Introduction

The history of physics involves the growth of knowledge outwards to ever larger scales and inwards to ever smaller ones, with ideas at the smallest and largest scales often viewed as bordering on philosophy because they lack empirical confirmation. Physicists with an antipathy to philosophy therefore regard such ideas disparagingly. However, this may be unwarranted since physics had its origin in natural philosophy, and the physics/philosophy boundary steadily shifts as fresh data expand the domain of physics. The criteria for what is regarded as legitimate physics have also changed.

An interesting example of this arises in the context of cosmology, which involves both the macro and micro extremes. While cosmography studies the structure of the universe on the largest scales, where gravity dominates, cosmogeny studies the origin of the universe and involves arbitrarily small scales, where the other forces are important. So, cosmology is doubly prone to accusations of being too philosophical and has often struggled to maintain its scientific respectability. Indeed, it only attained the status of a proper science in 1915, when the advent of general relativity gave the subject a secure mathematical basis. The discovery of the cosmological expansion in the 1920s then gave it a firm empirical foundation, and the detection of the cosmic microwave background radiation in 1965 established the hot Big Bang theory as a branch of mainstream physics. Nevertheless, more conservative physicists still regard some cosmological speculations as going beyond proper science. One example concerns the current debate over the multiverse.

Another topic that straddles the boundary between physics and philosophy is black holes. These objects were predicted by general relativity in 1916, but Albert Einstein thought they were mathematical artefacts, and it was 50 years before there was observational evidence for their existence. Black holes from stellar collapse were the first to be confirmed, but there is now evidence for increasingly massive ones, with “intermediate mass” black holes being associated with gamma-ray bursts and “supermassive” ones powering quasars. There may also be “primordial” black holes that formed shortly after the Big Bang, and these could be much smaller than a solar mass. However, the smallest ones would have evaporated by now, so their physical reality is hard to confirm. There are also objects termed “wormholes” with even more exotic properties than black holes, and therefore beloved by science fiction, that some physicists would relegate to philosophy.

Speculations about both cosmology and black holes have involved an extrapolation of theory to ever larger and smaller scales, with the physics involved being very speculative at the extremes. While they both derive from general relativity, they may also play a role in some final theory that unifies relativity and quantum mechanics. For example, they both involve singularities and anomalies in the nature of time, raising issues that go beyond currently understood physics but are conceivably part of future physics.

There is also a boundary between physics and theology. Indeed, one might regard physics, philosophy and theology as forming three overlapping magisteria, as indicated in Figure 1a. However, most physicists are even more uncomfortable with theology than philosophy, with the physics/theology boundary sometimes being regarded as a battlefield. They might therefore prefer to regard these magisteria as forming a sequence, with theology being further removed from physics than philosophy, as illustrated in Figure 1b.

Figure 1

Illustrating how cosmological and black hole research provides an interesting interface between physics, philosophy, and theology (a), although one might also regard these three disciplines as forming a sequence (b).

This physics/theology boundary is also illustrated by black holes and cosmology. As regards cosmology, it was a Belgian priest (Georges Lemaître) who introduced the idea of the Big Bang in 1931, and many questions addressed by cosmologists are traditionally regarded as being in the domain of religion. For example, all human cultures have their creation myths—a skeptic might claim the Big Bang theory is just the most recent one—and the earliest (prescientific) cosmological models explicitly reflected religious views. Of course, modern cosmologists would prefer to emphasize their links with science rather than religion. The theological aspects of black holes are not so explicit. However, it was an English priest (John Michell) who first introduced the idea in 1783, and we will see that black holes and cosmology raise similar conceptual issues. While the remit of religion goes well beyond the materialistic issues that are the focus of physics, in so much as religious and scientific truths overlap, they must be compatible.

This article first expands on the notion of the outward and inward journey of physics. Second, it discusses the link between cosmology, philosophy, and theology, introducing the concept of “metacosmology” to describe ideas on the border of cosmology and philosophy. Third, it focuses on the philosophical and theological aspects of black holes and shows that similar considerations apply. Fourth, it discusses time and singularities, these providing a link between cosmology and black holes and also residing on the physics/philosophy interface. Finally, it draws some general conclusions about the nature of science and the possible relevance of mind.

The Macro–Micro Connection and the Triumph of Physics

The outward journey into the macroscopic domain and the inward journey into the microscopic domain have revealed ever larger and smaller levels of structure in the universe, and these are summarized in the image of the cosmic uroboros in Figure 2. Planets, stars, galaxies, clusters of galaxies, and the entire observable universe are in the macroscopic domain; cells, DNA, atoms, nuclei, subatomic particles, and the Planck scale are in the microscopic domain.

Figure 2

The cosmic uroboros summarizes the different types of structure in the universe. Also shown are the cross-links associated with various forces. The macro and micro scales merge at the Big Bang, where new physics may arise. From Bernard Carr (2014).

The numbers at the edge indicate the sizes of these structures in centimeters. As one moves anticlockwise from the tail to the head, the scale increases from the Planck scale (10^–33cm) —the smallest meaningful distance allowed by quantum gravity—to the scale of the observable universe (10²⁷cm). So, the cosmic uroboros is like a clock, with each minute corresponding to one of sixty decades in scale. Although humans are not at the center of the universe geometrically, Figure 2 shows we are at the center of the scales of structure. This is because physics shows that the size of a human—or any living being—is roughly the geometric mean of the Planck length and the size of the observable universe.

The inward and outward journeys have also revealed the forces that determine the nature of these structures. These forces link the macroscopic and microscopic domains and are shown by the horizontal lines in Figure 2. For example, the “electric” line connects an atom to a planet because the force that binds the electron to a nucleus in an atom and the intermolecular force that binds solid objects are both electrical. The “strong” and “weak” lines connect a nucleus to a star because the strong force that holds nuclei together also provides the energy released in the nuclear reactions that power a star and the weak force that causes nuclei to decay also prevents stars from burning out too soon. The “SUSY” (supersymmetry) line connects certain types of particles to galaxies because these may provide the dark matter halos revealed by galactic rotation curves. The “GUT” (grand unified theory) line connects even smaller scales with galaxies and clusters because the density fluctuations generating these objects originated when the universe was hot enough for GUT interactions to be important.

So, progress of physics has connected the macroscopic and microscopic domains, revealing a surprising unity to the universe. The Big Bang is the ultimate macro–micro connection since it implies that the entire universe was once compressed to a tiny region of huge density. Since light travels at a finite speed, we can never see further than the distance light has travelled since the Big Bang; this is about 40 billion light-years, three times the age of the universe times the speed of light because the cosmic expansion helps light travel further. Near this cosmic horizon, more powerful telescopes probe to earlier times rather than larger distances, which is why the head of the snake meets the tail. This has led to an exciting collaboration between particle physicists and cosmologists. Although we now have a fairly complete picture of the history of universe after the first microsecond, our understanding becomes increasingly speculative at times earlier than that. In particular, we do not understand what happens as one approaches the top of the uroboros, where one encounters the multiverse on the macroscopic side and M-theory on the microscopic side.

The possibility of incorporating gravity into the unification of forces has led some physicists to proclaim that we are on the verge of obtaining a Theory of Everything. An intriguing feature of such a theory is the possibility of extra compactified dimensions. For example, Theodor Kaluza (1921) and Oskar Klein (1926) proposed that a fifth dimension could explain electromagnetism. Much later, “superstring” theory suggested there could be six extra dimensions, and the way they are compactified is described by the Calabi-Yau group. There were originally five superstring theories, but it was then realized that these are all embraced by “M-theory,” which has seven extra dimensions (Witten 1995). In a variant of this proposed by Lisa Randall and Raman Sundrum (1999), the eleventh dimension is extended so that the physical world is a four-dimensional “brane” in a higher-dimensional “bulk.” The development of these ideas is summarized in Figure 3. We have not yet detected these extra dimensions, as their effects only become noticeable at the top of the uroboros, where the energies are experimentally inaccessible.

Figure 3

The sequence of extra dimensions invoked in modern physics (a), one of which is extended in brane cosmology (b).

The inward and outward journeys have also led to dramatic changes in our worldview. The outward one has led to shifts from geocentric to heliocentric to galactocentric to cosmocentric worldviews and the radical change of view of space and time required by relativity theory. The inward journey has led to atomic theory, in which the atom is mainly empty space; quantum theory, in which particles are not solid but smeared out everywhere; and a unified view of the forces of nature through higher dimensions. These developments have shattered our common-sense view of reality, which has led more conservative physicists to reject them as philosophy rather than science. However, as demonstrated in the following section, the growth of knowledge has also entailed a change in our view of the nature of science.

Cosmology and the Philosophy/Theology Interface

Cosmology is now regarded as mainstream physics, but it is different from other branches of science: one cannot experiment with the universe or observe other ones, and speculations about processes at early times depend upon theories that have not been directly tested. In particular, we are clearly stretching physics to its limits when we speculate about the multiverse, as we cannot see further than the distance light has travelled since the Big Bang (10²⁵ m). Therefore, our belief in other universes might seem to be based on faith (like religion) rather than data, and some physicists are deeply uncomfortable with this proposal (Ellis and Silk 2014).

On the other hand, one might counterargue that the idea of other universes is consistent with the anthropic fine-tunings (Carter 1974; Carr and Rees 1979; Barrow and Tipler 1986). Although the multiverse proposal was not originally motivated by an attempt to explain these tunings, the two concepts are connected, for if there are many universes, the question arises as to why we inhabit this particular one, and our existence is clearly a relevant selection effect (Carr 2007). A huge number of universes will allow all combinations of constants to occur, so at least some of them must be life-supporting. Many physicists therefore regard the multiverse as providing the most natural explanation of the tunings (Tegmark 2003). If one wins the lottery, it is natural to infer that one is not the only person to have bought a ticket.

Of course, some physicists do not recognise anthropic speculations as proper physics, and a similar dilemma arises in other cosmological contexts. Therefore, I use the term “metacosmology” to describe aspects of cosmology that might be regarded as bordering on philosophy, reflecting the overlap represented in Figure 1. There is also an overlap with theology. However, since most cosmologists are more averse to theology than philosophy, it may be appropriate to regard cosmology, metacosmology, and theology as forming a sequence, with metacosmology occupying a middle ground. This is illustrated in Figure 4, which might be compared to Figure 1b.

Figure 4

This illustrates the sequence from cosmology to metacosmology to theology. The arrow indicates that the cosmology/metacosmology boundary evolves, with today’s metacosmology becomes tomorrow’s cosmology. From Carr (2014).

The perspective shown in Figure 4 can be applied to three possible explanations of the anthropic tunings, as indicated in Figure 5. The first is the multiverse proposal discussed earlier. At least some physicists would regard this as scientific and therefore put it in the cosmology circle of Figure 4a. The second possibility is based on the notion that consciousness is required to collapse the quantum wave function, so that the universe does not exist until consciousness has arisen. Once it has done so, it may reflect on the Big Bang, thereby forming a closed circuit and bringing the universe into existence (Wheeler 1977). This explanation is in the metacosmology circle because consciousness is not usually regarded as being in the domain of physics. The third possibility, clearly in the theology circle, is that God or some beneficent Creator made the universe specially for us by carefully placing a “pin” in the space of coupling constants (Holder 2004).

Figure 5

This indicates three explanations of the anthropic fine-tunings: the multiverse, consciousness collapsing the quantum wave function, and a fine-tuner. These relate to the three circles in Figure 4 and might be regarded as increasingly “wild” from a physics perspective. From Carr (2014).

These possibilities reflect increasing degrees of unpalatability for many physicists, with the A word (anthropic), the C word (consciousness), and the G word (God) being increasingly taboo. Even physicists uncomfortable with the notion of a multiverse would prefer it to invoking consciousness, but that is itself preferable to invoking God. On the other hand, all three explanations are logically possible, and the dichotomy between God and the multiverse is simplistic. While the fine-tunings certainly do not prove the existence God, nor would the multiverse preclude Him. I will not discuss such theological issues further here.

It should be stressed that the location of the cosmology/metacosmology boundary in Figure 4a is fuzzy. Some people would regard only a single self-created universe as proper physics—cf. the “universe in a nutshell” of Stephen Hawking (2001)—and dismiss the multiverse as philosophy. This issue was the focus of my dialogue with George Ellis, in which I defended and he opposed its scientific status (Carr and Ellis 2008). While conceding that the multiverse should currently be regarded as metacosmology, I argue that the cosmology/metacosmology boundary might eventually shift sufficiently for it to be reclassified. Perhaps one day we will create baby universes in a laboratory or visit other universes through wormholes!

The possibility that today’s metacosmology may become tomorrow’s cosmology is indicated by the right-pointing arrow in Figure 4. Indeed, the constant shift of the cosmology/metacosmology interface is illustrated by some historical examples:

• Even after Galileo had realized that the Milky Way is an assemblage of stars, the general opinion was that the region outside the solar system was beyond the domain of science. This is illustrated by comments of Auguste Comte (1835) on the study of stars: “We will never be able by any means to study their chemical compositions. The field of positive philosophy lies entirely within the Solar System, the study of the Universe being inaccessible in any possible science.” Comte had not foreseen the use of spectroscopy, which identifies chemical elements with absorption features in stellar spectra. New observational developments are hard to anticipate, so prescribing the limits of science is dangerous.

• Although general relativity gave cosmology a secure mathematical basis in 1915, resistance to extending physics beyond the galaxy continued for a further decade. Indeed, many astronomers did not believe there was anything beyond the galaxy. While Immanuel Kant had speculated as early as 1755 that some nebulae are “island universes” like the Milky Way, most astronomers adopted a galactocentric view until the 1920s. Indeed, Ernest Rutherford was so averse to the notion of the universe that he remarked, “Don’t let me hear anyone use the word ‘universe’ in my department!” The controversy led to a famous debate between Heber Curtis and Harlow Shapley in 1920. The issue was only resolved when Edwin Hubble measured the distance to M31 using Cepheid variable stars in 1924.

• A few years later, Hubble found that all galaxies are moving away from us with a speed proportional to their distance. This had been predicted by Alexander Friedmann in 1922 using the equations of general relativity, but Einstein himself still believed the Milky Way was the universe and invoked the cosmological constant to make it static. He only changed his mind several years after Hubble’s discovery. Georges Lemaître also derived Friedmann’s equations and was the first person to infer that the universe started in a highly compressed state. This is now almost universally accepted, and Lemaître is known as the father of the Big Bang theory, but the reaction of some eminent contemporaries is revealing. In 1927, Einstein told Lemaître: “Your maths is correct, but your physics is abominable.” Arthur Eddington (1931) rejected the Big Bang because it implied a fusion of physics and theology he found uncomfortable as a religious man: “Philosophically, the notion of a beginning of the present order of nature is repugnant to me.” This is an example of tensions on the physics/theology boundary.

• Even after Hubble’s discovery, cosmology was only accepted as a branch of mainstream physics when the cosmic microwave background was detected in 1964. Subsequent studies of this radiation have established cosmology as a precision science. Recent decades have brought two more important developments. First, observations of distant supernovae suggest that the expansion of the universe is accelerating (Riess et al. 1998; Perlmutter et al. 1999), although one expects it to slow down because of gravity. Some exotic form of “dark energy” is likely to be causing this, possibly related to the cosmological constant introduced by Einstein to allow a static model, leading to the concordance “LCDM” model. However, this is not certain, and many would prefer to relegate dark energy to the domain of metacosmology until we have determined its nature.

• Theory predicts that the early universe also underwent an accelerating phase—termed “inflation”—as a result of the vacuum energy (Guth 1981). This proposal initially seemed remote from observations, but then cosmic microwave background anisotropies were discovered by the cosmic background explorer satellite (Smoot et al. 1992) and subsequently measured with great precision with the Wilkinson Microwave Anisotropy Probe (Spergel et al. 2003) and Planck (2014). The fluctuations have exactly the form predicted by inflation, and the data determine various cosmological parameters very precisely. This illustrates how metacosmology can become cosmology because of new data.

Turning now to the theology boundary, cosmology addresses fundamental questions about the origin of matter and life, which are clearly relevant to religion, so theologians need to be aware of the answers it provides. In a sense, cosmology should provide the raw material from which religious belief is fashioned. Ellis (1993) uses the term “Cosmology” (with a capital C) to accommodate “the magnificent gestures of humanity,” whereas cosmology (with a lowercase c) just focuses on the universe’s physical features. On the other hand, astronomical revelations have sometimes clearly opposed theology. In particular, cosmology might appear to have removed the need for a Creator. The heavens have been progressively stripped of their divinity, and the extent of space is now so all-encompassing that there seems to be nowhere left for the God. Indeed, the more we understand the universe, from the vast expanses of the cosmos to the tiny world of particle physics, the more soul-less it seems to become.

Nor can we comfort ourselves with the delusion that humans are the focus of creation. The view that we have a direct link to the God (or Gods) who sustained the world was strongly challenged once science started to expand its domain of interest beyond the human scale. Indeed, the bigger the universe has grown, the more insignificant humans seem to have become, and modern cosmology might be regarded as the culmination of this process. The progress of physics has entailed our humbling and a loss of purpose. As Steven Weinberg (1977) says: “The more the Universe seems comprehensible, the more it seems pointless.”

However, recent decades have seen a reversal of this trend. As discussed in detail elsewhere (Carr 2006), this comes from the unity, beauty, and comprehensibility of the universe, the anthropic fine-tunings and the realization that mind may be a fundamental rather than incidental feature of the universe. Although humans are insignificant from a material perspective (i.e., compared to the huge length and time scales of the cosmos), we are hugely significant from a mental perspective because, as emphasized by the cosmic uroboros, our minds encompass the entire universe.

Black Holes and the Philosophy/Theology Interface

According to general relativity, when the matter in a region of mass M is sufficiently compressed, gravity causes it to collapse to a black hole. If there are no hidden dimensions, the size of the black hole (the Schwarzschild radius) is proportional to the mass (R_S = 2GM/c²), so the resulting density is inversely proportional to M². This result also arises in Newtonian theory, as first pointed out by John Michell. The sun would need to collapse to a radius of three kilometers and a density of 10¹⁹ kg m^–3 (i.e., 100 times nuclear density). Although the sun is not massive enough to do this, there are many situations in which black holes could form:

• The collapse of sufficiently massive stars that have finished their nuclear burning is the most likely mechanism for black hole formation. Stars smaller than 4M_☉ contract to white dwarfs, with collapse halted by electron degeneracy pressure. Those between 4M_☉ and about 10²M_☉ continue to burn in a stable manner until an iron/nickel core is formed, when nuclear reactions can release no more energy and the core collapses. If the core is small enough, it becomes a neutron star, with the collapse halted by neutron degeneracy pressure; at the same time, a hydrodynamic shock is reflected from the core and ejects the star’s envelope as a Type II supernova. However, if the core is large enough, collapse to a black hole ensues (MacFadyen et al. 2001).

• It is likely that the first stars to form were larger than 100 M_☉. During their hydrogen and helium burning phases, they would have been dominated by radiation, leading to large-amplitude pulsations. However, the pulsations are dissipated by the formation of shock waves, and the resulting loss of mass allows the stars to survive for the few million years of their main-sequence phase. They go unstable when oxygen begins to burn in the core, since the temperature becomes high enough for electron-positron pairs to be generated (Fowler & Hoyle 1964). Smaller cores explode, while larger ones collapse and form intermediate-mass black holes. This occurs for stars with mass larger than about 200 M_☉ (Woosley et al. 1982; Bond et al. 1984). The existence of such intermediate-mass black holes used to be regarded skeptically, but they are now believed to power ultra-luminous x-ray sources or gamma-ray bursts or be present in the middle of some globular clusters.

• The existence of much bigger stars has taken much longer to be accepted. Those larger than 10⁵ M_☉ are unstable to general relativistic instabilities, allowing them to collapse directly to “supermassive black holes” without undergoing nuclear burning (Fowler 1966). Such stars may possibly form in the centers of dense star clusters by dynamical relaxation. The stars would then be disrupted by collisions to form a single supermassive star from the newly released gas. Other routes to supermassive black hole formation may be coalescence of smaller black holes or accretion onto a single intermediate-mass black hole. Galactic nuclei have been shown to harbor supermassive black holes (Kormendy and Richstone 1995), with our own galaxy possessing one of 4 × 10⁶ M_☉. Quasars, which occur during the early evolution of galaxies, are powered by even larger black holes of mass between 10⁸ M_☉ and 4 × 10¹⁰ M_☉. supermassive black hole formation does not involve extreme physical conditions. For example, when a 10⁹ M_☉ object falls within its event horizon, it just has the density of water.

• Primordial black holes much smaller than a solar mass could have been produced in the early universe since the cosmological density rises indefinitely at early times, exceeding nuclear density within the first microsecond of the Big Bang. Comparing this with the Schwarzschild density implies that a primordial black hole produced at time t must have around the cosmological horizon mass c³t/G~10⁵(t/s)M_☉. Therefore, primordial black holes could span a huge mass range: from 10^–5 g for those forming at the Planck time to 10⁶ M_O for those forming at 10 s (the epoch of electron-positron annihilation). They may have formed from initial inhomogeneities or at some sort of cosmological phase transition (Zel’dovich and Novikov 1967; Hawking 1971; Carr and Hawking 1974). Those larger than 10²¹ kg (the mass of the moon) could have significant astrophysical consequences. For example, they could generate detectable lensing and dynamical effects or gravitational waves, and they might provide the dark matter (Carr et al. 2024).

In 1974, Hawking discovered that a black hole is not black after all but radiates thermally with a temperature inversely proportional to its mass (Hawking 1974). The temperature is around 10^–6 K and hence unobservable for a solar mass. But it is 10¹² K for 10¹² kg, corresponding to the mass of a mountain and the size of a proton. Such a black hole, which could only be primordial, radiates 100 MeV gamma-rays. However, as it loses mass as a result of this emission, it gets hotter and emits increasingly energetic particles. A black hole evaporates completely in a time proportional to the cube of its mass. This is unobservably long for a solar mass hole (10⁶⁶ y) but comparable to the age of the universe for 10¹² kg. So, such primordial black holes would be completing their evaporation today, and smaller ones would have done so much earlier. Black holes below 10²¹ kg can be regarded as quantum since they are hotter than the cosmic microwave background, so accretion does not swamp their evaporation. When the black hole mass gets down to about 10⁶ kg, the remaining energy is released in just a second, so the evaporation becomes explosive. These explosions are undetectable in the simplest picture, but according to James M. Cline and collaborators, primordial black hole explosions might explain some short timescale gamma-ray bursts (Cline et al. 1999).

Even if primordial black hole explosions are not detected, Hawking’s work was a tremendous conceptual advance because it unified three previously disparate areas of physics: general relativity, quantum theory, and thermodynamics. So, it has been useful to study primordial black holes even if they never formed. However, Hawking’s theory is only a first step toward a full quantum theory of gravity, since his analysis breaks down when the density reaches the Planck value of 10⁹⁷ kg m^–3 because of quantum gravitational fluctuations in the metric (Wheeler 1955). An evaporating black hole reaches this density when it gets down to the Planck mass of 10^–8 kg. A theory of quantum gravity would be required to understand the formation and evaporation of such an object. This might even allow black holes to leave stable Planck-mass relics rather than evaporate completely, in which case these relics could be dark matter candidates.

As indicated in Figure 3a, the existence of extra dimensions may come into play as a black hole shrinks towards the Planck scale. These are usually assumed to be compactified on the Planck scale, in which case their effects are unimportant for black holes heavier than the Planck mass. However, they are much larger than the Planck length in some models, with the consequence that gravity should grow much stronger at short distances than implied by the Newtonian inverse square law (Arkani-Ahmed et al. 2000). In other models, the extra dimensions are “warped” so that matter is confined to a 4D hypersurface (Randall and Sundrum 1999), as indicated in Figure 3b. In either case, the Planck energy (and hence the minimum black hole mass) is reduced. This has the important implication that black holes might be made in accelerators. For example, particles at the Large Hadron Collider reach an energy of roughly 10 TeV, which is equivalent to a mass of 10^–25 kg. When two such particles collide, the likelihood of forming a black hole is very small in the standard model because this is much less than the Planck mass of 10^–8 kg. However, if there are large extra dimensions, the Planck scale is lowered and the energy required to create black holes could lie within the LHC range. However, there is still no evidence for this.

Lee Smolin (1997) has pointed out an interesting link between black holes and cosmology. He argues that black hole formation can give birth to another expanding universe in which the fundamental constants are mutated. Our own universe may have been generated in this way (i.e., via gravitational collapse in some parent universe). Cosmological models with constants permitting the formation of black holes will therefore produce progeny (which may in turn produce further black holes, since the constants are nearly the same), whereas those with the wrong constants will be infertile. Through successive generations of universes, the physical constants will then naturally evolve to have the values for which black hole (and hence baby universe) production is maximized. Smolin’s proposal involves very speculative physics but there is no need for the anthropic principle because observers are just an incidental consequence of the universe being complex enough to give rise to black holes.

Figure 6 locates the various types of black holes around the cosmic uroboros according to their radius, this being proportional to their mass for three spatial dimensions. The well-established astrophysical black holes are on the right. The more speculative primordial black holes are on the left and possibly extend somewhat to the right. We have seen that black holes might be produced in accelerators if there are large extra dimensions.

Figure 6

The cosmic uroboros with black holes as a link between macro and micro physics. QSO stands for “quasi-stellar object,” MW for “Milky Way,” and IMBH for “intermediate-mass black hole.”

This discussion shows that the history of black holes—like cosmology—has entailed an evolving boundary between physics and philosophy. Their exotic properties resulted in their initial dismissal by many physicists; even today, they border on philosophy at the smallest and largest scales because the relevant physics is untestable (cf. metacosmology). In the first case, we have the possibility of black hole production in accelerators, but the energies required may not be attainable; in the second case, we have the possibility that our universe emerged from a black hole in some parent universe (Smolin 1997) or some previous cosmic cycle (Carr and Coley 2011), but neither of these can be observed. The theological implications of black holes are less clear than those of cosmology. However, as discussed in the following section, there are many links between black holes and cosmology, so such implications may still arise indirectly.

Time and Singularities: Linking Black Holes and Cosmology

Black holes and cosmology share two interesting features, both of which might themselves be regarded as being on the philosophy/theology interface: the existence of singularities and anomalous time behavior. Classical physics breaks down at a singularity, with the density perhaps becoming infinite there and the notion of space-time as a smooth continuum failing due to quantum gravity effects (Wheeler 1955). For a black hole, the singularity is at the center of the collapsing region and in the future (Penrose 1965); for cosmology, the singularity is associated with the Big Bang and in the past (Hawking 1966). There is a time anomaly in each case associated with both the singularity and the existence of horizons.

Let us first consider the time anomaly. The arena of Newtonian physics is three-dimensional space and time, both of which are absolute (i.e., the same for all observers). Newton’s paradigm is also mechanistic in the sense that the future and past are implicit in present. This was emphasized by Pierre Laplace, who pointed out that an omniscient intellect, knowing the position and velocity of every object in the universe, could predict its future and retrodict its past. This was the start of a trend in physics for the passage of time (i.e., the present moment) to become incidental rather than fundamental. I return to this issue later.

The arena of Einstein’s special relativity is four-dimensional spacetime, with objects being described by worldlines. Time is still different from space, because the distance in the time direction is mathematically imaginary, but there is no absolute present and moving clocks run slow. This time-dilation effect gives rise to the twin paradox, in which the twin who travels on a journey from Earth at high speed ages much less than one who remains on Earth. Time is more complicated in general relativity because space-time is curved by gravity, which means the duration experienced depends on the space-time path. Clocks run slow in a gravitational field, with the longest duration being experienced by a freely falling observer (e.g., an astronaut in orbit). The combination of special and general relativistic effects on time has been tested by flying atomic clocks on planes (Hafele and Keating 1972).

The effect of a gravitational field on clocks is most pronounced for a black hole. Time stops at the event horizon in the sense that an infalling astronaut appears to freeze there for external observers. However, it continues to pass in the astronaut’s own experience, and they may see the whole future of our universe while falling towards the central singularity. By orbiting close to the black hole without falling inside it, the astronaut can travel arbitrarily far into the future relative to someone on Earth, but time travel into the past is more challenging. In special relativity, this would require tachyons (i.e., objects moving faster than light), which are probably precluded. However, it may be possible in general relativity due the existence of closed time-like curves. For example, these arise in a rotating universe (Gödel 1949) and can be generated by a rotating cylinder (Tipler 1974). One can also travel into the past through a wormhole—different from a black hole because there is no singularity—but only to a time after it was created (Thorne 1994). It is not clear whether this is physically realistic, since one needs negative energy to hold the wormhole mouth open and the chronology protection conjecture (Hawking 1992) may preclude this. So, this notion is also on the physics/philosophy interface.

Another anomaly relates to the various arrows of time, each corresponding to some form of past/future asymmetry: cause and effect, birth and death, the cosmic expansion, retarded rather than advanced radiation, quantum collapse. There is also the psychological arrow, associated with consciousness, to which I return later. The puzzle is that the laws of fundamental physics are time reversible, apart from a tiny charge-parity violation. It is often argued that all these arrows arise from the second law of thermodynamics: entropy is always increasing because the environment is far from equilibrium. The most natural explanation for this increase is that the universe began in a low-entropy state (the Past Hypothesis), corresponding to the Big Bang, although the reason for this is not well understood.

This raises the issue of the origin of time. Aristotle argues there could be no beginning of time, whereas St. Augustine argues that God created time with the universe. Of course, neither knew about the Big Bang, which might seem to support the Augustinian view. However, some cosmologists envisage the universe undergoing a “big bounce” at some point in the past (e.g., due to a cosmological constant), so that the current expanding phase would have been preceded by a collapsing phase. One could even have a cyclic model with successive expansion and contraction phases (Tolman 1934), as arises in the ekpyrotic model (Steinhardt and Turok 2006). In this case, the universe would be eternal, supporting the Aristotelian view.

Let us now consider the singularity anomaly. Until a few decades ago, it was assumed that physics would break down at a singularity, but recent developments have changed this perspective. Indeed, quantum cosmology purports to describe the physics of the Big Bang itself. In this approach, one associates probabilities with three-dimensional spatial hypersurfaces and then determines the evolution of the universe by using a “sum-over-histories” calculation, which allows for all possible paths from some initial 3-space to some final one. The crucial development in this approach was the “no boundary” proposal of James B. Hartle and Hawking (1983). This removes the initial surface by making time imaginary (i.e., spacelike) at the Planck epoch (10^–43 s after Big Bang). This adroitly sidesteps the usual philosophical problems associated with a moment of creation and means the universe can be created as a quantum fluctuation out of nothing (Isham 1988).

This brings in the link with theology. Pope Pius XII once proclaimed that the Big Bang theory supports the account of Genesis, since the physicist’s description of creation must break down at a sufficiently early time. One might argue that God is required to “light the fuse.” On the other hand, cosmology seems to provide an ever more complete description. For example, one could envisage the following dialogue:

How did the universe originate? The universe started as a state of compressed matter. But where did the matter come from? The matter arose from radiation as a result of GUT processes occurring when the universe had the size of a grapefruit. But where did the radiation come from? The radiation was generated from empty space as a result of a vacuum phase transition. But where did space come from? Space appeared from nowhere as a result of quantum gravity effects. But where did the laws of quantum gravity come from? The laws of quantum gravity are probably no more than logical necessities.

Each step in this dialogue represents many years of theoretical work, but the implication is clear: no first cause is needed, because the universe contains its own explanation. There is an obvious connection here with the theological concept of creatio ex nihilo, and Willem B. Drees (1987; 1990) has explored the theological implications of quantum cosmology in some detail. Even if quantum gravity is necessary, it may not change the nature of the Big Bang predicted by classical theory, and the existence of Hilbert spaces etc. is perhaps more mysterious than the universe itself (Russell 1996). Also, there is a distinction between the question of how the universe came into existence and why it did so (Carr 2012). Even if the laws of quantum gravity are logically necessary, this need not imply there has to be a physical universe they describe.

We have seen that theological considerations may also arise in discussions of the anthropic tunings. The key issue here is whether some of the physical constants are contingent on accidental features of symmetry breaking and the initial conditions of our universe or whether some fundamental theory will determine them all uniquely (Rees 2001). The two cases correspond to the multiverse and single universe options, respectively. This relates to Einstein’s famous question: “Did God have any choice when he created the Universe?” If the answer is no, there would be no room for the anthropic principle. If the answer is yes, then trying to predict the values of the constants would be as forlorn as Johannes Kepler’s attempts to predict the spacing of the planets based on the properties of Platonic solids.

Another important problem on the interface of physics and philosophy is the passage of time. In the “block universe” of special relativity, nothing identifies the present moment (Savitt 2006). Past, present, and future coexist, so if consciousness is viewed as travelling along the world-line of the brain, as illustrated in Figure 7a, that motion itself cannot be described by relativity theory. Thus, the physical time of the outer world is distinct from the mental time of the inner world. This also relates to the problem of free will. At any experiential time, one feels that there are a number of possible future world-lines, as illustrated in Figure 7b, with one’s conscious will selecting one of these. This implies that the past is fixed but the future undetermined. But this contradicts the mechanistic block universe. These failures of relativity theory may also relate to quantum theory, because the collapse of the wave function to one of a number of possible states implies a basic irreversibility. Indeed, Figure 7b is reminiscent of the Everett “many worlds” picture (Everett 1957).

Figure 7

Illustrating two problems of consciousness from a relativistic perspective and their possible resolution: (a) the passage of time; (b) the selection of possible futures; (c) describing flow of conscious time with a second time.

The flow of time and collapse of the wave function seem to require what is termed a “growing block universe” (Ellis 2006). However, this does not describe the flow itself, so we need some extra ingredient. The philosopher C. D. Broad (1953) proposed that a second type of time (t₂), different from physical time (t₁), is required, and this is illustrated in Figure 7c. The progression of consciousness is then represented as a path in a five-dimensional space. At any value of t₂, a physical object has a unique future world-line in a mechanistic model or a number of possible world-lines in a quantum model. However, the intervention of consciousness or quantum collapse allows the future world-line to change or be selected from, respectively. So, the past in t₁ is uniquely prescribed, but the future is fuzzy. This interpretation may also be suggested by Figure 3b, in which space-time is viewed as a four-dimensional brane in a five-dimensional bulk. In the simplest case, the brane corresponds to flat space-time and is static. However, there is a cosmological case—called “brane cosmology”—in which the brane is curved and moves through the bulk (Maartens 2004), thereby generating the cosmic expansion. By identifying the extra dimension with t₂, one can link cosmology with an old philosophical problem (Carr 2021).

Concluding Remarks

In drawing conclusions about the physics/philosophy interface, I have stressed that the domain of legitimate physics changes with time, despite the resistance from more conservative physicists. The domain of legitimate physics is also sociologically determined. For example, one reason the anthropic principle has become more respectable in recent years is that it has been supported by physicists with the stature of Steven Weinberg (1987), Martin Rees (2001), Leonard Susskind (2005), Alexander Vilenkin (2006), and Frank Wilzcek (2007). The growth of knowledge has also entailed a change in the nature of science itself. In this context, Weinberg (2007) has remarked: “We usually mark advances in the history of science by what we learn about nature, but at certain critical moments the most important thing is what we discover about science itself. These discoveries lead to changes in how we score our work, in what we consider to be an acceptable theory.” Weinberg is referring specifically to M-theory and the multiverse, and the question of whether these proposals should be regarded as physics or philosophy is still contentious (Woit 2006; Smolin 2007). However, this insightful remark expresses a more general truth about the nature of science.

The current situation is very special in one sense: the macro and micro physics/philosophy boundaries in Figure 2 have now merged, with the very large and very small meeting at the top of the cosmic uroboros. Does this merging represent a transformation of physics—of the kind that tends to happen with every paradigm shift (Kuhn 1970)— or the completion of physics? I favor the former view and suggest that one feature of the new paradigm may be some reference to consciousness. This contrasts with the mainstream view that physics is concerned with a “third-person” account of the world (experiment) rather than a “first-person” account (experience), thereby excluding any reference to consciousness. On the other hand, some physicists are skeptical of claims of being close to a Theory of Everything when such a conspicuous aspect of the world is neglected. Thus, Roger Penrose (1994) predicts that “[w]e need a revolution in physics on the scale of quantum theory and relativity before we can understand mind,” and Andrei Linde (2004) suggests that “consciousness is as fundamental to the cosmos as space-time and mass-energy.”

Certainly, there are several hints from physics itself that mind may be a fundamental rather than incidental features of the universe, and I discuss this elsewhere (Carr 2006). A related point comes from contemplating the vast array of complex structures in Figure 2. These have evolved in the 14 billion years since the Big Bang, and the culmination of this complexity is the human brain. It is therefore curious that the most remarkable attribute of the brain—consciousness—is neglected by physics. It is also interesting that historically the uroboros represents the way in which we have systematically expanded our outermost and innermost limits of awareness through the progress of physics.

But how could the marriage of relativity theory and quantum theory at the top of the uroboros involve mind? I argue that most mental experiences involve some form of space different from ordinary physical space but maybe amalgamated with it. In particular, my proposal identifies this amalgamated space with the higher-dimensional space of M-theory (Carr 2021). After all, if the physical world is just a four-dimensional brane in a five-dimensional bulk, as indicated in Figure 3b, one is bound to ask what else resides in the bulk, and the only other entities of which I am aware are mental ones. This also relates to linking the passage of time with brane cosmology.

Let us conclude with some remarks about the physics/theology interface. The requirement that physics and religion should be compatible has two important implications. First, it makes a “God of the Gaps” view very unattractive from a theological perspective, since it implies that religion is always on the retreat as physics advances. Second, since physics progresses by a series of paradigm shifts, each providing a better approximation to reality than the previous but none representing ultimate truth, one should be wary of religious claims of possessing absolute (God-given) truths. Indeed, one might expect religion (like physics) to undergo paradigm shifts, so that some questions addressed in the past (e.g., the location of heaven and hell) become meaningless. Clearly, none of the pro- or anti-divine arguments from physics are decisive, and the evidence provided by the study of the physical world will probably always be equivocal. Even those physicists who are mystically inclined have not usually based their faith on scientific revelations (Wilbur 2001). Some merely take the view that the existence of God is more consistent with their experience than the nonexistence of God (Priest 2016). This article has stressed the involvement of Christian priests in black holes in cosmological research, but this need not imply any specific theological agenda. The faith connection may simply be that they are exploring the richness of God’s creation.