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As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended Bondi-Metzner-Sachs group. These include the Poincar\'e charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or center-of-mass charge, as well as extensions of these quantities associated with supertranslations and super-Lorentz transformations, namely supermomentum, superspin and super center-of-mass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole's charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $\sim M_i^2$ at late times, where $M_i$ is the initial mass (previously found by Page). (ii) The black hole mass $M$ has an uncertainty of order the mass $M$ itself at the epoch when $M \sim M_i^{2/3}$, well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $\sim M_i^2$. (iii) The supermomentum and superspin charges are not independent but are determined from the Poincare charges and the super center-of-mass charges. (iv) The supertranslation that characterizes the super center-of-mass charges has fluctuations at multipole orders $l$ of order unity that that are of order unity in Planck units. At large $l$, there is a power law spectrum of fluctuations that extends up to $l \sim M_i^2/M$, beyond which the fluctuations fall off exponentially, with corresponding total rms shear tensor fluctuations $\sim M_i M^{-3/2}$., Comment: 41 pages, 1 figure

The relationship between gravitational potential, black holes and squared light speed c²is examined aswell as the implications of the presented findings for the gravitational constant G and general relativitytheory. It is common knowledge that the velocity limit in our universe is defined by light speed c and asshown in this work c² plays a similar role for the gravitational potential since c² / G is linked to the massdensity of black holes, our local Hubble sphere and the overall universe. Furthermore, it is demonstratedthat the rift between cosmology and quantum physics can be reconciled by acknowledging the physicalmeaning of the Planck units which proposedly define the characteristics of quantized space-time. Thisnotion is also supported by the presented logarithmic relationships between the cosmological scale andthe quantum scale. Finally, the presented findings allow uncovering a physical relationship between theconstituents of Dirac’s contested large number hypothesis.

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it was already pointed out in 1987 that this led to a circular problem; namely, that one must know G to find the Planck units, and that it is therefore of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is held by the physics’ community. However, we will claim that the circular problem was solved a few years ago. In addition, when one expresses the mass from the Compton wavelength formula, this leads to the conclusion that the three universal constants of G, h, and c now can be replaced with only lp and c to predict observable gravitational phenomena. While there have been several review papers on the Newton gravitational constant, for example, about how to measure it, we have not found a single review paper on the composite view of the gravitational constant. This paper will review the history of, as well as recent progress in, the composite view of the gravitational constant. This should hopefully be a useful supplement in the ongoing research for understanding and discussion of Newton’s gravitational constant.

The subject matter of research in the article is a system-information approach to the uncertainty of the parameters of processes and systems of the technosphere as one of the scientific directions of using information theory in metrology and other scientific areas. The system-information approach is based on the definition of the term "information" of the properties of the system, its content and meaning. The solution of the basic problem in metrology, obtaining "information" of the quantitative characteristics of the true value of the properties of objects and phenomena that reveal the regularities of the environment, is a complex scientific problem. The instrument for obtaining information about the properties of the system is the measurement process. One of the directions in the development of measurement theory is the concept of uncertainty. The goal of the work is to research of non-traditional solutions to problems of technical-cybernetic systems based on the system-information approach to the uncertainty of the parameters of processes and systems. The article solves the following tasks: to analyze the assessment of the parameters of technological processes and systems based on the system-information approach; to develop system-information methods and algorithms for the effective use of discrete-probabilistic information in technical-cybernetic systems; to develop principles and approaches for using the system-information assessment of the uncertainty of the Planck units, use of system-information modeling in various scientific directions. The following methods are used: system-information approach to processes and systems, methodology of system-information modeling of the measured value; system information methodology for the assessment of the measured quantity and uncertainty. The following results were obtained: developed a system-information methodology for assessing the nominal parameter has been developed, which provides indirect control over the independent parameters associated with it; systemic and information methods for the effective use of discrete-probabilistic information in technical and cybernetic systems have been developed; a system-information methodology for calculating the energy equivalent of product performance indicators has been developed; the principle of calculating the efficiency of manufacturing a product based on the energy equivalent of Planck units is formulated. Conclusions: The solution of the set tasks on the basis of the system-information approach to the uncertainty of the parameters of processes and systems makes it possible, from the system-information point of view, to study the regularities of the stages of the life cycle of technical-cybernetic systems and conservation laws., Предметом исследования в статье является системно-информационный подход к неопределенности параметров процессов и систем техносферы как один из научных направлений использования теории информации в метрологии и других научных направлениях. В основе системно-информационного подхода лежит определение понятия термина "информация" свойств системы, ее содержание и значение. Решение базовой в метрологии задачи получение "информации" количественной характеристики истинного значения свойств объектов и явлений, которые раскрывают закономерности окружающей среды, является сложной научной проблемой. Инструментом для получения информации о свойствах системы является процесс измерения. Одно из направлений развития теории измерений является концепция неопределенности. Цель работы - исследование нетрадиционных решений задач технико-кибернетических систем на основе системно-информационного подхода к неопределенности параметров процессов и систем техносферы. В статье решаются следующие задачи: провести анализ оценки параметров технологических процессов и систем на основе системно-информационного подхода; разработать системно-информационные методы и алгоритмы эффективного использования дискретно-вероятностной информации в технико-кибернетических системах; разработать принципы и подходы использования системно-информационной оценки неопределенности планковских единиц, использование системно-информационного моделирования в различных научных направлениях. Используются следующие методы: системно-информационный подход к процессам и системам, методология системно-информационного моделирования измеряемой величины; системно-информационная методология оценки измеряемой величины и неопределенности. Получены следующие результаты: разработана системно-информационная методика определения точности измерения номинального параметра, которая обеспечивает максимальную информативность и качество результата измерения; разработаны системно-информационные алгоритмы эффективного использования дискретно-вероятностной информации в технико-кибернетических системах; разработана системно-информационная методика расчета планковского энергетического эквивалента технических показателей изделия; сформулирован принцип расчета эффективности производства изделия на основе планковского энергетического эквивалента физических величин. Выводы: Решение поставленных задач на основе системно-информационного подхода к неопределенности параметров процессов и систем дает возможность с системно-информационной точки зрения исследовать закономерности этапов жизненного цикла технико-кибернетических систем и законы сохранения., Предметом дослідження в статті є системно-інформаційний підхід до невизначеності параметрів процесів і систем техносфери як один із наукових напрямків використання теорії інформації в метрології та інших наукових напрямків. В основі системно-інформаційного підходу лежить визначення поняття терміна "інформація" властивостей системи, її зміст і значення. Вирішення базового в метрології завдання отримання "інформації" кількісної характеристики істинного значення властивостей об’єктів і явищ, які розкривають закономірності навколишнього середовища, є складною науковою проблемою. Інструментом для отримання інформації про властивості системи є процес вимірювання. Один із напрямків розвитку теорії вимірювань є концепція невизначеності. Мета роботи – дослідження нетрадиційних рішень завдань техніко-кібернетичних систем на основі системно-інформаційного підходу до невизначеності параметрів процесів і систем техносфери. В статті вирішуються наступні завдання: провести аналіз оцінювання параметрів технологічних процесів та систем на основі системно-інформаційного підходу; розробити системно-інформаційні методи і алгоритми ефективного використання дискретно-імовірнісної інформації в техніко-кібернетичних системах; розробити принципи та підходи використання системно-інформаційної оцінки невизначеності планківських одиниць, використання системно-інформаційного моделювання в різних наукових напрямках. Використовуються такі методи: системно-інформаційний підхід до процесів і систем, методологія системно-інформаційного моделювання вимірюваної величини; системно-інформаційна методологія оцінювання вимірюваної величини і невизначеності. Отримано наступні результати: розроблено системно-інформаційну методику визначення точності вимірювання номінального параметру, яка забезпечує максимальну інформативність непрямого контролю за пов’язаними з ним незалежними параметрами; розроблені системно-інформаційні алгоритми ефективного використання дискретно-імовірнісної інформації в техніко-кібернетичних системах; розроблено системно-інформаційну методику розрахунку планківського енергетичного еквіваленту технічних показників виробу; сформульований принцип розрахунку ефективності виготовлення виробу на основі планківського енергетичного еквіваленту фізичних величин. Висновки: Вирішення поставлених завдань дає можливість з інформаційного куту зору дослідити закономірності етапів життєвого циклу техніко-кібернетичних систем і закони перетворення і збереження.

We observe a direct relation between the existence of fundamental axionic strings, dubbed EFT strings, and infinite distance limits in 4d $\mathcal{N}=1$ EFTs coupled to gravity. The backreaction of EFT strings can be interpreted as RG flow of their couplings, and allows one to probe different regimes within the field space of the theory. We propose that any 4d EFT infinite distance limit can be realised as an EFT string flow. We show that along such limits the EFT string becomes asymptotically tensionless, and so the EFT eventually breaks down. This provides an upper bound for the maximal field range of an EFT with a finite cut-off, and reproduces the Swampland Distance Conjecture from a bottom-up perspective. Even if there are typically other towers of particles becoming light, we propose that the mass of the leading tower scales as $m^2\sim \mathcal{T}^w$ in Planck units, with $\mathcal{T}$ the EFT string tension and $w$ a positive integer. Our results hold even in the presence of a non-trivial potential, as long as its energy scale remains well below the cut-off. We check both proposals for large classes of 4d $\mathcal{N}=1$ string compactifications, finding that only the values $w=1,2,3$ are realised., Comment: 72 pages + appendices, 6 figures; v3: typos corrected

We perform a general analysis of the cosmological viability of Geometric Inflation. We show that the evolution of the universe, from inflation to the present day, can be seen from the addition of an infinite tower of curvature invariants into the Hilbert-Einstein action. The main epochs of the Universe can be reproduced: Inflation, Big Bang Nucleosynthesis, and Late-time acceleration driven by the cosmological constant. The slow-roll condition is a robust prediction of the theory. Inflation possesses a graceful exit with enough number of $e-$folds between the limit imposed by the Planck density and the exit of the exponential expansion to solve the horizon problem and the absence of topological defects. We also provide some scenarios where the energy scale of the theory can be calibrated., 17 pages, 4 figures. Accepted for publication in Physics of the Dark Universe (https://doi.org/10.1016/j.dark.2021.100887)

The Planck length is an object of the relativistic quantum-gravitational theory, therefore, a more general and consistent direction of the special relativity extension, seems to be the use of the postulate of the relativistically invariant and limiting nature of all Planck units, that was introduced by V.V. Korukhov at the end of the 90s. One of the examples of the implementation of this postulate in its methodological meaning is the model of a vacuum-like medium, the physical properties of which are characterized by relativistically invariant values, which qualita-tively distinguishes it from the known types of matter –matter and field.

We consider the cosmology obtained using scalar fields with a negative potential energy, such as employed to obtain an Ekpyrotic phase of contraction. Applying the covariant entropy bound to the tower of states dictated by the distance conjecture, we find that the relative slope of the potential $|V^{\prime}| / |V|$ is bounded from below by a constant of the order one in Planck units. This is consistent with the requirement to obtain slow Ekpyrotic contraction. We also derive a refined condition on the potential which holds near local minima of a negative potential., Comment: 8 pages, 2 figures; v2: 14 pages, 2 figures; references and comments on conformal diagrams added; matches published version

We have recently suggested a new quantum gravity theory that can be unified with quantum mechanics. We have coined this theory collision space-time. This new theory seems to be fully consistent with a 3-dimensional space-time, that is, three space dimensions and three time-dimensions, so some would call it six-dimensional. However, we have shown that collision-time and collision-length (space) are just two different sides of the same “coin” (space-time), so it is more intuitive to think of them as 3-dimensional space-time. In previous papers, we have not laid out a geometric coordinate system for our theory that also considers gravity, but we will do that here. We are pointing out that Einstein’s negative attitude towards relativistic mass can perhaps cause a weakness in the foundation of general relativity theory. When a relativistic mass is incorporated in the theory, this mass also seems to indicate one needs to move to three-dimensional space-time. Then, for example, our new theory matches fully up with all the properties of the Planck scale in relation to the mathematical properties of micro black holes, not only mathematically but also logically, something we demonstrate clearly that it is not the case of general relativity theory. Our new metric has many benefits as an alternative to the Schwarzschild metric and general relativity theory. It seems to be more consistent with the Planck units than the Schwarzschild metric. Most importantly, it seems to be fully consistent with a new quantum gravity theory that seems to unify gravity with quantum mechanics.

In a recent paper we have shown that a minimally coupled, self-interacting scalar field of mass $m$ can form black holes of mass $M=\sqrt{3}/(4m)$ (in Planck units). If dark matter is composed by axions, they can form miniclusters that for QCD axions have masses below this value. In this work it is shown that for a scenario in which the axion mass depends on the temperature as $m \propto T^{-6}$, minicluster masses above $0.32\,M_\odot$, corresponding to an axion mass of $3\times 10^{-10}$ eV, exceed $M$ and can collapse into black holes. If a fraction of these black holes is in binary systems, gravitational waves emitted during the inspiral phase could be detected by advanced interferometers like LIGO or VIRGO and by the planned Einstein Telescope. For a detection rate of one event per year, the lower limits on the binary fraction are $10^{-4}$ and $10^{-6}$ for LIGO and Einstein Telescope respectively., 6 pages, 2 figures. Version to appear in Eur. Phys. J. C

International audience; Starting from quantum theory (instead of general relativity) to approach quantum gravity within a minimal setting allows us here to describe the quantum space-time structure and the quantum light cone. From the classical-quantum duality and quantum harmonic oscillator (X, P) variables in global phase space, we promote the space-time coordinates to quantum noncommuting operators. The phase space instanton (X, P = iT) describes the hyperbolic quantum space-time structure and generates the quantum light cone. The classical Minkowski space-time null generators X = ±T disappear at the quantum level due to the relevant quantum [X, T] commutator which is always nonzero. A new quantum Planck scale vacuum region emerges. We describe the quantum Rindler and quantum Schwarzschild-Kruskal space-time structures. The horizons and the r = 0 space-time singularity are quantum mechanically erased. The four Kruskal regions merge inside a single quantum Planck scale “world.” The quantum space-time structure consists of hyper bolic discrete levels of odd numbers (X$^{2}$ — T$^{2}$)$_{n =}$ (2n + 1) (in Planck units ), n = 0,1, 2....(X$_{n}$, T$_{n}$) and the mass levels being v(2n + 1). A coherent picture emerges: large n levels are semiclassical tending towards a classical continuum space-time. Low n are quantum, the lowest mode (n = 0) being the Planck scale. Two dual (±) branches are present in the local variables (v2n + 1 ± v2n) reflecting the duality of the large and small n behaviors and covering the whole mass spectrum from the largest astrophysical objects in branch (+) to quantum elementary particles in branch (—) passing by the Planck mass. Black holes belong to both branches (+) and (—).

We derive a unified field theory based on a rotating de Broglie wave packet that combines electromagnetism, quantum mechanics, gravity and the strong force. We assume the already proven electro-weak force. This Planck units theory requires that t≈r and m=r.

On the evident tripartite equivalency of the light speed and time and distance as a natural paradigm introduced here it is deduced the natural metric tensor of the universe via Mach's mechanics (metric fully governed by measurable universe) included to the fully variable light speed and fully variable gravitational G accompanied with Planckian quantum gravity in natural quantization of the space-time and we see the quantum modes of the gravitational fields by combination of the Planck and Mach and Einstein-Riemannian physics introducing new universal constants. We see a new cosmology on the base of the variable light speed universe via conservation of the total matter of the universe expanding stationary via permanent cyclical transformation of the observable baryonic matter to background ether and the background ether to the observable baryonic matter required by equation of the continuity for equilibrium, creating homogeneity and isotropy and flattening of the universe and reasoning also a universal background minimum temperature creating cosmic microwave background as a black body radiation. Ultimately it is obvious that our universe is a large version of the Planckian mini universe and also we see variable Planck length correlated to the gravitational potential energy.

According to observations leptons are always produced in pairs. Both particles can be electrically charged, or just one, in which case the charged particle is accompanied by a particle specific neutrino. The period doubling process in nonlinear dynamical systems creates stable pair structures from the Planck units. The electron-positron pair is one of the stable structures, and the rest mass, electric charge and magnetic moment can be accurately calculated by the period doubling process. That the pair structure is stable means, that e.g., an electron and a positron are always born together. In the muon decay one of the pair is charged, while the other remains chargeless because there is only one charge available. It is suggested in this article that neutrino is the chargeless part of the lepton pair.

This is a short note to show how big G can be derived from dimensional analysis by assuming that the Planck length [1] is much more fundamental than Newton's gravitational constant.

It has been a long-standing goal in physics to present a physical model that may be used to describe and correlate the physical constants. We demonstrate, this is achieved by describing phenomena in terms of Planck Units and introducing a new concept, counts of Planck Units. Thus, we express the existing laws of classical mechanics in terms of units and counts of units to demonstrate that the physical constants may be expressed using only these terms. But this is not just a nomenclature substitution. With this approach we demonstrate that the constants and the laws of nature may be described with just the count terms or just the dimensional unit terms. Moreover, we demonstrate that there are three frames of reference important to observation. And with these principles we resolve the relation of the physical constants. And we resolve the SI values for the physical constants. Notably, we resolve the relation between gravitation and electromagnetism.

В работе рассмотрены три варианта выхода на закон Стефана – Больцмана в его записи с участием гравитационной постоянной. При проведении мысленного космологического эксперимента наряду с выходом на закон Стефана – Больцмана установлен закон падения температуры во Вселенной. Показано, что закон Стефана – Больцмана и планковские единицы имеют непосредственное отношение к описанию расширения Вселенной с охлаждением. Отмечена необходимость проведения дальнейших исследований., The paper considers three options for applying the Stefan-Boltzmann law in its recording with the participation of the gravitational constant. When conducting a mental cosmological experiment, along with the access to the Stefan – Boltzmann law, the law of temperature drop in the Universe is established. It is shown that the Stefan – Boltzmann law and Planck units are directly related to the description of the expansion of the Universe with cooling. The need for further research is noted.

В работе затронут вопрос космологической значимости фундаментальных физических постоянных и их комбинаций. Рассмотрены особенности организации и результаты проведения простейшего мысленного космологического эксперимента. В согласие с рекомендациями Цвибаха Бартона установленные в теории теплового излучения и в общей теории относительности закономерности представлены в безразмерных планковских единицах. Наблюдается согласие теоретических и экспериментальных данных. Приведены аргументы в пользу замкнутой модели Вселенной., The paper touches upon the question of the cosmological significance of fundamental physical constants and their combinations. The features of the organization and the results of the simplest mental cosmological experiment are considered. In accordance with the recommendations of Zwiebach Barton, the regularities established in the theory of thermal radiation and in the general theory of relativity are presented in dimensionless Planck units. The agreement of theoretical and experimental data is observed. The arguments in favor of a closed model of the Universe are presented.

We discuss cosmological solutions for a diffeomorphism invariant gauge theory of the non-compact Lorentz group $SO(1,3)$. Besides the gauge bosons our model of pregeometry contains a vector field in the vector representation of $SO(1,3)$ and a scalar singlet. General relativity and variable gravity emerge as effective theories for large distances and times in Planck units. We propose an approximation to the effective action with up to two derivatives. For a suitable range of parameters the universe approaches for large times stable Minkowski space. For late cosmology the model predicts dynamical dark energy and provides for a candidate for dark matter. Early cosmology is characterized by an inflationary epoch. The beginning of the universe in the infinite past is great emptiness, corresponding to an ultraviolet fixed point with the associated quantum scale symmetry. The beginning universe is a vacuum state with vanishing expectation values and finite non-vanishing correlation functions for the fluctuations of all fields. There is no physical big bang singularity., Comment: Further explanations, new references, 63 pages, 9 figures

В работе, в согласие с рекомендацией Ц. Бартона, закон всемирного тяготения представлен в безразмерных планковских единицах. Приведены доводы в пользу того, что и гравитационное поле, и силы всемирного тяготения во Вселенной возникли сразу же в след за планковским мгновением времени. Приведен результат оценки порядка величины «трудового стажа» закона всемирного тяготения., In the work, in accordance with the recommendation of C. Barton, the law of universal gravitation is presented in dimensionless Planck units. The arguments are given in favor of the fact that both the gravitational field and the forces of universal gravitation in the Universe arose immediately after the Planck instant of time. The result of estimating the order of magnitude of the "work experience" of the law of universal gravitation is given.

В работе рассмотрен событийный характер развития Вселенной. Учтено, что спектр регистрируемого на уровне радиошумов реликтового излучения представляет собой спектр излучения абсолютно черного тела. В согласие с рекомендациями Цвибаха Бартона физические законы чернотельного излучения представлены в безразмерных планковских единицах. Это позволяет вычленить глубинный физический смысл задачи описания космологической эволюции Вселенной. Приведены аргументы в поддержку гипотезы Гамова о том, что на смену эпохи Планка приходит период термоядерных реакций., The paper considers the event-based nature of the development of the Universe. It is taken into account that the spectrum of the relic radiation recorded at the radio noise level is the spectrum of the radiation of an absolutely black body. In accordance with the recommendations of Zwiebach Barton, the physical laws of blackbody radiation are presented in dimensionless Planck units. This allows us to isolate the deep physical meaning of the problem of describing the cosmological evolution of the Universe. The arguments in support of Gamov's hypothesis that the Planck epoch is being replaced by the period of thermonuclear reactions are presented.

When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking. However, deviations grow with time, and become of order unity after a time $t \sim M_i^{7/3}$, where $M_i$ is the initial mass in Planck units. After an evaporation time the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential fall off at high multipoles. Instead, the radiation is redistributed as a power law spectrum over a broad range of angular scales, all the way down to the scale $\Delta \theta \sim 1/M_i$, beyond which there is exponential falloff. This effect is is a quantum gravitational effect, whose origin is the spreading of the wavefunction of the black hole's center of mass location caused by the kicks of the individual outgoing quanta, discovered by Page in 1980. The modified angular distribution of the Hawking radiation has an important consequence: the number of soft hair modes that can effectively interact with outgoing Hawking quanta increases from the handful of modes at low multipoles $l$, to a large number of modes, of order $\sim M_i^2$. We argue that this change unlocks the Hawking-Perry-Strominger mechanism for purifying the Hawking radiation., Comment: 5 pages, no figures; v2 minor corrections; v3 minor clarifications and figure added

В работе, в согласие с рекомендацией Ц. Бартона, закон Стефана – Больцмана, закон падения температуры в расширяющейся Вселенной, а также одно и то же уравнение для объемной плотности энергии гравитационного излучения, которое известно из общей теории относительности и теории гравитации И. Ньютона, представлены в безразмерных планковских единицах. Или, иными словами, в космологическом исследовании реально реализована возможность связать понятия, используемые при словесном описании движения Вселенной «от» и «до», с их символами, фигурирующими в формулировках законов природы. Рассмотрены основания полагать, что и гравитационное излучение, и реликтовое фотонное излучение возникли сразу же в след за планковским мгновением времени. Приведен результат оценки порядка величины современной массы гравитационного излучения Вселенной., In this paper, in accordance with the recommendation of C. Barton, the Stefan – Boltzmann law, the law of temperature drop in the expanding Universe, as well as the same equation for the volume energy density of gravitational radiation, which is known from the general theory of relativity and the theory of gravity of I. Newton, are presented in dimensionless Planck units. Or, in other words, in cosmological research, it is really possible to link the concepts used in the verbal description of the movement of the Universe "from" and "to" with their symbols appearing in the formulations of the laws of nature. The reasons for believing that both gravitational radiation and relic photon radiation appeared immediately after the Planck instant of time are considered. The result of estimating the order of magnitude of the modern mass of gravitational radiation of the Universe is given.

The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck density, hinting that the spacetime singularity may be avoided if there is a non-zero torsion,i.e. if the collapsing dust particles possess intrinsic spin.

The Weak Gravity Conjecture proposes that a theory with a gauge field that is coupled to gravity must have charged matter on which gravity acts as the weakest force. It also proposes that there is an intrinsic cutoff on such an effective theory, which corresponds to a tower of charged states, that is set by the strength of the gauge coupling (in Planck units). This article is a brief introduction to the Weak Gravity Conjecture, covering aspects of the motivations for it as well as various extensions and refinements.

Planck units of length, mass, and time are fundamental constants of nature. Traditional constants including Planck's constant, the gravitational constant, the elementary charge, and many others are comprised of these three fundamental units. Physics equations are functions in which maximum potentials defined by the Planck units are reduced by one or more proportionality operators, producing observed quantities of natural phenomena. Natural symmetries constrain the relationships between length, mass, and time, yielding the physical dynamics of momentum, action, force, and energy. The Planck units quantify mechanical, gravitational, and electromagnetic properties of the universe and offer a common language for interpreting the standard model interactions. Units associated with the electromagnetic interaction are translated into units of length, mass, and time, including the coulomb, ampere, volt, tesla, henry, weber, farad, ohm, and siemen.

A new perspective on the Cosmological Constant Problem (CCP) is proposed and discussed within the multiverse approach of Quantum Cosmology. It is assumed that each member of the ensemble of universes has a characteristic scale a that can be used as integration variable in the partition function. An averaged characteristic scale of the ensemble is estimated by using only members that satisfy the Einstein field equations. The averaged characteristic scale is compatible with the Planck length when considering an ensemble of solutions to the Einstein field equations with an effective cosmological constant. The multiverse ensemble is split in Planck-seed universes with vacuum energy density of order one, thus, &Lambda, &tilde, &asymp, 8&pi, in Planck units and a-derivable universes. For a-derivable universe with a characteristic scale of the order of the observed Universe a&asymp, 8&times, 1060, the cosmological constant &Lambda, =&Lambda, /a2 is in the range 10&minus, 121&ndash, 10&minus, 122, which is close in magnitude to the observed value 10&minus, 123. We point out that the smallness of &Lambda, can be viewed to be natural if its value is associated with the entropy of the Universe. This approach to the CCP reconciles the Planck-scale huge vacuum energy&ndash, density predicted by QFT considerations, as valid for Planck-seed universes, with the observed small value of the cosmological constant as relevant to an a-derivable universe as observed.

A mirror builds here, by virtue of an iterative process, a geometry from a conceptual object.This dynamic, served by the Noether’s theorem, generates the universal constants, Un miroir construit ici, en vertu d’un processus itératif, une géométrie à partir d’un objet conceptuel. Cette dynamique, desservie par le théorème de Noether, génère les constantes universelles.

International audience; In this paper, we show how one can find the Planck length multiplied by the speed of light, lp*c, from a Newton force spring with no knowledge of the Newton gravitational constant G, the speed of light c, or the Planck constant h. This is remarkable, as for more than a hundred years, modern physics has assumed that one needs to know G, c, and the Planck constant in order to find any of the Planck units. We also show how to find other Planck units using the same method. To find the Planck time and the Planck length, one also needs to know the speed of light. To find the Planck mass and the Planck energy in their normal units, we need to know the Planck constant, something we will discuss in this paper. For these measurements, we do not need any knowledge of the Newton gravitational constant. It can be shown that the Planck length times the speed of light requires less information than any other Planck unit; in fact, it needs no knowledge of any fundamental constant to be measured. This is a revolutionary concept and strengthens the case for recent discoveries in quantum gravity theory completed by Haug [1].

Denis Bernardin Three fundamental dimensionless constants in physics.Abstract : This study highlights the fundamental role of three key dimensionless constants in physics. Two are already well known, they are: α, fine structure constant, and δ, ratio between the mass of the proton and that of the electron. The dimensionless constant, highlighted in this article, is the constant β whose order of magnitude is 2,39 x 1022 and which plays for gravitation a role similar to that of the fine structure constant for electromagnetism. This study also aims for define rigorously the mathematical structure of space containing any physical value whatever the units of measurement used and to express in this space, from the three dimensionless constants mentioned above, most of the constants of physics in a non-anthropocentric system of units., Denis Bernardin Trois constantes adimensionnelles clés en physique.Résumé : Cette étude met en lumière le rôle essentiel de trois constantes adimensionnelles clés en physique. Deux sont déjà bien connues, ce sont : α, constante de structure fine, et δ, rapport entre la masse du proton et celle de l’électron. La constante adimensionnelle, mise en lumière dans cet article, est la constante β dont l’ordre de grandeur est de 2,39 x 1022 et qui joue pour la gravitation un rôle analogue à celui de la constante de structure fine pour l’électromagnétisme. Cette étude a également pour objectif de définir rigoureusement la structure mathématique de l’espace contenant toute valeur physique quelles que soient les unités de mesure utilisées et d’exprimer dans cet espace, à partir des trois constantes adimensionnelles citées plus haut la plupart des constantes de la physique dans un système d’unités non anthropocentrique.

Providing for a comprehensive model of physics that describes both the discrete and non-discrete behavior of matter has proved difficult and elusive. Using a new approach, we express Heisenberg’s uncertainty principle in terms of measure and counts of those measures to resolve an expression consisting entirely of counts. Three arguments are presented each identifying one property of measure. Firstly, the three measures—length, mass and time—are each shown to have a physically significant lower bound. Secondly, each measure is shown to be discrete throughout the entire measurement domain. And thirdly, measure is shown to be the result of three frames of reference: the observer, the observed and the universe. Using these observations alone, the model resolves values for Planck’s constant, the gravitational constant and gravitational curvature.

The standard model of cosmology, although very successful, has problems with the very initial phase, such as the existence of a singularity when the density and curvature becomes infinite. In this work we propose a possible non-singular beginning of the Universe. From quantum considerations we set the earliest epoch to be the Planck epoch, which implies that the Universe did not begin with a singularity but with a finite minimal size of $10^{-3}~\mbox{cm}$. We suggest that the Universe initially began at the Planck length as a fluctuation having Planck energy expanding exponentially at constant Planck density, which then in turn accounts for the matter creation. All matter at the present epoch was created by the time the size of the Universe reached this minimal scale ($10^{-3}~\mbox{cm}$) starting from Planck length. We call this the Planck scale inflation. We also consider a time varying cosmological constant.

We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in $d>2$ spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a non-compact conformal manifold must diverge logarithmically in the higher-spin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions., 22 pages. v3: fixed compiling error

The study of de-Sitter Reissner–Nordstrøm black holes allows us to uncover a Weak Gravity Conjecture in de-Sitter space. It states that for a given mass [Formula: see text] there should be a state with a charge [Formula: see text] bigger than a minimal value [Formula: see text], depending on the mass and the de-Sitter radius [Formula: see text], in Planck units. This reproduces the well-known flat space–time result [Formula: see text] in the large radius limit (large [Formula: see text]). In the highly curved de-Sitter space, ([Formula: see text]) [Formula: see text] behaves as [Formula: see text]. Finally, we discuss the case of backgrounds from gauged R-symmetry in [Formula: see text] supergravity. This paper is based on [I. Antoniadis and K. Benakli, Fortsch. Phys. 68, 2000054 (2020), arXiv:2006.12512 [hep-th]].

The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-'t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond's holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson's derivation of Einstein's equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einstein's relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKN\cite{ckn} bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory., Comment: LaTeX2e 16 pages, 2 figures, to be published in Frontiers in Physics Research Topic, Qubits and Spacetime. Revised version has new figures, more explanation of HST formalism and Jacobson's derivation of Einstein equations, and added references

We propose a generalisation of the Weak Gravity Conjecture in de Sitter space by studying charged black-holes and comparing the gravitational and an abelian gauge forces. Using the same condition as in flat space, namely the absence of black-hole remnants, one finds that for a given mass $m$ there should be a state with a charge $q$ bigger than a minimal value $q_{\rm min}(m,l)$, depending on the mass and the de Sitter radius $l$, in Planck units. In the large radius flat space limit (large $l$), $q_{\rm min}\to m$ leading to the known result $q>m/\sqrt{2}$, while in the highly curved case (small $l$) $q_{\rm min}$ behaves as $\sqrt{ml}$. We also discuss the example of the gauged R-symmetry in $N=1$ supergravity., 15 pages, 2 figures

Denis Bernardin Three fundamental dimensionless constants in physics.Abstract : This study highlights the fundamental role of three key dimensionless constants in physics. Two are already well known, they are: α, fine structure constant, and δ, ratio between the mass of the proton and that of the electron. The dimensionless constant, highlighted in this article, is the constant β whose order of magnitude is 2,39 x 1022 and which plays for gravitation a role similar to that of the fine structure constant for electromagnetism. This study also aims for define rigorously the mathematical structure of space containing any physical value whatever the units of measurement used and to express in this space, from the three dimensionless constants mentioned above, most of the constants of physics in a non-anthropocentric system of units., Denis Bernardin Trois constantes adimensionnelles clés en physique.Résumé : Cette étude met en lumière le rôle essentiel de trois constantes adimensionnelles clés en physique. Deux sont déjà bien connues, ce sont : α, constante de structure fine, et δ, rapport entre la masse du proton et celle de l’électron. La constante adimensionnelle, mise en lumière dans cet article, est la constante β dont l’ordre de grandeur est de 2,39 x 1022 et qui joue pour la gravitation un rôle analogue à celui de la constante de structure fine pour l’électromagnétisme. Cette étude a également pour objectif de définir rigoureusement la structure mathématique de l’espace contenant toute valeur physique quelles que soient les unités de mesure utilisées et d’exprimer dans cet espace, à partir des trois constantes adimensionnelles citées plus haut la plupart des constantes de la physique dans un système d’unités non anthropocentrique.

We examine the dynamics of a closed cosmology whose matter source is that of a conformally coupled scalar field with a broken ${\rm SO}(1,1)$ symmetry, which correspond to the $\alpha$-attractors proposed by Linde and Kallosh. Following a field redefinition, such models give rise to "T-model" inflationary potentials, whose dynamics provide both an inflationary phase and a classical bounce. We show that the universe can undergo bounces far from the regime of quantum gravity. We analyse perturbations on this background with particular attention given to the effects of a double-bouncing scenario (with rapid recollapse between bounces) on the long wavelength modes. We demonstrate that the predictions of such models agree well with observations and might explain the suppression of power in the low multiples of the CMB., Comment: 29 pages, 7 figures

The recently introduced swampland criterion for de Sitter (arXiv:1806.08362) can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter $\epsilon_V$. This leads us to consider the other slow roll parameter $\eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $\epsilon_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${\cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $\epsilon_V$ need not necessarily be ${\cal O}(1)$, if $\eta_V \lesssim -{\cal O}(1)$ holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate arXiv:1806.08362, and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in $N$-flation., Comment: v2: many refs added, clarifications and comments added, improved wording regarding single/multi-field and potential/Hubble slow roll, typos fixed

Presenting a unified model of motion and gravity has proved difficult as current approaches to quantum and classical physics are incompatible. Using measurement quantization—a model that demonstrates the physical significance of Planck’s units of length, mass, and time—measure is expressed as counts of the fundamental units establishing a common framework for describing quantum and cosmological phenomena with expressions that are defined throughout the entire physical domain. Beginning with the Pythagorean Theorem, we demonstrate an understanding of measure with respect to static and moving references. The model is extended to include the measure of mass thus completing a single approach for describing the contraction and dilation of measure. With this new approach, relativistic effects are now described as properties of quantized finite units of measure. In support of the model, several descriptions of phenomena are resolved that match our most precise data such as the measure of dark energy, universal expansion, mass distribution, and the age of the Cosmic Microwave Background.

We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The limiting precision is $r^{-1}$ in Planck units, where $r$ is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states $S_1$ and $S_2$ cannot be experimentally distinguished from each other if they differ by a sufficiently small rotation. Experiments cannot exclude the possibility that the space of quantum state vectors (i.e., Hilbert space) is fundamentally discrete, rather than continuous. We discuss the implications for finitism: does physics require infinity or a continuum?, Comment: 10 pages. Version to appear in Physics Letters B

The notion of the dimensionless gravitational charge defined through the Planck mass and the fundamental constants specifying this mass itself is introduced. The Big Bang is related to the unified physical interaction decay and the drop of Newton’s gravitational constant by 40.67 orders of magnitude in comparison with the electromagnetic constant taken as unity. This causes an increase in theMetagalaxy curvature radius by the same value and a decrease in the average density of space–time curvature sources by 122 orders of magnitude: from the maximum allowable Planck density to the observed critical density. The microphysics appears naturally related to cosmology.

Recent cosmological measurements tend to confirm that the fine structure constant {\alpha} is not immutable and has undergone a tiny variation since the Big Bang. Choosing adequate units, this could also reflect a variation of Planck's constant h. The aim of this Letter is to explore some consequences of such a possible change of h for the pure and mixed states of quantum mechanics. Surprisingly enough it is found that not only is the purity of a state extremely sensitive to such changes, but that quantum states can evolve into classical states, and vice versa. A complete classification of such transitions is however not possible for the moment being because of yet unsolved mathematical difficulties related to the study of positivity properties of trace class operators., Comment: To appear in Phys. Lett. A

The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$., v2: 41 pages, typos fixed, references added, substantial revisions and clarifications (conclusions unchanged)

Hypothesis of friedmons as dark matter particles is proposed. Friedmons are stable particles with a mass of billion nucleon masses. These particles correspond to the not yet been discovered exact symmetry group dual to the SU(2) group: for the Standard model symmetries and dual symmetries, the roles of exact and broken symmetries and corresponding stable and unstable particles change places. The hypothesis of the decay of the primordial de Sitter vacuum of the Planck density to an asymptotic state of the expanding Universe with de Sitter vacuum of the observed critical density is proposed. The T -duality and S-duality hypotheses relating subgroups SU(3)×SU(2)×U(1) and dual subgroups S˜Ũ(3)× S˜Ũ(2) × ˜Ũ(1) with decay of the primordial symmetry group E(8) × ˜Ẽ(8) are proposed. In particular, these dualities relate the minimum Planck length 10−13 cm to the primordial curvature radius 10−13 cmof theMetagalaxy of the Planck density and its modern curvature radius of 1028 cm. That is, the probable relation of the Planck mass to the Metagalaxy mass of 1061 Planck masses is indicated.

The Hubble constant has been added in addition to the three fundamental constants (speed of light, gravitational constant and Planck constant) used by Max Planck, for derivation of the Planck mass by dimensional analysis. As a result, a general solution is found for the mass dimension expression m = γp m0, where m0 ≡ mp is the Planck mass, γ = 1.23×10-61 is a small dimensionless quantity and p is an arbitrary parameter in the interval [–1, 1]. The Planck mass mp = 2.17×10-8 kg, mass of the Hubble sphere MH ~ 1053 kg, minimum quantum of mass/energy mG = 2.68×10-69 kg, Weinberg mass mW = 1.08×10-28 kg, mass of hypothetical quantum gravity atom MG = 3.8×1012 kg, Eddington mass limit of stars ME = 6.6×1032 kg and some more masses potentially important for the physics and astrophysics represent particular solutions for values of p, expressed as fractions with small numerators and nominators.

The properties of symmetry of the Planck particle will be presented, and its magnetic charge will be extracted. This particle unifies the gravitational force, the electric force and the magnetic force into a single one, referred to as superforce. The phy...

Application of Maxwell’s equations and the theory of relativity on the processes in atoms with real oscillator leads to the structural constant of atoms s0 = 8.278692517. Measurements show that the ratio of energy of the photon and its frequency is not constant which means that Planck’s h is not constant. The theory which is consistent with these measurements, has been found. This theory covers processes in electron configuration and also at the core of atoms. Based on the structural constant s0 the maximum possible atomic number Z is determined. In order to encompass all atoms and all nuclides a new measurement unit has been proposed. That is the measurement unit for the order of substance. The introduction of structural constant s0 makes 11 fundamental constants redundant, including Planck’s h. The structural constant of atoms s0 stands up as the most stable constant in a very wide range of measurement, so it may replace variable Planck’s h well. Continuity of the bremsstrahlung is explained.