Throughout the 20th century, breakthroughs in cosmology brought humanity face-to-face with one of life’s biggest mysteries: how and why did the universe come into being? Thinkers from all walks of life—scientists, philosophers and theologians—wrestled with this question. For a while, naturalistic explanations for the universe’s origin felt puzzling and even counterintuitive. In contrast, the idea of a creator God—a transcendent and foundational consciousness—seemed to fit the attributes of the first cause.
Yet, as the sands of time continued to shift, the winds of intellectual revolution began to stir. Just as naturalistic explanations appeared to be dwindling, a bold and innovative perspective arose, challenging the long-standing dominance of the divine explanation.
Enter the realm of quantum cosmology, a daring and cutting-edge field born from the union of quantum mechanics and general relativity. Many naturalists are now turning to quantum cosmology, hoping that its advancements might provide naturalistic explanations for the existence of the universe.
Could quantum cosmology finally crack the code of how—and why—the universe began? Does it provide more persuasive, naturalistic explanations for why the universe exists?
Stephen Hawking believed so.
Now be prepared: quantum cosmology is a confusing and challenging field, known for its perplexing concepts and intricate theories that may seem baffling or even counterintuitive at times. Don’t be disheartened if certain aspects seem challenging to understand; after all, no one truly understands it in its entirety. The confusing nature of quantum cosmology is what makes it so interesting.
(*The following is an excerpt from “Does the Universe Paint God Out of the Picture?” by Luke Baxendale. This is part three of four in the book. It may be helpful to read part two first.)
Stephen Hawking and Quantum Cosmology
Stephen Hawking, an English theoretical physicist and cosmologist, was an extraordinary individual who defied the odds. Despite battling a rare early-onset, slow-progressing form of motor neurone disease that gradually paralysed him over decades, Hawking emerged as one of history’s most influential theoretical physicists. A mathematical prodigy, his groundbreaking work on the origin and structure of the universe, spanning the Big Bang to black holes, revolutionised the field.
Although Hawking played a crucial role in proving the singularity theorems alongside Roger Penrose in 1970 and George Ellis in 1973, he found their implications of an absolute beginning of spacetime philosophically unsettling. As a result, Hawking began to formulate a cosmological model that he hoped would dispel the implication of a beginning to our universe.
So, in 1981, Hawking gathered with some of the world’s leading cosmologists at the Pontifical Academy of Sciences, a vestige of the coupled lineages of science and theology located in a grand villa in the gardens of the Vatican. There, Hawking presented a revolutionary idea: a universe that emerged from nothing, but with no definitive beginning or end.
But how can a universe emerge from nothing and still have no clear beginning? Hawking proposed that near what might be considered the beginning of the universe, time behaves like a spatial dimension, resulting in a universe that is self-contained and without a boundary. This implies that there is no distinct point at which the universe began; instead, it simply “is” in a manner that does not require an external cause or a specific moment of creation.
Hawking’s bold proposal hinged on the application of quantum mechanics, the physics of the infinitesimally small, to analyse the universe at its nascent stage. In doing so, he contested the traditional notion of a ‘definite beginning’ and presented a formidable challenge to the foundation of the Kalam cosmological argument.
Quantum mechanics (QM) is the study of how the world operates at very small scales, where things can become quite strange. QM describes the interactions and motions of subatomic particles that exhibit both wave-like and particle-like behaviour. While the universe today is vast and expansive, at some point in the finite past, the universe would have been so small that physicists would need to consider how quantum mechanical effects would influence gravity. It is thought that in such a small space, Einstein’s theory of gravity (general relativity) would no longer be applicable.
Many physicists have proposed that gravitational attraction would have functioned differently in the early universe, as it would have been subject to quantum mechanical principles and unpredictable quantum fluctuations. Although no adequate theory of “quantum gravity” that coherently synthesises general relativity with QM has been formulated yet, Hawking applied quantum mechanical ideas about how gravity might operate on a subatomic scale to describe the universe in its earliest state. In collaboration with James Hartle, Hawking developed a quantum cosmological model based on the Wheeler-DeWitt equation. They called this their “no-boundary proposal,” which was fully formulated in a 1983 paper.[i]
Hawking and Hartle’s quantum cosmology applies quantum mechanics to understand the physics of the early universe, particularly focusing on the concept of wave-particle duality. The concept of wave-particle duality is not well understood. It was first observed in 1801 when Thomas Young conducted the famous “double-slit” experiment, which demonstrated that photons act as waves. This was peculiar because photons were typically considered particles, not waves. Subsequent experiments in the 1920s and later confirmed that electrons, atoms, and other subatomic particles could exhibit dual-nature properties, behaving as both particles and waves.
Physicists in the 1920s and 1930s sought to explain or at least accurately describe these strange results. Erwin Schrödinger developed a mathematical framework to characterise wave-particle duality, enabling physicists to predict or calculate the probability of a subatomic particle being in a particular location once detected.
When solved, the Schrödinger equation yields a “wave function,” allowing physicists to calculate the probability of a subatomic particle being found in a specific location upon detection. The wave function is a mathematical concept describing possibilities that may exist in spacetime once the photon, as a wave, encounters an observer or detector and the “probability wave” collapses. The wave function also portrays “superposition,” the strange idea that, prior to being observed, subatomic particles exist in a superposition of states, which means they are simultaneously in multiple possible states. However, when an observation or measurement is made, the wave function collapses, and the particle assumes a definite state in a specific location in space and time.
It’s important to clarify that the term “observed” in this context does not necessarily imply that a conscious observer is needed for the wave function to collapse. The collapse of the wave function can also occur through interaction with the environment, as described by decoherence theory. This aspect of quantum mechanics is still debated and open to interpretation. Admittedly, it’s all rather perplexing. The notion that a subatomic particle exists without a definite character, represented as a mathematical probability until it interacts or is observed, challenges both physicists and common sense alike. Indeed, the physics of the very small has proven to be the physics of the utterly bizarre.
So, how does this connect to cosmology? In the first fractions of a second after the Big Bang, the universe would have been so small that quantum mechanics would have been crucial for understanding how gravity functioned. To understand how gravity would have operated in such a confined space during the very earliest stage of the universe, scientists have crafted an equation that fuses mathematical concepts from quantum mechanics and general relativity. This equation is known as the Wheeler-DeWitt equation, named after its developers, John Wheeler and Bryce DeWitt. Many physicists consider this equation to be, at the very least, an initial step towards the development of a quantum theory of gravity. It represents an effort to unify general relativity and quantum mechanics within an approach known as “quantum geometrodynamics.” It’s an equation that describes the quantum state of the universe without any explicit time dependence. This absence of time is a peculiar feature that gives rise to what physicists call the “problem of time” in quantum gravity.
Let’s pause for a moment to recap so things stay clear. In standard quantum mechanics, various solutions to the Schrödinger equation enable physicists to create a mathematical expression known as a wave function. This wave function, in turn, allows them to calculate the probability of finding a particle at a given position and time, or to determine the probability of the particle possessing a specific momentum.
In quantum cosmology, however, the focus shifts to the universe as a whole, and this is where the Wheeler-DeWitt equation comes in. Solving this equation enables physicists to formulate a wave function for the entire universe. The Wheeler-DeWitt equation is conceptually similar to the Schrödinger equation in that it involves a wave function. However, while the Schrödinger equation’s wave function describes the quantum states of particles or fields, the wave function in the Wheeler-DeWitt equation describes quantum states of the entire universe. It describes a range of potential universes, each with distinct gravitational fields, which can be understood as different curvatures of space and unique mass-energy configurations. In other words, the universal wave function, derived from the Wheeler-DeWitt equation, outlines the various spatial geometries and matter configurations that a universe could assume, revealing the probability of a universe emerging with specific gravitational and mass properties.
By solving the Wheeler-DeWitt equation, physicists can determine the wave function for the entire universe and subsequently calculate the probability of a given universe with a particular gravitational field and a distinct curvature mass-energy pairing coming into existence.
So, to understand how quantum cosmology could be used as a theory that explains the existence of the universe, it’s crucial to focus on three key elements:
- The existence of our universe with its unique attributes—the phenomenon that needs to be explained.
- The universal wave function—the mathematical construct that provides the explanation.
- The Wheeler-DeWitt equation and the mathematical process for solving it—the justification for using the universal wave function as an explanation for the universe.
Stephen Hawking developed a quantum cosmological model based on the Wheeler-DeWitt equation to describe the universe as a consequence of a theory of quantum cosmology. His primary goal was to determine the wave function of the entire universe—a mathematical expression that encapsulates all possible states of the universe. By solving the Wheeler-DeWitt equation, they aimed to calculate the probability of a universe like ours, with its specific gravitational field and physical properties, coming into existence. If that probability showed that our universe is possible or even probable, Hawking believed this would provide a fundamental explanation for the universe’s existence based on the laws of quantum physics.
Together, Hartle and Hawking developed a formula that described a universe without a clear beginning—the so-called “wave function of the universe” that encompasses the entire past, present, and future. Their solution to the Wheeler-DeWitt equation suggested that space and time could emerge smoothly from a quantum state, bypassing the need for a singularity starting point like the traditional Big Bang. This concept challenges notions of creation and, consequently, the idea of a creator. In essence, they discovered a solution to the Wheeler-DeWitt equation that produced a universal wave function capable of generating a universe such as ours.
However, there were a few complications along the way…
The Limitations of Imaginary Time in Explaining the Universe
Hawking realised that accurately calculating the early universe’s likely state was impossible within the framework of real time. To address this problem, he introduced the concept of imaginary time. Here’s the gist: imagine real time as a straight arrow, moving through the past, present, and future in a line. In contrast, imaginary time runs perpendicular to this—almost like a second dimension of time. It opens the possibility for events to unfold in ways we don’t experience in our linear, real-time world. Here is a diagram I found to help explain:
But what exactly is imaginary time? In theoretical physics, its time treated as an imaginary number—specifically, real time multiplied by the square root of -1 (represented as “i” in mathematics). This concept is used in certain areas of theoretical physics to simplify calculations. Hawking applied the idea of imaginary time to Einstein’s spacetime metric, a mathematical framework that describes the geometry and curvature of spacetime. By equating time with imaginary time, Hawking could calculate probabilities associated with various early states of the universe.
This transformation, called the “Wick rotation,” is a mathematical technique that rotates the time axis in the complex plane by 90 degrees, simplifying calculations and making certain problems more tractable. It is important to note that the Wick rotation is a mathematical technique, and the concept of imaginary time should not be confused with a physical interpretation of time.
After performing the Wick rotation, his model of the universe no longer had a clear starting point—no singular moment of creation. In this imaginary-time universe, time became a dimension similar to space. It was “finite but unbounded,” by a specific temporal point of origin.
This reimagining led to Hawking’s famous “no boundary” proposal. This model avoided a cosmological singularity—an absolute beginning in time—while still preserving a finite past. He envisioned the early universe as having a rounded geometry, much like the curved surface of the Earth. In this analogy, the South Pole represents the “beginning” of the universe, and the circles of latitude represent the passage of time. Just as it is meaningless to ask what lies south of the South Pole, it becomes nonsensical to ask what occurred “before” the rounded-off section of spacetime in Hawking’s model. This model implies no need for a beginning as such, yet the past remains 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 suggested the universe would not need a transcendent creator to explain its existence. 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?”[ii]
Hawking’s proposal sparked widespread belief that he had dismantled the Kalam cosmological argument for God’s existence, particularly its claim that “the universe began to exist.” By the 1990s, Hawking single-handedly began to shift perceptions about the Big Bang Theory’s implications.
Nevertheless, Hawking’s approach relied on a clever but controversial mathematical move: replacing real time with “imaginary time.” While this substitution worked within the equations, it lacked physical justification beyond its mathematical convenience. Imaginary time, an abstract concept, doesn’t correspond to anything we observe in the physical universe. Essentially, it’s a tool for simplifying calculations, not a literal description of our reality.
In reality, Hawking’s mathematical trick altered the equations in such a way as to disassociate the new time variable from anything real in the physical universe. Imaginary time, a notion conceptually unintelligible if taken to depict reality as it is, should be understood as an anti-realist tool rather than an actual depiction of the real world. Hawking himself acknowledged that his view was not a realistic depiction of reality but rather a theory with instrumental value.
The problem wasn’t with Hawking’s maths—it was with how he interpreted it. His use of imaginary time produced a model that didn’t describe our universe’s actual spacetime geometry. Time, when confined to the imaginary axis of the complex plane, loses its physical meaning. He took a mathematical expression which lacks direct physical meaning (due to the incorporation of imaginary time) and spoke of it as if it bore physical significance. The concept of imaginary time is an abstract mathematical tool and is not directly observable or testable. It’s difficult to interpret what imaginary time would mean in the context of our universe, as our experience and understanding of time are based on real time. His model, therefore, belongs to the classification of useful fiction but did not undermine the justified belief in the universe’s beginning.
Hawking was aware of these issues, and in his Brief History, he candidly described his use of imaginary time as a “mathematical device (or trick).” He acknowledged that once his mathematical depiction of the geometry of space is transformed back into the real domain with a real-time variable, the domain of mathematics that applies to our universe, 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 spacetime and at which the laws of science break down.”[iii]
Questioning the Absence of a Singularity in Hawking and Hartle’s Universe Model
Another challenge arises in Hawking and Hartle’s model when considering their use of the path-integral method, a technique introduced by Richard Feynman in QM. This method is widely used in QM to sum up mathematical expressions describing the potential paths of quantum particles, like electrons or photons. For example, in QM, if a particle travels from point A to point B, it doesn’t follow a single path; rather, it simultaneously explores every possible path. The path integral method determines the probability of a particle’s movement by considering the contributions of all these paths, leading to the particle’s final behaviour as a combination of all possible paths.
When applying this concept to the universe’s history, Hawking and Hartle adapted the path-integral approach to account for all conceivable historical trajectories or ‘paths’ that the universe might have taken. This led them to propose a finite but boundaryless universe, utilising complex (imaginary) time paths, which contrasts with the singular origin suggested by classical Big Bang Theory. In their model, they construct a ‘universal wave function’ within ‘superspace’, a conceptual framework representing all possible geometries and matter configurations of the universe. This includes calculating the probabilities of various universe configurations, thereby including the likelihood of universes like ours emerging.
However, their model still assumes some form of pre-existing reality—such as physical laws, a quantum vacuum, or another fundamental structure. To apply the path-integral method—or any quantum mechanical approach—to the entire universe, there must already be a general concept of what constitutes the “universe.” This implies a need for some form of pre-existing structure or framework within which the mathematics can be applied. This reliance on pre-existing conditions means that the model does not really resolve the question of how or why the universe exists in the first place.
Although the “no-boundary” model replaces the classical Big Bang singularity with a quantum framework, the model itself depends on a specific set of initial conditions and physical laws that must already be in place for the universe to evolve as described. For instance, it presupposes boundary conditions such as Ψ = 1 at vanishing spatial volume (a → 0) and assumes the prior existence of quantum mechanical principles, including path integrals, configuration spaces, and wave function dynamics. These prerequisites effectively serve as a de facto origin point, as they establish the immutable rules governing how spacetime emerges from the quantum vacuum.
While the proposal smooths out the infinite density of a physical singularity by introducing a four-dimensional geometry in imaginary time, this merely replaces a temporal starting point with a conceptual one. The quantum formalism itself becomes a kind of non-physical “singularity,” requiring an irreducible mathematical foundation—such as superspace, quantum gravity axioms, and boundary rules. Hawking’s claim to have dismissed a temporal beginning relies on retroactive interpretations of the model’s multi-step formalism rather than eliminating the causal prerequisites altogether. This approach shifts rather than resolves the problem of origins: the proposed quantum emergence still relies on a structured, preconfigured framework that raises similar metaphysical questions about why these specific quantum preconditions exist in the first place.
In essence, while the mathematical framework would appear to avoid physical singularities, it does not remove the need to explain why these particular quantum preconditions are there at all. Hawking’s dismissal of a temporal beginning occurs only at a later stage in this multi-step calculation process, leaving the question of ultimate origins unresolved.
I’m not going to lean too hard on this argument—there are bigger issues to consider. For those with a background in quantum cosmology, you can decide for yourself if this reasoning holds water, though we could spend much more time here. This argument isn’t as widely debated as the challenges tied to their use of imaginary time. That said, there’s an interesting tension here: while the Hartle-Hawking model offers a valuable perspective in quantum cosmology, its reliance on a pre-existing notion of the universe (however vaguely defined) and the conceptual leap involved in using imaginary time raise significant questions about whether this model really explains the existence of our universe from nothing.
Constraints on Mathematical Freedom: The Role of Information in Quantum Cosmological Models
The Hartle-Hawking model, for all its elegance, faces another fascinating challenge: the need for constraints. This isn’t just a technical detail; it cuts to the heart of what we mean by “explaining” the universe.
Think of it this way: to solve the Wheeler-DeWitt equation and find the universe’s “wave function,” scientists have to sift through a mind-boggling number of possibilities and narrow them down to a smaller, more manageable selection for analysis.
Hartle and Hawking used a clever shortcut, the “path integral” approach (which sums over all possible spacetime geometries), but in practice, they focused on universes with specific properties: isotropic (uniform in every direction), closed (self-contained and curved), spatially homogeneous (uniform in composition), and possessing a positive cosmological constant.
This naturally helped narrow the infinite possibilities to a manageable few, making calculations possible. But did it also bake in assumptions? Does the resulting wave function truly arise from the math itself, or does it rely on preconceived choices that steer the outcome?
To address the inherent complexity of these problems, Hawking and Hartle developed a technique called the ‘mini-superspace’ approximation. Rather than wrestling with all possible spatial geometries, this technique restricts the analysis to a limited set of geometrical configurations. By cutting down the “degrees of freedom,” researchers can systematically zero in on specific gravitational field configurations and explore how certain universes—like the one we live in—might emerge as possible solutions.
These assumptions and simplifications feed into a broader issue: The Wheeler-DeWitt equation allows for an infinite number of solutions, and to arrive at a unique solution—a unique universal wave function—theoretical physicists must judiciously select boundary conditions and apply them to the equation from the start. But by limiting the mathematical degrees of freedom, these models unintentionally infuse additional information into their calculations as they attempt to explain it. Alexander Vilenkin highlights the necessity for boundary conditions to limit the degrees of mathematical freedom on possible solutions to the Wheeler-DeWitt equation. He notes:
“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 external to the universe, and a boundary condition should be added to the Wheeler-DeWitt equation.”[iv]
This passage highlights a crucial point that physicists encounter when working with the Wheeler-DeWitt equation: the need to limit its infinite mathematical possibilities to arrive at a solution. The universal wave function that supposedly explains the existence of our universe is entirely an artefact of the constraints that the theoretical physicists themselves have placed on the possible solutions to the Wheeler-DeWitt equation.
The challenge in quantum cosmology arises from the lack of a physical theory that justifies the specific limitations imposed on ‘superspace’ by the techniques used by Hawking and Hartle. ‘Superspace’ is a concept in theoretical physics representing the space of all conceivable spatial geometries and gravitational field configurations. For a quantum cosmological model to realistically explain the existence of our universe, naturalistic physicists must go beyond arbitrarily choosing constraints. They need to provide a solid, non-circular physical reasoning for the specific constraints they apply.
James Hartle himself acknowledged this limitation, stating,
“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.”[v]
Daily bread or not, Hawking and Hartle’s assumptions about the universe were modelled based on the properties of our own universe. By narrowing the scope of superspace to universes like ours, they risked circular reasoning – essentially building the answer into their initial assumptions.
Whenever you select one option over others, a bit of information is invariably introduced into the system. In quantum cosmology, specifically in relation to the Wheeler-DeWitt equation, the choice to exclude nearly an infinite number of potential mathematical solutions—whether through directly imposed boundary conditions, limiting the possible universes under consideration, or both—amounts to a significant injection of information into the mathematical frameworks used to model and explain the existence of the universe. This infusion of extra information lies at the heart of a major issue.
Philosopher Stephen C. Meyer has advanced this argument, emphasising that the selection of these constraints is not determined by the Wheeler-DeWitt equation, a deeper theorem of gravity, or other fundamental physical theories. Rather, these decisions rest solely in the hands of the theoretical physicist, an intelligent agent acting with a specific goal.
We tend to think of the universe as governed by cold, hard laws of physics. But here there seems to be more to the story. Intelligence—foresight, the ability to choose a specific outcome—might have played a role in shaping the cosmos. It’s a mind-bending idea, and for some, it’s a non-starter. But why is that?
Think about it this way: Intelligent agents possess foresight and can input specific information to achieve desired outcomes. A computer program, for example, doesn’t arise spontaneously from the computer’s circuits or the physical laws it’s built on, but by the programmer’s directives. Similarly, in all models that seek to explain the existence of the universe using quantum cosmology, scientists must confine the degree of mathematical freedom to yield a desired outcome: a wave function that includes our universe. This act of selection introduces information, nudging the equations toward a particular result: a universe like ours.
This raises a valid question: Where does this crucial information come from? It’s not enough to ask where matter, energy, or even space-time originated. We must also ask about the origin of the information needed to build the very equations that describe existence. Can the laws of physics alone fully account for this?
Quantum cosmology opens the door to the idea that intelligence might be fundamental to both modelling the universe and explaining its origins. If these theories indeed succeed in explaining the universe’s existence, they suggest that mind—not just matter—had a hand in bringing about this ultimate event. Far from being an argument rooted in ignorance, this perspective highlights the indispensable role of information, foresight, and specificity—hallmarks commonly associated with intelligent agents.
So, I don’t think quantum cosmology excludes theism as a valid interpretive framework. In fact, it arguably underscores the necessity of an intelligent agent as central to the existence of the universe. As Stephen Hawking once mused, something—or dare I say someone—must “fire into the equations” the precise specificity and information needed to bring the universe into existence. This concept echoes the biblical notion that “in the beginning was the Word,” implying an origin rich in intent.
Quantum cosmology pushes us to rethink how we approach the universe’s origin, highlighting the critical role intelligence plays in shaping its foundational models. This reliance on intelligence to provide the necessary information and specificity challenges the notion that the universe can be fully explained through “blind” and unguided natural processes. In light of this, Hawking’s claim to have eliminated the need for an ultimate intelligence in the context of quantum cosmology is therefore misleading. The very nature of these models and the requirement for an intelligent agent to shape them suggests that theism remains a viable framework for the existence of the universe.
Vilenkin’s Quantum Tunnelling Proposal
Soon after Hawking and Hartle’s initial publication on quantum cosmology, another visionary physicist, Alexander Vilenkin, introduced a theory that would challenge our fundamental understanding of the universe. His model of quantum cosmology was based on the concept of “tunnelling wave functions,” which held that the universe could emerge from nothingness through a process of quantum tunnelling. This theory, along with the Hartle-Hawking no-boundary proposal, has become one of the most prominent theories in the field of quantum cosmology. Some believe that quantum tunnelling could offer a quasi-mechanistic explanation for the existence of the universe.
To grasp Vilenkin’s idea, we first need to understand quantum tunnelling, a phenomenon unique to the strange world of QM. In classical physics, objects are bound by strict energy constraints. Imagine a ball rolling toward a hill: if it doesn’t have enough energy to climb over, it will stop or roll back. However, in the quantum realm, particles behave more like waves than solid objects. Thanks to their wave-like nature and the inherent uncertainties of quantum mechanics, there’s a small but real probability that a particle can “tunnel” through an energy barrier and appear on the other side—even if it doesn’t have enough energy to cross it in classical terms.
Vilenkin took this challenging concept and applied it on a cosmic scale. In his model, the universe itself behaves like a subatomic particle. Before its existence, there was no space, time, matter, or energy—just “nothingness.” But in quantum mechanics, even “nothing” is unstable and subject to fluctuations. Vilenkin proposed that through quantum tunnelling, the universe could overcome an energy barrier and transition from this state of nothingness into existence.
In this context, “nothingness” doesn’t mean an empty void but rather a state with no classical spacetime or physical laws as we know them. The emergence of the universe through tunnelling would mark the birth of spacetime itself—a moment when existence as we understand it began. Once the universe tunnelled into being, it didn’t remain tiny for long. Vilenkin’s model then incorporates inflation—a phase of rapid exponential expansion that occurred in the universe’s earliest moments.
So, according to Vilenkin, the universe comes into being from a state of nothingness through quantum tunnelling. This process allows it to suddenly appear with a definite size, overcoming a classical barrier in a way that traditional physical laws can’t explain. Vilenkin’s theory contrasts with the Hartle-Hawking No Boundary proposal, which views time as finite but without a definite beginning or end, thus not pinpointing a specific commencement for the universe.
While Vilenkin’s quantum tunnelling model is celebrated for its innovative approach to explaining the universe’s emergence, I struggle with his interpretation of “nothingness.” For most of us, “nothing” means a complete absence—no properties, no laws, no anything. But Vilenkin’s version of “nothing” includes pre-existing quantum laws. Quantum mechanics, which underpins the tunnelling process, presupposes a framework within which these laws operate. This creates a paradox: if space-time itself only arises with the universe’s emergence, how could there be a pre-existing quantum field or set of rules before space-time existed? For instance, the reliance on physical laws in Vilenkin’s model would seem to imply the presence of a matter field prior to the universe’s existence, which introduces a paradox. In physics, a matter field, which permeates space and can generate particles, presupposes a structured entity within a space-time framework. Yet Vilenkin’s model suggests that space-time emerges after the tunnelling event. This apparent contradiction implies that some form of pre-universal structure or law must exist, undermining the notion of an absolute beginning from “nothing.”
Furthermore, the ‘tunnelling wave function’ in Vilenkin’s model calculates the probability of the universe transitioning from a singularity (or near-singular state) to an expanding state through quantum tunnelling. This model describes how the nascent universe, facing a gravitational energy barrier, could overcome this barrier to facilitate expansion. However, it’s not clear to me that it really explains how tunnelling occurs immediately following the universe’s emergence, leaving the precise nature of the initial creation act somewhat unclear.
In summary, as I understand it, while Vilenkin’s model offers an innovative mechanism for the universe’s development post-origin, it does not clearly explain the initial emergence from a true state of “nothingness.” The theory’s reliance on pre-existing laws and the notion of a pre-existing matter field shifts its focus towards explaining the early development of the universe.
Previously, we questioned whether the Hawking-Hartle model truly explains the universe’s emergence from ‘nothing’. A similar issue arises with the Vilenkin model, as both seem to presuppose a pre-existing reality, thus sidestepping the ultimate origin of the universe. The complex mathematics in these theories assume the pre-existence of the universe, albeit vaguely defined. The notion that these models start from “nothing” is misleading; this “nothing” is not an absolute void but a state at the universe’s inception, such as a quantum vacuum or a pre-geometric state with inherent properties. Claiming that quantum mechanics allows for creation from absolute nothingness is a misnomer, as this “nothing” still possesses certain properties, implying that only “something” can have properties. Therefore, suggesting that something arises from nothing through quantum principles subtly introduces “something” into the equation of “nothing.” This is a point of contention noted by philosopher of physics Willem B. Drees:
“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.”[vi]
The notion of a universe with possible properties must first exist before quantum cosmologists can construct the universal wave function describing those properties as a superposition. Consider the double-slit experiment: when a photon encounters the double-slit barrier, the photon demonstrates characteristics of being in multiple states simultaneously, a phenomenon known as superposition. The Schrödinger equation comes into play by providing a mathematical description of the photon’s probable behaviour in this setup. It calculates the probabilities of various outcomes, such as where the photon will be detected on the screen, based on its superposition. However, the point is that the existence of the photon precedes and informs the solutions derived from the Schrödinger equation.
Similarly, a universe with certain possible properties precedes the mathematical procedures that produce a solution to the Wheeler-DeWitt equation—a universal wave function that assigns definite probabilities to the different possible attributes the universe could possess. While these models offer interesting insights into the universe’s developmental stages, they appear to start from a point where the universe, in some form, already exists.
Quantum cosmology can feel like a wild frontier—fascinating, puzzling, and sometimes downright contradictory. It’s one of those scientific fields where we’re still very much in the process of figuring things out, so it’s wise to take any sweeping claims or criticisms with a pinch of scepticism. I’ll be the first to admit that my understanding of quantum cosmology is far from complete—none of ours really is. But that’s the nature of exploring the unknown, right? The good news is, in this section, we’ll shift gears and dive into topics that are more grounded, focusing on philosophical ideas that are not only easier to wrap your head around but also deeply thought-provoking.
In his influential work, “The Grand Design,” Stephen Hawking proposes a thought-provoking idea: “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. It is not necessary to invoke God to light the blue touch paper and set the universe going.” Similarly, Lawrence M. Krauss, drawing inspiration from Alexander Vilenkin’s work, argues that “The laws themselves require our universe to come into existence, to develop and evolve.”
When Hawking speaks of “a law such as gravity” being central to the universe’s creation, he’s referencing the entire mathematical edifice of quantum cosmology, including the universal wave function, the Wheeler-DeWitt equation, and modern theories of quantum gravity. Underlying his claim is the assumption that these physical laws can act as causal agents, explaining events such as the origin of the universe.
Now, when scientists suggest that mathematical models can account for the existence of the universe, they might be unknowingly aligning with the ancient philosophies of Plato and Pythagoras. These thinkers wondered that if we can use mathematics to describe the effects of various phenomena, perhaps the underlying causes are mathematical too. This raises a crucial question: can mathematical models actually cause physical phenomena?
Professor John Lennox points out that it’s important to differentiate between causes and scientific laws. Causes refer to specific events that lead to other outcomes, whereas laws describe the general relationships between different events or variables. For example, the law of gravity does not cause material objects to fall, but rather it describes and explains how material objects interact with one another when influenced by mass and energy. Similarly, the laws of physics are interpretations of nature’s behaviour, not initiators of phenomena. Take the simple arithmetic equation of 1 + 1 = 2. While accurate and straightforward, this equation doesn’t create anything. If I save $100 one month and another $100 the following month, arithmetic will confirm I have $200. However, without the act of saving, arithmetic on its own won’t grow my savings. Believing that the laws of physics can create the universe is like thinking money can be made just by doing calculations.
The idea that complex mathematical laws alone can conjure up the universe and life within a purely naturalistic frame borders on science fiction. Theories and laws don’t have the power to create matter or energy. Claiming that the laws of nature can explain the origin of all matter, energy, and spacetime is like saying that the lines of longitude and latitude on a map are responsible for the location of the Hawaiian Islands in the Pacific Ocean. While these laws may explain the universe’s structure and make its existence possible, it’s a completely different leap to suggest they’re responsible for creating it.
Stephen Hawking’s assertion that the laws of science—specifically “the law of gravity”—can explain “why there is something rather than nothing” reflects a deeper philosophical misunderstanding about the role and limits of physical laws. These laws, expressed in mathematical terms, are descriptive tools that explain how nature behaves and how its components interact. However, they do not possess the power to cause the natural world to exist in the first place. This distinction underscores why even a “theory of everything” or the discovery of a new natural law is unlikely to bridge the gap between nothingness and the emergence of existence. No law of nature can resolve this divide.
Think about it this way, the universal wave function essentially outlines potential universes with varying gravitational fields. It describes the “superposition” of all conceivable universes, each with its own spatial geometry and mass-energy configuration. While this is a fascinating framework, it does not specify why any one universe should emerge from this spectrum of possibilities—or why anything should exist at all. In scenarios where spacetime, matter, and energy are absent, there is no physical mechanism within this framework to account for their sudden appearance.
In other words, these models do not provide a causal mechanism for the emergence of the universal wave function or the potential universes it describes. They describe what might be possible but fail to explain how or why these possibilities transition into reality.
The Wheeler-DeWitt equation and the concept of curvature-matter pairings in superspace represent theoretical constructs or potential physical realities, but they remain, fundamentally, mathematical abstractions. This mathematical characterisation of possible universes does not equate to their actual physical existence. The inherently theoretical nature of quantum cosmology, even when viewed as a foundational element of quantum gravity, does not pinpoint a physical cause for why the universe exists.
This limitation highlights a broader issue: while quantum cosmology excels at mapping out potential universes and their properties, it struggles to explain why any particular universe materialised—or why there is something rather than nothing at all. Abstract mathematical models are invaluable for describing physical phenomena but lack the creative power to generate material reality. As far as I am aware, there is no evidence that mathematical entities possess the capacity to create existence itself. They describe; they do not cause.
This raises an important question: If mathematical laws cannot create the universe, where does their apparent explanatory power originate? Alexander Vilenkin pondered this, suggesting the possibility of a “mind” behind it all. He wondered:
“Does this mean that the laws are not mere descriptions of reality and can have an independent existence of their own? 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?”[vii]
Many physicists agree that mathematical laws are simply descriptive tools—powerful frameworks that exist in the minds of physicists but lack generative power. Quantum cosmology thus suggests two possibilities: either mathematics somehow “creates” the universe (a position bordering on the mystical) or aligns with Mathematical Platonism, which claims that mathematical ideas exist in a non-physical realm.
I can think of three ways to think about the relationship between the mathematics of quantum cosmology and the material universe:
- Mathematics is a post-universal mental phenomenon. It is merely a useful description of reality, which is not fundamentally mathematical.
- Mathematics exists prior to the universe in an abstract, immaterial realm independent of mind.
- Mathematics is a mental phenomenon and exists prior to the universe.
Among the three options, I argue that the third makes the most sense based on our uniform experience. This is because:
- The world appears to fundamentally conform to mathematical principles independent of human minds, excluding the first conception. This conception would also rule out the idea under discussion—that mathematical laws cause the universe’s conception.
- There is no logical reason to believe the contents of an abstract realm independent of mind would be accessible to minds. As mathematics is accessible to our minds, this rules out the second conception.
- Mathematics is a mental phenomenon and the universe fundamentally conforms to mathematical principles, so this fits with the third conception.
If mathematical principles must have existed causally prior to the universe, yet mathematics is accessible to minds, not abstract from them, then doesn’t that imply a mind causally prior to the universe within which mathematical principles hold shape? Unlike a realm of disconnected mindless abstract mathematics, our minds can interact with mathematics because our minds are of the same kind as the mathematics generating Mind.
Of course, here we’re going well beyond the realms of empirical observation and scientific inquiry into deeply speculative philosophy. However, the argument is that the concept of a transcendent Mind is a reasonable extension of the cosmological data, and provides a more logically robust explanation for the universe than abstract, mindless mathematics.
And to be clear, to say that mathematics is a mental phenomenon is not to say that we ‘invent’ mathematics. I view mathematical truths as human discoveries. The proposal is that mathematical laws and principles exist independently of human minds, and that these were put in place by a transcendent Mind as part of the created order. Humans, through their intellectual capacities, discover these pre-existing truths. The ability of the human mind to understand and uncover mathematical truths reflects being made in the image of that transcendent Mind. This belief suggests a compatibility and connection between the human mind and the ‘divine’ mind.
The existence of a mind capable of conceiving complex mathematical concepts and the existence of a cosmos that operates on these principles are not coincidental, as it would be if mathematics pre-existed in an abstract, mindless realm. It is logical to hold that this alignment points toward a universe that is a product of an intelligent mind, and that our minds are therefore somehow attuned (or attracted) to this underlying order.
We also have plenty of experience of ideas originating in the mental realm and, through acts of volition, producing entities that embody those ideas. Even if you could explain the existence of matter and energy from “nothing,” the origin of the information that gives structure to our universe implies some sort of intelligence. So, while general relativity predicts a beginning for the universe, quantum cosmology provides rationale for a consciousness behind it all.
If quantum cosmology points to a realm where mathematical concepts exist independently of our universe, it makes sense to think these ideas come from a higher mental source—a mind “above” the universe. This perspective resonates with Alexander Vilenkin’s thoughts, as he briefly considers a theistic interpretation of quantum cosmology, suggesting these mathematical ideas might reflect a higher intelligence.
Between Speculation and Certainty: Stephen Hawking’s Contributions and the Debate on Quantum Cosmology
Stephen Hawking was a titan of science and an inspiring symbol of the remarkable accomplishments someone with a disability can achieve. His pioneering work in the 1960s and 1970s set the stage for research areas that continue to flourish today. Hawking inspired millions, myself included, to delve into the mysteries of the universe. However, it is crucial to acknowledge his shortcomings, particularly those he failed to overcome. Like many brilliant scientific minds, Hawking was prone to becoming captivated by his own speculative ideas, discussing them with a certainty best reserved for well-established, robust theories.
Hawking’s no-boundary proposal, though speculative, was often presented with unyielding certainty. Concepts such as baby universes, a unifying theory of everything, and higher dimensions may be widespread, but they lack definitive evidence. Some aspects of these ideas remain untested, while others have failed to yield supporting evidence. Despite these shortcomings, Hawking championed them, much to the dismay of more cautious scientists. He seldom differentiated between validated theories and speculative ones, particularly when discussing his own conjectures. He portrayed his speculations as fact and made sweeping statements based on them.
Hawking, along with physicists like Laurence Krauss, sought to employ quantum cosmology as an alternative to the theistic implications of the Big Bang Theory and the cosmological singularity. They maintained that the mathematics behind solving the wave function demonstrated that our universe did not necessarily have a beginning and could have arisen from “nothing.” In this light, Hawking contended that quantum cosmology negated the necessity for a transcendent creator, positioning it as the ultimate scientific rebuttal to the God hypothesis.
However, this perspective is not without its weaknesses. For instance, imagine if I told you I could build a house from nothing, but still requiring pre-existing building codes; an infinite Home Depot with all possible materials, and a first construction rule like “Start with door frames”. Have I truly created something from nothing? Or have I simply disguised the starting points by hiding them in the requirements? Hawking and James Hartle were able to solve the Wheeler-DeWitt wave equation for the universe by substituting imaginary time into the formula, resulting in a theoretical model of a universe akin to our own. Yet, it would also seem that their calculations inadvertently presuppose the existence of a universe (vaguely defined). Also, their calculations necessitated the intelligent selection of conditions compatible with a universe like ours. As a result, their work did not explain the existence of the universe from unaided nothing; it needed a pre-existent something, and it needed intelligence to add information and foresight. Additionally, mathematics is a mental phenomenon that appears to exist prior to the universe, suggesting an intelligent mind that preceded the universe. So, as far as I can tell, quantum cosmology intriguingly tilts in favour of theistic expectations over purely naturalistic and other atheistic ones. When examined closely, these quantum models seem to presuppose prior intelligence, thus bearing significant theistic implications.
[i] https://journals.aps.org/prd/abstract/10.1103/PhysRevD.28.2960
[ii] Hawking, S. A Brief History of Time: From the Big Bang to Black Holes (1988). London, UK: Bantam, 140-141.
[iii] A Brief History of Time, 136.
[iv] Vilenkin, A. “Quantum Cosmology”, 7.
[v] Hartle, J. “What Is Quantum Cosmology?” Closer to Truth. Retrieved from https://www.youtube.com/watch?v=s6wPcq5yb7s
[vi] https://link.springer.com/article/10.1007/BF00670817
[vii] Vilenkin, A. ‘Many Worlds in One’, 205.
