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

Associate DIETRICH BELITZ, University of Oregon Editors: Condensed Matter Physics (Theoretical) J. IGNACIO CIRAC, Max-Planck-Institut für Quantenoptik Quantum Information RAYMOND E. GOLDSTEIN, University of Cambridge Biological Physics ARTHUR F. HEBARD, University of Florida Condensed Matter Physics (Experimental) RANDALL D. KAMIEN, University of Pennsylvania Soft Condensed Matter DANIEL KLEPPNER, Massachusetts Institute of Technology Atomic, Molecular, and Optical Physics (Experimental) PAUL G. LANGACKER, Institute for Advanced Study, Princeton University Particle Physics (Theoretical) VERA LÜTH, Stanford University Particle Physics (Experimental) DAVID D. MEYERHOFER, University of Rochester Physics of Plasmas and Matter at High-Energy Density WITOLD NAZAREWICZ, University of Tennessee, Oak Ridge National Laboratory Nuclear Physics JOHN H. SCHWARZ, California Institute of Technology Mathematical Physics FRIEDRICH-KARL THIELEMANN, Universität Basel Astrophysics Senior Assistant Editor: DEBBIE BRODBAR, APS Editorial Office American Physical Society

Reviews of Modern Physics

Lectures on Physics

Quantum Processes, Systems, and Information: Quantum information processing

Using the divergence theorem and the coordinate transformation theory for the general Fickian second law, fundamental diffusion problems are investigated. As a result, the new findings are obtained as follows. The unified diffusion theory is reasonably established, including a self-diffusion theory and an N (N ≥ 2) elements system interdiffusion one. The Fickian first law is incomplete without a constant diffusion flux corresponding to the Brown motion in the localized space. The cause of Kirkendall effect and the nonexistence of intrinsic diffusion concept are theoretically revealed. In the parabolic space, an elegant analytical method of the diffusion equation is mathematically established, including a nonlinear diffusion equation. From the Schr?dinger equation and the diffusion equation, the universal expression of diffusivity proportional to the Planck constant is reasonably obtained. The material wave equation proposed by de Broglie is also derived in relation to the Brown motion. The fundamental diffusion theories discussed here will be highly useful as a standard theory for the basic study of actual interdiffusion problems such as an alloy, a compound semiconductor, a multilayer thin film, and a microstructure material.

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Mathematical Physics in Diffusion Problems

This paper argues that a hypothetical “dark” particle (a black hole
with the reduced Planck mass and arbitrary temperature) gives a simple
explanation to the open question of dark energy and has a relic density of only
17% more than the commonly accepted value. By considering an additional near-horizon
boundary of the black hole, set by its quantum length, the black hole can
obtain an arbitrary temperature. Black-body radiation is still present and fits
as the source of the Universe’s missing energy. Support for this hypothesis is
offered by showing that a stationary solution to the black hole’s length scale
is the same if derived from a quantum analysis in continuous time, a quantum
analysis in discrete time, or a general relativistic analysis.

/pdf/dark-particles-answer-dark-energy-1grgyxlozz.pdf

Dark Particles Answer Dark Energy

In the governing thought, I find an equivalence between the classical information in a quantum system and the integral of that system’s energy and time, specifically , in natural units. I solve this relationship in four ways: the first approach starts with the Schrodinger Equation and applies the Minkowski transformation; the second uses the Canonical commutation relation; the third through Gabor’s analysis of the time-frequency plane and Heisenberg’s uncertainty principle; and lastly by quantizing Brownian motion within the Bernoulli process and applying the Gaussian channel capacity. In support I give two examples of quantum systems that follow the governing thought: namely the Gaussian wave packet and the electron spin. I conclude with comments on the discretization of space and the information content of a degree of freedom.

/pdf/measuring-a-quantum-system-s-classical-information-4biiyz3ic6.pdf

Measuring a Quantum System’s Classical Information

The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle’s temperature, (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of which is a combination of quantum and classical diffusion. The solution to the quantum diffusion of a free particle is derived from the equation for kinetic energy and its associated imaginary diffusion constant; a real diffusion constant (representing classical diffusion) is shown to be . We find the entropy of the initial state is one natural unit, which is the same amount of entropy the process generates after the de-coherence time, .

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Entropy Rate of Thermal Diffusion

With super-luminal neutrinos being observed in 2011 then refuted in 2012 we present an argument, based on Jensen’s inequality, that they might still exist only with a smaller excess speed than initially thought. Specifically, the quantity measured by OPERA and ICARUS is the average of the length of the displacement over time which is greater than the length of the average velocities - which determines and does not break Lorenz invariance. We examine quantum diffusion to explain the physics behind the particle’s variance resulting in an excess average velocity of ℏ⁄(mc^2 (t+τ) ), where t is the baseline and τ is the coherence time. We examine the experimental setup at OPERA to estimate the excess velocity and show it is within the error as observed in the tighter re-run. We also show consistency with Fermilab 1979 and supernova 1987A. In conclusion we comment on arguments refuting superluminal neutrinos and note a similar consequence of quantum mechanics that conservation of energy can be violated, if only for a short time.

Superluminal Consequences of Quantum Diffusion on Special Relativity

This paper argues a hypothetical �dark� particle (a black hole with the reduced Planck mass) gives a simple explanation to the open question of dark energy and has a relic density of only 17% more than the commonly accepted value. By considering an additional near horizon boundary of the black hole, set by its quantum length, the black hole can obtain an arbitrary temperature. Black body radiation is still present and fits as the source of the Universe�s missing energy. Support for this hypothesis is offered by showing a stationary solution to the black hole�s length scale is the same if derived from a quantum analysis in continuous time, a quantum analysis in discrete time, or a general relativistic analysis.

/pdf/dark-particles-black-holes-with-the-reduced-planck-mass-3vuul2dwwt.pdf

John L. Haller

Papers

Dark Particles Answer Dark Energy

Measuring a Quantum System’s Classical Information

Entropy Rate of Thermal Diffusion

Superluminal Consequences of Quantum Diffusion on Special Relativity

Dark Particles (Black Holes with the Reduced Planck Mass) Answers Dark Energy