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Science Fiction Meets Science Fact: Black Holes and the Feasibility of Dr. Who’s TARDIS


Do black holes, akin to fading old soldiers, simply dissipate? Do they burst like hyperdimensional balloons? Perhaps they undergo a cosmic transformation, crossing a threshold that reverses their inherent nature, turning them into inverse anomalies. These anomalies may defy entry through their event horizons but continuously emit energy and matter back into the universe.

In his recent work, “White Holes,” physicist and philosopher Carlo Rovelli directs his expertise toward these enigmatic cosmic phenomena. Delving beyond the event horizon, he explores the theoretical intricacies and speculates on what might lie at the core of these infinitesimally small yet infinitely captivating gravitational points. In this excerpt from “Hitting the Books,” Rovelli delves into a scientific divide within the astrophysics community regarding the fate of information that, based on our current understanding of the universe’s rules, cannot be destroyed once trapped within an inescapable black hole.

Riverhead Books

In 1974, Stephen Hawking made an unexpected theoretical breakthrough: black holes are compelled to emit heat. This phenomenon, akin to a quantum tunnel effect, is simpler than the bounce of a Planck star. Photons confined within the horizon manage to escape through a quantum physics-enabled process, “tunneling” beneath the horizon.

Much like a stove, black holes release heat, and Hawking calculated their temperature. The emitted heat carries away energy, causing the black hole to progressively lose mass (since mass is energy). Consequently, it becomes lighter and smaller, and its horizon contracts. In technical terms, we describe this process as the “evaporation” of the black hole.

Heat emission stands out as a distinctive feature of irreversible processes—those that unfold in one time direction and cannot be reversed. When a stove emits heat, it warms a cold room, showcasing an irreversible event. Conversely, one wouldn’t observe the walls of a cold room emitting heat to warm a preheated stove. Irreversible processes are invariably accompanied by heat production or an analogous phenomenon. Heat serves as the hallmark of irreversibility, distinguishing the past from the future.

Hence, in the life of a black hole, there is at least one unequivocally irreversible aspect: the gradual reduction of its horizon.

However, it’s crucial to note that the shrinking of the black hole’s horizon does not imply a reduction in the size of its interior. The interior largely maintains its size, with the volume continuously expanding. The contraction specifically applies to the horizon itself, a nuanced aspect that often leads to confusion. The phenomenon of Hawking radiation primarily concerns the horizon, not the profound interior of the black hole. Consequently, an aging black hole exhibits a distinctive geometry: an expansive interior that continues to grow alongside a minute (due to evaporation) horizon enveloping it. Imagine an aged black hole resembling a glass bottle skillfully manipulated by a Murano glassblower, where the volume of the bottle expands while its neck narrows.

During the transition from black to white, an old black hole may possess an exceedingly small horizon coexisting with an extensive interior—a miniature shell containing vast spaces, reminiscent of a fable.

Fables often depict small huts that, when entered, reveal hundreds of spacious rooms—an seemingly implausible scenario, reminiscent of fairy tales. However, in reality, enclosing a vast space within a small sphere is entirely possible.

The seeming peculiarity arises from our familiarity with the notion that space’s geometry is straightforward, following the principles of Euclidean geometry studied in school. Yet, in the real world, gravity distorts the geometry of space. This distortion enables a substantial volume to be confined within a diminutive sphere. The gravitational influence of a Planck star induces such a profound distortion.

An ant accustomed to residing on a vast, flat plaza would experience astonishment upon discovering that a small hole grants access to a sizable underground garage. Similarly, for us with a black hole, the lesson from such marvels is a reminder not to blindly adhere to familiar ideas— the world is more peculiar and diverse than our imaginations can conceive.

This existence of extensive volumes within confined horizons has stirred confusion in the scientific realm, sparking a heated and ongoing debate within the scientific community. In the following section, I delve into this dispute. It’s more technical than the preceding content, so feel free to skip it, but it provides insight into a dynamic scientific discourse.

The contention revolves around the capacity to encode information within an entity featuring a substantial volume but a limited surface. One faction within the scientific community firmly asserts that a black hole with a modest horizon can only accommodate a limited amount of information, while another faction disagrees.

But what does it mean to “contain information”?

In a sense, it’s comparable to determining whether there are more items in a box holding five large and heavy balls or in a box containing twenty small marbles. The answer hinges on the interpretation of “more things.” The five balls are larger and weigh more, indicating that the first box contains more matter, substance, energy, and overall stuff. In this context, the box of balls has “more things.”

However, the quantity of marbles surpasses that of the balls. In this context, there are “more things,” more intricacies, in the box of marbles. If we aimed to convey signals by assigning a unique color to each marble or ball, we could transmit more signals, more colors, and more information with the marbles due to their greater number. To be precise: describing the marbles would require more information than describing the balls because of their higher quantity. In technical terms, the box of balls holds more energy, while the box of marbles contains more information.

As an old black hole undergoes substantial evaporation, its energy diminishes significantly due to Hawking radiation. The contentious question arises: Can it still harbor considerable information after losing a substantial portion of its energy? This is where the debate unfolds.

Some colleagues have convinced themselves that it’s implausible to store a substantial amount of information beneath a small surface. In other words, they firmly believe that when most of the energy is depleted, and the horizon has dwindled, only a minimal amount of information can persist within.

On the contrary, another faction of the scientific community, to which I am affiliated, staunchly asserts the opposite. They argue that even in the case of a significantly evaporated black hole, the information it contains can still be substantial. Each side is unwavering in its conviction that the other has veered off course.

Such disagreements are commonplace in the annals of scientific history; one might say they are the essence of the discipline. They can endure for extended periods, marked by scientists splitting, quarreling, debating, and challenging one another. Eventually, however, clarity emerges, with some proving to be correct and others conceding their errors.

In the late nineteenth century, the field of physics was deeply divided into two opposing factions. One faction, following Mach, asserted that atoms were merely convenient mathematical constructs, while the other, adhering to Boltzmann, argued that atoms exist in reality. The debates were intense, and although Ernst Mach was a prominent figure, it was ultimately Boltzmann who was proven correct. Today, we can even observe atoms through a microscope.

I believe that my colleagues who are steadfast in their belief that a small horizon can only accommodate a limited amount of information have made a significant error, despite the apparent persuasiveness of their arguments. Let’s examine these arguments.

The first contention is that it is possible to calculate the number of elementary components (such as molecules) comprising an object by considering the relationship between its energy and temperature. Since we know the energy of a black hole (its mass) and its temperature (computed by Hawking), we can perform the calculations. The outcome suggests that the smaller the horizon, the fewer elementary components it possesses.

The second argument is based on explicit calculations derived from the two most studied theories of quantum gravity—string theory and loop theory. Both of these rival theories independently completed this computation around 1996, revealing that the number of elementary components decreases when the horizon is small.

While these arguments may appear robust, many physicists have embraced a “dogma” (a term they use themselves) on their basis: the notion that a small surface can only contain a limited number of elementary components, equating to minimal information. If the evidence supporting this “dogma” is compelling, where does the mistake lie?

The mistake lies in the fact that both arguments exclusively focus on the components of the black hole that are observable from the outside, as long as the black hole maintains its current state. These observable components are confined to the horizon. Essentially, both arguments disregard the potential existence of components within the extensive interior volume. They are articulated from the viewpoint of an observer positioned far from the black hole, incapable of witnessing its interior, and assuming that the black hole will persist in its current state indefinitely. If the black hole remains unchanged forever—remember—observers at a distance will only perceive what is outside or immediately on the horizon. It’s as if, for them, the interior doesn’t exist.

However, the interior does exist! Not only for those, like us, who venture inside, but also for those who exercise patience, awaiting the transformation of the black horizon into white, enabling the release of what was previously trapped within. In essence, considering the calculations of the number of components in a black hole provided by string theory or loop theory as comprehensive overlooks Finkelstein’s 1958 article. The portrayal of a black hole from an external standpoint is incomplete.

The computation in loop quantum gravity is enlightening: the number of components is precisely determined by counting the quanta of space on the horizon. Yet, upon closer examination, the string theory calculation achieves the same by assuming the black hole is stationary and is grounded in observations from a distance. It, by hypothesis, neglects what is inside and what will be observable from afar after the hole has completed its evaporation—once it is no longer in a stationary state.

I believe that certain colleagues err due to impatience, seeking resolution before the end of evaporation when quantum gravity becomes inevitable, and because they overlook considerations beyond immediate observation—a pair of common mistakes in life.

Adherents to the dogma encounter a dilemma known as the “black hole information paradox.” They firmly believe that once a black hole has evaporated, there is no residual information inside. However, anything entering a black hole inherently carries information, posing the question of where this information goes. Information cannot simply disappear. So, how is it resolved?

In attempting to address the paradox, proponents of the dogma propose imaginative and intricate scenarios for the escape of information from the black hole. They suggest that it might exit through mysterious channels, such as within the folds of Hawking radiation—drawing parallels to Ulysses and his companions hiding beneath sheep to escape the cave of the cyclops. Alternatively, they speculate about hypothetical invisible canals connecting the interior of the black hole to the outside. Essentially, they resort to grasping at straws, seeking convoluted ways to uphold their dogmatic beliefs when faced with challenges.

However, the information that enters the black hole’s horizon doesn’t need to employ arcane or magical means for its escape. Instead, it simply emerges after the horizon undergoes transformation from a black to a white state.

In his final years, Stephen Hawking reassured that there’s no need to fear life’s black holes; sooner or later, a way out will be found. This exit, he suggested, lies in the form of the child white hole.

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