Phase diagram of solid hints new fundamental constant and sees atomic orbital

Cold and pressure transform gas into liquid and then into solid. Van der Waals understood the phase diagram of liquefiable gas with the molecular volume and intermolecular attraction, however, was silent on how solid behaved1. Unfortunately, solid-state phase diagram have remained uncomprehended mystery; only its straight boundary2,3 was explained by struggle of order vs. chaos. Here we show that the volume of orbital overlap has its own energy, with the universal density 8.941 eV/Å3 announced as new fundamental atomic constant that determines the transition temperature TC. Furthermore, we devised solid-state tomography, valid to 5 TPa, - imaging orbital through the baric dependencies of TC. Triangle-shaped pattern of the diagram is explained by the only possible way, just as only one plane passes through triangle: -inflation of the intersection volume during the transition determines hysteresis, but its disappearance does triple point; -approaching ions, whose orbitals overlap, curves the line from zero-field-cooling (ZFC) TC to triple point; -the straight line between zero-field-heating (ZFH) TC and triple point is a consequence of straightening tilting angle. Diamond melting point, calculated from volumes of the tetrahedral covalent bonds, excellently agrees with real; furthermore, the points up to 2 TPa agree with experiment4. Our findings open up way to interpret antiferromagnetism and steric effect in mono, binary, and ternary transition-metal oxides and sulfides5-11, and advance in unravelling unconventional superconductivity12,13, ascertaining the roles of s- and p-hybridizations. Thereby, the importance of the solid-state tomography for organic conductors12,13 being high-compressible and interior of stars can scarcely be exaggerated.

Phase diagram senses orbitals and prompts a fundamental constant

Van der Waals’ discovery of that the volumes of molecules and their intermolecular attraction between them cause the peculiarities of the phase diagrams of gases and liquids1 gave the greatest impact on the progress of science and industry. Unfortunately, the phase charts of solids capable to advance scientific and technical progress remain uncomprehended mystery. Only the certain linear phase boundaries are understood by the struggle of magnetic field B against the thermal agitation2,3. Here we show that the intersection volume of internal atomic orbitals determines the form of phase boundary and, furthermore, energy per unit volume of the intersection is a new fundamental constant v = 8.941 eV/Å3. Together with the known struggle contribution2,3 to TC(B), we found a term proportional to the intersection volume of 3deg and 2p orbitals in the Sm0.55Sr0.45MnO3 manganite. Hysteresis of TC is described by the avalanche-like widening of the intersection volume due to reducing the Coulomb distortion with double-exchange ferromagnetism. The pressure-TC diagram4 of (Sm1-xNdx)0.55Sr0.45MnO3 (x=0, 0.2, 0.4, 0.5) is approximated with the same parameters as the TC(B) diagram of Sm0.55Sr0.45MnO3. Furthermore, the diamond’s melting point 4157oC calculated from the intersection volume of sp3-orbitals is in excellent agreement with the real 4000oC. Tips explaining the puzzling pressure-TN diagrams5-10 of NiS, Ni1-xS1-ySey, BaVS3, V2O3, RNiO3 and ferrites were given. Our discovery is the beginning of condensed-matter geometrodynamics and marks an era of studying phase diagrams to advance condensed-matter physics and tailor new materials with predicted properties necessary in sunrise industries. Moreover, internucleon, interquark and intergluon orbital intersections would be useful for understanding the properties of nuclei, nucleons and quarks.

The Physical Essence of Time

The article considers the model of the space-frequency-time continuum, according to which the physical essence of Time is manifested as a fraction of electromagnetic energy spent on updating a material object in a cyclic process of copying-incarnation. For all structural levels of physical reality, the value of this fraction is a fundamental constant, which can be represented as the tangent of the loss angle, or expressed in radians, as the angle of inclination of the evolutionary spiral, which characterizes the rate of change of states or the duration of events and processes. The value of this constant can be calculated, and its value turns out to be identically equals to the square of the fine structure Constant (α2). The description of the method for identifying a new constant allows us to present the formula of Scientific Discovery as the Physical Essence of Time.

The universal acceleration scale from stellar feedback

ABSTRACT It has been established for decades that rotation curves deviate from the Newtonian gravity expectation given baryons alone below a characteristic acceleration scale $g_{\dagger }\sim 10^{-8}\, \rm {cm\, s^{-2}}$, a scale promoted to a new fundamental constant in MOND. In recent years, theoretical and observational studies have shown that the star formation efficiency (SFE) of dense gas scales with surface density, SFE ∼ Σ/Σcrit with $\Sigma _{\rm crit} \sim \langle \dot{p}/m_{\ast }\rangle /(\pi \, G)\sim 1000\, \rm {M_{\odot }\, pc^{-2}}$ (where $\langle \dot{p}/m_{\ast }\rangle$ is the momentum flux output by stellar feedback per unit stellar mass in a young stellar population). We argue that the SFE, more generally, should scale with the local gravitational acceleration, i.e. that SFE ${\sim}g_{\rm tot}/g_{\rm crit}\equiv (G\, M_{\rm tot}/R^{2}) / \langle \dot{p}/m_{\ast }\rangle$, where Mtot is the total gravitating mass and $g_{\rm crit}=\langle \dot{p}/m_{\ast }\rangle = \pi \, G\, \Sigma _{\rm crit} \approx 10^{-8}\, \rm {cm\, s^{-2}} \approx \mathit{ g}_{\dagger }$. Hence, the observed g† may correspond to the characteristic acceleration scale above which stellar feedback cannot prevent efficient star formation, and baryons will eventually come to dominate. We further show how this may give rise to the observed acceleration scaling $g_{\rm obs}\sim (g_{\rm baryon}\, g_{\dagger })^{1/2}$ (where gbaryon is the acceleration due to baryons alone) and flat rotation curves. The derived characteristic acceleration g† can be expressed in terms of fundamental constants (gravitational constant, proton mass, and Thomson cross-section): $g_{\dagger }\sim 0.1\, G\, m_{\mathrm{ p}}/\sigma _{\rm T}$.

Improved model-independent constraints on the recombination era and development of a direct projection method

ABSTRACT The unparalleled precision of recent experiments such as Planck have allowed us to constrain standard and non-standard physics (e.g. due to dark matter annihilation or varying fundamental constants) during the recombination epoch. However, we can also probe this era of cosmic history using model-independent variations of the free electron fraction, Xe, which, in turn, affects the temperature and polarization anisotropies of the cosmic microwave background. In this paper, we improve on the previous efforts to construct and constrain these generalized perturbations in the ionization history, deriving new optimized eigenmodes based on the full Planck 2015 likelihood data, introducing the new module Fearec++. We develop a direct likelihood sampling method for attaining the numerical derivatives of the standard and non-standard parameters, and discuss complications arising from the stability of the likelihood code. We improve the amplitude constraints of the Planck 2015 principal components constructed here, μ1 = −0.09 ± 0.12, μ2 = −0.17 ± 0.20, and μ3 = −0.30 ± 0.35, finding no indication for departures from the standard recombination scenario. The error constraint on the third mode has been improved by a factor of 2.5. We utilize an efficient eigenanalyser that keeps the cross-correlations of the first three eigenmodes to ${\rm Corr\left(\mu \, \mu ^{\prime }\right)}\lt 0.1$ per cent after marginalization for all the considered data combinations. We also propose a new projection method for estimating constraints on the parameters of non-standard recombination scenarios. As an example, using our eigenmode measurements, this allows us to recreate the Planck constraint on the two-photon decay rate, A2s1s = 7.60 ± 0.64, giving an error estimate to within ≃ 0.05σ of the full MCMC result. The improvements on the eigenmode analysis using the Planck data will allow us to implement this new method for analysis with fundamental constant variations in the future.

Updated fundamental constant constraints from Planck 2018 data and possible relations to the Hubble tension

ABSTRACT We present updated constraints on the variation of the fine structure constant, αEM, and effective electron rest mass, me, during the cosmological recombination era. These two fundamental constants directly affect the ionization history at redshift z ≃ 1100 and, thus, modify the temperature and polarization anisotropies of the cosmic microwave background (CMB) measured precisely with Planck . The constraints on αEM tighten slightly due to improved Planck 2018 polarization data but otherwise remain similar to previous CMB analysis. However, a comparison with the 2015 constraints reveals a mildly discordant behaviour for me, which from CMB data alone is found below its local value. Adding baryon acoustic oscillation data brings me back to the fiducial value, $m_{\rm e}=(1.0078\pm 0.0067)\, m_{\rm e,0}$, and also drives the Hubble parameter to H0 = 69.1 ± 1.2(in units of ${\rm km \, s^{-1} \, Mpc^{-1} }$). Further adding supernova data yields $m_{\rm e}=(1.0190\pm 0.0055)\, m_{\rm e,0}$ with H0 = 71.24 ± 0.96. We perform several comparative analyses using the latest cosmological recombination calculations to further understand the various effects. Our results indicate that a single-parameter extension allowing a slightly increased value of me (≃3.5σ above me, 0) could play a role in the Hubble tension.

Precision and consistency of astrocombs

ABSTRACT Astrocombs are ideal spectrograph calibrators whose limiting precision can be derived using a second, independent, astrocomb system. We therefore analyse data from two astrocombs (one 18 GHz and one 25 GHz) used simultaneously on the HARPS (High Accuracy Radial velocity Planet Searcher) spectrograph at the European Southern Observatory. The first aim of this paper is to quantify the wavelength repeatability achieved by a particular astrocomb. The second aim is to measure wavelength calibration consistency between independent astrocombs, that is to place limits or measure any possible zero-point offsets. We present three main findings, each with important implications for exoplanet detection, varying fundamental constant and redshift drift measurements. First, wavelength calibration procedures are important: using multiple segmented polynomials within one echelle order results in significantly better wavelength calibration compared to using a single higher order polynomial. Segmented polynomials should be used in all applications aimed at precise spectral line position measurements. Secondly, we found that changing astrocombs causes significant zero-point offsets (${\approx}60\, {\rm cm\, s}^{-1}$ in our raw data) which were removed. Thirdly, astrocombs achieve a precision of ${\lesssim }4\, {\rm cm\, s}^{-1}$ in a single exposure (${\approx }10{{\,\rm per\,cent}}$ above the measured photon-limited precision) and 1 cm s−1 when time-averaged over a few hours, confirming previous results. Astrocombs therefore provide the technological requirements necessary for detecting Earth–Sun analogues, measuring variations of fundamental constants and the redshift drift.

LIBRETTO OF THE OPERA THE MAGIC FLUTE BY W. A. MOZART IN THE GENRE OF FAIRY-TALE

The Magic Flute by W. A. Mozart occupies a special place in the treasury of the world musical art. The article for the first time explores the specifics of the embodiment of the genre model of the fairy-tale underlying the libretto. The reconstruction of its basic, static and dynamic elements is based on methodological approaches developed in the study of folk and literary fairy-tales. The analysis of the verbal text of the opera demonstrates: canonized set of personages that possess the definite semantic functions in the plot-syntagmatic line, invariant fairytale situations, typical parameters of the fairy-tale space-time continuum. In the semantics of the fairy-tale by W. A. Mozart the categories of paths (wanderings), trials, value indicators and the totemic rite of initiation acquire conceptual meaning. The plot line of the libretto, as well as of the fairy-tale, reflects the theme of marriage and family relations but in the cosmic foreshortening. The deep symbolic paradigm witnesses the mythical, cosmogonic gist of the fairy-tale plot. The semiotic model of the artistic world of the fairy-tale singspiel is organized by the binary oppositions of Light and Darkness. Darkness is metaphorically personified in the anthropomorphic image of the fundamental constant of being — Queen of the Night. The world of the sage Zarastro personifies Light. In the verbal artistic text of the opera the composer and the librettist exhibit deep and bright knowledge of the genre canons of the classical folk and literary fairy-tale and reflect the idea of the spiritual search of perfection in the world.

Testing bound dark energy with cosmological parameter and fundamental constant evolution

ABSTRACT A new bound dark energy (BDE) cosmology has been proposed where the dark energy is the binding energy between light meson fields that condense a few tens of years after the big bang. It is reported that the correct dark energy density emerges using particle physics without fine-tuning. This alone makes the BDE cosmology worthy of further investigation. This work looks at the late-time BDE predictions of the evolution of cosmological parameters and the values of fundamental constants to determine whether the cosmology’s predictions are consistent with observation. The work considers the time period between a scale factor of 0.1 and 1.0. A model BDE cosmology is considered with current-day values of the cosmological parameters well within the observational limits. The calculations use three different values of the current-day dark energy equation of state close to −1. All three cases produce evolutions of the cosmological parameters and fundamental constants consistent with the observational constraints. Analytic relations between the BDE and cosmological parameters are developed to insure a consistent set of parameters.

5. The quantum world of the atom

‘The quantum world of the atom’ considers the profound discoveries of the early twentieth century that exposed the inner structure of the atom and the revolutionary new physics of quantum mechanics—the behaviour of matter on very small scales. At the microscopic level, ‘particles’ of matter resemble waves, a feature that enables us to understand the structure, stability, and properties of atoms. Key discoveries and concepts are described: the fundamental constant of nature, Planck’s constant; Heisenberg’s uncertainty principle; the Schrödinger equation; quantum tunnelling; the wavelike characteristics of microscopic particles; and the two types of particles, fermions and bosons.