Hawking Radiation Explained

Hawkings radiation

Stephen Hawking is one of the most influential scientists of the 20th century. He is well known for not letting a motor neuron disease stop him from pushing the frontiers of his knowledge of the universe. Stephen Hawking has made several profound contributions to physics, ranging from quantum mechanics to cosmology. While he is vividly famous for writing the book “A Brief History of Time,” there is also an astronomical phenomenon that bears his name, “Hawking Radiations.” Soon after Albert Einstein formulated his theory of general relativity in 1915, physicists realized that the mathematics behind it allows for the gravitational collapse in areas of extreme density, such as a massive star’s dead center. Karl Schwarzschild, in particular, represented the first solution of the general theory of relativity and named these massive stars “frozen stars.” Today, we know them by the name first used by Wheeler in 1967, “black holes.” These supermassive dead stars are known for their immense gravitation pull, through which even light can not escape. In 1975, by taking into account the outcomes of quantum mechanics, Hawking presented a theory that black holes should emit radiations for the underlying physics to hold. In other words, the black hole should lose mass over time by giving off Hawking Radiations. If proved to be factual, Hawking radiation would mean black holes can emit energy, and therefore, shrink in size, with the tiniest of these insanely dense objects exploding rapidly in a puff of heat (and the largest slowly evaporating over trillions of years in a cold breeze). Hawking’s proposition of blackholes emitting radiation is a mathematically established concept; however, there is no practical observation of this phenomenon. The mathematics that Stephen hawking employed for this theory resulted in a puzzle called “information paradox,” which is discussed later in this article. To understand the concept of “Hawking Radiation,” let’s first discuss black holes.

Black holes

Black holes are one of the strangest celestial objects. Their immense gravitational pull does not allow anything to escape from its vicinity, and therefore, there is no direct way to confirm all the theoretical propositions about black holes. There is a common misconception of viewing a black hole as a literal hole in space; however, that’s not the case. The formation of black holes occurs when a star with a mass greater than 2.16 times the mass of our sun enters the last stage of its stellar evolution. During the stellar evolution, the core of a star undergoes nuclear fusion, changing from hydrogen to helium and subsequently up to iron over several billion years. This fusion process produces a tremendous amount of energy in the form of radiation, which in turn creates a radiation pressure force that pushes against gravity, preventing a star from collapsing under its own gravity. As long as the fusion continues inside the core, the star remains in a stable hydrostatic equilibrium. For stars with a mass greater than around 2.16 solar masses, the fusion stops when the core becomes entirely of iron. The balance between gravitational and radiation pressure forces collapses when the mass (or density) of the iron core reaches a critical value, and the entire star implodes, adding more mass to the core in a fraction of seconds, accompanied by an explosion of tremendous energy and heavier (atomic mass greater than iron) elements into space. This phenomenon is observed as a supernova in cosmology, and it either leaves behind a neutron star (for stars less than 2.16 solar masses) or a black hole (for stars greater than 2.16 solar masses).

The black sphere that astronomers observe as a black hole is not the surface of a dead star but a region of space-time called the event horizon, beyond which our natural laws of physics may or may not hold, and the applied physics is purely hypothetical. The center of this sphere is believed to be a point called the singularity, where all the mass of a black hole is supposedly concentrated. It is a common misbelief that anything that passes through the event horizon is drawn into the black hole and ultimately vanishes as it hits the singularity; instead, the space-time continuum within the event horizon is so warped that even light appears to be trapped within it, and therefore, it is difficult to tell with absolute certainty about what happens to the thing that passes the event horizon. Einstien’s general theory of relativity effectively explains why nothing can escape an event horizon of a black hole; however, Stephen Hawking suggested that the quantum field theory enables energy and information to escape from a black hole. Hawking’s insight was based on a phenomenon of quantum physics known as virtual particles and their behavior near the event horizon. To understand the role of virtual particles in Hawking’s theory of black holes emitting radiations, let’s first understand what we anticipate as virtual particles.

How do Black Holes emit Hawking Radiations?

Quantum Field Theory (QFT) is one of the most revolutionary theoretical frameworks in physics that has provided us with a distinct and more accurate perspective to understand the fundamental nature of reality. At its core, QFT is the combination of classical field theory, special relativity, and quantum mechanics. The basic idea of quantum field theory suggests that space is filled with quantum fields that oscillate with different frequencies, and the particles that we observe are the excitations in the underlying quantum field associated with that particle. For instance, an electron is an excitation in the electronic field that has a zero value everywhere else except where the electron is being observed. These excitations are quanta (packets of specific energies) of waves that can have several modes of vibrations (one quantum can vibrate with different frequencies and behave differently). According to Heisenberg’s uncertainty principle, these vibrational modes must go through a temporary random change in the amount of energy as they progress through time. These energy fluctuations are known as quantum fluctuations, the transient disturbances in quantum fields that govern the interaction of real particles. For instance, two electrons (excitations in an electric field) will repel each other by exchanging energy through causing a transient disturbance (quantum fluctuation) in an underlying electromagnetic field. In general, a quantum fluctuation in an electromagnetic field represents the elementary particle photon; however, we do not observe any photon (light) when two electrons repel each other. Physicists work around this inconsistency by employing an abstract mathematical concept of “virtual particles” that arises from the perturbation theory of the quantum field theory. It is important to not consider virtual particles as real particles, since they are best explained as a mathematical tool to represent the infinite ways in which a fluctuating quantum field can behave. The objective existence of virtual photons is limited by Heisenberg’s uncertainty principle; however, some physically real effects, such as the Unruh effect and the Casimir effect, can not be explained without considering virtual particles. Moreover, quantum field theory also suggests that a quantum fluctuation can have both positive and negative frequencies. A negative frequency can be thought of as a vibrational mode that propagates backward in time (referred to as antiparticles). Extending these ideas to a vacuum state, physicists found that a quantum vacuum state corresponds to the continuous creation and annihilation of virtual particle-antiparticle pairs, which results in the lowest possible finite energy of a vacuum.

Stephen Hawking tried to apply this idea to a curved space-time and wondered what would happen to the quantum fluctuation near an event horizon of a black hole. To answer this question accurately, the requirement is the full union of quantum mechanics and the general theory of relativity (the theory of everything), which we still don’t have. Hawking came up with an ingenious workaround for this problem. He considered a quantum field in a vacuum state, extending across the universe, and suggested that when a black hole is formed, the surrounding quantum field’s vacuum state is disrupted in such a way that virtual particle-antiparticle pairs, whose existence and annihilation previously kept the energy to the lowest finite possible value, can no longer recombine to annihilate. One of the pair falls into the black hole while the other escapes. The particle that fell into the black hole must have had a negative energy (an antiparticle) to conserve total energy. This would cause the black hole to lose mass. To an outside “future” observer (in reference to the moment of black hole creation), it would appear that the black hole has just emitted a particle,” the Hawking’s Radiation.” Stephen Hawking employed the mathematics of Bogoliuvob transformation to approximate the effect of curved space-time on quantum fluctuations by connecting them to the region of flat space-time. There are, however, several equally valid physical interpretations of the result that this mathematics concludes. One of the most profound interpretations tells that the wavelength of the out-scattered quantum fluctuation should be of a similar order to the Schwarzschild radius of the black hole (radius of the event horizon). In other words, large black holes should appear cold (red) and the small ones should appear extremely hot (blue). Nonetheless, the radiation of such a huge wavelength would cause an enormous delocalization of the wave ( because of the Heisenberg Uncertainty Principle). This also suggests that the particles emitted by black holes as Hawking’s radiations must be photons or other massless particles since particles with mass would have higher energy and correspondingly low wavelength. Although hawking’s idea of black holes emitting radiations is undoubtedly brilliant, the origin, the splitting of vacuum fluctuations, is purely hypothetical and does not have any physical consequence to support it; however, it has raised several interesting questions about the mysteries of the black holes. One of these most interesting enigmas is the black hole information paradox in which hawking radiations appear to destroy what should be a conserved quantity in quantum mechanics.

The Black Hole Information Paradox

(Note:- The word “information,” in this context, is used simultaneously for any parameter that describes the state of a system)

Stephen Hawking tried to demystify the nature of the black hole with Hawking’s radiations using the general theory of relativity and quantum mechanics, but these same radiations contradict the very foundation of quantum mechanics. The fundamental question that later became the information paradox was “what happens to the objects that pass the event horizon?” In technical words, what happens to the entropy, “the information,” of an object that falls in the vicinity of the black hole’s event horizon? In physics, if we have the information for a given state of a particle (i.e. its momentum, position, energy, etc.), we can calculate the future state of the particle by using laws of physics and equations of motion. For instance, if we know the mass of a ball, the forces acting on it, and the air resistance, we can precisely calculate its trajectory using projectile equations. In other words, perfect knowledge of a system in the present perfectly predicts how the system will evolve in the next instant, and so on; however, this deterministic nature of laws of physics does not guarantee that the same laws can perfectly predict the states backward in time, the past. This concept is known as time-reversal symmetry (or asymmetry) in the language of physics. Another important concept of physics that supports its predictive accuracy is the “conservation laws.” For instance, the verification of any equation of motion in classical mechanics is done by checking if the energy and momentum are conserved for the initial and the final state. If we cannot predict the past states of a system using the information of its current state, we say that the information has been destroyed; in other words, the law of conservation of information has been violated. In quantum mechanics, the state of any particle is defined by the wave function of the wave associated with that particle, and the behavior of that wave function is governed by the Schrödinger equation. It can perfectly predict how a quantum wave function should progress, both backward and forward in time, for a given environment (quantum potential). In other words, quantum mechanics suggests that information is time-reversal invariant, even if we cannot access it for the past, i.e, information may change over time, but it can neither be created nor be destroyed. This is known as the law of conservation of quantum information. According to Stephen Hawking, the black holes should decrease in size over time by emitting Hawking radiations. Nevertheless, if the entity disrupted by the creation of a black hole was a pure quantum state (quantum fluctuations), the transformation of that state into the mixed state of Hawking radiation (splitting of virtual particles) would destroy information about the original quantum state because of the black hole evaporation. This violates the law of conservation of information and thus presents the black hole information paradox. In simpler terms, if we assume that both the general theory of relativity and the quantum field theory is completely correct, as we currently understand them, then Hawking’s radiations must exist, and they must violate the law of conservation of information via black hole evaporation. During the last few decades, physicists have proposed several solutions to this paradox; however, none of them completely explain the phenomenon due to the lack of a proper mathematical framework. One of the most profound solutions to this paradox is the holographic principle proposed by physicist Gerard ‘t Hooft, which suggests that the information of all the objects which will ever fall in is entirely contained in surface fluctuations of the event horizon and does not get destroyed. Although physicists are not certain about the above-mentioned theories, Stephen Hawking has proved mathematically that if quantum mechanics is taken into account, the black holes are not entirely black. Let’s discuss the role of Hawking’s radiation in enhancing our understanding of the universe.

Why is Hawking Radiation Important

The laws of physics are made such that they should hold for any given case. Since the dawn of black hole physics, the physicists had this thought that since nothing can escape the gravitational vicinity of a black hole, there is no way to confirm whether our usual laws of physics apply to black holes or not. The concept of Hawking’s radiation provided physicists with a new insight to understand the physics of the black hole. It provides a more consistent view of black hole thermodynamics by showing how black holes interact thermally with the rest of the universe. By attempting to connect the laws of gravity, thermodynamics, quantum mechanics, and relativity, the study of  Hawking’s radiation also pointed that there should be a “theory of everything” — a single, unified theory of physics that described the behavior of the universe. Although there is no experimental evidence of the existence of Hawking’s radiation, most of the physicist consider it to be true and believe that further study on Hawking’s radiation would unveil a deeper understanding of the universe.


Is Hawking Radiation Dangerous

The mathematics of Hawking’s radiation suggests that its wavelength should be of a similar order to the Schwarzschild radius of the black hole, and therefore, it should be a low-energy photon or another massless particle. In other words, for Hawking’s radiations to be ionizing (dangerous), they should be of very high energy (i.e., high frequency/ low wavelength), which could only be possible if the radiation is originating from an extremely small black hole.


Interesting Facts

  • Stephen Hawking was 21 years old when he was first diagnosed with a motor neuron disease called amyotrophic lateral sclerosis (ALS). The doctors predicted that he would only live for a couple of years. Instead, he lived for 55 more years and then died on 14 March 2018. When asked about the study of physics taking him “beyond physical limitations,” Hawking famously answered, “The human race is so puny compared to the universe, that being disabled is not of much cosmic significance.”
  • Hawking was initially perplexed by the idea of Hawking’s radiations because he thought black holes were celestial traps that absorb energy; however, he discovered that there was scope for this phenomenon by combining quantum theory, general relativity, and thermodynamics in 1974, distilling it into one (relatively) basic yet elegant formula. Hawking later said that he wanted this equation engraved on his tombstone.
  • Stephen was always keen for his work to be accessible to everyone, not just scientists. He wrote books that explained his theories in simple terms for everyone to understand, including a children’s book. His most famous book, “A brief history of time,” sold more than 10 million copies worldwide.
  • Although Hawking’s radiations are not experimentally confirmed yet, a similar phenomenon has been recreated in the laboratory. A team of researchers at the Israel Technion Institute of Technology have generated analogs of tiny black holes that work with sound rather than light, and they have managed to demonstrate something similar to Hawking radiation. These experiments have confirmed two of the physicist’s predictions: that the radiation is spontaneous, i.e., it is generated from space, and it is stationary, i.e., does not change in intensity over time.
  • In 2018, Stephen W Hawking, Malcolm J. Perry, and their collaborators found a theoretical way to propose that black holes can have “soft hair,” an infinite collection of extra properties that a black hole can have. This metaphorical hair “suggests ways in which black holes may keep track of information at their surfaces so that this information is ultimately recovered.”
  • Although Stephen Hawking was never awarded Nobel Prize for his scientific contribution, he has earned plenty of other awards including the Fundamental Physics prize (2013), Copley Medal (2006), and the Wolf Foundation prize (1988). He is a Fellow of the Royal Society and a member of the US National Academy of Sciences and the Pontifical Academy of Sciences. Stephen Hawking was also awarded Order of the British Empire by Queen Elizabeth II in person, and therefore, he is Sir Stephen Hawking.

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