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God and Stephen Hawking. Is Quantum Cosmology God’s Undertaker?

This essay is intended as an ongoing debate about God and the origin of the universe. In our previous essay, we explained how the rise of evidence that the universe had a beginning posed a great threat to materialistic worldviews. Eroding the foundations of atheism, the idea that the universe had an origin appeared to have strong theistic implications – with God as the best-known explanation for the first cause.

But is this still the case? Have newer advances in science, especially in the field of quantum cosmology, provided better, more plausible explanations for the origin of the universe? Is it time to dismiss God from the realm of rationality, at last?

Stephen Hawking thought so.

Now be prepared. We are going to be talking about quantum cosmology. Things will get complicated, whacky, and blimmin confusing at times. So sit up, grab your coffee and let’s dive in.

Stephen Hawking and quantum cosmology

Stephen Hawking was an English theoretical physicist and cosmologist who passed away in 2018. He had a rare early-onset, slow-progressing form of motor neurone disease, a fatal neurodegenerative disease that affects the motor neurons in the brain and spinal cord, which gradually paralysed him over decades. And yet, despite his severely disabled condition, Hawking went on to become one of the most influential theoretical physicists in history. He was a mathematical genius, and his work on the origins and structure of the universe, from the Big Bang to black holes, revolutionised the field.

Though Stephen Hawking had helped to prove the singularity theorems with Roger Penrose in 1970 and George Ellise in 1973, he found their implication of an absolute beginning of time and space philosophically disturbing and unsatisfying. As a result, Hawking began to formulate a cosmological model that he hoped would eliminate the implication of a beginning to our universe.

He did so by applying the physics of the very small, known as “quantum mechanics,” to analyse the universe when it was very small. In so doing, he challenged that idea that the universe had a definite beginning, and posed an objection to the evidential basis for the cosmological argument discussed in our previous essay.

Quantum mechanics describes the interactions and motions of subatomic particles that manifest both wavelike and particle-like behaviour (here’s our introductory essay on the subject). Whereas the expansion of the universe has produced a vast spatial volume in the present, at some point in the finite past the universe would have been small enough that physicists would need to consider how quantum mechanical effects would influence gravity. Physicists think that, in that small space, Einstein’s theory of gravity (general relativity) would effectively break down.

Instead, many physicists have suggested that gravitational attraction would have worked differently since the early universe would have been subject to quantum mechanical principles and unpredictable quantum fluctuations. So far physicists have not formulated an adequate theory of “quantum gravity” that coherently synthesises general relativity with quantum mechanics. Nevertheless, Hawking applied quantum mechanical ideas about how gravity might work on a subatomic scale to describe the universe in its earliest state.

Hawking found, however, that in order to make a precise mathematical calculation about the probable state of affairs in the early universe, he needed to use a calculating device that required introducing the concept of imaginary time. He introduced imaginary time into one of Einstein’s mathematical expressions (called the spacetime metric) that describes the geometry (or curvature) of spacetime. Since this expression includes a time variable, Hawking simply equated time with ‘imaginary time’ to make it possible to calculate the probabilities associated with different possible early states of the universe. Mathematicians call this transformation a “Wick rotation.”

When hawking performed the Wick rotation, the resulting mathematical construct depicted a universe with spatial dimensions but no preferred temporal direction and no temporal beginning. Basically, the resulting mathematical depiction of the universe treated time as essentially another dimension of space. Consequently, Hawking eliminated the temporal singularity – at least as long as he continued to describe the geometry of space using imaginary rather than real time. His description of spacetime depicted a universe that is “finite but unbounded” by a specific temporal point of origin.

Basically, Stephen Hawking, using imaginary time, developed a “no boundary” model of the “beginning of the universe” to avoid a cosmological singularity, that is, an absolute beginning, while still retaining a finite past. His model depicted the initial segment of space-time as rounded off very much like the South Pole being the “beginning” of the earth and various circles of latitude playing the role of time itself. Just as you cannot ask what is south of the South pole, you can’t ask what came before the rounded off section of the initial segment of space-time. So there is no need for a beginning as such, and yet the past is finite.

In ‘A Brief History of Time’, Hawking presented this result as a challenge to the idea that the universe had a definite beginning in time. He argued that this mathematical model implied the universe would not, therefore, need a transcendent creator to explain its origin. After he explained how this mathematical manipulation eliminated the singularity, he famously observed:

“So long as the universe had a beginning, we would suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end; it would simply be. What place, then, for a creator?”

Hawking’s proposal also created the widespread impression that he has refuted the Kalam (first cause) cosmological argument for the existence of God. Certainly, Hawking presented this model as a challenge to the second premise of that argument, the statement that “the universe began to exist.” By the 1990s, Hawking single-handedly began to shift perception about the implications of the Big Bang theory.

Nevertheless, his key claim to have eliminated the need for a temporal beginning in the depiction of the universe proved vulnerable to an obvious critique. Physicists and philosophers pointed out that his decision to equate time with imaginary time has no physical justification apart from its expediency in making the calculations that Hawking wanted to make. Consequently, Hawking’s mathematical description of the geometry of spacetime lacks the applicability and intelligibility as a physical description of our universe. When Hawking substituted imaginary time for real time in Einstein’s mathematical expression, the resulting depiction of the geometry of spacetime did not correspond to anything in the real universe.

The use of imaginary time is a notion that is literally conceptually unintelligible if taken to depict reality as it really is – the model should be understood in an anti-realist way rather than an actual depiction of the real world. In fact, Hawking has acknowledged that his view is, indeed, not a realistic depiction of reality but, rather, a theory that merely has instrumental value. His model, therefore, belongs to the classification of useful fiction but did nothing whatsoever to undermine justified belief in the universe’s beginning.

So, the problem with Hawking’s proposition was not the mathematical technique he used, but instead the metaphysical interpretation that he assigned to the intermediate steps in his mathematical manipulations. The intermediate steps in his mathematical procedure produced an expression that does not describe the spacetime geometry of the real universe. Time, when confined to the imaginary axis of the complex plane, has no physical meaning. Hawking himself admitted this, and in his Brief History candidly described his use of imaginary time as a “mathematical device (or trick).”

Hawking acknowledged that once his mathematical depiction of the geometry of space is transformed back into the real domain with a real-time variable, that is, the domain of mathematics that does apply to our universe, then the singularity reappears. In his own words: “When one goes back to the real time in which we live, however, there will still appear to be singularities… Only if we lived in imaginary time would we encounter no singularities… In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down.”

Now there is also a second, obvious critique. The specific mathematical transformation that Hawking performed allowed him to treat time as a dimension of space for the purposes of his calculations. But collapsing time into space in this way, again, does not result in a mathematical expression with physical meaning, still less one that changes over time as our universe does. Though in general relativity, time and space are linked, they are treated differently. Time is not the same thing as space. Events occur in space, but also in temporal sequence. Collapsing time into space (or “spatializing time”) eliminates the possibility of describing the reality of our universe and renders Hawking’s mathematical description of the geometry of “spacetime” inapplicable as a description of our universe.

Therefore, the claim that Hawking disputed the basis for the cosmological argument is not true at all. The need for an initial singularity has not been eliminated.

But the story continues…

Hawking & quantum cosmology, round two 

Five years after the publication of Hawking and Hartle’s first technical paper on quantum cosmology, theoretical physicist Alexander Vilenkin formulated another version of quantum cosmology. Vilenkins’ theory did not attempt to eliminate the singularity. Instead, it presupposed the singularity and sought to explain how the universe came from it – indeed, from nothing physical at all. In effect, Vilenkin tried to describe the emergence of the universe as a physical process that does not require an external cause, therefore eliminating the cause of God in the cosmological argument.

Following Vilenkin, Hawking gave it another shot. Vilenkin’s formulation of quantum cosmology, like Hawking’s, depends upon an application of quantum mechanics to the physics of the early universe – specifically ‘wave-particle’ duality.

No one really understands wave-particle duality. It all started in 1801 when Thomas Young performed the famous “double-slit” experiment which showed that photons act as a wave. This is strange because photons are typically understood as particles, not waves. Since then, experiments performed in the 1920s (and later) confirmed that electrons, atoms, and other subatomic particles can behave as both particles and waves – exhibiting dual nature properties. Now, this doesn’t really make sense; how can a particle act as a wave? Or a wave as a particle?

The task of explaining, or at least accurately describing these bizarre results fell to physicists in the 1920s and 1930s. Physicist Erwin Schrödinger rose to the challenge and proposed a mathematical apparatus to characterise the phenomenon of wave-particle duality. The equation devised to do so – known as the Schrödinger equation (up there as one of the biggest scientific achievements of the 20th century), allowed physicists to predict, or better yet, calculate the probability that a subatomic particle would manifest itself at any given location once detected.

When solved, the Schrodinger equation generates what is known as a “wave function” which allows physicists to calculate the probability of the subatomic particle having a particular location upon detection. The wave function is a mathematical concept describing possibilities that may exist in space and time once the photon as a wave encounters an observer or detector and the “probability wave” collapses. The wave function also portrays what physicists call “superposition,” the wacky idea that prior to being observed subatomic particles “exist” as mathematical possibilities in multiple indeterminate states at once, occupying an actual location in space and time only after detection or being observed.

I know that probably sounded very confusing, and it is. The idea that a subatomic particle would have no definite character, but exists as a sort of mathematical probability until observed by a conscious agent puzzled physicists as well as common sense. The physics of the very small has turned out to be the physics of very, very weird.

Now, what’s all this got to do with cosmology? What does the physics of the tiny realm of subatomic particles have to do with the origin of the largest object we know – the universe? Well, as we mentioned before, since the universe is expanding, this implies a much smaller universe in the remote past. If we rewind all the way back, astrophysicists envision a time in the first fractions of a second after the big bang, when the universe would have been so small that quantum mechanics would have been relevant for understanding how gravity might work.

To describe how gravity would have worked in such a tiny space during the very earliest period of the universe, quantum cosmologists have developed an equation that synthesises mathematical concepts from quantum mechanics and general relativity. That equation is called the Wheeler-DeWitt equation, named after John Wheeler and Bryce DeWitt who developed it. Some physicists regard the equation as at least the first step in the development of a quantum theory of gravity.

Now before we move on too quickly, let’s recap. We mentioned that in ordinary quantum mechanics, the different solutions to the Schrödinger equation allow physicists to construct a mathematical expression called a wave function. The wave function, in turn, allows physicists to calculate the probability of finding a particle at a given position and time or to determine the probability of that particle having a specific momentum. Now in quantum cosmology, solving the Wheeler-DeWitt equation allows physicists to construct a wave function for the universe. That wave function then describes different possible universes with different possible gravitational fields – in other words, different curvatures of space and different mass-energy configurations. So, the universal wave function, which is the solution to the Wheeler-DeWitt equation, describes the different possible spatial geometries and configurations of matter that a universe could adopt. 

Solving the Wheeler-DeWitt equation allows physicists to determine the wave function of the entire universe and then to calculate the probability that a given universe exhibiting a specific gravitational field with a specific curvature mass-energy pairing will emerge. Now what does this have to do with the question of the origin of the universe? Understanding how we would use quantum cosmology as an origins theory of the universe requires keeping just three main elements in view:

  1. First, the origin of our universe with its specific attributes – the thing to be explained.
  2. Second, the universe wave function – the mathematical entity that does the explaining.
  3. Third, the Wheeler-DeWitt equation and the mathematical procedure for solving it – the alleged justifications for treating the universal wave function as an explanation for the origin of the universe.

With these three elements, Hawking developed a quantum cosmological model based on the Wheeler-DeWitt equation. This time, not so much to eliminate the singularity as the beginning of the universe, but instead to describe the origin of the universe as a consequence of a fundamental physical theory – a theory of quantum cosmology. Thus, Hawking mainly wanted to determine the wave function of the entire universe by solving the Wheeler-DeWitt equation. If he could do that, he could then calculate the probability that a universe such as ours with its specific gravitational field would emerge. If that probability shows that our universe is possible, or even probable, then Hawking would consider the origin of the universe explained by reference to a fundamental theory of physics.

Nevertheless, Hawking realised that solving the Wheeler-DeWitt equation would be intractable in the domain of real numbers. That’s where the mathematical calculating device involving imaginary time came in, again. When using imaginary time, the resulting mathematical expression – though one without physical meaning – temporarily depicted the geometry of spacetime without a temporal singularity.

Now it turned out that Hawking (and Hartle) did come up with a solution to the Wheeler-DeWitt equation that gave them a universal wave function that could generate a universe such as ours. Even so, there were a couple of catches.

First, Hawking and Hartle’s new quantum cosmology model did not actually eliminate the singularity at the beginning of the universe. Their use of what’s called “the path integral method” actually presupposed a spacetime singularity out of which numerous possible universes could emerge. Hawking only eliminates the depiction of a temporal beginning in one of the subsequent steps of a multistep calculating procedure, and only then by interpreting a mathematical expression with no physical meaning (due to the use of imaginary time) as if it had physical significance.

Another catch is that to solve the Wheeler-DeWitt equation and construct a universal wave function, Hawking needed to limit the number of possible universes under consideration. Hawking and Hartle constructed a wave function using the “the path integral method.” But they chose to do so only using certain paths. In particular, they only included paths that they knew would enable their mathematical formalism to produce a viable wave function that included universes such as our own. They chose, for example, only isotropic, closed, and spatially homogeneous universes and only those with a positive cosmological constant. These restrictions allowed a much smaller number of gravitational fields to emerge. Furthermore, Hawking and Hartle had to use approximation techniques that further restricted the degrees of mathematical problems. Nevertheless, after multiple mathematical steps, Hawking and Hartle did succeed in producing a wave function that included a universe like ours as a possible outcome.

Limiting degrees of mathematical freedom

Now, here is my main criticism. The crucial problem in the quantum cosmological models of Hawking-Hartle (And Vilenkin), is that by limiting degrees of mathematical freedom they are smuggling information into the mathematical calculation as they seek to explain it.

The Wheeler-DeWitt equation allows for an infinite number of solutions. To determine a unique solution – a unique universal wave function – theoretical physicists must carefully choose boundary conditions and impose them on the equation at the outset. Vilenkin describes the need for boundary conditions to restrict degrees of mathematical freedom on possible solutions to the Wheeler-DeWitt equation. He remarks:

“In ordinary quantum mechanics, the boundary conditions for the wave function are determined by the physical setup external to the system under consideration. In quantum cosmology, there is nothing to the universe, and a boundary condition should be added to the wheeler-DeWitt equation.”

This passage is revealing. It shows that physicists must arbitrarily restrict the infinite degrees of mathematical freedom inherent in the Wheeler-DeWitt equation in order to solve it. Yet the specific universal wave function that “explains” the origin of the universe in this way is entirely an artefact of the restrictions that the theoretical physicists themselves have placed on the possible solution to the Wheeler-DeWitt equation.

Hawking and Hartle also restricted degrees of mathematical freedom as a result of the approximation techniques used in their sum-over-histories method. The use of these techniques further constricted “superspace” in the process of finding approximate solutions to the path integral. Without these techniques, Hawking and Hartle could not solve the Wheeler-DeWitt equation.

My issue with this is that no physical theory justified the specific constriction of superspace that the use of the techniques entailed. To generate a realistic quantum cosmological model that in some sense explains the origin of our universe, physicists can’t just choose those constraints arbitrarily. Instead, to explain our universe as a possible outcome of a natural physical process, they must provide some non-question-begging physical rationale for the constraints that they choose.

From the standpoint of fundamental physics, the use of these methods and certainly the assumptions about the universe that Hawking and Hartle used to restrict superspace constitute ad hoc constraints on the process of constructing the universal wave function. As James Hartle himself said, “every time when we do one of those calculations, we have to use very simple models in which lots of degrees of freedom are just eliminated. It’s called mini-superspace… It’s how we make our daily bread, so to speak.”

Daily bread or not, Hawking and Hartle’s assumption about the kind of universe they could consider in the construction of the universal wave function clearly appropriated knowledge of the properties of our universe in a question-begging way. They effectively smuggled information into their calculation by winnowing the region of superspace under consideration, so as to ensure that the paths through superspace that they summed would produce a universal wave function that included universes with properties similar to our own. In other words, they designed  a mathematical procedure and limited inputs into it, so as to give “the right answer.” 

Anytime someone elects one option and excludes another, they input a bit of information into the system. Thus, the choice to exclude a nearly infinite number of possible mathematical solutions to the Wheeler-DeWitt equation, whether by a) directly imposing boundary conditions on the equation, b) limiting the possible universes under consideration when constructing the universal wave function (Limiting paths through superspace) or c) both, represents an enormous input of information into the mathematical equations and procedures that quantum cosmologists use to model the origin and development of the universe. The source of that “extra information” is precisely what is the issue. While Hawking and Hartle tacitly acknowledged this issue, Hawking seemed to sweep it under the rug and never addressed it in his books.

Significantly, the choice of these constraints occurs entirely because of the decision of an intelligent agent – in particular, that of a theoretical physicist. Neither the Wheeler-DeWitt equation itself nor any deeper theorem of gravity or other fundamental physical theory determines the choice of these boundary conditions and constraints. They are selected with a goal in mind. In all modelling of the origin of the universe using quantum cosmology, intelligent agents must restrict the degree of mathematical freedom to generate a desired outcome, a wave function that includes our universe. Both Hawking-Hartle and Vilenkin inadvertently model the need for a designing intelligence to exclude some options and select others – that is, to input information – in order to achieve an intended outcome.

The point is, even if you could explain the origin of matter, energy, space and time from nothing, or from nothing but the mathematically expressed laws of physics, you would still not be able to explain the origin of the information necessary to express and solve the equations that supposedly explain the origin of the universe. Therefore, these Quantum cosmological theories still subtly depend upon the activity of a mind to model the origin of the universe. So if quantum cosmology provides the correct model for the origin of the universe, then mind, not just matter, played a causal role in the ultimate origin event. A prior intelligent design is implied, which has strong theistic implications.

In this theme, quantum cosmology does not dispense with theism as an explanation for the origin of the universe, but instead implies the need for an intelligent agent to breathe, if not “fire into the equations,” as Hawking wondered, then certainly specificity and information. Thus, it invokes something akin to the biblical idea that “in the beginning was the Word.” And that’s not nothing.

The origin of the universe as a consequence of physical law

As you may have found so far, quantum cosmology can seem puzzling and paradoxical, to put it mildly. Now in this section I am going to divert our attention to more obvious issues, one’s more easily understood.

Hawking, in his book ‘The Grand Design’, wrote “because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist.”

This was not the slam dunk statement he thought it was.

Firstly, attempting to explain how everything came from nothing by claiming that because of the principles of quantum mechanics, something will come from nothing, is really just smuggling something into “nothing.” This supposed “nothing” has specific properties but only “things” have properties.

Secondly, like Hawking, proponents of quantum cosmology often attempt to model the origin of the universe as a consequence of a deeper physical law or theory. Now when Hawking says “a law such as gravity” explains the origin of the universe, he refers to the whole mathematical superstructure of quantum cosmology, the universal wave function, the Wheeler-DeWitt equation, and current ideas about quantum gravity. He also assumes that the laws of physics cause or explain specific events, including the origin of the universe.

This is a category mistake. 

Causes and scientific laws are not the same thing. Causes are typically particular events that precede other events. Laws, by contrast, describe general relationships between different types of events or variables. The law of gravity does not cause material objects or space and energy to come into existence; instead, it describes how material objects interact with each other once they already exist. The laws of physics represent only our description of nature. Descriptions in themselves do not cause things to happen.

For example, the simple law of arithmetic: 1+1 = 2, never brought anything into existence. If I saved £100 one month, and then £100 the next, the laws of arithmetic will explain how I now have £200. But if I don’t save any money and simply leave it to the laws of arithmetic to increase my savings, I’ll be disappointed. To think that laws can produce the universe is like saying you can create money by simply doing sums.

The world of strict naturalism in which clever mathematical laws all by themselves bring the universe and life into existence is pure (science) fiction. Theories and laws do not bring matter or energy into existence. To say that the laws of nature can explain where all the matter, energy, space and time of the universe came from is like saying the longitude and latitude lines on the map explain how the Hawaiian Islands ended up in the middle of the Pacific Ocean. The laws of nature may allow for the universe and give rise to its structure, but create it? That would be a  misunderstanding.

So Stephen Hawking’s claim that the laws of science or “the law of gravity” can explain “why there is something rather than nothing” betrays a deep philosophical confusion about what the laws of physics can do. Laws of nature describe, typically in mathematical terms, how nature operates and how different parts of nature interact with one another, but they don’t cause the natural world to come into existence in the first place. This suggests the futility of waiting for the discovery of some new law of nature or a “theory of everything.”

No law of nature can close the causal discontinuity between nothing and the origin of nature itself.

Now you might ask, couldn’t quantum cosmology include a law that specifies some material antecedent event as the cause of the origin of the universe? Couldn’t the universal wave function and/or the Wheeler-DeWitt equation, conceived as a proto-law of quantum gravity, specify a material antecedent cause for the origin of matter, space, time and energy?

The answer is no.

The universal wave function merely describes the possible universes with different gravitational fields that could arise from the singularity. Without the wave function, no physical universe, and thus no possible physical causal antecedent, would have existed.

Recall that the universal wave function merely describes possible universes with different possible gravitational fields.  These possible universes represent outcomes – universes that could come into existence. The universal wave function just describes the “superposition” of all the universe with different spatial geometries and configurations of mass-energy that could exist without specifying any antecedent that might cause one of those universes, as opposed to all the others, to come into existence. How could it? Before matter, space, time and energy first arose, no such entities existed. Moreover, in the main models of quantum cosmology, the outcomes described by the universal wave function arise from an initial temporal singularity of zero spatial volume. Quantum cosmology presupposes this singularity but does not provide a physical cause or explanation for the origin of the universal wave function or the possible universes it describes that may emerge out of the singularity.

Both the Wheeler-DeWitt equation and the curvature-matter pairings in superspace represent purely mathematical realities or physical possibilities. But these mathematically possible universes have no necessary physical existence. The purely mathematical character of quantum cosmology – even if conceived as a proto-law of quantum gravity – renders it incapable of specifying any material antecedent as a physical cause of the origin of the universe.

How, then, do naturalists maintain that purely mathematical entities bring a material universe into being in time and space? In other words, how can a mathematical equation create an actual physical universe? In A Brief History of Time, Stephen Hawking asked, “what is it that breathes fire into the equations and makes a universe for them to describe?”

This all got me wondering, what really is the relationship between the mathematics of quantum cosmology and the material universe? Alexander Vilenkin asks whether laws are not mere descriptions of reality and whether they can have an independent existence on their own? He continues, “In the absence of space, time, and matter, what tablets could they be written upon? The laws are expressed in the form of mathematical equations. If the medium of mathematics is the mind, does this mean that mind should predate the universe?”

It seems that the laws that some physicists invoke to explain the origin of space (and energy) are mathematical descriptions that exist only in the minds of physicists – in which case they have no power to generate anything in the natural world external to our minds, let alone the whole universe. In other words, quantum cosmology suggests either a kind or magic where human maths creates a universe, or Mathematical Platonism. 

Mathematical Platonism asserts that mathematical concepts or ideas exist independently of the human mind. This view suggests two possibilities, either mathematical ideas exist in an abstract transcendent realm of pure ideas, or mathematical ideas reside in and are from a transcendent intelligent mind.

Putting this all together, we have three distinct ways of thinking about the relationship between the mathematics of quantum cosmology and the material universe: 

  1. These mathematical expressions exist solely in the human mind and somehow produce a material universe; or
  2. These equations represent pure mathematical ideas that exist independently of the human mind in a transcendent, immaterial realm of pure ideas; or
  3. These equations exist in and issue from a preexisting transcendent mind.

Of those three options, I would argue, based on our uniform experience, that the third makes the most sense scientifically. Maths can help us describe the universe, yet we have no experience of mathematical equations actually creating material reality. Material stuff can’t be conjured out of mathematical equations, since in our experience maths has no causal powers by itself apart from intelligent agents who use it to understand and act upon nature. Our experience shows that only minds can use mathematical ideas to influence the structure of matter. Therefore, by claiming that the laws of physics explain why there is something rather than nothing, these physicists implicitly affirm a metaphysics that comports better with theism than with scientific atheism or materialism. 

We also have no experience of mathematics existing apart from our minds. Yet we do have a wealth of experience of ideas that start in the mental realm and by acts of volition produce entities that embody those ideas. The laws of physics are themselves information-rich expressions that imply prior mental activity, so even if you could explain the origin of matter and energy from ‘nothing’, you can’t explain the origin of information that gives us the structured universe we have.

The nature of information found in the physical laws is inseparable from the reality of an intelligent source. So whilst General Relativity predicts a beginning for the universe, Quantum Mechanics instead gives us evidence for a consciousness behind it all. Thus, Hawking’s attempt to explain the origin of the universe within a naturalistic worldview failed, but instead, did quite the opposite.

To summarise: if quantum cosmology implies a realm of mathematical ideas and objects preexisting the universe, then those ideas must have a transcendent mental source – they must reflect the contents of a preexisting mind. When Vilenkin himself tumbles to this realisation, however briefly, he raises the possibility of a decidedly theistic interpretation of quantum cosmology.

What about quantum tunnelling?

But what about the process of quantum tunnelling to which quantum cosmologists refer? Does that provide a physical mechanism, rather than just a mathematical equation, for explaining the origin of the universe?

Now you may be asking, “what even is quantum tunnelling?” Quantum tunnelling in ordinary quantum mechanics refers to a process by which a physically bounded subatomic particle can overcome a potential energy barrier even though the particle in question lacks sufficient kinetic energy to do so. It’s tricky to explain, so perhaps this one-minute video will help – What is Quantum Tunneling?

In the subatomic realm of quantum mechanics, the wave function that allows physicists to determine the probability of finding a given subatomic particle in a given place also admits the possibility of finding that particle on the other side of a potential energy barrier, a barrier that the subatomic particle cannot overcome based solely on its kinetic energy (if only classical mechanics is applied).

Quantum cosmologists have appropriated this idea by drawing an analogy between energy barriers to enclosed subatomic particles, and energy barriers to the development of an expanding universe. In his quantum cosmological model, Vilenkin posits the existence of a universe beginning in a singularity. As soon as the universe begins to expand, its continued expansion would, according to Einstein’s field equation, be opposed by an increasing gravitational energy barrier resulting from a matter field that Vilenkin assumes would be present in that expanding universe. But that energy barrier would push the universe back to a singularity. Therefore, Vilenkin’s “tunnelling wave function” suggests the possibility that the initial universe that emerges out of the singularity could overcome the gravitational energy barrier, thus allowing it to continue expanding.

He constructs his “tunnelling wave function” by assuming a singularity (i.e. a universe with a beginning) that can tunnel into an expanding universe. Vilenkin’s “tunnelling wave function” determines the probability that the nascent universe he presupposes will tunnel into a particular state. Hawking and Hartle envision tunnelling as an event that converts a preexisting closed universe (described by a wave function) into a continually expanding universe. In their case, they construct a wave function that describes possible universes that could exist before the postulated tunnelling event would occur. Yet, in both cases, quantum cosmologists must presuppose the existence of a universe. But that presupposes the very thing, the origin of which, they are attempting to explain. Philosopher of physics Willem Drees notes: “Hawking and Hartle interpreted their wave function of the universe as giving the probability for the universe to appear from nothing. However, this is not a correct interpretation, since the normalisation presupposes a universe, not nothing.”

To summarise: a universe must first exist with possible properties before quantum cosmologists can construct the universal wave function that describes those properties as a superposition. In fact, the mathematics of quantum cosmology begins by describing a universe already presupposed to exist. It has to. As the tunnelling event that Hawking and Hartle invoke occurs after the origin of the universe, quantum tunnelling scenarios attempt to account for the evolution, not the origin, of the universe.

Recall that in the double-slit experiment a photon in superposition within that experimental apparatus logically precedes the solution to the Schrödinger equation – a wave function that enables physicists to describe the probable behaviour/properties of the photon. In the same way, a universe with certain possible properties logically precedes the mathematical procedures that produce a solution to the Wheeler-DeWitt equation – a universal wave function that allows assigning definite probabilities to the different possible properties of attributes that the universe could possess. Thus, the mathematical properties that quantum cosmologists use to produce a wave function to explain the origin of the universe tacitly presuppose the existence of a universe.

Conclusion: Quantum tunnelling does not provide a quasi-mechanistic explanation for the origin of the universe.

Is quantum cosmology God’s undertaker or God’s servant?

If we are willing to be honest with ourselves, then we should admit the growing verdict from quantum cosmological models provides a far better support for theistic worldviews than atheistic. Quantum cosmology has not foiled the return of the God hypothesis. Not even close.

Quantum cosmologists, in particular Stepehen Hawking, posed quantum cosmology as an alternative to the manifestly theistic implications of the big bang theory and Hawking’s own proof of a cosmological singularity. Hawking argued that quantum cosmology had undermined the case for the existence, or at least the need to posit the existence, of a transcendent creator. As presented by Hawking, quantum cosmology provided the ultimate scientific counterargument to the God hypothesis. And yet, in truth, the opposite has been the case. Quantum cosmological models appear to presuppose prior intelligence, therefore having strong theistic implications.

Put both atheism and theism side by side and quantum cosmology leans to the theists, not the materialistic or naturalistic worldviews of atheism. Hawking did not trounce the requirement for a transcendent cause to our universe. God still stands as the best explanation so far, as shown in our previous essay.

For more on quantum cosmology and the God hypothesis, read Chapter 17 – 19 of ‘Return of the God Hypothesis’ by Philosopher of Science, Stephen C.Meyer.

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