Search

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time and a new state equation was developed to determine precise, realistic values for a number of cosmological parameters, such as the energy of the universe U, cosmological constant Λ, the curvature of space k, energy density ρΛe, age of the universe tΩ etc. The development of the state equation highlights the importance of not neglecting any of the differential terms given the very large amounts in play that can counterbalance the infinitesimals. Some assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, tp, the universe contained a single photon at Planck temperature TP, almost Planck energy EP in the Planck volume. During the photon inflation phase (before characteristic time ~10-9 [s]), the number of original photons (alphatons) increased at each unit of Planck time tp and geometrical progression~n3, where n is the quotient of cosmic time over Planck time t/tp. Then, the primordial number of photons reached a maximum of N~1089, where it remained constant. These primordial photons (alphatons) are still present today and represent the essential of the energy contained in the universe via the cosmological constant expressed in the form of energy EΛ. Such geometric growth in the number of photons can bring a solution to the horizon problem through γγ exchange and a photon energy volume that is in phase with that of the volume energy of the universe. The predicted total mass (p, n, e, and ν), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 1050 [kg]. The predicted cosmic neutrino mass is ≤8.69 × 10-32 [kg] (≤48.7 [keV·c-2]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (ΔU/U) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons).

In SETI, when searching for "beacons" -- transmissions intended for us and meant to get our attention -- one must guess the appropriate frequency to search by considering what frequencies would be universally obvious to other species. This is a well known concept in game theory, where such solutions to a non-communicative cooperative game (such as a mutual search) are called "Schelling points." It is noteworthy, therefore, that when developing his eponymous units, Planck called them "natural" because they "remain meaningful for all times and also for extraterrestrial and non-human cultures." Here, I apply Planck's suggestion in the context of Schelling points in SETI with a "Planck Frequency Comb," constructed by multiplying the Planck energy by integer powers of the fine structure constant. This comb includes a small number of frequencies in regions of the electromagnetic spectrum where laser and radio SETI typically operates. Searches might proceed and individual teeth in the comb, or at many teeth at once, across the electromagnetic spectrum. Indeed, the latter strategy can be additionally justified by the transmitter's desire to signal at many frequencies at once, to improve the chances that the receiver will guess one of them correctly. There are many arbitrary and anthropocentric choices in this comb's construction, and indeed one can construct several different frequency combs with only minor and arbitrary modifications. This suggests that it may be fruitful to search for signals arriving in frequency combs of arbitrary spacing. And even though the frequencies suggested here are only debatably "better" than others proposed, the addition of the Planck Frequency Comb to the list of "magic frequencies" can only help searches for extraterrestrial beacons., Comment: 14 tables, 5 tables, accepted to the International Journal of Astrobiology. v4. Has minor language corrections and a correction to equations 5 and 7, and proper number of significant figures in the tables. v5. adds a relevant reference

To derive invariant forms of conservation equations, a scale invariant statistical mechanics model is used. A modified form of the Cauchy stress tensor for fluid is presented, which leads to a modified Stokes assumption and thus a finite bulk viscosity coefficient. Brownian motion is defined as the state of equilibrium between suspended particles and molecular clusters that also have Brownian motion. Physical space, also known as the Casimir vacuum, is a tachyonic fluid that is Dirac's "stochastic ether" or de Broglie's "hidden thermostat," and it is compressible according to Planck's compressible ether. The stochastic definitions of the Planck h and Boltzmann k constants are shown to be related to the spatial and temporal aspects of vacuum fluctuations, respectively. As a result, a modified definition of thermodynamic temperature is introduced, resulting in predicted sound velocity that agrees with observations. Boltzmann combinatoric method was employed to derive invariant forms of Planck energy and Maxwell-Boltzmann speed distribution functions. In addition, the universal gas constant is identified as a modified value of the Joule-Mayer mechanical equivalent of heat known as De Pretto number 8338, which appeared in his mass-energy equivalence equation. Invariant versions of Boltzmann, Planck, and Maxwell-Boltzmann distribution functions for equilibrium statistical fields, including those of isotropic stationary turbulence, are determined using Boltzmann's combinatoric methods. The latter leads to the definitions of (electron, photon, neutrino) as the most likely equilibrium sizes of (photon, neutrino, tachyon) clusters, respectively. The physical basis for the coincidence of the Riemann zeta function's normalized spacing between zeros and the normalized Maxwell-Boltzmann distribution, as well as its connections to the Riemann hypothesis are investigated. Through Euler's golden key, the zeros of the Riemann zeta function are related to the zeros of particle velocities or "stationary states," providing a physical explanation for the location of the critical line. It is proposed that, because the energy spectrum of the Casimir vacuum will be determined by the Schrodinger equation of quantum mechanics, physical space should be characterised by noncommutative spectral geometry of Connes in light of Heisenberg matrix mechanics. Invariant forms of transport coefficients implying finite values of gravitational viscosity, as well as hierarchies of vacua and absolute zero temperatures, are described. Some of the implications of the results for the problem of thermodynamic irreversibility and the Poincare recurrence theorem are discussed. An invariant modified form of the first law of thermodynamics is obtained, as well as a modified definition of entropy, which closes the gap between radiation and gas theory. Finally, in quantum mechanics, new paradigms for the hydrodynamic foundations of both Schrodinger and Dirac wave equations, as well as transitions between Bohr stationary states, are examined.

Padmanabhan elucidated the concept of super radiance in black hole physics which would lead to loss mass of a black hole, and loss of angular momentum due to space-time infall of material into a black hole. As Padmanabhan explained it, to avoid super radiance, and probable break down of black holes, from in fall, one would need in fall material frequency, divided by mass of particles undergoing in fall in the black hole to be greater than the angular velocity of the black hole event horizon in question. We should keep in mind we bring this model up to improve the chance that Penrose’s conformal cyclic cosmology will allow for retention of enough information for preservation of Planck’s constant from cycle to cycle, as a counterpart to what we view as unacceptable reliance upon the LQG quantum bounce and its tetrad structure to preserve memory. In addition, we are presuming that at the time of z = 20 in red shift that there would be roughly about the same order of magnitude of entropy as number of operations in the electro weak era, and that the number of operations in the z = 20 case is close to the entropy at redshift z = 0. Finally, we have changed Λ with the result that after redshift = 20; there is a rapid collapse to the present-day vacuum energy value i.e. by z = 12 the value of the cosmological constant, Λ likely being the same, today, as for what it was when z = 12. And z = 12 is the redshift value about when Galaxies form.

This paper attempts to reason about the propositions of photons and its movement in space according to the known axiom of the definition, and by some simple logical method. The light is by the space motion photon component. The space motion photon has the energy and the quality. Photon in space along straight line direction movement speed identically equal in c. A photon moves in space with uniform helical motion, which is a combination of uniform circular motion and uniform linear motion in which the speed of the linear motion and the linear speed of the circular motion are always equal to c. Photon’s Planck energy formula E=hv=2πhv, h is the approximate Planck constant, which is the angular momentum of photons moving along the circumference plane direction mcr, r is the photon along the circumference plane motion radius; v is photon each second completes the circular motion by link speed c the number of times c/2πr, also is the photon frequency. By replacing the mcr and c/2πr with the Planck energy formula, it may obtain Einstein mass energy formula E=mc2. The greater its mass and energy, the smaller the radius of its circular motion, the higher its frequency, and the shorter its wavelength. The lower its mass and energy, the greater the radius of its circular motion, the lower its frequency, and the longer its wavelength. The uncertainty principle is essentially caused by our misunderstanding of the motion of light. The existence and motion of light can be determined.

We consider five dimensional conformal gravity theory which describes an anisotropic extra dimension. Reducing the theory to four dimensions yields Brans–Dicke theory with a potential and a hidden parameter α which implements the anisotropy between the four dimensional spacetime and the extra dimension. We find that a range of value of the parameter α can address the current dark energy density compared to the Planck energy density. Constraining the parameter α and the other cosmological model parameters using the recent observational data consisting of the Hubble parameters, type Ia supernovae, and baryon acoustic oscillations, together with the Planck or WMAP 9-year data of the cosmic microwave background radiation, we find α > − 2 . 05 for Planck data and α > − 2 . 09 for WMAP 9-year data at 95% confidence level. We also obtained constraints on the rate of change of the effective Newtonian constant ( G eff ) at present and the variation of G eff since the epoch of recombination to be consistent with observation.

We investigate how the universal constants, including the fine structure constant, have varied since the early universe close to the Planck energy scale ($E_P\sim 10^{19}$GeV) and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. We have already shown that the speed of light was much higher close to the Planck scale. In the present work, we will go further, first by showing that both the Planck constant and the electron charge were also too large in the early universe. However, we conclude that the fine structure constant ($\alpha\cong 1/137$) has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data. Furthermore, we will obtain the divergence of the electron (or proton) mass and also the gravitational constant ($G$) at the Planck scale. Thus, we will be able to verify the veracity of Dirac's belief about the existence of "coincidences" between dimensionless ratios of sub-atomic and cosmological quantities, leading to a variation of $G$ with time, i.e., the ratio of the electrostatic to gravitational force between an electron and a proton ($\sim 10^{41}$) is roughly equal to the age of the universe divided by an elementary time constant, so that the strength of gravity, as determined by $G$, must vary inversely with time just in the approximation of lower temperature or for times very far from the early period, in order to compensate for the time-variation of the Hubble parameter ($H\sim t^{-1}$). In short, we will show the validity of Dirac's hypothesis only for times very far from the early period or $T\sim T_P\sim 10^{32}$K., Comment: 6 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1211.1936, arXiv:2009.05397, arXiv:1205.2298

Planck scale acts as a threshold where a new description of spacetime is expected to appear. Such a scale should be invariant which is achieved by modifying the algebra. For the exotic spacetimes appearing at Planck scale, the phase-space is also expected to modify. Considering such a modification in a relativistic theory with an invariant Planck scale as an ultraviolet cut-off, we study the thermodynamics of ideal gases. In case of ideal photon gas this leads to the modification of Planck energy density distribution and Wien’s displacement law. We also study various equilibrium thermodynamic properties of blackbody radiation.

We rediscuss the main Cosmological Problems as illusions originated from our ignorance of the hidden information holographically stored in vacuo. The Cosmological vacuum state is full of a large number of dynamical quantum hairs, dubbed hairons, which dominate the Cosmological Entropy. We elaborate on the Cosmological Constant (CC) problem, in both the dynamical and time-constant possibilities. We show that all dangerous quantum mixings between the CC and the Planck energy scales are exponentially suppressed as an entropic collective effect of the hairon environment. As a consequence, the dark energy scale is UV insensitive to any Planckian corrections. On the other hand, the inflation scale is similarly stabilized from any radiative effects. In the case of the Dark energy, we show the presence of a holographic entropic attractor, favoring a time variation of $$\Lambda \rightarrow 0$$ in future rather than a static CC case, i.e., the $$w>-1$$ Dynamical DE is favored over a CC or a $$w

In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,\epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated., Comment: 12 pages, 8 figures

In this epilogue we place the theories of semiclassical and stochastic gravity in perspective, exploring their linkage with quantum gravity, defined as theories for the microscopic structures of spacetime, not necessarily and most likely not from quantizing general relativity. We distinguish two categorical approaches, ‘top-down’ (Planck energy) and ‘bottom-up’. The tasks of the ‘top-down’ approach, which include string theory and other proposed theories for the microstructures of spacetime, lie in explaining how the micro-constituents give rise to macroscopic structure. They are thus more appropriately called emergent gravity. warnings are issued not to blindly follow the dogma that quantizing general relativity naturally yields a microscopic structure of spacetime, or to accept, without checking the emergent mechanisms, the dictum that some micro-constituent is the theory that gives us everything. Stochastic gravity takes the more conservative ‘bottom-up’ approach. For the linkage with quantum gravity we mention (a) the kinetic theory approach, relying on the structure of a correlation hierarchy and the role played by noise and fluctuations, and (b) the effective theory approach, using large N techniques. The ingredients of both approaches have been developed in earlier chapters systematically. We end with a description of the advantages and limitations of stochastic gravity.

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.

Some models of quantum gravity predict that the very structure of spacetime is `frothy' due to quantum fluctuations. Although the effect is expected to be tiny, if these spacetime fluctuations grow over a large distance, the initial state of a photon, such as its energy, is gradually washed out as the photon propagates. Thus, in these models, even the most monochromatic light source would gradually disperse in energy due to spacetime fluctuations over large distances. In this paper, we use science verification observations obtained with ESPRESSO at the Very Large Telescope to place a novel bound on the growth of spacetime fluctuations. To achieve this, we directly measure the width of a narrow Fe II absorption line produced by a quiescent gas cloud at redshift z=2.34, corresponding to a comoving distance of ~5.8 Gpc. Using a heuristic model where the energy fluctuations grow as sigma_E / E = (E/E_P)^alpha, where E_P = 1.22 x 10^28 eV is the Planck energy, we rule out models with alpha < 0.634, including models where the quantum fluctuations grow as a random walk process (alpha = 0.5). Finally, we present a new formalism where the uncertainty accrued at discrete spacetime steps is drawn from a continuous distribution. We conclude, if photons take discrete steps through spacetime and accumulate Planck-scale uncertainties at each step, then our ESPRESSO observations require that the step size must be at least >10^13.2 L_P, where L_P is the Planck length., 7 pages, 2 figures, Submitted for publication in Monthly Notices of the Royal Astronomical Society

In the projection gravitation theory, the center of a gravitational source is an empty hole, not black hole. The gravitation can be understood as a new kind of Lorentz symmetry breaking. Multiple empty holes can merge together to form a large empty hole. So the empty holes form a thermodynamic system. So the empty hole has thermodynamic properties, such as entropy and temperature. We discuss two models of empty holes merging. The first model derives out a result that empty hole entropy is proportional to the radius of the empty hole. The second model can simply derive out the formula of black hole entropy in General Relativity. The black hole entropy is just a special case in empty hole. Two models get the same result that the temperature of the empty hole is inversely proportional to its radius. The empty hole has a new statistical distribution mode, that is the empty hole distribution. In the new projection gravitation, the Planck energy and the Planck length have a new and different physical meaning. The two constants represent a special kind of association relationship that has not yet been understood by humans.

International audience; Since the baryonic matter of the observable Universe consists mainly of protons and neutrons, then the numerical value of its mass can be represented and calculated on the basis of an additive-multiplicative golden algebraic fractal, based on golden algebraic fractals of the masse of proton, neutron, and muon. Based on an analytical estimate of the mass of the observable Universe, using the law “Planck’s Universal Proportions”, an analytical estimate of the Hubble constant and the main spatial-energy characteristics of the observed Universe is obtained. An analytical estimate of the Hubble constant is consistent with the experimental data of Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration. The objectivity of the experimental estimation of the Hubble constant from the H0LiCOW, Riess et al, Hubble Space Telescope collaborations does not raise any doubts. This means that the Hubble constant describes two similar, but different physical processes and has at least two values. The value of the Hubble constant from the collaborations Planck’s mission, SDSS-III Baryon Oscillation Spectroscopic Survey, DES Collaboration describes the process of rotation of the space of the observed Universe, and the value of the Hubble constant from the collaborations H0LiCOW, Riess et al, Hubble Space Telescope describes the process of rotation of substance in the space of the observed Universe. New estimates of the values of Dirac's large energy numbers are presented. It is confirmed that all coefficients in Planck’s proportions, which are calculated on the basis of Planck’s constants — length, mass, time, are equal to similar coefficients, which are calculated on the basis of the main characteristics of the observed Universe. Estimation of the numerical values of the Schwarzschild and Hubble radii for the observable Universe suggests that the Hubble sphere is inside the Schwarzschild sphere, therefore the observable Universe is a black hole. The presence of a redshift from distant objects of the observable Universe suggests that this is a rotating black hole. It has been shown that the vacuum pressure cannot be a source of dark energy. It is shown that the force of imaginary dark energy is equal in magnitude to the force of gravitational compression of the observed Universe and is equal to the Planck force. It is shown that after the Big Bang, the space of the observable Universe made one incomplete revolution of at 345 degrees, and the substance in it made one complete revolution of approximately 379 degrees. Estimates are given for the energy of dark matter, as the kinetic energy of rotation of the space of the observable Universe, as well as the equivalent mass of dark matter. New estimates are given: of the gravitational constant, of the Planck energy, of the Planck acceleration, of the Planck force, of the gravity factor of the observable Universe, of the Planck temperature, of the angular velocity of rotation of the space of the observable Universe. Estimates of temperature and wavelength of thermal radiation of the observable Universe, as the Hubble sphere, are given.

The Brown-York quasi-local energy of a charged rotating black hole described by the Kerr-Newman metric and enclosed by a fixed-radius surface is computed. No further assumptions on the angular momentum or the radial coordinate in Boyer-Lindquist coordinates were made. The result can be expressed in terms of incomplete elliptic integrals and is used to analyze the self-energy of an electron which is assumed to be described by the Kerr-Newman metric. For this purpose the small sphere limit is investigated thoroughly comparing the analysis with known results. Evaluating the energy using the mass, angular momentum and charge of an electron a value in the order of the Planck energy is obtained in the small sphere limit as long as the Kerr-Newman metric acting as exterior solution can be used as a description of spacetime., Comment: 11 pages, 9 figures

Due to the high energies and long distances to the sources, astrophysical observations provide a unique opportunity to test possible signatures of Lorentz invariance violation (LIV). Superluminal LIV enables the decay of photons at high energy. The High Altitude Water Cherenkov (HAWC) Observatory is among the most sensitive gamma-ray instruments currently operating above 10 TeV. HAWC finds evidence of 100 TeV photon emission from at least four astrophysical sources. These observations exclude, for the strongest of the limits set, the LIV energy scale to $2.2\times10^{31}$ eV, over 1800 times the Planck energy and an improvement of 1 to 2 orders of magnitude over previous limits., Accepted for publication in Physical Review Letters

Using Relativistic Quantum Geometry we study back-reaction effects of space-time inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of space-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of space-time. We found that temperature and entropy are dependent on the number of sub-states on each energy's level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p\,c^2$, and a B-H temperature: $T_{BH}=\left(\frac{\hbar\,c}{2\pi\,l_p\,K_B}\right)$., Comment: Version accepted in EPJC. arXiv admin note: text overlap with arXiv:1904.11599

We present a detailed analysis of the stacked frequency spectrum of a large sample of galaxy clusters using Planck data, together with auxiliary data from the AKARI and IRAS missions. Our primary goal is to search for the imprint of relativistic corrections to the thermal Sunyaev-Zeldovich effect (tSZ) spectrum, which allow to measure the temperature of the intracluster medium. We remove Galactic and extragalactic foregrounds with a matched filtering technique, which is validated using simulations with realistic mock data sets. The extracted spectra show the tSZ signal at high significance and reveal an additional far-infrared (FIR) excess, which we attribute to thermal emission from the galaxy clusters themselves. This excess FIR emission from clusters is accounted for in our spectral model. We are able to measure the tSZ relativistic corrections at $2.2\sigma$ by constraining the mean temperature of our cluster sample to $4.4^{+2.1}_{-2.0} \, \mathrm{keV}$. We repeat the same analysis on a subsample containing only the 100 hottest clusters, for which we measure the mean temperature to be $6.0^{+3.8}_{-2.9} \, \mathrm{keV}$, corresponding to $2.0\sigma$. The temperature of the emitting dust grains in our FIR model is constrained to $\simeq 20 \, \mathrm{K}$, consistent with previous studies. Control for systematic biases is done by fitting mock clusters, from which we also show that using the non-relativistic spectrum for SZ signal extraction will lead to a bias in the integrated Compton parameter $Y$, which can be up to 14% for the most massive clusters. We conclude by providing an outlook for the upcoming CCAT-prime telescope, which will improve upon Planck with lower noise and better spatial resolution., Comment: matches the article published in MNRAS; 22 pages, 16 figures

Extremal rotating black holes can be formed in the Planck energy scattering of Dirac spin parallel neutrinos in the mass state m2 (assuming m1=0), owing to the repulsive interaction between their magnetic dipoles, induced by vacuum fluctuations. Assuming that some recent results of loop-quantised Schwarzschild black holes would be also applicable for the Kerr case, we show that the resulting black hole has Planck mass and angular momentum ħ, and that its horizon area is in the spectrum of the Loop Quantum Gravity area operator. Moreover, we argue that such black holes could be produced at the reheating, with an abundance that allows their interpretation as forming the presently observed dark matter component, provided that the energy scale at inflation is ≈1017 GeV. This scale can be lower if we attribute a high chemical potential to primordial neutrinos. As extremal black holes have zero surface gravity, there is no limits on their abundance from Hawking evaporation.

The tiny modification of dispersion relation induced by Lorentz violation (LV) is an essential issue in quantum gravity (QG) theories, which can be magnified into significant effects when dealing with astrophysical observations at high energy and long propagation distance. LV would lead to photon decay at high energies, therefore, observations of high-energy photons could constrain LV or even QG theories. The Large High Altitude Air Shower Observatory (LHAASO) is the most sensitive gamma-array instrument currently operating above 100 TeV. Recently, LHAASO reported the detection of 12 sources above 100 TeV with maximum photon energy exceeding 1 PeV. According to these observations, the most stringent restriction is achieved in this paper, i.e., limiting the LV energy scale to $1.7\times10^{33} $ eV, which is over 139,000 times that of the Planck energy and achieve an improvement of about 1.9 orders of magnitude over previous limits., Comment: AMS-LaTeX 2.0, 7 pages, 3 figures

Dynamical systems methods are used to investigate a cosmological model with non-minimally coupled scalar field and asymptotically quadratic potential function. We found that for values of the non-minimal coupling constant parameter $\frac{3}{16}, Comment: 11 pages; 2 multiple figures; (v2) published version

The evolution of a quantum gravitational system (QGS) with the maximally symmetric geometry in the epoch close to the Planck one is investigated. The state vector of the QGS satisfies the set of wave equations which describes the time evolution of the quantum system in the space of quantum fields. It is shown that, for the time arrow from past to future, the state vector describes the QGS contracting for the negative values of the cosmic scale factor and expanding for its positive values. The intensity distributions of matter for two exactly solvable models of spatially closed and flat QGSs formed by dust and radiation are calculated. The analogies with known phenomena in quantum mechanics and optics are drawn., Дослiджено еволюцiю квантової гравiтацiйної системи (КГС) з максимально-симетричною геометрiєю в епоху, близьку до планкiвської. Вектор стану КГС задовольняє систему хвильових рiвнянь, якi описують еволюцiю квантової системи у часi в просторi квантових полiв. Показано, що для стрiли часу, спрямованої з минулого в майбутнє, вектор стану описує КГС, яка стискається для вiд’ємних значень космiчного масштабного фактора та розширюється для його додатних значень. Обчислено розподiл iнтенсивностi матерiї для двох моделей, що допускають точний розв’язок, а саме для просторово замкненої та плоскої КГС, якi утворенi пилом та випромiнюванням. Наведенi аналогiї з вiдомими явищами з квантової механiки та оптики.

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.

We find that π represents dual attributes. One is within the purely mathematical domain and can be derived for example, from infinite series, among several other methods. The other is within a 2D geometric-physical domain. This paper analyzes several physical constants from an analogous perspective where they are defined solely by mathematical and 2D geometric properties independent of any actual physical scaling data. The constants are evaluated as natural unit frequency equivalents of the neutron, electron, Bohr radius, Rydberg constant, Planck’s constant, Planck time, a Black hole with a Schwarzschild radius, the distance light travels in one time unit; and the fine structure constant. These constants are defined within two inter-related harmonic domains. In the linear domain, the ratios of the frequency equivalents of the Rydberg constant, Bohr radius, electron; and the fine structure constant are related to products of 2 and π. In the power law domain, their partial harmonic fraction powers, and the integer fraction powers of the fundamental frequency for Planck time are known. All of the constants are then derived at the point where a single fundamental frequency simultaneously fulfills both domains independent of any direct physical scale data. The derived values relative errors from the known values range from 10-3 to 10-1 supporting the concept and method.

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.

In quantum gravity theories, when the scattering energy is comparable to the Planck energy the Heisenberg uncertainty principle breaks down and is replaced by the minimal length uncertainty relation. In this paper, the consequences of the minimal length uncertainty relation on one-dimensional quantum scattering are studied using an approach involving a recently proposed second-order differential equation. An exact analytical expression for the tunneling probability through a locally-periodic rectangular potential barrier system is obtained. Results show that the existence of a non-zero minimal length uncertainty tends to shift the resonant tunneling energies to the positive direction. Scattering through a locally-periodic potential composed of double-rectangular potential barriers shows that the first band of resonant tunneling energies widens for minimal length cases when the double-rectangular potential barrier is symmetric but narrows down when the double-rectangular potential barrier is asymmetric. A numerical solution which exploits the use of Wronskians is used to calculate the transmission probabilities through the Poschl–Teller well, Gaussian barrier, and double-Gaussian barrier. Results show that the probability of passage through the Poschl–Teller well and Gaussian barrier is smaller in the minimal length cases compared to the non-minimal length case. For the double-Gaussian barrier, the probability of passage for energies that are more positive than the resonant tunneling energy is larger in the minimal length cases compared to the non-minimal length case. The approach is exact and applicable to many types of scattering potential.

We show that, Schwarzschild radius of Planck mass plays a vital role in electroweak and strong interactions. With reference to the observed large proportionality ratio, , it seems appropriate to consider a large nuclear gravitational constant, . Qualitatively this idea is in agreement with 'Strong gravity' concept proposed by Abdus Salam and C.Sivaram [Mod. Phys. Lett., A8(4), 321- 326. (1993)]. We would like to suggest that, by replacing the Newtonian gravitational constant with the proposed nuclear gravitational constant, predicted high energy levels of String theory can be brought down to the current hadronic scale. Based on this idea, we defined the nuclear Planck mass, and proposed a quantized model mechanism for understanding the hadronic mass spectrum.

In this work, we first propose a cosmological scenario inherently based on the effective Nambu--Jona-Lasio (NJL) model near the infrared (IR) limit of the Ho\v{r}ava-Lifshitz (HL) theory. Having used the one-loop correction, we employ the NJL framework in the ultraviolet (UV) limit of the HL theory, with critical exponent $z=3$, to demonstrate in the IR limit that the symmetry of the potential at the critical coupling value is broken at $z=1$. We also derive the effective Higgs-like potential in the low energy regimes. Here the symmetry of the effective potential will be broken near $z=1$ at a certain value of the critical coupling. In our scenario, the scalar channel of the NJL model plays the role of a composite inflaton. We find that the Lorentz invariance (LI) appears at the IR regime of the HL theory and employ the standard inflationary (slow-roll) paradigm as a probe of physics at very high energy. We compute inflationary parameters and compare them with recent Planck 2015 data. Interestingly, we discover that the predictions of the model are in perfect agreement with the Planck analysis. Our salient feature is that we used inflation to quantify the IR and UV fixed points of the underlying theory. We discover that the IR fixed point of HL gravity is compatible with the grand unified energy scale; whilst the UV fixed point is the Planck energy scale., Comment: v3: 15 pages, 2 figures, texts modified, references added, version accepted for publication by Physics Letters B

Due to the high energies and long distances involved, astrophysical observations provide a unique opportunity to test possible signatures of Lorentz Invariance Violation (LIV). Superluminal LIV enables the decay of photons at high energy over relatively short distances, giving astrophysical spectra that have a hard cutoff above this energy. The High Altitude Water Cherenkov (HAWC) observatory is the most sensitive currently-operating gamma-ray observatory in the world above 10 TeV. Together with the recent development of an energy-reconstruction algorithm for HAWC using an artificial neural network, HAWC can make detailed measurements of gamma-ray energies above 100 TeV. With these observations, HAWC can limit the LIV energy scale greater than $10^{31}$ eV, over 800 times the Planck energy scale. This limit on LIV is over 60 times more constraining than the best previous value for $\rm E_{LIV}$.

A cosmological model was developed using the equation of state of photon gas, as well as cosmic time. The primary objective of this model is to see if determining the observed rotation speed of galactic matter is possible, without using dark matter (halo) as a parameter. To do so, a numerical application of the evolution of variables in accordance with cosmic time was developed to determine precise, realistic values for a number of cosmological parameters, such as energy, cosmological constant Λ, curvature of space k, energy density ρΛe, etc. Several starting assumptions were put forth in order to solve these equations. The current version of the model partially explains several of the observed phenomena that raise questions. Numerical application of the model has yielded the following results, among others: Initially, during the Planck era, at the very beginning of Planck time, tp, the universe contained a single photon at Planck temperature and Planck energy in the Planck volume. During the photon inflation phase (before characteristic time ~10-9 [s]), the number of photons increased at each unit of Planck time and geometrical progression ~n3, where n is the quotient of cosmic time over Planck time (t/tp). Then, the primordial number of photons reached a maximum of ~1089, where it remained constant. Such geometric growth in the number of photons can bring a solution to the horizon problem through photon-photon exchange and a photon energy volume that is in phase with that of the universe. The age of the universe in cosmic time that is in line with positive energy conservation (in terms of conventional thermodynamics) and the creation of proton, neutron, electron, and neutrino masses, is ~76 [Gy]. The predicted total mass (p, n, e and n), based on the Maxwell-Juttner relativistic statistical distribution, is ~7 × 1050 [kg]. The predicted cosmic neutrino mass is ≤ 8.69 × 10−32 [kg]. (≤ 48.7 [keVc−2]) if based on observations of SN1987A. The temperature variation of the cosmic microwave background (CMB), as measured by Planck, can be said to be partially due to energy variations in the universe (DE/E) during the primordial baryon synthesis (energy jump from the creation of protons and neutrons), through a process called baryon asymmetry and the Maxwell-Juttner relativistic distribution. In this model, what is usually referred to as dark energy actually corresponds to the energy of the universe that has not been converted to mass, and which acts on the mass created by the mass-energy equivalence principle and the cosmological gravity field, FΛ, associated with the cosmological constant, which is high during primordial formation of the galaxies (

The project of \emph{"quantum spacetime phenomenology"} focuses on searching pragmatically for the Planck scale quantum features of spacetime. Among these features is the existence of a characteristic length scale addressed commonly by effective approaches to quantum gravity (QG). This characteristic length scale could be realized, for instance and simply, by generalizing the standard Heisenberg uncertainty principle (HUP) to a \emph{"generalized uncertainty principle"} (GUP). While usually it is expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a \emph{"cold atomic ensemble recoil experiment"} (CARE) as a low energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high finesse optical cavity which is supported by a new class of low power consumption integrated devices known as \emph{"micro-electro-opto-mechanical systems"} (MEOMS). The proposed system comprises of a micro mechanical oscillator instead of spherical confocal mirrors as one of the components of high finesse optical cavity. In the framework of a bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant (FSC) from the Rubidium ($^{87}$Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint as $0.999978, Comment: 12 pages, 2 figures, Revised Version, Accepted for publication in Progress of Theoretical and Experimental Physics

The goal of this contribution is to present the properties of a class of quantum bouncing models in which the quantum bounce originates from the Dirac canonical quantization of a midi-superspace model composed of a homogeneous and isotropic background, together with small inhomogeneous perturbations. The resulting Wheeler-DeWitt equation is interpreted in the framework of the de Broglie-Bohm quantum theory, enormously simplifying the calculations, conceptually and technically. It is shown that the resulting models are stable and they never get to close to the Planck energy, where another more involved quantization scheme would have to be evoked, and they are compatible with present observations. Some physical effects around the bounce are discussed, like baryogenesis and magnetogenesis, and the crucial role of dark matter and dark energy is also studied.

In quantum gravity theories, when the scattering energy is comparable to the Planck energy, the usual Heisenberg uncertainty principle breaks down and is replaced by generalized uncertainty principle (GUP). In this paper, the Dirac equation is studied for a single particle with spin and pseudospin symmetry in the presence of GUP, in [Formula: see text] dimensions. For arbitrary wave [Formula: see text], the Dirac equation with multiparameter exponential-type potential is solved by applying the approximation of the centrifugal term and the Nikiforov–Uvarov method. The corresponding energy spectra and eigenvalue function are obtained in the closed form and depend on the GUP parameter. In addition, several interesting cases have been discussed.

Based on the functional dependence of entropy on energy, and on Wien's distribution for black-body radiation, Max Planck obtained a formula for this radiation by an interpolation relation that fitted the experimental measurements of thermal radiation at the Physikalisch Technishe Reichanstalt (PTR) in Berlin in the late 19th century. Surprisingly, his purely phenomenological result turned out to be not just an approximation, as would have been expected, but an exact relation. To obtain a physical interpretation for his formula, Planck then turned to Boltzmann's 1877 paper on the statistical interpretation of entropy, which led him to introduce the fundamental concept of energy discreteness into physics. A novel aspect of our account that has been missed in previous historical studies of Planck's discovery is to show that Planck could have found his phenomenological formula partially derived in Boltzmann's paper in terms of a variational parameter. But the dependence of this parameter on temperature is not contained in this paper, and it was first derived by Planck.

We find the highest symmetry between the fields intrinsic to free particles (free particles having only mass, charge and spin), and show these fields symmetries and their close relationship to force and entropy. The Boltzmann Constant is equal to the natural entropy, in that it is The Planck Energy over The Planck Temperature. This completes a needed symmetry in The Bekenstein-Hawking Entropy. Upon substitution of Planck Units into The Schwarzschild Radius, we find that the mass and radius of any black hole define both the gravitational constant and the natural force. We find that the Gaussian Surface area about a particle is equal to the surface area of an equally massed black hole if we define the gravitational field of that particle to be the quotient of The Planck Force and the particles mass. By these simple substitutions we find that gravity is quantized in units of surface entropy. We also find Pythagorean Triples are resting within the dimensional parameters of Special Relativity, and show this to be the dimensional aspects of single particles observing one another, coupled with the intrinsic Hubble nature of the universe.

We evaluate three of the quantum constants of hydrogen, the electron, e-, the Bohr radius, a0, and the Rydberg constants, , as natural unit frequency equivalents, v. This is equivalent to Planck’s constant, h, the speed of light, c, and the electron charge, e, all scaled to 1 similar in concept to the Hartree atomic, and Planck units. These frequency ratios are analyzed as fundamental coupling constants. We recognize that the ratio of the product of 8π2, the ve- times the vR divided by va0 squared equals 1. This is a power law defining Planck’s constant in a dimensionless domain as 1. We also find that all of the possible dimensionless and dimensioned ratios correspond to other constants or classic relationships, and are systematically inter-related by multiple power laws to the fine structure constant, α; and the geometric factors 2, and π. One is related to an angular momentum scaled by Planck’s constant, and another is the kinetic energy law. There are harmonic sinusoidal relationships based on 2π circle geometry. In the dimensionless domain, α is equivalent to the free space constant of permeability, and its reciprocal to permittivity. If any two quanta are known, all of the others can be derived within power laws. This demonstrates that 8π2 represents the logical geometric conversion factor that links the Euclid geometric factors/three dimensional space, and the quantum domain. We conclude that the relative scale and organization of many of the fundamental constants even beyond hydrogen are related to a unified power law system defined by only three physical quanta of ve-, vR, and va0.

When initial radius Rinitial →0 if Stoica actually presents Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. We present entanglement entropy in the early universe with a shrinking scale factor, due to Muller and Lousto, and show that there are consequences due to initial entangled SEntropy = 0.3r2h/a2 for a time dependent horizon radius rH = in cosmology, with (flat space conditions) for conformal time. Even if the 3 dimensional spatial length goes to zero, this construction preserves a minimum non-zero L vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial →0 . We state that the presence of computational bits is necessary for cosmological evolution to commence.

In the year 1900, Max Planck was led by experimental observations to propose a strange formula for the intensity as a function of frequency for light emitted by a cavity made in a hot substance such as a metal. Planck provided a derivation based on peculiar properties to be obeyed by the emitters and absorbers in the cavity, introducing a new fundamental constant in the process. I attempt to point out some nuts and bolts reasoning that could have provided a clue.

Two of the major open questions in particle physics are: (1) Why do the elementary fermionic particles that are so far observed have such low mass-energy compared to the Planck energy scale? (2) What mechanical energy may be counterbalancing the divergent electrostatic and strong force energies of point-like charged fermions in the vicinity of the Planck scale? In this paper, using a hitherto unrecognised mechanism derived from the non-linear amelioration of the Dirac equation known as the Hehl&ndash, Datta equation within the Einstein&ndash, Cartan&ndash, Sciama&ndash, Kibble (ECSK) extension of general relativity, we present detailed numerical estimates suggesting that the mechanical energy arising from the gravitationally coupled self-interaction in the ECSK theory can address both of these questions in tandem.

Astrophysical observations provide a unique opportunity to test possible signatures of Lorentz Invariance Violation (LIV), due to the high energies and long distances involved. In quantum theory of gravity, one may expect the modification of the dispersion relation between energy and momentum for photons, which can be probed with the time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs). In this paper, by using the detailed time-delay measurements of GRB 160625B at different energy bands, as well as 23 time-delay GRBs covering the redshifts range of $z=0.168-2.5$ (which were measured at different energy channels from the light curves), we propose an improved model-independent method (based on the newly-compiled sample of $H(z)$ measurements) to probe the energy-dependent velocity due to the modified dispersion relation for photons. In the framework of a more complex and reasonable theoretical expression to describe the time delays, our results imply that the intrinsic time lags can be better described with more GRBs time delay data. More importantly, through direct fitting of the time-delay measurements of a sample of GRBs, our limit on the LIV energy scale is comparable to that with unknown constant for the intrinsic time lag, much lower than the Planck energy scale in both linear LIV and quadratic LIV cases., 7pages,3figures,Accepted for publication in ApJ