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).

/pdf/recognition-by-components-a-theory-of-human-image-2d038hmxno.pdf

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

Foreword by Michael Atiyah vii Acknowledgments ix CHAPTER ONE Classical Theory, Stephen Hawking 3 CHAPTER TWO Structure of Spacetime Singularities, Roger Penrose 27 CHAPTER THREE Quantum Black Holes, Stephen Hawking 37 CHAPTER FOUR Quantum Theory and Spacetime, Roger Penrose 61 CHAPTER FIVE Quantum Cosmololgy, Stephen Hawking 75 CHAPTER SIX The Twistor View of Spacetime, Roger Penrose 105 CHAPTER SEVEN The Debate, Stephen Hawking and Roger Penrose 121 AFTERWORD TO THE 2010 EDITION The Debate Continues, Stephen Hawking and Roger Penrose 139 References 143

The Nature of Space and Time

Proposals for describing the initial state of the universe hardly ever address a certain fundamental conundrum [1] — yet this is a conundrum whose significance is, in a certain sense, obvious. The issue arises from one of the most fundamental principles of physics: the Second Law of thermodynamics. According to the Second Law, roughly speaking, the entropy of the universe increases with time, where the term “entropy” refers to an appropriate measure of disorder or lack of “specialness” of the state of the universe. Since the entropy increases in the future direction of time, it must decrease in the past time-direction. Accordingly, the initial state of the universe must be the most special of all, so any proposal for the actual nature of this initial state must account for its extreme specialness. Proposals have been put forward from time to time (such as in various forms of “inflationary cosmology” and the previously popular “chaotic cosmology”) in which it is suggested that the initial state of the universe ought to have been in some sense “random”, and various physical processes are invoked in order to provide mechanisms whereby the universe might be driven into the special state in which it appears actually to have been in, at slightly later stages. But “random” means “non-special” in the extreme; hence the conundrum just referred to. Sometimes theorists have tried to find an explanation via the fact that the early universe was very “small”, this smallness perhaps allowing only a tiny number of alternative initial states, or perhaps they try to take refuge in the anthropic principle, which would be a selection principle in favour of certain special initial states that allow the eventual evolution of intelligent life. Neither of these suggested explanations gets close to resolving the issue, however. It may be seen that, with timesymmetrical dynamical laws, the mere smallness of the early universe does not provide a restriction on its degrees of freedom. For we may contemplate a universe model in the final stages of collapse. It must do something, in accordance with its dynamical laws, and we expect it to collapse to some sort of complicated space-time singularity, a singularity encompassing as many degrees of freedom as were already present in its earlier nonsingular collapsing phase. Time-reversing this situation, we see that an initial singular state could also contain as many degrees of freedom as such a collapsing one. But in our actual universe, almost all of those degrees of freedom were somehow not activated. What about the anthropic principle? Again, this is virtually no help to us whatever in resolving our conundrum. It is normally assumed that life had to arise via complicated evolutionary processes, and these processes required particular conditions, and particular physical laws, including the Second Law. The Second Law was certainly a crucial part of evolution, in the way that our particular form of life actually came about. But the very action of this Second Law tells us that however special the universe may be now, with life existing in it now, it must have been far more special at an earlier stage in which life was not present. From the purely anthropic point of view, this earlier far more special phase was not needed; it would have been much more likely that our present “improbable” stage came about simply by chance, rather than coming about via an earlier even more improbable stage. When the Second Law is a crucial component, there is always a far more probable set of initial conditions that would lead to this same state of affairs, namely one in which the Second Law was violated prior to the situation now! As another aspect of this same issue, we may think of the vastness of our actual universe, most of which had no actual bearing on our existence. Though very special initial conditions were indeed required for our existence in our particular spatial location, we did not actually need these same special conditions at distant places in the universe. Yet as we look out at the universe, we see the same kind of conditions, acting according to the same Second Law of thermodynamics, no matter how far out we look. If we take the view that the Second Law was introduced in our vicinity merely for our own benefit, then we are left with no explanation for the extravagance of this same Second Law having to be invoked uniformly throughout the universe, as it appears to be as far as our powerful instruments are able to probe.

/pdf/before-the-big-bang-an-outrageous-new-perspective-and-its-13mkv5zl1n.pdf

Before the big bang: An outrageous new perspective and its implications for particle physics

10 exact gravitationally-conserved quantities

http://www.quantumconsciousness.org/sites/default/files/Hameroff%2C%20Penrose%20-%20Reply%20to%20the%20seven%20commentaries%2C%20March%202014.pdf

Reply to seven commentaries on “Consciousness in the universe: Review of the ‘Orch OR’ theory”

We present a test of General Relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS and LAGEOS 2 laser-ranged satellites together with the Earth's gravity field model GGM05S produced by the space geodesy mission GRACE. We measure $\mu = (0.994 \pm 0.002) \pm 0.05$, where $\mu$ is the Earth's dragging of inertial frames normalized to its General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the estimated systematic error mainly due to the uncertainties in the Earth's gravity model GGM05S. Our result is in agreement with the prediction of General Relativity.

/pdf/a-test-of-general-relativity-using-the-lares-and-lageos-3u2on97aw2.pdf

Roger Penrose

Papers

The Nature of Space and Time

Before the big bang: An outrageous new perspective and its implications for particle physics

10 exact gravitationally-conserved quantities

Reply to seven commentaries on “Consciousness in the universe: Review of the ‘Orch OR’ theory”

A Test of General Relativity Using the LARES and LAGEOS Satellites and a GRACE Earth's Gravity Model