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Theo M. Nieuwenhuizen

Publications and source records attributed to Theo M. Nieuwenhuizen.

At least 19 recordsLinked to original sources
arXiv2024

Teaching ideal quantum measurement, from dynamics to interpretation

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.

quant-ph↗
arXiv2021

The interior of hairy black holes in standard model physics

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.

gr-qc↗
arXiv2017

Simultaneous measurement of two non-commuting quantum variables: Solution of a dynamical model

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.

quant-ph↗
arXiv2016

On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics

de la Peña 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 Peña-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.

quant-ph↗
arXiv2016

A sub-ensemble theory of ideal quantum measurement processes

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 Schrödinger'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.

quant-ph↗
arXiv2015

Simulation of the hydrogen ground state in Stochastic Electrodynamics

Stochastic electrodynamics is a classical theory which assumes that the physical vacuum consists of classical stochastic fields with average energy $\frac{1}{2}\hbar ω$ 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.

quant-ph↗
arXiv2014

A subquantum arrow of time

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 $\frac{1}{2}\hbarω$ 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.

quant-ph↗
arXiv2014

Veelvoudige verstrooiing van golven

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.

cond-mat.mes-hall↗
arXiv2014

Lectures on dynamical models for quantum measurements

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.

quant-ph↗
arXiv2013

Are observations of the galaxy cluster Abell 1689 consistent with a neutrino dark matter scenario?

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.

astro-ph.CO↗
arXiv2013

Understanding quantum measurement from the solution of dynamical models

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]

quant-ph↗
arXiv2013

Model for common growth of supermassive black holes, bulges and globular star clusters: ripping off Jeans clusters

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.

astro-ph.CO↗
arXiv2012

The Mass Function of Primordial Rogue Planet MACHOs in quasar nanolensing

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.

astro-ph.CO↗
arXiv2012

Do the Herschel cold clouds in the Galactic halo embody its dark matter?

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.

astro-ph.CO↗
arXiv2012

Why don't clumps of cirrus dust gravitationally collapse?

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 $μ$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).

astro-ph.CO↗
arXiv2012

Why are so many primitive stars observed in the Galaxy halo?

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.

physics.gen-ph↗
arXiv2011

Note on the chemical potential of decoupled matter in the Universe

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 $μ=αk_BT$, where $α$ is the usual parameter of the Fermi-Dirac or Bose-Einstein distribution function.

astro-ph.CO↗