In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature$\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K$ where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.

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Particle Creation by Black Holes

Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.

Black holes and entropy

were proposed in the early 1980’s [Benioff80] and shown to be at least as powerful as classical computers an important but not surprising result, since classical computers, at the deepest level, ultimately follow the laws of quantum mechanics. The description of quantum mechanical computers was formalized in the late 80’s and early 90’s [Deutsch85][BB92] [BV93] [Yao93] and they were shown to be more powerful than classical computers on various specialized problems. In early 1994, [Shor94] demonstrated that a quantum mechanical computer could efficiently solve a well-known problem for which there was no known efficient algorithm using classical computers. This is the problem of integer factorization, i.e. testing whether or not a given integer, N, is prime, in a time which is a finite power of o (logN) . ----------------------------------------------

A fast quantum mechanical algorithm for database search

The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recognition-by-components (RBC), is that a modest set of generalized-cone components, called geons (N £ 36), can be derived from contrasts of five readily detectable properties of edges in a two-dimensiona l image: curvature, collinearity, symmetry, parallelism, and cotermination. The detection of these properties is generally invariant over viewing position an$ image quality and consequently allows robust object perception when the image is projected from a novel viewpoint or is degraded. RBC thus provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition: The constraints toward regularization (Pragnanz) characterize not the complete object but the object's components. Representational power derives from an allowance of free combinations of the geons. A Principle of Componential Recovery can account for the major phenomena of object recognition: If an arrangement of two or three geons can be recovered from the input, objects can be quickly recognized even when they are occluded, novel, rotated in depth, or extensively degraded. The results from experiments on the perception of briefly presented pictures by human observers provide empirical support for the theory. Any single object can project an infinity of image configurations to the retina. The orientation of the object to the viewer can vary continuously, each giving rise to a different two-dimensional projection. The object can be occluded by other objects or texture fields, as when viewed behind foliage. The object need not be presented as a full-colored textured image but instead can be a simplified line drawing. Moreover, the object can even be missing some of its parts or be a novel exemplar of its particular category. But it is only with rare exceptions that an image fails to be rapidly and readily classified, either as an instance of a familiar object category or as an instance that cannot be so classified (itself a form of classification).

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Recognition-by-Components: A Theory of Human Image Understanding.

Chandrasekhar, black holes, and singularities

Despite almost a century's worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as `quantizing gravity', resulting in a theory of `quantum gravity'. The opposite approach is `gravitizing QT' where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using a Bose-Einstein condensate (BEC) to search for clues. In particular, we study how a single BEC in a superposition of two locations could test a gravitizing QT proposal where wavefunction collapse emerges from a unified theory as an objective process, resolving the measurement problem of QT. Such a modification to QT due to general relativistic principles is testable near the Planck mass scale, which is much closer to experiments than the Planck length scale where quantum, general relativistic effects are traditionally anticipated in quantum gravity theories. Furthermore, experimental tests of this proposal should be simpler to perform than recently suggested experiments that would test the quantizing gravity approach in the Newtonian gravity limit by searching for entanglement between two massive systems that are both in a superposition of two locations.

Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate

Within the scheme of conformal cyclic cosmology (CCC), information can be transmitted from aeon to aeon. Accordingly, the “Fermi paradox” and the SETI programme --of communication by remote civilizations-- may be examined from a novel perspective: such information could, in principle, be encoded in the cosmic microwave background. The current empirical status of CCC is also discussed.

CCC and the Fermi paradox

A key obstruction to the twistor programme has been its so-called googly problem, unresolved for nearly 40 years, which asks for a twistor description of right-handed interacting massless fields (p...

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2014.0237

Palatial twistor theory and the twistor googly problem

The LARES satellite was successfully launched in 2012 for tests of General Relativity and gravitational physics including the accurate measurement of frame-dragging. It is currently very well observed all over the world by the stations of the International Laser Ranging Service. Its preliminary orbital analyses show that LARES behaves as the best artificial massive test particle today available in the solar system, providing an optimal approximation to the time-like geodesic motion of General Relativity. Furthermore, on the basis of a test using almost three years of observations of LARES, we concluded that LARES, together with the LAGEOS and LAGEOS 2 satellites, provides excellent preliminary results for testing General Relativity.

Roger Penrose

Papers

Chandrasekhar, black holes, and singularities

Exploring the unification of quantum theory and general relativity with a Bose-Einstein condensate

CCC and the Fermi paradox

Palatial twistor theory and the twistor googly problem

Preliminary orbital analysis of the LARES space experiment