Black Holes, Hawking Radiation, and Quantum Mechanics: A Solution to the Information Paradox

Kaden Oqueli-White Pioneer Research Program Dr. Jones 8/13/21

Black Holes, Hawking Radiation, and Quantum Mechanics: A Solution to the Information Paradox ——————————————————————————————————————————

Author’s Background: Kaden Oqueli-White was born in New York City and lived in Brooklyn before moving to Louisiana right outside of New Orleans. He is a senior at Jesuit High School. His Pioneer Research concentration was in the field of astrophysics and titled “Black Holes, Hawking Radiation, and Quantum Mechanics: A Solution to the Information Paradox.”

Introduction The cosmos is vast, teeming with innumerable planets, stars, and other bodies, from neutron stars to the (until rather recently) incredibly elusive black holes. These “star corpses,” some of the greatest cosmic engines present in the known universe, have been theorized as an idea only rather recently in the human history. Black holes were first deemed nothing more than a possible side effect of Einstein’s calculations within his own theory of relativity, a concept not even he himself considered anything worth investigating beyond the most basic acknowledgment. Yet from simply a basic idea, Einstein’s early calculations within relativity spawned an entire discipline dedicated to studying some of the most mysterious yet impactful cosmic objects in the universe. Black holes serve as a window into a state of being that is difficult to comprehend using simple logic. Yet, they seem to do what the fundamental laws (as we know them to be) of our universe have dictated should not be possible: they appear to destroy matter itself. Though many theories of how to resolve this dilemma have arisen, the most realistically observable and “neat” method of resolving this clash of black holes and human laws of physics involves the introduction of Hawking radiation.

Hawking radiation (named after Stephen Hawking, who first theorized its existence) follows a basis in a quantum mechanical idea that even in a “true vacuum” where absolutely no matter exists within a given space, the space is not truly empty, as fluctuations on the quantum level still occur. Hawking radiation uses this foundation to stipulate that at the event horizon of a black hole (the “point-of-no-return” for any object unable to surpass the speed of light), virtual particles manifesting into existence in pairs split off from one another, with one leaving the black hole, and the other falling beyond the event horizon.

All of this comes to a head within a theory of quantum mechanics known as the Information Paradox. This paradox stipulates that black holes appear to violate a fundamental law of quantum mechanics: all matter possesses intrinsic information, which can neither be created nor destroyed. The goal of this paper is to examine the theories regarding how Hawking radiation relates to the information paradox, evaluate the associated experiments and data, and to demonstrate Hawking radiation as the solution to the information paradox.

Background Much of the foundation of modern physics lies upon the study of quantum mechanics, a field dedicated to mathematically examining and studying the realm of sub-atomic particles and how they interact on a fundamental level. Most of the field involves theorizing about particles beyond direct observation, such as quarks (which make up protons and neutrons) and bosons (which include photons and the crucial Higgs Boson), all of which remain smaller than even the primary particles which make up atoms. The field is crucial to the modern understanding physics in our universe but has yet to be fully realized, as attempts to unite the general theory of quantum mechanics with the world of Einstein’s theory of relativity (and by extension the general theory of gravity) into a universal theory of quantum gravity remain to be entirely explored.

A key aspect of Hawking radiation is that it involves two obscure phenomena present in the universe, one of which is black holes, which are cosmic bodies formed in a variety of ways, usually from the collapse of a large star of approximately 3 or more solar masses, or from the collision of other black holes, neutron stars, or white dwarfs (Mangum, 2014, para. 1). Such a collapse against the force of gravity results in the matter of the parent body (or bodies) being compressed infinitely into an infinitely dense point, termed a “singularity” (Ouellette, 2018, para. 2) The gravitational force of this singularity remains so intense that even light is unable to escape once it has fallen beyond the event horizon, a boundary within the black hole beyond which no object unable to move greater than the speed of light can escape.

It should be noted that the outer edge of what would appear to be a black hole’s outer edge is often located at a separate point than the boundary of the event horizon. The true physics of what lies beyond the event horizon have yet to be fully understood, and the apparent destruction of any matter which enters a black hole remains a major issue when considering how they interact in quantum mechanics.

The second crucial aspect of Hawking radiation concerns virtual particles. According to quantum mechanics, most interactions in the universe require the presence of quantum fluctuations, which manifest into virtual particles.

These pairs form even in the emptiest regions of deep space and would be present even in a theoretical “true vacuum” devoid of all other influences and objects. At the event horizon of a black hole, these particles form a matter and anti-matter particle pair, with one falling into the black hole and the other escaping to carry away energy from a black hole, leading the black hole to eventually evaporate away its mass (Baez, 1994, para. 3). This blackbody radiation proposed by Stephen Hawking in 1974 has served as the foundation for numerous approaches to the solve the information paradox.

Modern interpretations of the black hole take place in a universe governed by de Sitter space, a state of the universe in which the cosmological constant (what modern physicists term the “energy density of the universe”) is positive, and where the fabric of space time takes the shape of an expanding sphere (Griswold, 2012, para. 2). This variation of the general theory of relativity has a counterpart in which the cosmological constant is instead negative, called anti-de Sitter space, which forms the basis of how some modern theories interpret the spatial geometry within a black hole.

All of these components build into the main issue facing cosmologists and quantum physicists studying black holes: the information paradox, a theoretical issue with the way that black holes supposedly interact with matter that falls beyond their event horizons, and it first emerged alongside Stephen Hawking’s original theory of Hawking radiation in 1974. The paradox pertains to a basic law of quantum mechanics, one that forms the basis of our entire understanding of the field: information. According to the quantum mechanics, all matter intrinsically possesses information, which is the pattern of quantum structure within any amount of matter.

Essentially, information is what distinguishes one quantity of matter from another, such as a sponge from a rock or a cup from a plate, on a fundamental level. A fundamental principle of quantum mechanics is that information, like matter and energy, cannot be created nor destroyed.

By Hawking’s original proposal, the information of all of the matter to have fallen into the black hole must be destroyed, irrecoverable once the black hole evaporates away all of its mass, and the idea that information is a fundamental aspect of the study of quantum mechanics itself. The paradox in question arises when one tries to conceive how black holes interact with matter (and therefore information itself) with their incredible gravitational influence.

By conventional theories, the infinitely collapsing singularity of a black hole takes matter which falls beyond the event horizon and makes all of it the same, essentially destroying information and violating this principle The Page Curve, offered by physicist Don Page, is built upon the idea that information does not leave in significant or reasonable measurable quantities through the early life of a black hole. In the black hole subsystem with dimension n ~ esh, where sh = A/4 is the semiclassical Hawking entropy of a black hole of area A, and the radiation subsystem is assumed to have a dimension m ~ eSr, where sr represents thermodynamic radiation entropy.

The hypothesis states no information is lost in black hole formation and evaporation, that these subsystems form a total system in a pure state in a Hilbert space of dimension mn, with density matrix prh = p.

If the black hole and the radiation are indeed correlated, each of these subsystems would be in a mixed state:

pr = pr h, ph = pr h

(Equation 1)

with the entanglement entropy:

Sr = -(pr ln pr) = Sh =- (ph ln ph)

(Equation 2)

and information (representing the deviation from the entanglement entropy maximum) (Don Page, 1993):

Ir = ln m – Sr ≃ sr – Sr , Ih = ln n – Sh ≃ sh – Sh

(Equation 3)

Finally, this paper’s main focus with these topics is how they relate to the Information paradox, a prominent issue within the study of quantum mechanics. Throughout the universe, very few phenomena appear to violate the conservation of information except for black holes, which in theory would destroy information and erase the identity of its matter. Numerous theories and ideas have arisen in order to reconcile this violation of one of the basic laws of the universe.

Research into the effects of Hawking radiation and its implications has remained constant since Stephen Hawking published his original theory in 1975.

Proving its existence, however, has remained more difficult than most concepts in physics. Observing Hawking radiation, even if one could approach a black hole directly, would require temperature measurements able to detect temperatures in the order of 10-8 K, well below the temperature of Cosmic Background Radiation (CBT) of approximately 2.7K (Aguero-Santacruz and Bermudez, 2020, p. 3). This, in addition our obvious inability to directly reach or observe the environment of black holes has led researchers to attempt to simulate black holes through analogue means, such as creating sonic black holes in laboratory environments or approaching the existence of information in Hawking radiation through mathematical theory.

I.

Sonic Black Holes and Their Implications In 1981, a physicist named William Unruh determined, using Hawking’s work, that the event horizon of an astrophysical black hole and the horizon of a hypothetical sonic black hole could both not only be described by a “waterfall” analogy, but also by the same equations (Wolchover, 2016, para. 3). This proposal led a number of researchers to delve into the depths of manufacturing such a sonic black hole to confirm Unruh’s mathematical conclusions.

In 2009, Jeff Steinhauer reported his findings from an experiment where he had created a “sonic black hole” using super-cooled rubidium atoms taking the form of a Bose-Einstein condensate and superheating the material with a laser, creating a “sonic horizon” (Wolchover, 2016, para. 12).

Steinhauer and his colleagues used 8000 rubidium atoms to create the artificial black hole, which was approximately 0.1 millimeters long (Fadelli, 2021, para. 5).

Steinhauer describes his experiment in creating the horizon “by a very sharp potential step, achieved by short-wavelength laser light (0.442 µm),” and this resulted in an environment where, as indicated by Figure 1, the region to the left of the step (or horizon) represents an area where the condensate remains relatively unperturbed, while the region to the right of the step represents the actual analogue black hole, and the fluid flows at supersonic speed (Steinhauer, 2016, p. 7). This black hole is created once the fluid reaches a flowrate velocity of 1.02 mm sec-1, a velocity great enough to exceed the speed of sound within the fluid, 0.25 mm sec-1 (Steinhauer, 2016, p. 7). This results in phonons at the horizon being unable to escape from beyond the sonic horizon of the fluid, forced inward into the condensate itself, as shown by Figure 1.

Fig. 1. Diagram of Steinhauer’s analog black hole process Source: Reading-Ikkanda, 20

Yet, to the left of the horizon, phonons are generated quite near the horizon and move outward into the outer region. These phonon patterns appear to mimic those originally proposed by Hawking, where pairs of particles of discrete energy form at the boundary of a black hole, with one escaping and bringing energy away from the black hole, and the other falling beyond the event horizon inducing negative energy and lowering the energy present in the black hole’s gravitational system.

Thus, Steinhauer claims that this demonstration of Hawking’s principle proves the existence of Hawking radiation within astrophysical black holes, with sound being the stand-in for photons or virtual particles. The entanglement of particles at a black hole’s event horizon could be reflected in the similar pattern of phonon pairs at a sonic horizon, and thus Hawking radiation most likely follows this pattern in actual black holes. Yet Steinhauer believes that this still confirms Hawking’s original claim that information is destroyed in the process, even with the existence of Hawking radiation demonstrated in his experiments, despite Hawking himself joining the school of thought believing there must be a way to reconcile this apparent violation.

II.

Unruh Radiation Additionally, physicists have been working to confirm another conclusion by Unruh

concerning equivalent radiation. In 1976, Unruh hypothesized that the same kind of radiation as Hawking proposed could be observed if one were moving at a high enough acceleration, which remains consistent with Einstein’s theory of relativity (Lerner, 2019, para 2.).

Naturally, this has never been truly observed, as the acceleration required would have to be a G force on the order of a billion-billion. To prove this, a team of UChicago physicists constructed an experiment in which 60,000 cesium atoms are first cooled down to 10 nano-Kelvin and are struck with an oscillating magnetic field (Fadelli, 2019, para. 7). The material, much like the previous experiment, utilized atoms in a Bose-Einstein condensate, and researchers such as Cheng Chin, the physicist who led the experiment, observed streams of atoms which matched the temperatures predicted by Unruh’s radiation theory.

III. The Page Curve These conclusions are crucial to understanding the fundamental ideas with how Hawking radiation interacts with the event horizon of a black hole, and by extension, the information potentially preserved beyond the black hole’s infinite depth. Rather than seeking purely practical interpretations of Hawking’s theory like Steinhauer or Chin, some mathematical theorists have even taken to amending Hawking’s semiclassical approach to the relationship between radiation, the event horizon, and information through mathematical speculation. One such theory has proposed that Hawking radiation takes on different qualities during different points of a black hole’s lifespan, as seen in Figure 2. This progression is highlighted by the relationship between Equation 2 and Equation 3, which demonstrate the inverse relationship between entanglement entropy and information.

Fig 2. Simplified Diagram of the Page Curve Source: Samuel Velasco/Quanta Magazine

Physicist Don Page has concluded that particles of radiation (with their information included) maintain quantum entanglement “with the place of their origin,” allowing the information within the black hole to be emitted in a sort of encrypted fashion, which may appear unorganized independently but could “exhibit a pattern” when observed together (Musser, 2020, para. 15).

Additionally, Page theorized that the relationship between the entanglement of the black hole and the radiation would follow a consistent relationship, termed “entanglement entropy,” with the radiation increasing as information spills from the black hole, all the while the entanglement entropy builds and then gradually shrinks along the “Page Curve,” as demonstrated by Figure 2.

Another caveat of this theory is that, instead of remaining consistent with the idea that a black hole only experiences such exotic effects once it reaches a subatomic state very near the end of its life, it proposes that the turning point of this exotic relationship would occur approximately halfway through the black hole’s life span, when the black hole itself is still enormous (Musser, 2020, para. 17-18).

Recent efforts in the last two years have confirmed Page’s conclusions, including new calculations which offer a relatively unconventional perspective: black holes act as a kind of shell around what is called a “quantum extremal surface,” essentially embracing the interpretation of black holes as pocket universes governed by their own sets of physics (Musser, 2020, para. 31). This novel advancement of the theory reconciles the main issue many physicists held with Page’s original proposal: how to deal with the decrease of entropy within the system, seen in Figure 3.

Fig. 3. Progression of black hole information content along the Page curve.

Source: Samuel Velasco/Quanta Magazine

By offering a system by which the entanglement entropy can decrease, the quantum extremal surface allows information to leak out of the black hole via quantum entangled radiation. This would allow the information to leave the black hole through being encoded by the individual particles leaving the black hole and could serve as the method through which information is returned to the greater universe and provide a method by which information is preserved rather than destroyed, solving the paradox. Researchers have already provided as much proof of decreasing entropy by examining the inner black hole as functioning in the anti-de Sitter spacetime instead of de Sitter space-time unlike the rest of the universe, allowed for the extremal surface to function as an island within the black hole through which radiation can siphon from past the event horizon to the outer universe, allowing information to escape.

The pursuit of a solution to the information is a vast and varied discipline, with innumerable theories and methods binding the coalition of researchers determined to finally crack, in some small way, the foundational nature of the universe in its most enigmatic forms. Some theories that are not covered in this research paper include the Holographic Theory, which, while working in tandem with many other approaches, examines the subject from the lens of information existing upon the surface of a black hole as a virtual projection (which also demonstrates that the same could be true for information present within the outer boundary of the observable universe.

Importance The information paradox and its associated phenomena have implications spanning some of the largest scientific disciplines in the modern world. Quantum mechanics and many aspects of our understanding of physics is built upon the fundamental principle of the conservation of information in the universe, which cannot truly be a foundational principle if violations are allowed to occur, as would happen if black holes truly destroy information as Hawking had proposed in 1974. Without information, matter loses its identity, the very core aspect of its nature and our understanding of how the universe functions is in dire need of reassessment if there exists a state without information.

Additionally, many of the phenomena examined in the search for a resolution to the information paradox have given rise to new pursuits regarding how Einstein’s seemingly all-encompassing theory of relativity, the gravitational concepts of which are fully functional on the macroscopic level yet appear to break down on the quantum level. Uniting these two fundamental theories through a “unified theory of quantum gravity” is crucial to understanding not only the origin of these forces but also how their interactions shape the entire expanse of the cosmos. Without basic principles governing our scientific processes, we cannot hope to draw any conclusions about what occurs in the world around us, and the pursuit of the effects of Hawking radiation could lead to remarkable breakthroughs in the greater scope of physics and cosmology when it comes to observing such forces at the greatest physical extremes present in the universe.

Evaluation I have always seen the discussion of both black holes and quantum mechanics as a truly fascinating subject , something I have always wanted to pursue in my career as both an astrophysicist and theoretical physicist. Both subjects involve incredibly diverse and unique perspectives on the some of the strangest (at least to our current understanding or how the universe operates) events in the cosmos, and I have wanted to join the frontier to scientists seeking to fully figure them out. Though I have done more casual independent research in my own curiosity (simply for the sake of having a greater awareness of the progress being made in these endeavors), through the more deliberate research necessary for this paper, I have learned that the schools of thought surrounding these efforts are even more fascinating than I had thought them to be. Simply seeing the creation of a sonic black hole, something which I had not even conceived of before, reignited my desire to study black holes in the hopes that I, with the countless other individuals seeking these truths, may truly come to know the universe more intimately. And even if that day may not come in my career, I hope to set the foundation for the next scientists to pursue the same goal.

Additionally, my time with Professor Jones first gave me the idea to pursue this research project during our time covering black holes in class, however brief. I wanted to go beyond the typical questions asked about these fascinating cosmic events and more deeply examine the research behind how these behemoths behave on the fundamental levels of our universe.

Works Cited Aguero-Santacruz, Raul, and David Bermudez. “Hawking Radiation in Optics and Beyond.”

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 378, no. 2177, 2020, pp. 1–17., https://doi.org/10.1098/ rsta.2019.0223. This research paper explains the minute mathematical details of how

Hawking radiation functions in the terms of thermodynamics and details how a semiclassical approach is necessary to truly determine the nature of Hawking radiation.

Baez, John. “Hawking Radiation.” Edited by Ilja Schmelzer, Hawking Radiation, 1994, https:// math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html. This article provides

information on the blackbody radiation nature of Hawking radiation as well as the anti-particle/particle nature of the radiation which occurs at the event horizon of black holes.

Fadelli, Ingrid. “A Quantum Simulation of Unruh Radiation.” Phys.org, Phys.org, 7 June 2019, https://phys.org/news/2019-06-quantum-simulation-unruh.html. This article provides

further details the UChicago experiment on Unruh radiation as well as the properties of Unruh radiation.

Griswold, Britt. “WMAP- Cosmological Constant or Dark Energy.” NASA, NASA, 21 Dec. 2012, https://map.gsfc.nasa.gov/universe/uni_accel.html. This article provides background

information on the nature of the scientific consensus on the cosmological constant and its influences on the wider universe.

Lerner, Louise. “Scientists Use Atoms to Simulate Quantum Physics in Curved Spacetimes.”

University of Chicago News, 18 June 2019, https://news.uchicago.edu/story/scientistsuse-atoms-simulate-quantum-physics-curved-spacetimes. This article details the

proposed radiation as following William Unruh's hypothesis that one could observe Hawking radiation when travelling at immense G forces, as well as providing basic details concerning the experiment itself.

Mangum, Jeff. “What Is the Critical Mass at Which a Star Becomes a Black Hole?” National Radio Astronomy Observatory, 21 Feb. 2014, https://public.nrao.edu/ask/what-is-thecritical-mass-at-which-a-star-becomes-a-black-hole/. This small article provides insight

on the mass limitations on the formation of black holes in terms of established physical constants, such as the speed of light and gravitational constant.

Musser, George. “The Most Famous Paradox in Physics Nears Its End.” Quanta Magazine, 29 Oct. 2020, https://www.quantamagazine.org/the-most-famous-paradox-in-physics-nears-itsend-20201029. This article details the theory of the Page curve with regards to the

information output of black holes, including citations of the calculations done to demonstrate the viability of the theory.

Ouellette, Jennifer. “Why Stephen Hawking's Black Hole Puzzle Keeps Puzzling.” Quanta Magazine, 16 Oct. 2020, https://www.quantamagazine.org/stephen-hawkings-black-holeparadox-keeps-physicists-puzzled-20180314/ . This article discusses recent

breakthroughs in the pursuit of a solution to the black hole information paradox as well as providing background information about the nature of black holes and their properties. It provides background information on Stephen Hawking's original contribution to the subject and how researchers have continued to seek the solution in his legacy.

Steinhauer, Jeff. (2014). “Observation of self-amplifying Hawking radiation in an analogue black-hole laser.” Nature Physics, 10(11), 864–869. https://doi.org/10.1038/ nphys3104. This scientific paper demonstrates the mathematical calculations behind his experimental process in creating the sonic black holes, as well as the data and results from the experiment itself.

Wolchover, Natalie. “What Sonic Black Holes Say about Real Ones.” Quanta Magazine, 18 May 2020, https://www.quantamagazine.org/what-sonic-black-holes-say-about-realones-20161108/. This is an article explaining the background on William Unruh's

original proposal for relating sonic black holes and astrophysical black holes, as well as the materials and methods as described by Jeff Steinhauer on how his team created the first artificial sonic black holes.

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Research Cite this article: Aguero-Santacruz R, Bermudez D. 2020 Hawking radiation in optics and beyond. Phil. Trans. R. Soc. A 378: 20190223. http://dx.doi.org/10.1098/rsta.2019.0223 Accepted: 4 March 2020 One contribution of 12 to a discussion meeting issue ‘The next generation of analogue gravity experiments’.

Subject Areas: vacuum physics, optics Keywords: analogue gravity, Hawking radiation, optical fibres Author for correspondence: David Bermudez e-mail: dbermudez@fis.cinvestav.mx

Hawking radiation in optics and beyond Raul Aguero-Santacruz and David Bermudez Departamento de Física. Cinvestav, A.P. 14-740, 07000 Ciudad de México, Mexico RA-S, 0000-0001-6897-7633; DB, 0000-0002-2977-0303 Hawking radiation was originally proposed in astrophysics, but it has been generalized and extended to other physical systems receiving the name of analogue Hawking radiation. In the last two decades, several attempts have been made to measure it in a laboratory, and one of the most successful systems is in optics. Light interacting in a dielectric material causes an analogue Hawking effect, in fact, its stimulated version has already been detected and the search for the spontaneous signal is currently ongoing. We briefly review the general derivation of Hawking radiation, then we focus on the optical analogue and present some novel numerical results. Finally, we call for a generalization of the term Hawking radiation.

This article is part of a discussion meeting issue ‘The next generation of analogue gravity experiments’.

1. Introduction The fascinating phenomenon of Hawking radiation was proposed over 45 years ago by Stephen W. Hawking [1]. Using a semi-classical approximation, i.e. considering quantum fields around a classical geometry, Hawking realized that the event horizon of a black hole in the Schwarzschild metric [2] should emit massless particles.

Black holes are not entirely black.

This is a significant phenomenon because it gives black holes—known as the ultimate devourers—some thing unthinkable, a mechanism to lose mass. This black hole evaporation could dramatically change the cosmological evolution and the final state of the universe.

However, astrophysical Hawking radiation is too small to be directly detected by any conceivable experiment, satellite, or telescope up to now. This is partly because gravity is the weakest known force [3].

For example, in the Millikan oil drop experiment, a single electron charge can counteract the gravitational attraction of the whole planet Earth. A quantum effect due to gravity would be extremely hard to measure.

2020 The Author(s) Published by the Royal Society. All rights reserved.

[Physics FAQ] - [Copyright] Modified by Ilja Schmelzer 1997.

Original by John Baez 1994.

Hawking Radiation In 1975 Hawking published a shocking result: if one takes quantum theory into account, it seems that black holes are not quite black! Instead, they should glow slightly with "Hawking radiation", consisting of photons, neutrinos, and to a lesser extent all sorts of massive particles. This has never been observed, since the only black holes we have evidence for are those with lots of hot gas falling into them, whose radiation would completely swamp this tiny effect. Indeed, if the mass of a black hole is M solar masses, Hawking predicted it should glow like a blackbody of temperature 6 × 10-8/M kelvins,

so only for very small black holes would this radiation be significant. Still, the effect is theoretically very interesting, and folks working on understanding how quantum theory and gravity fit together have spent a lot of energy trying to understand it and its consequences. The most drastic consequence is that a black hole, left alone and unfed, should radiate away its mass, slowly at first but then faster and faster as it shrinks, finally dying in a blaze of glory like a hydrogen bomb. But the total lifetime of a black hole of M solar masses works out to be 1071 M3 seconds

so don't wait around for a big one to give up the ghost. (People have looked for the death of small ones that could have formed in the big bang, but they haven't seen any.)

How does this work? Well, you'll find Hawking radiation explained this way in a lot of "pop-science" treatments: Virtual particle pairs are constantly being created near the horizon of the black hole, as they are everywhere. Normally, they are created as a particle-antiparticle pair and they quickly annihilate each other. But near the horizon of a black hole, it's possible for one to fall in before the annihilation can happen, in which case the other one escapes as Hawking radiation.

In fact this argument also does not correspond in any clear way to the actual computation. Or at least I've never seen how the standard computation can be transmuted into one involving virtual particles sneaking over the horizon, and in the last talk I was at on this it was emphasized that nobody has ever worked out a "local" description of Hawking radiation in terms of stuff like this happening at the horizon. I'd gladly be corrected by any experts out there... Note: I wouldn't be surprised if this heuristic picture turned out to be accurate, but I don't see how you get that picture from the usual computation.

The usual computation involves Bogoliubov transformations. The idea is that when you quantize (say) the electromagnetic field you take solutions of the classical equations (Maxwell's equations) and write them as a linear combination of positive-frequency and negative-frequency parts. Roughly speaking, one gives you particles and the other gives you antiparticles. More subtly, this splitting is implicit in the very definition of the vacuum of the quantum version of the theory! In other words, if you do the splitting one way, and I do

A quantum simulation of Unruh radiation 7 June 2019, by Ingrid Fadelli The Unruh effect, or Unruh radiation, is closely connected to Hawking radiation. In 1974, theoretical physicist Stephen Hawking predicted that the strong gravitational force near black holes leads to the emission of a thermal radiation of particles, which resembles the heat wave emitted by an oven. This phenomenon remains speculative with no direct experimental confirmation.

A few years later, in 1976, physicist William Unruh hypothesized that a person could observe the same radiation when she is moving with a high acceleration. The equivalence between Hawking and Unruh radiation is based on Einstein's equivalence principle, which has now been confirmed by many experiments.

Despite Unruh's predictions, no one has yet observed Unruh radiation, which is not surprising, as this phenomenon is particularly difficult to capture. In fact, a person would need to endure a Gforce of 25 billion billion (25*1018) to see a weak (a) illustrates how Unruh radiation is expected to emerge radiation of 1 Kelvin. This is an astounding number when considering that, for instance, the G-force in an accelerating frame. (b) shows the image of our experiment that simulates Unruh radiation. Credit: Hu et experienced by a fighter jet pilot is no more than a.

10.

"In our lab, we simulate Unruh physics by precisely modulating a Bose-Einstein condensate with the Researchers at the University of Chicago magnetic field," Chin said. "Even through our (UChicago) have recently reported an experimental sample is not moving, the modulation has the same observation of a matter field with thermal effect as boosting the sample to an accelerating fluctuations that is in accordance with Unruh's reference frame. We observe radiation at 2 microradiation predictions. Their paper, published in Kelvin, and the measurement excellently agrees Nature Physics, could open up new possibilities for with the Unruh's prediction and confirms the research exploring the dynamics of quantum quantum nature of the radiation field." systems in a curved spacetime.

In their experiment, Chin and his colleagues "Our team at UChicago has been investigating a prepared 60,000 cesium atoms and cooled them to new quantum phenomena called Bose fireworks about 10 nano-Kelvin, then started the modulation that we discovered two years ago," Cheng Chin, of the magnetic field. A few milliseconds after the one of the researchers who carried out the study, modulation, they observed a thermal emission of told Phys.org. "Our paper reports its hidden atoms in all directions. To confirm the thermal connection to a gravitational phenomenon called distribution of atoms, the researchers collected a Unruh radiation." larger number of samples and showed that the atom number fluctuates precisely according to the

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Wilkinson Microwave Anisotropy Probe

What is a Cosmological Constant?

Einstein first proposed the cosmological constant (not to be confused with the Hubble Constant) usually symbolized by the greek letter "lambda" (Λ), as a mathematical fix to the theory of general relativity. In its simplest form, general relativity predicted that the universe must either expand or contract. Einstein thought the universe was static, so he added this new term to stop the expansion. Friedmann, a Russian mathematician, realized that this was an unstable fix, like balancing a pencil on its point, and proposed an expanding universe model, now called the Big Bang theory. When Hubble's study of nearby galaxies showed that the universe was in fact expanding, Einstein regretted modifying his elegant theory and viewed the cosmological constant term as his "greatest mistake".

Many cosmologists advocate reviving the cosmological constant term on theoretical grounds. Modern field theory associates this term with the energy density of the vacuum. For this energy density to be comparable to other forms of matter in the universe, it would require new physics: the addition of a cosmological constant term has profound implications for particle physics and our understanding of the fundamental forces of nature.

The main attraction of the cosmological constant term is that it significantly improves the agreement between theory and observation. The most spectacular example of this is the recent effort to measure how much the expansion of the universe has changed in the last few billion years. Generically, the gravitational pull exerted by the matter in the universe slows the expansion imparted by the Big Bang. Very recently it has become practical for astronomers to observe very bright rare stars called supernova in an effort to measure how much the universal expansion has slowed over the last few billion years. Surprisingly, the results of these observations indicate that the universal expansion is speeding up, or accelerating! While these results should be considered preliminary, they raise the possibility that the universe contains a bizarre form of matter or energy that is, in effect, gravitationally repulsive. The cosmological constant is an example of this type of energy. Much work remains to elucidate this mystery!

There are a number of other observations that are suggestive of the need for a cosmological constant. For example, if the cosmological constant today comprises most of the energy density of the universe, then the extrapolated age of the universe is much larger than it would be without such a term, which helps avoid the dilemma that the extrapolated age of the universe is younger than some of the oldest stars we observe! A cosmological constant term added to the standard model Big Bang theory leads to a model that appears to be consistent with the observed large-scale distribution of galaxies and clusters, with WMAP's measurements of cosmic microwave background fluctuations, and with the observed properties of X-ray clusters.

WMAP AND THE COSMOLOGICAL CONSTANT By characterizing the detailed structure of the cosmic microwave background fluctuations, WMAP is able to accurately determine the basic cosmological parameters, including the cosmological constant, to better than 1% (as of the year 2013).

FURTHER READING: Donald Goldsmith, "Einstein's Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe", (Harvard University Press: Cambridge, Mass.) A well written, popular account of the cosmological constant and the current state of cosmology. wmap.gsfc.nasa.gov Webmaster: Britt Griswold NASA Official: Dr. Edward J. Wollack Page Updated: Friday, 12-21-2012

Scientists use atoms to simulate quantum physics in curved spacetimes

By Louise Lerner (/taxonomy/term/49911) Jun 18, 2019

UChicago team glimpses phenomena that underlie black holes, other extreme physics

B

lack holes fascinate the public and scientists alike because they are where it all breaks down: matter, unlucky stars and space flotsam, and our understanding of physics.

And while scientists have chipped away at their mysteries—from capturing the first image of one (https://news.uchicago.edu/story/uchicago-scientistshelp-capture-first-image-black-hole), to detecting the ripples in space-time they create (https://news.uchicago.edu/story/gravitational-waves-detected-100years-after-einsteins-prediction) when colliding—key parts of understanding black holes have escaped them. For example, Stephen Hawking suggested in 1974 that black holes actually emit a stream of warm radiation created by their extremely strong gravity; but of course, no one has been able to get close enough to a black hole to observe it.

Physicist William Unruh later suggested that the same type of radiation would appear if you were moving at a high enough acceleration; Einstein’s theory of general relativity confirms the equivalence between the two types of radiation. But Unruh radiation also has not been observed, since you would need to be accelerating tremendously fast just to see a tiny bit of the radiation—a G force on the order of a billion billion. (Fighter pilots top out at 10 Gs).

A team of physicists at the University of Chicago has built a quantum system to simulate the physics of this Unruh radiation. The breakthrough (https://www.nature.com/articles/s41567-019-0537-1) advances our understanding of these complex physics—and could ultimately help us explain how the largest and smallest phenomena in the universe fit together.

“This experiment shows a novel way to simulate physics in curved spacetimes,” said Prof. Cheng Chin, co-author of the study and a pioneer (https://news.uchicago.edu/story/exotic-gigantic-molecules-fit-inside-each-other-russian-nesting-dolls) in using ultracold atoms to study (https://news.uchicago.edu/story/same-rules-apply-some-experimental-systems-regardless-scale-0) the quantum (https://news.uchicago.edu/story/cesiumatoms-shaken-not-stirred-create-elusive-excitation-superfluid) phenomena (https://news.uchicago.edu/story/ultracold-experiments-heat-quantum-research) that underlie the behavior of other particles in the universe. “Our scheme is a bit like building a flight simulator, which allows you to experience what it’s like to experience enormously large G forces while staying on the ground,” he said.

In Chin’s lab, a sample of atoms are first cooled down to near-zero temperature. Next, researchers apply an oscillating magnetic field on the sample and observe jets of atoms shooting outwards, which they termed “Bose fireworks (https://news.uchicago.edu/story/uchicago-scientists-see-fireworks-atomsultra-low-temperatures).”

“This experiment shows a novel way to simulate physics in curved spacetimes.”

—Prof. Cheng Chin

They also saw a coherence to the jets which reflects the quantum properties of Unruh radiation. “We realized that these emissions could also provide a new view into the quantum origin of Unruh radiation,” said Lei Feng, a graduate student and co-author on the study.

the-most-famous-paradox-in-physics-nears-its-end-20201029

10/24/21, 9:15 PM

SERIES

The Most Famous Paradox in Physics Nears Its End

By George Musser

October 29, 2020 In a landmark series of calculations, physicists have proved that black holes can shed information, which seems impossible by definition. The work appears to resolve a paradox that Stephen Hawking first described five decades ago.

https://www.quantamagazine.org/print

Page 1 of 27

Why Stephen Hawking’s Black Hole Puzzle Keeps Puzzling

By Jennifer Ouellette

March 14, 2018 The renowned British physicist, who died at 76, left behind a riddle that could eventually lead his successors to the theory of quantum gravity.

The physicist Stephen Hawking in 1979 in Princeton, New Jersey.

Santi Visalli/Getty Images

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Published: 12 October 2014

Observation of self-amplifying Hawking radiation in an analogue black-hole laser

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Jeff Steinhauer Nature Physics 10, 864–869 (2014) 12k Accesses

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Abstract

International Year of Light 2015

By a combination of quantum field theory and general relativity, black holes have been predicted to emit Hawking radiation. Observation from an actual black hole is,

A black-hole laser

however, probably extremely difficult, so attention has turned to analogue systems in

Giovanni Modugno

the search for such radiation. Here, we create a narrow, low density, very low

News & Views 12 Oct 2014

temperature atomic Bose–Einstein condensate, containing an analogue black-hole horizon and an inner horizon, as in a charged black hole. We report the observation

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of Hawking radiation emitted by this black-hole analogue, which is the output of the

Abstract

black-hole laser formed between the horizons. We also observe the exponential

References

growth of a standing wave between the horizons, which results from interference

Acknowledgements

between the negative-energy partners of the Hawking radiation and the negative-

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energy particles reflected from the inner horizon. We thus observe self-amplifying

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Hawking radiation.

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Download references

Acknowledgements I thank R. Parentani, I. Carusotto, A. Ori and F. Michel for helpful discussions. This work is supported by the Russell Berrie Nanotechnology Institute and the Israel Science Foundation.

Author information Affiliations Department of Physics, Technion—Israel Institute of Technology, Technion City, Haifa 32000, Israel

Jeff Steinhauer

Corresponding author Correspondence to Jeff Steinhauer.

Ethics declarations Competing interests The author declares no competing financial interests.

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About this article Cite this article Steinhauer, J. Observation of self-amplifying Hawking radiation in an analogue black-hole laser. Nature Phys 10, 864–869 (2014). https://doi.org/10.1038/nphys3104 Download citation Received

Accepted

Published

14 July 2014

19 August 2014

12 October 2014

Issue Date November 2014 DOI https://doi.org/10.1038/nphys3104

Subjects Bose–Einstein condensates

Ultracold gases

Further reading Quantum-circuit black hole lasers Haruna Katayama Scientific Reports (2021)

The life of an analogue black hole Giovanni Modugno Nature Physics (2021)

Amplification of waves from a rotating body Marion Cromb, Graham M. Gibson[…] & Daniele Faccio Nature Physics (2020)

Resonant frequencies of a massless scalar field in the canonical acoustic black hole spacetime H. S. Vieira & V. B. Bezerra General Relativity and Gravitation (2020)

Observation of thermal Hawking radiation and its temperature in an analogue black hole Juan Ramón Muñoz de Nova, Katrine Golubkov[…] & Jeff Steinhauer Nature (2019)

Nature Physics (Nat. Phys.) ISSN 1745-2481 (online) ISSN 1745-2473 (print)

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what-sonic-black-holes-say-about-real-ones-20161108

10/24/21, 9:17 PM

What Sonic Black Holes Say About Real Ones

By Natalie Wolchover

November 8, 2016 Can a fluid analogue of a black hole point physicists toward the theory of quantum gravity, or is it a red herring?

Olena Shmahalo/Quanta Magazine

In a 1972 lecture at the University of Oxford, a young physicist named William Unruh asked the audience to imagine a fish screaming as it https://www.quantamagazine.org/print

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