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The **Thorne–Hawking–Preskill bet** was a public bet on the outcome of the black hole information paradox made in 1997 by physics theorists Kip Thorne and Stephen Hawking on the one side, and John Preskill on the other, according to the document they signed February 6, 1997^{ [1] }, as shown in Hawking's * The Universe in a Nutshell *.

The **black hole information paradox** is a puzzle resulting from the combination of quantum mechanics and general relativity. Calculations suggest that physical information could permanently disappear in a black hole, allowing many physical states to devolve into the same state. This is controversial because it violates a core precept of modern physics—that *in principle* the value of a wave function of a physical system at one point in time should determine its value at any other time. A fundamental postulate of the Copenhagen interpretation of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses. The evolution of the wave function is determined by a unitary operator, and unitarity implies that information is conserved in the quantum sense.

**Kip Stephen Thorne** is an American theoretical physicist and Nobel laureate, known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech) until 2009 and is one of the world's leading experts on the astrophysical implications of Einstein's general theory of relativity. He continues to do scientific research and scientific consulting, most notably for the Christopher Nolan film *Interstellar*.

**Stephen William Hawking** was an English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his death. He was the Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009.

Thorne and Hawking argued that since general relativity made it impossible for black holes to radiate, and lose information, the mass-energy and information carried by Hawking radiation must be "new", and must not originate from inside the black hole event horizon. Since this contradicted the idea under quantum mechanics of microcausality, quantum mechanics would need to be rewritten. Preskill argued the opposite, that since quantum mechanics suggests that the information emitted by a black hole relates to information that fell in at an earlier time, the view of black holes given by general relativity must be modified in some way. The winning side of the bet would receive an encyclopedia of their choice, "from which information can be retrieved at will".^{ [2] }

**General relativity** is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the *curvature of spacetime* is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.

**Hawking radiation** is black-body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. It is named after the theoretical physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974.

In astrophysics, an **event horizon** is a boundary beyond which events cannot affect an observer on the opposite side of it. An event horizon is most commonly associated with black holes, where gravitational forces are so strong that light cannot escape.

In 2004, Hawking announced that he was conceding the bet, and that he now believed that black hole horizons should fluctuate and leak information, in doing so providing Preskill with a copy of *Total Baseball, The Ultimate Baseball Encyclopedia*.^{ [3] } Comparing the useless information obtainable from a black hole to "burning an encyclopedia", Hawking later joked, "I gave John an encyclopedia of baseball, but maybe I should just have given him the ashes."^{ [4] } Thorne, however, remained unconvinced of Hawking's proof and declined to contribute to the award.^{ [5] } As of 2008, Hawking's argument that he has solved the paradox has not yet been accepted by the community, and a consensus has not yet been reached that Hawking has provided a strong enough argument that this is in fact what happens.

Hawking had earlier speculated that the singularity at the centre of a black hole could form a bridge to a "baby universe", into which the lost information could pass; such theories have been very popular in science fiction. But according to Hawking's new idea, presented at the 17th International Conference on General Relativity and Gravitation, on 21 July 2004 in Dublin, black holes eventually transmit, in a garbled form, information about all matter they swallow:

A **gravitational singularity**, **spacetime singularity** or simply **singularity** is a location in spacetime where the gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system. The quantities used to measure gravitational field strength are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter. Since such quantities become infinite within the singularity, the laws of normal spacetime cannot exist.

The **International Society on General Relativity and Gravitation** (ISGRG) is a learned society established in 1971 with the goal to promote research on general relativity (GR) and gravitation. To that end, it encourages communication between relativity researchers, in particular by organizing the triennial international GR conferences, sponsoring the Hyperspace website, and publishing the journal *General Relativity and Gravitation*. The society also serves as the Affiliated Commission 2 (AC.2) of the International Union of Pure and Applied Physics.

**Dublin** is the capital and largest city of Ireland. Situated on a bay on the east coast, at the mouth of the River Liffey, it lies within the province of Leinster. It is bordered on the south by the Dublin Mountains, a part of the Wicklow Mountains range. It has an urban area population of 1,173,179, while the population of the Dublin Region as of 2016 was 1,347,359. The population of the Greater Dublin Area was 1,904,806 per the 2016 census.

The Euclidean path integral over all topologically trivial metrics can be done by time slicing and so is unitary when analytically continued to the Lorentzian. On the other hand, the path integral over all topologically non-trivial metrics is asymptotically independent of the initial state. Thus the total path integral is unitary and information is not lost in the formation and evaporation of black holes. The way the information gets out seems to be that a true event horizon never forms, just an apparent horizon.

^{ [6] }

Euclidean spaceis the fundamental space of geometry. Originally, this was the three-dimensional space of Euclidean geometry, but, in modern mathematics, there are Euclidean spaces of any nonnegative integer dimension, including the three-dimensional space and theEuclidean plane. It has been introduced by the Ancient Greek mathematician Euclid of Alexandria, and the qualifierEuclideanhas been added for distinguishing it from other spaces that are considered in physics and modern mathematics.

Functional integrationis a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differential equations, and in the path integral approach to the quantum mechanics of particles and fields.In mathematics, a

metricordistance functionis a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.

An older bet from 1974 – about the existence of black holes – was described by Hawking as an "insurance policy" of sorts:

This was a form of insurance policy for me. I have done a lot of work on black holes, and it would all be wasted if it turned out that black holes do not exist. But in that case, I would have the consolation of winning my bet, which would win me four years of the magazine

Private Eye. If black holes do exist, Kip will get one year ofPenthouse. When we made the bet in 1975, we were 80% certain that Cygnus X-1 was a black hole. By now, I would say that we are about 95% certain, but the bet has yet to be settled.

is a British fortnightly satirical and current affairs news magazine, founded in 1961. It is published in London and has been edited by Ian Hislop since 1986. The publication is widely recognised for its prominent criticism and lampooning of public figures. It is also known for its in-depth investigative journalism into under-reported scandals and cover-ups.Private Eye

is a men's magazine founded by Bob Guccione. It combines urban lifestyle articles and softcore pornographic pictorials that, in the 1990s, temporarily evolved into hardcore.Penthouse

Cygnus X-1(abbreviatedCyg X-1) is a galactic X-ray source in the constellation Cygnus, and the first such source widely accepted to be a black hole. It was discovered in 1964 during a rocket flight and is one of the strongest X-ray sources seen from Earth, producing a peak X-ray flux density of 2.3×10^{−23}Wm^{−2}Hz^{−1}(2.3×10^{3}Jansky). It remains among the most studied astronomical objects in its class. The compact object is now estimated to have a mass about 14.8 times the mass of the Sun and has been shown to be too small to be any known kind of normal star, or other likely object besides a black hole. If so, the radius of its event horizon has 300 km "as upper bound to the linear dimension of the source region" of occasional X-ray bursts lasting only for about 1 ms.— Stephen Hawking,A Brief History of Time (1988)^{ [7] }

In the updated and expanded edition of *A Brief History of Time*, Hawking states, "Although the situation with Cygnus X-1 has not changed much since we made the bet in 1975, there is now so much other observational evidence in favour of black holes that I have conceded the bet. I paid the specified penalty, which was a one year subscription to * Penthouse *, to the outrage of Kip's liberated wife."

While Hawking described the bet as having been made in 1975, the written bet itself—in Thorne's handwriting, with his and Hawking's signatures—bears witness signatures under the legend "Witnessed this tenth day of December 1974".^{ [8] } Thorne confirmed this date on the January 10, 2018 episode of * Nova * on PBS.^{ [9] }

The weak and the strong **cosmic censorship hypotheses** are two mathematical conjectures about the structure of gravitational singularities arising in general relativity.

A **wormhole ** is a speculative structure linking disparate points in spacetime, and is based on a special solution of the Einstein field equations solved using a Jacobian matrix and determinant. A wormhole can be visualized as a tunnel with two ends, each at separate points in spacetime.

**Timeline of black hole physics**

* A Brief History of Time: From the Big Bang to Black Holes* is a popular-science book on cosmology by British physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for non-specialist readers with no prior knowledge of scientific theories.

The **no-hair theorem** states that all black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three *externally* observable classical parameters: mass, electric charge, and angular momentum. All other information about the matter which formed a black hole or is falling into it, "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers. Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair" which was the origin of the name. In a later interview, John Wheeler says that Jacob Bekenstein coined this phrase.

* The Universe in a Nutshell* is a 2001 book about theoretical physics by Stephen Hawking. It is generally considered a sequel and was created to update the public concerning developments since the multi-million-copy bestseller

In black hole theory, the **black hole membrane paradigm** is a simplified model, useful for visualising and calculating the effects predicted by quantum mechanics for the exterior physics of black holes, without using quantum-mechanical principles or calculations. It models a black hole as a thin, classically radiating surface at or vanishingly close to the black hole's event horizon. This approach to the theory of black holes was created by Kip S. Thorne, R. H. Price and D. A. Macdonald.

The **chronology protection conjecture** is a conjecture first proposed by Stephen Hawking which hypothesizes that the laws of physics are such as to prevent time travel on all but submicroscopic scales. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some exact solutions to General Relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the **causal violation**.

A **scientific wager** is a wager whose outcome is settled by scientific method. They typically consist of an offer to pay a certain sum of money on the scientific proof or disproof of some currently-uncertain statement. Some wagers have specific date restrictions for collection, but many are open. Wagers occasionally exert a powerful galvanizing effect on society and the scientific community.

**John Phillip Preskill** is an American theoretical physicist and the Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech).

**James Burkett Hartle** is an American physicist. He has been a professor of physics at the University of California, Santa Barbara since 1966, and he is currently a member of the external faculty of the Santa Fe Institute. Hartle is known for his work in general relativity, astrophysics, and interpretation of quantum mechanics.

* Black Holes & Time Warps: Einstein's Outrageous Legacy* is a 1994 popular science book by physicist Kip Thorne. It provides an illustrated overview of the history and development of black hole theory, from its roots in Newtonian mechanics until the early 1990s.

* Gravitation* is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973. It is frequently abbreviated

The following outline is provided as an overview of and topical guide to black holes:

* Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics * is a 2008 popular science book by American theoretical physicist Leonard Susskind. The book covers the black hole information paradox, and the related scientific dispute between Stephen Hawking and Susskind. Susskind is known for his work on string theory and wrote a previous popular science book,

- ↑ Preskill, John. "Black hole information bet".
*California Institute of Technology*. Retrieved 14 March 2018. - ↑ Capri, Anton Z (2007).
*From Quanta to Quarks: More Anecdotal History of Physics*. Hackensack, NJ: World Scientific. p. 139. ISBN 978-981-270-916-5. - ↑ Hawking, S. W. (October 2005). "Information loss in black holes".
*Physical Review D*.**72**(8): 4. arXiv: hep-th/0507171 . Bibcode:2005PhRvD..72h4013H. doi:10.1103/PhysRevD.72.084013. - ↑ Hawking, Stephen. "Into a Black Hole".
*Stephen Hawking Official Website*. Retrieved 6 October 2015. - ↑ Preskill, John (24 July 2004). "On Hawking's Concession". California Institute of Technology . Retrieved 19 May 2008.
- ↑ "17th International Conference". GR17. Archived from the original on 3 December 2007. Retrieved 19 May 2008.
- ↑ Hawking, Stephen (1988).
*A Brief History of Time*. Bantam Books. ISBN 0-553-38016-8. - ↑ Vaughan, Simon. "Hawking–Thorne wager".
*University of Leicester*. Retrieved 9 February 2018. - ↑ "Black Hole Apocalypse".
*PBS.org*. Retrieved 4 February 2018.

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