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Quantum fluctuations at the Planck scale

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arXiv 2019年

作者： Melia, Fulvio Department of Physics Applied Math Program and Department of Astronomy University of Arizona TucsonAZ85721 United States

The recently measured cutoff, kmin = 4.34 ± 0.50/rcmb (with rcmb the comoving distance to the last scattering surface), in the fluctuation spectrum of the cosmic microwave background, appears to disfavor slow-roll inflation and the associated transition of modes across the horizon. We show in this Letter that kmin instead corresponds to the first mode emerging out of the Planck domain into the semi-classical universe. The required scalar-field potential is exponential, though not inflationary, and satisfies the zero active mass condition, ρφ + 3pφ = 0. Quite revealingly, the observed amplitude of the temperature anisotropies requires the quantum fluctuations in φ to have classicalized at ∼ 3.5 × 1015 GeV, consistent with the energy scale in grand unified theories. Such scalar-field potentials are often associated with Kaluza-Klein cosmologies, string theory and even supergravity. Copyright © 2019, The Authors. All rights reserved.

关键词： Cosmology

The origin of rest-mass energy

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arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

Today we have a solid, if incomplete, physical picture of how inertia is created in the standard model. We know that most of the visible baryonic 'mass' in the Universe is due to gluonic back-reaction on accelerated quarks, the latter of which attribute their own inertia to a coupling with the Higgs field-a process that elegantly and self-consistently also assigns inertia to several other particles. But we have never had a physically viable explanation for the origin of rest-mass energy, in spite of many attempts at understanding it towards the end of the nineteenth century, culminating with Einstein's own landmark contribution in his Annus Mirabilis. Here, we introduce to this discussion some of the insights we have garnered from the latest cosmological observations and theoretical modeling to calculate our gravitational binding energy with that portion of the Universe to which we are causally connected, and demonstrate that this energy is indeed equal to mc2 when the inertia m is viewed as a surrogate for gravitational mass. © 2021, CC BY.

关键词： Binding energy

The Apparent (Gravitational) Horizon in Cosmology

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arXiv 2018年

作者： Melia, Fulvio Department of Physics Applied Math Program Department of Astronomy University of Arizona TucsonAZ85721 United States

In general relativity, a gravitational horizon (more commonly known as the "apparent horizon") is an imaginary surface beyond which all null geodesics recede from the observer. The Universe has an apparent (gravitational) horizon, but unlike its counterpart in the Schwarzschild and Kerr metrics, it is not static. It may eventually turn into an event horizon—an asymptotically defined membrane that forever separates causally connected events from those that are not—depending on the equation of state of the cosmic fluid. In this paper, we examine how and why an apparent (gravitational) horizon is manifested in the Friedmann-Robertson-Walker metric, and why it is becoming so pivotal to our correct interpretation of the cosmological data. We discuss its observational signature and demonstrate how it alone defines the proper size of our visible Universe. In so doing, we affirm its physical reality and its impact on cosmological models. Copyright © 2018, The Authors. All rights reserved.

关键词： Cosmology

Thermodynamics of the Rh = ct Universe: A simplification of cosmic entropy

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arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

In the standard model of cosmology, the Universe began its expansion with an anomalously low entropy, which then grew dramatically to much larger values consistent with the physical conditions at decoupling, roughly 380,000 years after the Big Bang. There does not appear to be a viable explanation for this ‘unnatural’ history, other than via the generalized second law of thermodynamics (GSL), in which the entropy of the bulk, Sbulk, is combined with the entropy of the apparent (or gravitational) horizon, Sh. This is not completely satisfactory either, however, since this approach seems to require an inexplicable equilibrium between the bulk and horizon temperatures. In this paper, we explore the thermodynamics of an alternative cosmology known as the Rh = ct universe, which has thus far been highly successful in resolving many other problems or inconsistencies in ΛCDM. We find that Sbulk is constant in this model, eliminating the so-called initial entropy problem simply and elegantly. The GSL may still be relevant, however, principally in selecting the arrow of time, given that Sh ∝ t2 in this model. © 2021, CC BY.

关键词： Entropy

Reassessing dust's role in forming the CMB

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arXiv 2020年

作者： Melia, F. Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

The notion that dust might have formed the cosmic microwave background (CMB) has been strongly refuted on the strength of four decades of observation and analysis, in favour of recombination at a redshift z ∼ 1080. But tension with the data is growing in several other areas, including measurements of the Hubble constant H(z) and the BAO scale, which directly or indirectly impact the physics at the surface of last scattering (LSS). The Rh = ct universe resolves at least some of this tension. We show in this paper that-if the BAO scale is in fact equal to the acoustic horizon-the redshift of the LSS in this cosmology is zcmb ∼ 16, placing it within the era of Pop III star formation, prior to the epoch of reionization at 15 z 6. Quite remarkably, the measured values of zcmb and H0 ≡ H(0) in this model are sufficient to argue that the CMB temperature today ought to be ∼ 3 K, so H0 and the baryon to photon ratio are not independent free parameters. This scenario might have resulted from rethermalization of the CMB photons by dust, presumably supplied to the interstellar medium by the ejecta of Pop III stars. Dust rethermalization may therefore yet resurface as a relevant ingredient in the Rh = ct universe. Upcoming high sensitivity instruments should be able to readily distinguish between the recombination and dust scenarios by either (i) detecting recombination lines at z ∼ 1080, or (ii) establishing a robust frequency-dependent variation of the CMB power spectrum at the level of ∼ 2−4% across the sampled frequency range. Copyright © 2020, The Authors. All rights reserved.

关键词： Cosmology

Classicalization of quantum fluctuations at the Planck scale in the Rh = CT universe

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arXiv 2021年

作者： Melia, Fulvio Department of Physics The Applied Math Program Department of Astronomy The University of Arizona TucsonAZ85721 United States

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result on the question of classicalization, and demonstrate that the birth of quantum fluctuations at the Planck scale would have been a 'process' supplanting the need for a 'measurement' in quantum mechanics. Emerging with a single wavenumber, these fluctuations would have avoided the interference between different degrees of freedom in a superposed state. Moreover, the implied scalar-field potential had an equation-of-state consistent with the zero active mass condition in general relativity, allowing the quantum fluctuations to emerge in their ground state with a time-independent frequency. They were therefore effectively quantum harmonic oscillators with classical correlations in phase space from the very beginning. © 2021, CC BY.

关键词： Degrees of freedom (mechanics)

On the transversal vibrations of a conveyor belt using a string-like equation

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On the transversal vibrations of a conveyor belt using a str...

18th Biennial Conference on Mechanical Vibration and Noise

作者： Suweken, Gede Van Horssen, W.T. Dept. of Applied Math. Analysis Faculty of Info. Technol. and Syst. Delft University of Technology Mekelweg 4 2628 CD Delft Netherlands Program Studi Pend. Matematika STKIP Singaraja Bali Indonesia

In this paper an initial-boundary value problem for a linear wave (string) equation is considered. This problem can be used as a simple model to describe the vertical vibrations of a conveyor belt, for which the velocity is small with respect to the wave speed. In this paper the belt is assumed to move with varying speed. Formal asymptotic approximations of the solutions are constructed to show the complicated dynamical behavior of the conveyor belt. It also will be shown that for this problem, the truncation method is not valid on long time scales.

关键词： Vibrations (mechanical)

Acousto-conformational phase transitions in the cytoskeleton, adaptive resonance networks with nonlinear synapses and trainable intraneuronal pattern recognition

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Acousto-conformational phase transitions in the cytoskeleton...

International Joint Conference on Neural Networks (IJCNN)

作者： A. Samsonovich A. Scott S. Hameroff Appl. Math. Program Arizona Univ. Tucson AZ USA Laboratory of Applied Mathematical Physics Technical University of Denmark Lyngby Denmark Applied Mathematics Program University of Arizona Tucson Tucson AZ USA

A possible role for phonon excitations of the cytoskeleton in intraneuronal pattern recognition and learning is discussed. Biophysical support is presented for molecular implementation of adaptive resonant theory neural network principles. Relations between pattern recognition by neural network and symmetry breaking second order phase transitions are discussed.< >

关键词： Intelligent networks Adaptive systems Resonance Phonons Proteins Pattern recognition Neurons Neural networks Biomembranes mathematics

Hyperbolic Diffusion Procrustes Analysis for Intrinsic Representation of Hierarchical Data Sets

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Hyperbolic Diffusion Procrustes Analysis for Intrinsic Repre...

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Ya-Wei Eileen Lin Yuval Kluger Ronen Talmon Viterbi Faculty of Electrical and Computer Engineering Technion Interdepartmental Program in Computational Biology and Bioinformatics Yale University Applied Math Program Yale University Department of Pathology School of Medicine Yale University

In this paper, we present Hyperbolic Diffusion Procrustes Analysis (HDPA), a new method for informative representation of hierarchical datasets based on hyperbolic geometry, diffusion geometry, and Procrustes analysis. Our method jointly embeds multiple datasets in a product manifold of hyperbolic spaces, where the data's hidden common hierarchical structure is provably recovered. In addition, our method generates an intrinsic embedding that accommodates the joint representation of multiple datasets with different features, acquired by different equipment, at different sites, or under different environmental conditions. Experimental results demonstrate the efficacy of HDPA on three biomedical datasets comprising heterogeneous gene expression and mass cytometry data.

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