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 is best to read part two first.
Throughout the 20th century, groundbreaking advances in cosmology converged to confront humanity with a profound enigma: the origin of the universe. Theologians, philosophers, and scientists tirelessly grappled with this conundrum. Amidst the unfolding narrative, naturalistic explanations for the universe’s origin seemed increasingly nonsensical and counterintuitive. In contrast, the concept of God emerged as a fitting explanation for the universe’s genesis, aligning with 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 divine explanation’s dominance.
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.
Do recent breakthroughs in quantum cosmology provide more persuasive, naturalistic explanations for the universe’s beginning? Might it be time to relinquish the notion of God?
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.
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.
He 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 wavelike and particlelike behaviour. The expansion of the universe has produced a vast spatial volume in the present, but 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 relies on the application of quantum mechanics to the physics of the early universe — specifically, the 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 proposed a mathematical framework to characterise the phenomenon of wave-particle duality. The Schrödinger equation, which he developed, enabled 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.
To be clear, it is important to note that the term “observed” in this context does not necessarily imply that a conscious observer is needed for the wave function to collapse. Measurement or interaction with the environment can also cause the wave function collapse, 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.
Now, you might be wondering: how does all of this relate 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 depict how gravity would have operated in such a confined space during the very earliest stage of the universe, quantum cosmologists 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. The equation is an attempt to combine general relativity with quantum mechanics, specifically within the canonical approach to quantum gravity 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 and significant feature of the equation, leading to what’s often termed the “problem of time” in quantum gravity.
Before we proceed, let’s take a moment to recap so we don’t get lost. 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.
Moving into the realm of quantum cosmology, the focus shifts to the Wheeler-DeWitt equation. 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 fundamental physical theory — a theory of quantum cosmology. His primary goal was to determine the wave function of the entire universe by solving the Wheeler-DeWitt equation. By doing so, he could calculate the probability of a universe like ours, with its specific gravitational field, coming into existence. If that probability showed that our universe is possible or even probable, Hawking would consider the existence of the universe to be explained by a fundamental theory of 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. This concept challenges traditional 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 discovered that making precise mathematical calculations about the early universe’s probable state of affairs was intractable in the domain of real time. To overcome this challenge, he introduced the concept of imaginary time. In simple terms, while real time encompasses the past, present, and future, imaginary time is perpendicular to the present, allowing for multiple events to occur simultaneously. Here is a diagram I found to help explain:
Imaginary time arises when time is treated as an imaginary number, obtained by multiplying real time by the square root of -1 (denoted as “i”). This concept is used in certain areas of theoretical physics to simplify calculations and explore complex systems. Hawking incorporated imaginary time into one of Einstein’s mathematical expressions, known as the spacetime metric, which describes spacetime’s geometry or curvature. 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, Hawking’s mathematical construct depicted a universe with spatial dimensions but no preferred temporal direction and no temporal beginning. This model treated time as essentially another dimension of space, eliminating the temporal singularity as long as the geometry of space continued to be described using imaginary rather than real time. Hawking’s spacetime description depicted a universe that is “finite but unbounded” by a specific temporal point of origin.
Using imaginary time, Hawking developed a “no boundary” model of the universe’s beginning to avoid a cosmological singularity — an absolute beginning — while still maintaining a finite past. His model illustrated the initial segment of spacetime as rounded off, similar to how the South Pole represents the “beginning” of Earth, with various circles of latitude playing the role of time. Just as you cannot ask what is south of the South Pole, it also becomes nonsensical to ask what came before the rounded-off section of the initial segment of spacetime. 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 also created the widespread impression that he had refuted the Kalam (first cause) cosmological argument for God’s existence. He presented this model as a challenge to the argument’s second premise: “the universe began to exist.” By the 1990s, Hawking single-handedly began to shift perceptions about the Big Bang Theory’s implications.
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. As many have pointed out, Hawking’s decision to equate time with imaginary time, however, lacked physical justification beyond its mathematical convenience. As a result, his depiction of spacetime geometry lacked applicability and intelligibility as a physical description of our universe. When he substituted imaginary time for real time in Einstein’s mathematical expression, the resulting depiction did not correspond to anything in the real universe.
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.
So, the challenge lies not in the mathematical technique employed by Hawking, but in the metaphysical interpretation he assigned to the intermediate steps in his mathematical manipulations. These intermediate steps produced an expression that failed to describe the spacetime geometry of the real universe. Time, when confined to the imaginary axis of the complex plane, loses its physical meaning. 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 well aware of these issues, and in his Brief History, he 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, 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]
Additionally, the specific mathematical transformation that Hawking applied enabled him to treat time as a spatial dimension for his calculations’ purposes. However, collapsing time into space in this way doesn’t result in a mathematical expression with physical meaning, particularly one that changes over time like our universe does. Collapsing time into space is an abstract mathematical concept without clear physical justification. Treating time as another dimension of space disconnects Hawking’s model from the real-world experience and understanding of time.
While time and space are indeed linked in general relativity, they are still treated differently. Time is not the same thing as space. Events occur within space but also follow a temporal sequence. Collapsing time into space (or “spatialising time”) eliminates the possibility of accurately describing our universe’s reality, rendering Hawking’s mathematical description of spacetime geometry inapplicable to our universe.
Questioning the Absence of a Singularity in Hawking and Hartle’s Universe Model
Furthermore, there are other reasons I remain sceptical about whether the quantum cosmology model proposed by Hawking and Hartle truly explains the origin of the universe. Let me explain: Their model utilises the ‘path-integral’ method, a technique introduced by Richard Feynman in quantum mechanics. This method is widely used in quantum mechanics to sum up mathematical expressions describing the potential paths of quantum particles, like electrons or photons. For example, in quantum mechanics, 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 encompass 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 posited 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 encompassing the likelihood of universes like ours emerging.
However, this model presupposes a pre-existing reality, such as a set of physical laws, a quantum vacuum, or some other fundamental structure. While Hartle-Hawking’s model attempts to circumvent an initial singularity by proposing a finite but boundaryless universe using complex time paths, this approach doesn’t entirely negate the need for an originating condition or a pre-existing framework.
To apply the path integral method, or any quantum mechanical formalism, to the universe as a whole, an initial concept or understanding of the ‘universe’ is necessary, even in a generalised form. This implies a need for some form of pre-existing structure or framework within which the mathematics can be applied. Thus, while innovative, the Hartle-Hawking model may not fully address the issue of the universe’s existence without some unexplained conditions. How these initial conditions came to be remains unaddressed by the model. The model starts with a certain set of conditions and laws of physics that must already be in place for the universe to evolve as described. This initial setup could be tantamount to acknowledging a concept of a universe emerging from a singularity with zero spatial volume. Hawking only dismissed the notion of a temporal beginning at a later stage in this multi-step calculation process. And this is only through interpreting a mathematical expression which lacks direct physical meaning (due to the incorporation of imaginary time), as if it bore physical significance.
To be clear, I wouldn’t assert this too strongly. Questioning the absence of a singularity in Hawking and Hartle’s model isn’t as broadly recognised as the challenges associated with the use of imaginary time. However, as we will explore, there are additional, more evident disputes to consider.
Constraints on Mathematical Freedom: The Role of Information in Quantum Cosmological Models
Another challenge with the Hartle-Hawking model stems from the necessity to impose certain arbitrary constraints on these models. For instance, in the pursuit of solving the Wheeler-DeWitt equation and constructing a universal wave function, there’s a critical need to filter the numerous potential universes into a more manageable subset for analysis. In this context, Hawking and Hartle employed the ‘path integral’ approach, focusing only on specific paths. This method involves summing the amplitudes of all possible spacetime geometries, allowing for the exploration of the quantum properties of the early universe. However, their focus was notably selective, zeroing in on specific types of universes: those that are isotropic (uniform in all directions), closed (self-contained and curved), spatially homogeneous (uniform in composition), and possessing a positive cosmological constant.
While this approach is instrumental in narrowing down the field, it inadvertently introduces a layer of pre-determined information into the quantum cosmological models. This aspect is particularly pivotal because it subtly challenges the ability of these models to independently explain the existence of the universe. It implies foresight in explaining the universe’s existence, raising questions about the self-sufficiency of these cosmological models.
Stephen Hawking and James Hartle developed a technique known as ‘mini-superspace’ to tackle the complexities of quantum cosmology. This method simplifies the problem by significantly reducing the degrees of freedom. Instead of grappling with the entire spectrum of possible spatial geometries, ‘mini-superspace’ focuses on a limited, more manageable set. This reduction in variables allows theoretical physicists to explore a narrower range of gravitational field configurations, a crucial step in developing a wave function that includes a universe resembling ours as a possible outcome.
The challenge with the quantum cosmological models lies in this very simplification. By limiting the mathematical degrees of freedom, these models unintentionally infuse additional information into their calculations as they attempt to explain it. 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. Alexander Vilenkin, a theoretical physicist, 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 excerpt reveals that physicists must arbitrarily restrict the infinite degrees of mathematical freedom inherent in the Wheeler-DeWitt equation to solve it. However, the specific universal wave function that apparently explains the existence of the universe in this manner 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]
And there lies the problem: the assumptions made by Hawking and Hartle about the type of universe they considered in constructing the universal wave function were based on the properties of our own universe, creating a circular reasoning. They effectively inserted specific information into their calculations by narrowing the scope of superspace. This narrowing ensured that the paths through superspace they considered would lead to a universal wave function encompassing universes similar to ours. In doing so, they crafted a mathematical procedure and restricted inputs to arrive at ‘the right answer’, a method that, while ingenious, raises questions about the objectivity of their approach.
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 objective.
Intelligent agents possess foresight and can input specific information to achieve desired outcomes. For example, a computer programmer can write code that directs a computer to perform specific tasks. The information in the code is not a product of the computer’s hardware or the laws of physics governing its operation, but rather an input from the programmer’s mind.
Similarly, in all models that seek to explain the existence of the universe using quantum cosmology, such intelligent agents must confine the degree of mathematical freedom to yield a desired outcome: a wave function that includes our universe. This demonstrates the need for a designing intelligence to select specific options over others, thereby introducing information to achieve a particular result.
The core issue extends beyond explaining the existence of matter, energy, or spacetime. It delves into the origin of the information required to formulate and solve the equations that claim to explain the existence of the universe. This information cannot be solely explained by the laws of physics, suggesting a deeper involvement of intelligence in the process.
Thus, quantum cosmological theories subtly imply the necessity of intelligence in modelling and explaining the existence of the universe. If these theories accurately explain the existence of the universe, then mind, not just matter, played a causal role in this ultimate event. This perspective doesn’t stem from ignorance but rather acknowledges the essential role of information and foresight that originates from intelligent agents.
Quantum cosmology does not rule out theism as a viable explanation for the universe’s existence. In fact, it can be argued that quantum cosmology underscores the need for an intelligent agent to be involved in the creation of the universe. The need for specificity and information is a key aspect of this argument. Quantum cosmology suggests that the universe may require an intelligent agent to “fire into the equations” (as Hawkings mused) the necessary specificity and information to bring it into existence. This notion echoes the biblical idea that “in the beginning was the Word,” indicating a presence far from nothingness.
By highlighting the critical role of intelligence in constructing these cosmological models, quantum cosmology poses a significant challenge to naturalistic and strictly atheistic interpretations of the universe’s existence. The need for an intelligent agent to provide the necessary information and specificity undermines the claim that the universe can be explained solely through natural, unguided processes. Stephen 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 suggest that theism remains a viable explanation for the existence of the universe.
Vilenkin’s Quantum Tunnelling Proposal
Five years 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.
In simple terms, quantum tunnelling is a quantum mechanical phenomenon in which a subatomic particle, seemingly trapped and lacking the energy to escape, penetrates a potential energy barrier. Imagine a ball rolling towards a hill on a flat surface. In the everyday world governed by classical mechanics, if the ball lacks the energy to climb the hill, it won’t make it over; it will either stop or roll back. However, quantum mechanics introduces a fascinating twist: there’s a slight chance that the ball could ‘tunnel’ through the hill and emerge on the other side, defying the energy limitation. This is due to the wave-like nature of particles in the quantum realm and the inherent uncertainties of quantum mechanics.
In quantum mechanics, the ‘wave function’ of a particle helps physicists predict where it might be found. It indicates that, against all odds, a particle could end up on the other side of an energy barrier that it couldn’t surmount by classical energy measures. Quantum cosmologists like Vilenkin see a parallel between this phenomenon and the expansion of the universe. In his model, the universe is akin to a subatomic particle that tunnels through an energy limitation from a state of nothingness into existence, filled with spacetime, matter, and energy. Vilenkin’s model suggests the universe emerged through quantum tunnelling. Once it appeared, it expanded rapidly in a phase known as ‘inflation.’ Inflation is like blowing up a tiny balloon very quickly to a huge size. This rapid expansion is described through the concept of a ‘de Sitter space,’ a concept in physics that describes a universe that’s constantly expanding.
So, according to Vilenkin, the universe comes into being from a state of complete 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.
Vilenkin’s approach posits that ‘nothingness’ is not entirely devoid of properties. It presupposes the existence of quantum mechanical laws that facilitate the tunnelling process. This interpretation of ‘nothingness’ deviates from the traditional philosophical view, which defines ‘nothing’ as a complete absence of properties or characteristics. The reliance on physical laws in Vilenkin’s model implies 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. However, according to Vilenkin’s model, space-time itself emerges with the universe. This scenario suggests some form of pre-universal structure or law, challenging the notion of an absolute beginning from ‘nothing.’
The ‘tunnelling wave function’ in Vilenkin’s model calculates the probability of the universe transitioning from a singularity 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, the specifics of how tunnelling occurs immediately following the universe’s emergence remain unaddressed, leaving the initial act of creation 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 development of the universe. This critique highlights the philosophical and scientific difficulties in reconciling the concept of ‘nothingness’ with quantum mechanics and the established properties 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. The mathematics of quantum cosmology begins by describing a universe already presupposed to exist. For instance, think about the double-slit experiment: When a photon encounters the double-slit barrier, the photon exhibits 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. They open up philosophical discussions about the assumptions regarding the universe’s initial state.
Quantum cosmology is a complex and sometimes contradictory area of study. It’s a part of science that we still have a lot to learn about. Because of this, any ideas or conclusions that come from quantum cosmology, as well as any criticisms of it, should be approached with a healthy dose of scepticism. In this section, you’ll be glad to hear that we’ll pivot to discussing issues that are more grounded in philosophical concepts that are easier to grasp.
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. He presupposes that these laws of physics can be causal agents, explaining events like the universe’s inception.
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 believed that since mathematics adeptly manages quantities, it must be the key to understanding the universe’s very existence. This idea initially appears logical: if we can quantify the effects of various phenomena mathematically, perhaps the causes themselves are rooted in mathematics. However, there’s a significant oversight here. Mathematical models are constructs within the minds of physicists, lacking the capacity to manifest anything in the physical world, much less the entire universe. This raises a crucial question: can these mathematical descriptions actually be the causes of phenomena? I remain sceptical.
As Professor John Lennox points out, 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 doesn’t cause material objects to exist; it simply explains how material objects that already exist interact with one another. 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 is akin to science fiction. Theories and laws don’t have the power to create matter or energy. To assert that the laws of nature can explain the genesis 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 might permit the universe’s existence and explain its structure, they cannot be credited with its creation.
Stephen Hawking’s claim that the laws of science, or specifically “the law of gravity,” can explain “why there is something rather than nothing,” betrays a philosophical misunderstanding about the capabilities of physical laws. These laws, often articulated in mathematical language, are tools for describing how nature functions and how its various components interact. They do not, however, have the capability to cause the natural world to exist. This distinction highlights the unlikelihood that the discovery of a new natural law or a “theory of everything” could explain the existence of nature. No law of nature can overcome the fundamental gap between the non-existence of everything and the emergence of the natural world. Quite simply, laws of nature presuppose the existence of nature, so cannot be invoked as the cause of nature.
This brings us to question whether quantum cosmology could offer an alternative explanation by introducing a law that points to a material event as the cause of the universe’s inception. Could the universal wave function or the Wheeler-DeWitt equation, seen as foundational elements of quantum gravity, identify a material precursor to the universe?
I am doubtful of this. 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, yet it does not pinpoint any specific event that would cause one of these universes to materialise over the others. In the absence of matter, spacetime, and energy, there are no such entities in existence.
In quantum cosmology models that correctly use real time, the scenarios depicted by the universal wave function typically begin from a temporal singularity with zero spatial volume. These models assume this singularity but fall short of providing a physical cause or explanation for the birth of the universal wave function, or the potential universes it suggests could emerge from this singularity.
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 enable it to identify a material precedent as the physical cause for the existence of the universe.
Consequently, quantum cosmology encounters a challenge in pinpointing material precursors for the universe’s emergence. It’s adept at delineating possible universes and their attributes but lacks the capacity to clarify how or why a particular universe materialised instead of others.
This brings us to an intriguing query: how can purely mathematical entities be responsible for the manifestation of a material universe in time and space? Put another way, how does a mathematical equation give rise to an actual, tangible universe? This echoes Stephen Hawking’s contemplation in A Brief History of Time: “What is it that breathes fire into the equations and makes a universe for them to describe?” It’s a fundamental question that bridges the gap between abstract mathematical models and the concrete reality of our universe.
The argument that the mathematics underpinning the laws of nature have the power to create reality raises profound philosophical questions, one of which concerns the source of this supposed creative power of mathematics. Alexander Vilenkin contemplated this question, drawn to the concept of a “mind”:
“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]
The laws some physicists invoke to explain the existence of space and energy are mathematical descriptions that exist in the minds of physicists. In this case, they lack the power to generate anything in the natural world, let alone the entire universe. In essence, quantum cosmology implies either a kind of magic where mathematics creates a universe or Mathematical Platonism. Mathematical Platonism posits that mathematical concepts or ideas exist in a non-physical, abstract realm.
In summary, we can consider three distinct perspectives on the enigmatic 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, we must posit 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.
It’s also worth reiterating our previous point, that while mathematics is an invaluable tool for describing the universe, there’s a significant distinction between description and creation. Our experiences show that mathematical equations, while powerful in explanation, don’t possess the ability to generate material reality. Material entities don’t spring forth from mathematical formulas; instead, it’s through the application of intelligent minds that mathematics becomes a tool to understand the natural world.
Furthermore, we possess a wealth of experience of ideas originating in the mental realm and, through acts of volition, producing entities that embody those ideas. Even if one could explain the existence of matter and energy from “nothing,” the origin of the information that gives structure to our universe implies the reality of an intelligent source. So, while general relativity predicts a beginning for the universe, quantum cosmology provides rationale for a consciousness behind it all.
If quantum cosmology suggests a realm where mathematical ideas and objects exist independently of our universe, then it seems logical to deduce that these ideas originate from a transcendent mental source — a mind “above” the universe. This perspective finds an echo in Alexander Vilenkin’s musings, as even he briefly entertains the possibility of a theistic interpretation of quantum cosmology, opening a door to the idea that these mathematical concepts may be reflections of 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 viewpoint is not without its flaws. 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 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) with a singularity. 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. 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.
