks could be representative of the origin of the physical (which is not necessarily the same thing as the origin of time).

If I need have no prejudice against beginnings nor see a necessity to have a full quantum gravity primordial era, where am I led? I am again attracted by the idea that GTR+ models can capture the “origin of clocks,” and thus, capture the “origin of the physical” sufficiently for our purposes.

Summary

What do we make of this? I think we’re led in two radically different directions. If I embrace time as fundamental, I seem led to something such as a GTR+ model (QG inspired corrections to GTR, within a GTR framework). The very problems we see with having a temporal dimension in QG physics are indicators toward a conclusion of a beginning to the physical (and perhaps time itself). Perhaps this comes in concert with a “tunneling-from-nothing” result, which one interprets as a genuine “creation-ex-nihilo.” Or I’m going to believe in quasi-classical trajectories (with QG-inspired features and endpoints) as the entities that comprise my ontology. My multiverse is real (not imagined), with an origin to independent trajectories.

One could summarize the options:

But one could drop my presupposition and deny the reality of time. In fact, theorists today are often talking in terms of synchronic emergence (bottom-up ontological structure with time acting similar to a spatial dimension in a 4D bloc) rather than diachronic emergence (arrival of the metric time of GTR from some more primitive temporal entity). In a synchronic view, a breakdown of space-time in quantum gravity doesn’t inform any discussion of a primordial era; rather, it refers to the problem of how there can appear to be space-time and scientists who do science in an evolutionary world, when the true ontology has entities that may be nothing like that. Where is the connection? The animating discussions deal with empirical coherence and the (in)dispensability of space-time. In short, could such a thing be true, but we can’t know it? Can space-time really be dispensed within a so-called “background independent” theory? The “nature of time” should be the topic for a future Greer-Heard event.

In short, if the world works the way we appear to experience it, I believe the Kalām argument ultimately goes through and one can embrace its conclusion of a transcendent cause for physical reality. To defeat the argument, one must argue convincingly how common terms such as “cause,” “time,” “nothing,” or “evolution” mean something very different from how the typical intelligent layman normally thinks of them. As Groucho Marx might have said, “who are you going to believe, me or your lying eyes?”

Sean Carroll’s Response

Much has been made of the claim that whether or not the universe had a beginning or is eternal is a theologically neutral statement; it is a physics statement. That may well be true. But let me give you a potentially relevant fact: if you go to Google, and you search for “Borde-Guth-Vilenkin Theorem,” 98 percent of the results are from theology. Not from cosmology.

Now, why would that be? It’s not because cosmologists don’t recognize the theorem as something true; it’s that: (1) they recognize that it is only a statement about the regime in which classical descriptions of space-time are good approximations, not a full statement about the actual universe; and (2) cosmologists are not invested in the answer. Cosmologists are invested in knowing the answer, they want to know whether or not the universe had a beginning or not. But they recognize we’re nowhere near being able to answer that question. And the BGV Theorem doesn’t get us very close to it. Whereas some theologians seem to be very invested in this, and therefore, they make a big deal about the BGV Theorem, I don’t think that the tendency to pick pieces of evidence that favor your position and bring them to prominence is something that distinguishes theists and atheists in any way; atheists do that much of the time. But it does seem to distinguish the subset of theists who make a big deal out of the BGV Theorem.

Remember, I told you about the Aguirre-Gratton Model. This is a classical space-time model that is absolutely eternal, that obeys the laws of the BGV Theorem, and would tend to be completely well-defined, and it never enters the quantum regime. I asked for an explanation of what sense that model is supposed to have a beginning in, and I haven’t yet heard one.

The issue with the Aguirre-Gratton model, just as with the Carroll and Chan model, is that there is a moment in time where the entropy is lowest. So, in our conventional understanding of time moving away from the period of lowest entropy, there is a point in time to the one direction of time and to the other direction, and we both call it time, moving forward. But this again, as I mentioned before, equivocates on the fact that there is no place for God to have created such a universe. So, unless this universe is fit into our explanatory framework, we have not really done our work here.

But the real issue, as Tim Maudlin alluded to, is that we all (physicists, theologians, people on the street) tend to reify the concept of space-time far too much. We live in a universe that is fundamentally quantum-mechanical, and the notion of space-time is fundamentally classical. But it is so useful (the classical space-time notion) that we tend to try to fit it into the framework of an ultimate theory even though we know that’s not the right language to use. If you want to get right the fundamental rules of reality, you have to talk the language of quantum mechanics, the language of wave functions, and Schrödinger’s equation. And you see this problem when James Sinclair quoted Quentin Smith. To the extent that I can appeal to myself as an authority, I promise you, everything in that quote by Quentin Smith was wrong. But I don’t blame him, because he was probably reading papers by physicists who were extremely sloppy in talking about what their theories meant. Hartle, Hawking, Vilenkin; whatever it was, we tend to talk in space-time terminology, even though what we are describing are wave functions and quantum states. The real answer is not that there is Euclidian time at one point and real time at another point; what there are are wave functions at all points. Sometimes, you can calculate them most effectively by using Euclidian time methods; other times, by using real time methods.

Remember, I gave you a theorem, the Quantum-Eternity Theorem, which seems to tell you in an ironclad way that the universe should be eternal, if it obeys the rules of quantum mechanics. I don’t recall any of the folks on the other side of the debate referencing that theorem. But you might want to know how is it even possible to have a universe that had a beginning, given that theorem, if quantum mechanics is the right answer. Well, every theorem has a little condition. The BGV Theorem’s says if the universe has an average expansion rate greater than zero. It sounds like a little technicality, but it’s actually crucially important. The Quantum-Eternity Theorem has a little condition that says, if the energy of the universe is not zero; if the energy of the universe is zero, then there is no strictly defined notion of time. And that is exactly the condition that applies to the Hartle-Hawking quantum universe, the quantum cosmology universe that does have a first moment. In that picture, time is emergent, not fundamental. So, as a cosmologist, I’m happy, no matter which way it turns out, but I know that we’re nowhere close to knowing the final answer.

William Lane Craig’s Response

I’m going to resist the temptation to respond to Sean Carroll’s remarks because that’s Jim Sinclair’s duty. But let me simply say that I was careful in my opening statement in the debate earlier to present the Borde-Guth-Vilenkin theorem as simply one of the most recent theorems that show that classical space-time had to have a beginning. Recall the boundary in superspace, which is implied by that theorem. The question is, is that the beginning of the universe, or is there something on the other side of the boundary? If there is something on the other side of the boundary, that’s the quantum gravity regime.

Here, Jim touches on very deep philosophical questions about what time is—or what Christopher Isham calls the “problem of time”—and this notion of space-time as an emergent reality.^[17] There’s a good deal of talk today in the philosophical literature about space-time as emergent. But as Reiner Hedrich explains, the notion of emergence here has to do with different levels at which physical reality is described.^[18] An emergent feature is one that doesn’t appear in the description of reality at the fundamental level, but at a higher level. The difficulty is, in these quantum cosmogonies, the quantum gravity era does appear to be temporally and causally prior to classical space-time, to the Planck time. And yet, that is incoherent, as Jim says. You can’t have diachronic emergence of time itself because you would have to already have time in order for time to emerge. So, you have to say that this is merely a synchronic emergence—that is to say, that this quantum gravity description is a description of the same reality, but just at a deeper level, or at a microscopic rather than a macroscopic level. And in that deeper reality, you could get rid of the initial singularity. But it is still the same reality; it’s just different levels of description. So, if classical space-time is finite in the past, so must be the quantum gravity era. It’s not as if the quantum gravity era can “stick out” before the classical space-time. That would be incoherent. It’s just different descriptions of reality at different levels.

Now what we must not do—and this leads me to comment on Dr. Carroll’s remarks—is privilege the fundamental level of description as somehow more real than what is in a higher-level description. I call this mistake “fundamentalism.” I think that people such as Dr. Carroll are guilty of being fundamentalists in this regard, thinking that because something doesn’t appear in a more fundamental description of reality (say, on a microscopic scale), it is less real, or even unreal, if it then appears on a higher level. That simply doesn’t follow. There’s no reason to privilege the lower level over the upper level.

Indeed, I would say that time is one of the most evident realities to us, inescapably real. The reality of time is even more evident than the reality of the eternal world. For I could be a brain in a vat with illusions of an external world around me, but my stream of contents of consciousness in succession, one after another, is undeniable and inescapable. Even the illusion of temporal passage is temporal passage. So, the reality of time, it seems to me, is one of the most basic, undeniable realities of metaphysics that there can possibly be. If time doesn’t appear on a fundamental, quantum level, then so much the worse for the ontology of that level! That simply implies that a description of reality on that sort of a scale doesn’t capture reality fully.

If you insist that this quantum gravity regime is, in some sense, temporal, even though not classically temporal, then, as I argued yesterday from Aguirre and Kehayias, it cannot be infinite in the past. A quantum state cannot endure forever doing nothing because it’s unstable. It would either produce the universe from eternity, if it’s causally sufficient for it, or it would never produce it. But it wouldn’t be possible that the universe—classical space-time—would appear just 14 billion years ago after having waited in a quantum state from eternity past.

James Sinclair’s Response

Thank you Dr. Carroll, it is a privilege to be criticized by you. [Tongue-in-cheek] Bill’s been criticizing me for years, so I’m used to that.

There are four salient points that I want to address. The first, about being theologically neutral—you brought it up in the context of BGV—I’m pretty sure I could have gotten Dr. Vilenkin to hold up a sign, saying, “It’s theologically neutral,” because he’s told me that many times. But certainly, I can’t deny what you’re saying about Google. It is of significant interest to people like me. As I said earlier, the notion of incomplete geodesics is relevant to the concept of a beginning, but as I was careful to say in my discussion of model tool sets, we do have to be careful about a naïve commitment to a particular toolset. And I think you’re on board with me on that, as per the discussion we had ourselves in our email.

One other thing I want to mention, and this actually addresses a point that I think several of the speakers on this side made, with regard to, especially, Dr. Maudlin, I believe he made this point. With regard to the practice of science and whether cosmology has anything to say; the fact that there isn’t certainty regarding this subject of a beginning, and therefore, we shouldn’t arrive at any conclusions. Well you see, in the realm that I live in, we practice a very different kind of science, but I think that the way it’s done is just as valid as what is done in academia. In my realm, you have to produce the best answer you can on a deadline, because there are decision makers who are making decisions on what is going to happen with building jets fifteen years in the future that are hopefully going to save the lives of pilots. And the key thing is that those decision makers are going to make their decisions whether I help them or not—whether they get the critical input they need or not. I don’t have the option to say, “I don’t know” just because the knowledge base is incomplete. I have to give them the best possible answer at the time, using the data, incomplete as it is. And being honest about it, about the error volume, or the different sizes of trade’s spaces, or assumptions, limitations, and constraints. So I look at that type of topic from a philosophy of science perspective very differently than you do. I think that you have to give the best answer you can right now. And part of the talk that I was going to give, that I had to cut out, had to do with the fact that we’re living our lives right now. I guess I’m disagreeing with Dr. Maudlin on another point. I very much believe that discerning the existence of God does help me make life choices. I call myself the problem child of Christianity: you’re not argued into the kingdom of God, essentially. I believe that it’s true. What I mean by calling myself a problem child is that I think that if you did have a universe that was created by God, there ought to be evidence of it.

And the other thing that I believe is that in the public square, if we’re going to deal with issues as to whether religious truth claims should have any currency at all, the only information we have to share with each other is publicly available information, which would have to be reason and evidence. I can’t show you my heart, and say, “Look, I believe I have the Holy Spirit.” I have to share with you this public evidence. So, that’s another reason why I’m interested in generating that.

I’m going to cede you the point with regard to Aguirre-Gratton. Dr. Vilenkin has written papers on this. He believes that model does have a beginning, but he uses what I would term an idiosyncratic definition of “beginning.”

Now however, I did talk to Dr. Aguirre, and he said, if I got him correct, that most of the geodesics do hit the boundary in his model. And that very few of them go past infinity, so I don’t know whether that leads to a conceptual difficulty or not, or whether I misinterpreted him. The relevant issue is that if “measure zero” worldlines trace to past infinite times, that can be an indication that the model shouldn’t be taken literally here, as per my earlier discussion of instrumental vice realist models.

But it’s very important when Dr. Craig spoke about whether universe concepts that are past eternal are viable. Well, he was repeating what Dr. Vilenkin said at Stephen Hawking’s conference for his birthday party in 2013—Dr. Vilenkin made that very strong claim. In the Blackwell Companion article that Dr. Craig and I wrote, what we said is that it was difficult to envision—not that it was impossible to envision—past eternal models. So, I’ll be willing to cede that point to you, and my last point will have to stop.

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