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We present a graduate course on ideal measurements, analyzed as dynamical processes of interaction between the tested system S and an apparatus A, described by quantum statistical mechanics. The apparatus A=M+B involves a macroscopic measuring device M and a bath B. The requirements for ideality of the measurement allow us to specify the Hamiltonian of the isolated compound system S+M+B. The resulting dynamical equations may be solved for simple models. Conservation laws are shown to entail two independent relaxation mechanisms: truncation and registration. Approximations, justified by the large size of M and of B, are needed. The final density matrix $\hat{\cal D}(t_f)$ of S+A has an equilibrium form. It describes globally the outcome of a large set of runs of the measurement. The measurement problem, i.e., extracting physical properties of individual runs from $\hat{\cal D}(t_f)$, then arises due to the ambiguity of its splitting into parts associated with subsets of runs. To deal with this ambiguity, we postulate that each run ends up with a distinct pointer value $A_i$ of the macroscopic M. This is compatible with the principles of quantum mechanics. Born's rule then arises from the conservation law for the tested observable; it expresses the frequency of occurrence of the final indications $A_i$ of M in terms of the initial state of S. Von Neumann's reduction amounts to updating of information due to selection of $A_i$. We advocate the terms $q$-probabilities and $q$-correlations when analyzing measurements of non-commuting observables. These ideas may be adapted to different types of courses., Comment: 32 pages

A large class of stationary, non-rotating black hole metrics is proposed, in which the interior is regular with a core consisting of a condensate of Higgs and $Z$ bosons generated from the nuclear binding energy of the initial H atoms. Gravitational collapse is prevented by negative pressures from the Higgs condensate and a small imbalance in the distribution of electric charges. Non-condensed, thermal particles are present as well. The approach holds for masses exceeding 0.75 $10^{-4}M_\odot$. The inner horizon sets an inner core of 11 cm, while the characteristic radius of the full core is 270 $(M/M_\odot)^{1/3}$ cm. For increasing charge, the core expands; in the extremal case, it fills the interior. While the net charge is easily shielded, the build up of horizons may prevent this in the interior, and consequently avoid a singularity. In black hole merging, the core of a nearly extremal one may be exposed, forming a new class of events. The approach is a stepping stone towards rotating black holes., Comment: 6 pages revtex

Two types of quantum measurements, measuring the spins of an entangled pair and attempting to measure a spin at either of two positions, are analysed dynamically by apparatuses of the Curie-Weiss type. The outcomes comply with the standard postulates., Comment: 6 pages. This work was carried out during the master thesis research of M. P.-L. at the University of Amsterdam in 2012

de la Pe\~na 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics are stable. Though the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Pe\~na-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an $1/r^2$ potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium., Comment: 18 pages latex, 1 figure

The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-$\frac{1}{2}$ system simultaneously interacting with two magnets, which act as measuring apparatuses of two different spin components. We work out the dynamics of this process and determine the final state of the measuring apparatuses, from which we can find the probabilities of the four possible outcomes of the measurements. The measurement is found to be non-ideal, as (i) the joint statistics do not coincide with the one obtained by separately measuring each spin component, and (ii) the density matrix of the spin does not collapse in either of the measured observables. However, we give an operational interpretation of the process as a generalised quantum measurement, and show that it is fully informative: The expected value of the measured spin components can be found with arbitrary precision for sufficiently many runs of the experiment., Comment: 24 pages, 9 figures; close to published version

Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar \omega$ in each mode, i.e., the zero-point Planck spectrum. While this classical theory explains many quantum phenomena related to harmonic oscillator problems, hard results on nonlinear systems are still lacking. In this work the hydrogen ground state is studied by numerically solving the Abraham -- Lorentz equation in the dipole approximation. First the stochastic Gaussian field is represented by a sum over Gaussian frequency components, next the dynamics is solved numerically using OpenCL. The approach improves on work by Cole and Zou 2003 by treating the full $3d$ problem and reaching longer simulation times. The results are compared with a conjecture for the ground state phase space density. Though short time results suggest a trend towards confirmation, in all attempted modelings the atom ionises at longer times., Comment: 20 pages, 9 figures. Published version, minor changes

The outcome of a single quantum experiment is unpredictable, except in a pure-state limit. The definite process that takes place in the apparatus may either be intrinsically random or be explainable from a deeper theory. While the first scenario is the standard lore, the latter implies that quantum mechanics is emergent. In that case, it is likely that one has to reconsider radiation by accelerated charges as a physical effect, which thus must be compensated by an energy input. Stochastic electrodynamics, for example, asserts that the vacuum energy arises from classical fluctuations with energy $\frac{1}{2}\hbar\omega$ per mode. In such theories the stability of the hydrogen ground state will arise from energy input from fluctuations and output by radiation, hence due to an energy throughput. That flux of energy constitutes an arrow of time, which we call the "subquantum arrow of time". It is related to the stability of matter and it is more fundamental than, e.g., the thermodynamic and cosmological arrows., Comment: 10 pages Latex

These are notes (in Dutch) of lectures on multiple scattering of waves, given at the University of Amsterdam in 1993. At request of some of the students, now professors, they are made publicly available. The main part of the material is covered in the review paper: {\it Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,} by M. C. W. van Rossum and myself, Rev. Mod. Phys. {\bf 71} (1999) 313 - 371., Comment: 156 pages, many figures. To be printed 2 pages per sheet, two sided

In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for the interpretation of quantum mechanics. Here we analyse an ideal measurement as a process of interaction between the tested system S and an apparatus A, so as to derive the properties postulated in textbooks. We thus consider within standard quantum mechanics the measurement of a quantum spin component $\hat s_z$ by an apparatus A, being a magnet coupled to a bath. We first consider the evolution of the density operator of S+A describing a large set of runs of the measurement process. The approach describes the disappearance of the off-diagonal terms ("truncation") of the density matrix as a physical effect due to A, while the registration of the outcome has classical features due to the large size of the pointer variable, the magnetisation. A quantum ambiguity implies that the density matrix at the final time can be decomposed on many bases, not only the one of the measurement. This quantum oddity prevents to connect individual outcomes to measurements, a difficulty known as the "measurement problem". It is shown that it is circumvented by the apparatus as well, since the evolution in a small time interval erases all decompositions, except the one on the measurement basis. Once one can derive the outcome of individual events from quantum theory, the so-called "collapse of the wave function" or the "reduction of the state" appears as the result of a selection of runs among the original large set. Hence nothing more than standard quantum mechanics is needed to explain features of measurements. The employed statistical formulation is advocated for the teaching of quantum theory., Comment: 43 pages, 5 figures. Lectures given in the "Advanced School on Quantum Foundations and Open Quantum Systems", Joao Pessoa, Brazil, summer 2012. To appear in the proceedings and in IJMPB

Recent weak and strong lensing data of the galaxy cluster A1689 are modelled by dark fermions that are quantum degenerate within some core. The gas density, deduced from X-ray observations up to 1 Mpc and obeying a cored power law, is taken as input, while the galaxy mass density is modelled. An additional dark matter tail may arise from cold or warm dark matter, axions or non-degenerate neutrinos. The fit yields that the fermions are degenerate within a 430 kpc radius. The fermion mass is a few eV and the best case involves 3 active plus 3 sterile neutrinos of equal mass, for which we deduce $1.51 \pm 0.04$ eV. The eV mass range will be tested in the KATRIN experiment., Comment: 5 pages latex, 5 figures. Accepted for MNRAS Letters

To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is tackled with two guidelines. On the one hand, the dynamics of the macroscopic apparatus A coupled to the tested system S is described mathematically within a standard quantum formalism, where "q-probablities" remain devoid of interpretation. On the other hand, interpretative principles are introduced to account for the expected features of ideal measurements. Most of the five principles, which relate the quantum formalism to physical reality, are straightforward and refer to macroscopic variables. The process can be identified with a relaxation of S+A to thermodynamic equilibrium, not only for a large ensemble $\scriptE$ of runs but even for its sub-ensembles. The different mechanisms of quantum statistical dynamics that ensure the relaxation are exhibited. The additional information provided by the sub-ensembles remove Schr\"odinger's quantum ambiguity of the final density operator for $\scriptE$ which hinders its direct interpretation, and bring out a commutative behaviour of the pointer observable at the final time. The latter property supports the introduction of a last principle, needed to switch from the statistical ensembles and sub-ensembles described by quantum theory to individual experimental events. It amounts to identify some formal "q-probabilities" with ordinary frequencies, but only those which refer to the final pointer indications. The desired properties of ideal measurements, in particular the uniqueness of the result for each individual run and von Neumann's reduction, are thereby recovered with economic interpretations. The status of Born's rule involving both A and S is re-evaluated, and contextuality is made obvious., Comment: Matches published version. 24 pages revtex

The recent Sumi et al (2010, 2011) detection of free roaming planet mass MACHOs in cosmologically significant numbers recalls their original detection in quasar microlening studies (Schild 1996, Colley and Schild 2003). We consider the microlensing signature of such a population, and find that the nano-lensing (microlensing) would be well characterized by a statistical microlensing theory published previously by Refsdal and Stabel (1991). Comparison of the observed First Lens microlensing amplitudes with the theoretical prediction gives close agreement and a methodology for determining the slope of the mass function describing the population. Our provisional estimate of the power law exponent in an exponential approximation to this distribution is $2.98^{+1.0}_{-0.5}.$ where a Salpeter slope is 2.35., Comment: 12 pages, 1 figure

We consider the Herschel-Planck infrared observations of presumed condensations of interstellar material at a measured temperature of approximately 14 K (Juvela et al., 2012), the triple point temperature of hydrogen. The standard picture is challenged that the material is cirrus-like clouds of ceramic dust responsible for Halo extinction of cosmological sources (Finkbeiner, Davis, and Schlegel 1999). Why would such dust clouds not collapse gravitationally to a point on a gravitational free-fall time scale of $10^8$ years? Why do the particles not collide and stick together, as is fundamental to the theory of planet formation (Blum 2004; Blum and Wurm, 2008) in pre-solar accretion discs? Evidence from 3.3 $\mu$m and UIB emissions as well as ERE (extended red emission) data point to the dominance of PAH-type macromolecules for cirrus dust, but such fractal dust will not spin in the manner of rigid grains (Draine & Lazarian, 1998). IRAS dust clouds examined by Herschel-Planck are easily understood as dark matter Proto-Globular-star-Cluster (PGC) clumps of primordial gas planets, as predicted by Gibson (1996) and observed by Schild (1996)., Comment: 8 pages, 2 figures, Conference FQMT'11

Recent Herschel/SPIRE maps of the Small and Large Magellanic Clouds (SMC, LMC) exhibit in each thousands of clouds. Observed at 250 microns, they must be cold, T ~ 15 K, hence the name "Herschel cold clouds" (HCCs). From the observed rotational velocity profile and the assumption of spherical symmetry, the Galactic mass density is modeled in a form close to that of an isothermal sphere. If the HCCs constitute a certain fraction of it, their angular size distribution has a specified shape. A fit to the data deduced from the SMC/LMC maps supports this and yields for their radius 2.5 pc, with a small change when allowing for a spread in HCC radii. There are so many HCCs that they will make up all the missing Halo mass density if there is spherical symmetry and their average mass is of order 15,000 Mo. This compares well with the Jeans mass of circa 40,000 Mo and puts forward that the HCCs are in fact Jeans clusters, constituting all the Galactic dark matter and much of its missing baryons, a conclusion deduced before from a different field of the sky (Nieuwenhuizen, Schild and Gibson 2011). A preliminary analysis of the intensities yields that the Jeans clusters themselves may consist of some billion MACHOs of a few dozen Earth masses. With a size of dozens of solar radii, they would mostly obscure stars in the LMC, SMC and towards the Galactic center, and may thus have been overlooked in microlensing., Comment: Revised and corrected version, matches published version. Conclusions unchanged

Small values of lithium observed in a small, primitive, Galaxy-Halo star SDSS J102915 + 172927 cannot be explained using the standard cold dark matter CDM theory of star formation, but are easily understood using the Gibson/Schild 1996 hydrogravitationaldynamics (HGD) theory. From HGD, primordial H-4He gas fragments into Earth-mass planets in trillion-planet proto-globular-star-cluster (PGC) clumps at the 300 Kyr time of transition from the plasma epoch, soon after the big bang. The first HGD stars formed from pristine, frictionally-merging, gas-planets within the gently stressed clumps of the early universe, burning most available lithium in brown-dwarfs and hot-stars before creating metals that permit cooler burning. The Caffau halo star is a present day example. CDM first stars (Population III) were massive and promptly exploded, reionizing the gas of the universe and seeding it with metals, thus making the observed star unexplainable. From HGD, CDM and its massive first stars, and re-ionization by Pop III supernovae, never happened. All stars are formed from planets in primordial clumps. HGD first stars (Pop III) were small and long-lived, and the largest ones were hot. We suggest such small HGD (Pop III) stars still form in the gently stressed Galaxy halo., Comment: 7 pages 3 figures, for the Journal of Cosmology Volume 16

Textbooks on cosmology exhibit a thermodynamic inconsistency for free streaming, decoupled matter. It is connected here to the chemical potential, which deviates from its equilibrium value $\mu=\alpha k_BT$, where $\alpha$ is the usual parameter of the Fermi-Dirac or Bose-Einstein distribution function., Comment: 4 pages latex

The workshop "New directions in modern cosmology", organized by Theo Nieuwenhuizen, Rudy Schild, Francesco Sylos Labini and Ruth Durrer, was held from September 27 until October 1, 2010, in the Lorentz Center in Leiden, the Netherlands. A transcript of the final round table discussion, chaired by Theo Nieuwenhuizen and Rudy Schild, is presented. The subjects are: 0) spread in data; 1) back reaction; 2) $N$-body simulations; 3) neutrinos as the dark matter; 4) gravitational hydrodynamics, 5) missing baryons and lensing in an inhomogeneous universe, and 6) final points., Comment: 14 pages

It is assumed that a galaxy starts as a dark halo of a few million Jeans clusters (JCs), each of which consists of nearly a trillion micro brown dwarfs, MACHOs of Earth mass. JCs in the galaxy center heat up their MACHOs by tidal forces, which makes them expand, so that coagulation and star formation occurs. Being continuously fed by matter from bypassing JCs, the central star(s) may transform into a super massive black hole. It has a fast $t^3$ growth during the first mega years, and a slow $t^{1/3}$ growth at giga years. JCs disrupted by a close encounter with this black hole can provide matter for the bulge. Those that survive can be so agitated that they form stars inside them and become globular star clusters. Thus black holes mostly arise together with galactic bulges in their own environment and are about as old as the oldest globular clusters. The age 13.2 Gyr of the star HE 1523-0901 puts forward that the Galactic halo was sufficiently assembled at that moment. The star formation rate has a maximum at black hole mass $\sim4 \ 10^7M_\odot$ and bulge mass $\sim5\,10^{10}M_\odot$. In case of merging supermassive black holes the JCs passing near the galactic center provide ideal assistance to overcome the last parsec., Comment: 6 pages latex. Matches published version

The quantum measurement problem, understanding why a unique outcome is obtained in each individual experiment, is tackled by solving models. After an introduction we review the many dynamical models proposed over the years. A flexible and rather realistic model is introduced, describing the measurement of the $z$-component of a spin through interaction with a magnetic memory simulated by a Curie--Weiss magnet, including $N \gg1$ spins weakly coupled to a phonon bath. Initially prepared in a metastable paramagnetic state, it may transit to its up or down ferromagnetic state, triggered by its coupling with the tested spin, so that its magnetization acts as a pointer. A detailed solution of the dynamical equations is worked out. Conditions are found, which ensure that the process satisfies the features of ideal measurements. Various imperfections are discussed, as well as attempts of incompatible measurements. The first steps consist in the solution of the Hamiltonian dynamics for the spin-apparatus density matrix $D(t)$. On a longer time scale, the trend towards equilibrium of the magnet produces a final state $D(t_{\rm f})$ that involves correlations between the system and the indications of the pointer, thus ensuring registration. A difficulty lies in a quantum ambiguity: There exist many incompatible decompositions of the density matrix $\scriptD(t_{\rm f})$. This difficulty is overcome by dynamics due to suitable interactions within the apparatus. Any subset of runs thus reaches over a brief delay a stable state which satisfies the same hierarchic property as in classical probability theory. Standard quantum statistical mechanics alone appears sufficient to explain the occurrence of a unique answer in each run. Finally, pedagogical exercises are proposed while the statistical interpretation is promoted for teaching. [Abridged], Comment: Minor changes, matches published version. 201 pages Latex, 377 references, 15 figures

One of the tests of nucleosynthesis theory is the $^3$He abundance in the Galaxy. $^3$He$^+$ is observed through its 3.46 cm hyperfine level in Hii regions and the $^3$He/H ratio compares well with theory. Since $^3$He can be created or destroyed in nuclear reactions, one would expect that its abundance shows a trend with the amount of such reactions, so with distance to the Center of the Galaxy and with metallicity. Such trends are lacking in observations. This is explained by assuming that the Hii clouds are recently formed out of the primordial micro brown dwarfs of earth mass predicted by gravitational hydrodynamics. If indeed existing, they would preserve their primordial $^3$He/H ratio and spread this when evaporating into Hii clouds, independent of the location in the Galaxy. In the development of the argument, it is also explained that wide binaries do not rule out the MACHO dark matter predicted by gravitational hydrodynamics, but are rather immersed as visible partners in Jeans clusters of dark micro brown dwarfs., Comment: 4 pages

The KATRIN experiment in Karlsruhe Germany will monitor the decay of tritium, which produces an electron-antineutrino. While the present upper bound for its mass is 2 eV/$c^2$, KATRIN will search down to 0.2 eV$/c^2$. If the dark matter of the galaxy cluster Abell 1689 is modeled as degenerate isothermal fermions, the strong and weak lensing data may be explained by degenerate neutrinos with mass of 1.5 eV$/c^2$. Strong lensing data beyond 275 kpc put tension on the standard cold dark matter interpretation. In the most natural scenario, the electron antineutrino will have a mass of 1.5 eV/$c^2$, a value that will be tested in KATRIN., Comment: 13 pages, 5 figures

Context: The baryonic dark matter dominating the structures of galaxies is widely considered as mysterious, but hints for it have been in fact detected in several astronomical observations at optical, infrared, and radio wavelengths. We call attention to the nature of galaxy merging, the observed rapid microlensing of a quasar, the detection of "cometary knots" in planetary nebulae, and the Lyman-alpha clouds as optical phenomena revealing the compact objects. Radio observations of "extreme scattering events" and "parabolic arcs" and microwave observations of "cold dust cirrus" clouds are observed at 15 - 20 K temperatures are till now not considered in a unifying picture. Aims: The theory of gravitational hydrodynamics predicts galactic dark matter arises from Jeans clusters that are made up of almost a trillion micro brown dwarfs (mBDs) of earth weight. It is intended to explain the aforementioned anomalous observations and to make predictions within this framework. Methods: We employ analytical isothermal modeling to estimate various effects. Results: Estimates of their total number show that they comprise enough mass to constitute the missing baryonic matter. Mysterious radio events are explained by mBD pair merging in the Galaxy. The "dust" temperature of cold galaxy halos arises from a thermostat setting due to a slow release of latent heat at the 14 K gas to solid transition at the mBD surface. The proportionality of the central black hole mass of a galaxy and its number of globular clusters is explained. The visibility of an early galaxy at redshift 8.6 is obvious with most hydrogen locked up in mBDs. Conclusions: Numerical simulations of various steps would further test the approach. It looks promising to redo MACHO searches against the Magellanic clouds., Comment: 12 pages A&A tex, 3 pdf figures

Given the state of a quantum system, one can calculate the expectation value of any observable of the system. However, the inverse problem of determining the state by performing different measurements is not a trivial task. In various experimental setups it is reasonably straightforward to reconstruct the state of a quantum system employing linear tomographic technique. In this way the elements of the density matrix can be linearly related to a set of measured quantities. But since different observables of a quantum system are not commuting with each other, one often has to perform series of successive measurements of observables which cannot be done simultaneously. Simultaneous measurement of observables cost less time and energy and is more beneficial. In this paper we review the strategy of quantum state tomography with simultaneous measurement of commuting observables. This can be done by introducing an assistant system of which the state is known. We show that the interaction between the assistant and the system of interest within different frame works allows the reconstruction of the state of the system. Specifically, we consider a two-level system and reconstruct its initial state by introducing an assistant which can be either another two-level system or a single cavity mode of the electromagnetic field., Comment: 11 pages, to be appear in journal of computational and theoretical nanoscience

The lensing data of the galaxy cluster Abell 1689 can be explained by an isothermal fermion model with a mass of 1-2 eV. The best candidate is the 1.5 eV neutrino; its mass will be searched down to 0.2 eV in KATRIN 2015. If its righthanded (sterile) modes were created too, there is 20% neutrino hot dark matter. Their condensation on clusters explains the reionization of the intercluster gas without Pop. III stars. Baryonic structure formation is achieved by gravitional hydrodynamics alone, without dark matter trigger., Comment: 3 pages, Proceedings Marcel Grossmann XII, Paris, 2009

Gravitational hydrodynamics acknowledges that hydrodynamics is essentially nonlinear and viscous. In the plasma, at $z=5100$, the viscous length enters the horizon and causes fragmentation into plasma clumps surrounded by voids. The latter have expanded to 38 Mpc now, explaining the cosmic void scale $30/h=42$ Mpc. After the decoupling the Jeans mechanism fragments all matter in clumps of ca 40,000 solar masses. Each of them fragments due to viscosity in millibrown dwarfs of earth weight, so each Jeans cluster contains billions of them. The Jeans clusters act as ideal gas particles in the isothermal model, explaining the flattening of rotation curves. The first stars in old globular clusters are formed by aggregation of milli brown dwarfs, without dark period. Star formation also happens when Jean clusters come close to each other and agitate and heat up the cooled milli brown dwarfs, which then expand and coalesce to form new stars. This explains the Tully-Fischer and Jackson-Faber relations, and the formation of young globular clusters in galaxy mergers. Thousand of milli brown dwarfs have been observed in quasar microlensing and some 40,000 in the Helix planetary nebula. While the milli brown dwarfs, i.e., dark baryons, constitute the galactic dark matter, cluster dark matter consists probably of 1.5 eV neutrinos, free streaming at the decoupling. These two types of dark matter explain a wealth of observations., Comment: 3 pages, Proceedings Marcel Grossmann XII, Paris 2009

This paper investigates the question whether a realistic black hole can be in principal similar to a star, having a large but finite redshift at its horizon. If matter spreads throughout the interior of a supermassive black hole with mass $M\sim10^9M_\odot$, it has an average density comparable to air and it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field describing H atoms is coupled to the curvature scalar with dimensionless coupling $\xi$. In the Bose-Einstein condensed groundstate an exact, self-consistent solution for the metric occurs for a certain large value of $\xi$, quadratic in the black hole mass. It is put forward that $\xi$ is set by proper choice of the background metric as a first step of a renormalization approach, while otherwise the non-linearities are small. The black hole has a hair, the binding energy. Fluctuations about the ground state are considered., Comment: 18 pages Latex Physica E style

The gravitational hydrodynamics of the primordial plasma with neutrino hot dark matter is considered as a challenge to the bottom-up cold dark matter paradigm. Viscosity and turbulence induce a top-down fragmentation scenario before and at decoupling. The first step is the creation of voids in the plasma, which expand to 37 Mpc on the average now. The remaining matter clumps turn into galaxy clusters. Turbulence produced at expanding void boundaries causes a linear morphology of 3 kpc fragmenting protogalaxies along vortex lines. At decoupling galaxies and proto-globular star clusters arise; the latter constitute the galactic dark matter halos and consist themselves of earth-mass H-He planets. Frozen planets are observed in microlensing and white-dwarf-heated ones in planetary nebulae. The approach also explains the Tully-Fisher and Faber-Jackson relations, and cosmic microwave temperature fluctuations of micro-Kelvins., Comment: 6 pages, no figures

The Schwarzschild metric has a divergent energy density at the horizon, which motivates a new approach to black holes. If matter is spread uniformly throughout the interior of a supermassive black hole, with mass $M\sim M_\star= 2.34 10^8M_\odot$, it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field is coupled to the curvature scalar. In the Bose-Einstein condensed groundstate an exact, selfconsistent solution for the metric is presented. It is regular with a specific shape at the origin. The redshift at the horizon is finite but large, $z\sim 10^{14}$$M_\star/M$. The binding energy remains as an additional parameter to characterize the BH; alternatively, the mass observed at infinity can be any fraction of the rest mass of its constituents., Comment: 6 pages, no figures

Within the Relativistic Theory of Gravitation it is shown that the equation of state $p=\rho$ holds near the center of a black hole. For the stiff equation of state $p=\rho-\rho_c$ the interior metric is solved exactly. It is matched with the Schwarzschild metric, which is deformed in a narrow range beyond the horizon. The solution is regular everywhere, with a specific shape at the origin. The gravitational redshift at the horizon remains finite but is large, $z\sim 10^{23}$$M_\odot/M$. Time keeps its standard role also in the interior. The energy of the Schwarzschild metric, shown to be minus infinity in the General Theory of Relativity, is regularized in this setup, resulting in $E=Mc^2$., Comment: 12 pages newFNLstyle. 4 figures

The standard model of glasses is an ensemble of two-level systems interacting with a thermal bath. The general origin of memory effects in this model is a quasi-stationary but non-equilibrium state of a single two-level system, which is realized due to a finite-rate cooling and very slow thermally activated relaxation. We show that single particle memory effects, such as negativity of the specific heat under reheating, vanish for a sufficiently disordered ensemble. In contrast, a disordered ensemble displays a collective memory effect [similar to that described by Kovacs for glassy polymers], where non-equilibrium features of the ensemble are monitored via a macroscopic observable. An experimental realization of the effect can be used to further assess the consistency of the model., Comment: 4 pages, 6 figures

Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const. $\times$ {\it total energy momentum tensor}. For flat space cosmology the gravitational energy is negative and cancels the material energy. In the relativistic theory of gravitation a bimetric coupling between the Riemann and Minkowski metrics breaks general coordinate invariance. The case of a positive cosmological constant is considered. A singularity free version of the Schwarzschild black hole is solved analytically. In the interior the components of the metric tensor quickly die out, but do not change sign, leaving the role of time as usual. For cosmology the $\Lambda$CDM model is covered, while there appears a form of inflation at early times. Here both the total energy and the zero point energy vanish., Comment: 5 pages, 1 figure

The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement, regarded as a process of quantum statistical mechanics. Schr\"odinger cat terms involving both the system and the apparatus, die out very quickly, while the registration is a process taking the apparatus from its initially metastable state to one of its stable final states. The occurrence of Born probabilities can be inferred at the macroscopic level, by looking at the pointer alone. Apparent non-unitary behavior of the measurement process is explained by the arisal of small many particle correlations, that characterize relaxation., Comment: 13 pages, discussion of pre-measurement added. World Scientific style. To appear in proceedings "Beyond The Quantum", Th.M. Nieuwenhuizen et al, eds, (World Scientific, 2007)

This is a transcript of the round table that took place during the conference Quantum Theory: Reconsideration of Foundations - 3, June 2005, Vaxjo, Sweden. There are presented opinions of leading experts in quantum foundations on such fundamental problems as the origin of quantum fluctuations and completeness of quantum mechanics., Comment: Proceedings of Conference Quantum Theory: Reconsideration of Foundations-3, American Institute of Physics, Ser. Conference Proceedings, Melville, NY, 2006, vol. 810

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs and applied on glassy polymers, is implemented in an exactly solvable model with facilitated dynamics. This model is based on interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property and to slow dynamics, the model reproduces the characteristic non-monotonic evolution known as the ``Kovacs effect'', observed in polymers, spin glasses, in granular materials and models of molecular liquids, when similar experimental protocols are implemented., Comment: Contribution to the Proceedings of the Summerschool "Ageing and the glass transition", Luxembourg 14-25 Sept. 2005. To appear in a special issue of Journal of Physics

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs for glassy polymers, is implemented in an exactly solvable dynamical model. This model is characterized by interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property, the model reproduces the characteristic non-monotonic evolution known as the ``Kovacs effect'', observed in polymers, in granular materials and models of molecular liquids, when similar experimental protocols are implemented., Comment: 8 pages, 6 figures

On the basis of Galilean invariance and the Doppler formula, combined with an observational condition, it is shown that the constancy of the velocity of light {\it in vacuo} can be derived, together with time-dilatation and Lorentz contraction. It is not necessary to take the constancy as a postulate., Comment: 5 pages AIP-tex. Conference "Quantum Theory: Reconsideration of Foundations 3", Vaxjo Sweden, June 2005. To appear in AIP conference series

In a quantum measurement, a coupling $g$ between the system S and the apparatus A triggers the establishment of correlations, which provide statistical information about S. Robust registration requires A to be macroscopic, and a dynamical symmetry breaking of A governed by S allows the absence of any bias. Phase transitions are thus a paradigm for quantum measurement apparatuses, with the order parameter as pointer variable. The coupling $g$ behaves as the source of symmetry breaking. The exact solution of a model where S is a single spin and A a magnetic dot (consisting of $N$ interacting spins and a phonon thermal bath) exhibits the reduction of the state as a relaxation process of the off-diagonal elements of S+A, rapid due to the large size of $N$. The registration of the diagonal elements involves a slower relaxation from the initial paramagnetic state of A to either one of its ferromagnetic states. If $g$ is too weak, the measurement fails due to a ``Buridan's ass'' effect. The probability distribution for the magnetization then develops not one but two narrow peaks at the ferromagnetic values. During its evolution it goes through wide shapes extending between these values., Comment: 12 pages, 2 figures

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (aster-like) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusion leads to the coexistence of regions of high and low densities of bound motors corresponding to motor traffic jams, which grow upon increasing the overall motor concentration. These jams are insensitive to the motor behavior at the end of the filament. In centered systems, traffic jams remain small and an increase in the motor concentration leads to a flattening of the profile, if the motors move inwards, and to the build-up of a concentration maximum in the center of the aster if motors move outwards. In addition to motors density patterns, we also determine the corresponding patterns of the motor current., Comment: 48 pages, 8 figures

Processive molecular motors which drive the traffic of organelles in cells move in a directed way along cytoskeletal filaments. On large time scales, they perform motor walks, i.e., peculiar random walks which arise from the repeated unbinding from and rebinding to filaments. Unbound motors perform Brownian motion in the surrounding fluid. In addition, the traffic of molecular motors exhibits many cooperative phenomena. In particular, it faces similar problems as the traffic on streets such as the occurrence of traffic jams and the coordination of (two-way) traffic. These issues are studied here theoretically using lattice models., Comment: latex, uses elsart.cls and phyeauth.cls (included), 10 pages, 6 figures, to appear in the proceedings of FQMT'04, Prague

We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the apparatus is macroscopic. This implies to treat it with quantum statistical mechanics. The relevant time scales of the process are exhibited. It begins with a very rapid disappearance of the off-diagonal blocks of the overall density matrix of the tested system and the apparatus. Possible recurrences are hindered by the large size of the latter. On a much larger time scale the apparatus registers the outcome: Correlations are established between the final values of the pointer and the initial diagonal blocks of the density matrix of the tested system. We thus derive Born's rule and von Neumann's reduction of the state from the dynamical process., Comment: 18 pages, no figures; conference talk of R. Balian

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation. Results are obtained for the fraction of bound motors, their average velocity and displacement. Enclosing the system in a finite geometry (tube, slab) leads to an experimentally realizable problem, that is studied in a continuum description and also numerically in a lattice simulation., Comment: 10 pages, uses elsart.cls (included), to appear in the proceedings of StatPhys-Taiwan 2004

An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The $z$-component $\hat s_z$ of a spin-1/2 is measured with an apparatus, which itself consists of magnet coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state according to the sign of $s_z$ of the tested spin. The quantum measurement goes in two steps. On a timescale $1/\sqrt{N}$ the off-diagonal elements of the spin's density matrix vanish due to a unitary evolution of the tested spin and the $N$ apparatus spins; on a larger but still short timescale this is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is a quantum process which can already be understood from classical statistical mechanics. The von Neumann collapse and the Born rule are derived rather than postulated., Comment: 7 pages revtex, 2 figures

Movements of molecular motors on cytoskeletal filaments are described by directed walks on a line. Detachment from this line is allowed to occur with a small probability. Motion in the surrounding fluid is described by symmetric random walks. Effects of detachment and reattachment are calculated by an analytical solution of the master equation in two and three dimensions. Results are obtained for the fraction of bound motors, their average velocity and displacement. The diffusion coefficient parallel to the filament becomes anomalously large since detachment and subsequent reattachment, in the presence of directed motion of the bound motors, leads to a broadening of the density distribution. The occurrence of protofilaments on a microtubule is modeled by internal states of the binding sites. After a transient time all protofilaments become equally populated., Comment: 20 pages Phys Rev E format + 11 figures

The spin-boson model, often used in NMR and ESR physics, quantum optics and spintronics, is considered in a solvable limit to model a spin one-half particle interacting with a bosonic thermal bath. By applying external pulses to a non-equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale T_2 inherent to transversal (`quantum') fluctuations. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a violation of the Clausius inequality and the Thomson formulation of the second law (cycles cost work) for the two-level system., Comment: 5 pages Latex, uses aip-proceedings style files. Proceedings `Quantum Limits to the Second Law', San Diego, July 2002

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics., Comment: 6 pages Latex, uses aip-proceedings style files. Proceedings `Quantum Limits to the Second Law', San Diego, July 2002