Compton Wavelength Research Articles

Superradiant production of heavy dark matter from primordial black holes

Rotating black holes (BHs) can efficiently transfer energy to the surrounding environment via superradiance. In particular, when the Compton length of a particle is comparable to the gravitational radius of a BH, the particle's occupation number can be exponentially amplified. In this work, we investigate the effect of the primordial-black-hole (PBH) superradiant instabilities on the generation of heavy bosonic dark matter (DM) with mass above $\sim$ 1 TeV. Additionally, we analyze its interplay with other purely gravitational and therefore unavoidable DM production mechanisms such as Hawking emission and the ultraviolet freeze-in. We find that superradiance can significantly increase the DM density produced by PBHs with respect to the case that only considers Hawking emission, and hence lower initial PBH densities are required.

Superradiance in massive vector fields with spatially varying mass

Superradiance is a process by which massive bosonic particles can extract energy from spinning black holes, leading to the build up of a condensate if the particle has a Compton wavelength comparable to the black hole's Schwarzschild radius. One interesting possibility is that superradiance may occur for photons in a diffuse plasma, where they gain a small effective mass. Studies of the spin-0 case have indicated that such a build up is suppressed by a spatially varying effective mass, supposed to mimic the photons' interaction with a physically realistic plasma density profile. We carry out relativistic simulations of a massive Proca field evolving on a Kerr background, with modifications to account for the spatially varying effective mass. This allows us to treat the spin-1 case directly relevant to photons, and to study the effect of thinner disk profiles in the plasma. We find similar qualitative results to the scalar case, and so support the conclusions of that work: either a constant asymptotic mass or a shell-like plasma structure is required for superradiant growth to occur. We study thin disks and find a leakage of the bosonic condensate that suppresses its growth, concluding that thick disks are more likely to support the instability.

Double copy of spontaneously broken Abelian gauge theory

Similarity in the structure of scattering amplitudes in Yang-Mills theories and General Relativity led to the idea that graviton could be described as the double copy of a vector gauge field. In this letter we discuss a realization of this idea emerging directly from solutions of equations of General Relativity. A general form of the energy momentum tensor for the electric field is derived that leads to the metric tensor in terms of the double copy of a corresponding gauge potential. We then use this general property to find the double copy of spontaneously broken scalar electrodynamics. The result is a screened Reissner-Nordström-like metric. When the horizon radius and the Compton wavelength of the massive photon become comparable the black hole becomes a quantum object. An exact solution of the horizon wave equation is found and the corresponding energy spectrum is described. It turns out that highly excited states show a characteristic string-like behavior.

The effect of dark matter discreteness on light propagation

Light propagation in cosmology is usually studied in the geometrical optics approximation which requires the spacetime curvature to be much smaller than the light wavenumber. However, for non-fuzzy particle dark matter the curvature is concentrated in widely separated spikes at particle location. If the particle mass is localised within a Compton wavelength, then for masses ≳104 GeV the curvature is larger than the energy of CMB photons.We consider a post-geometrical optics approximation that includescurvature. Photons gain a gravity-induced mass when travelling throughdark matter, and light paths are not null nor geodesic. We find thatthe correction to the redshift is negligible. For the angular diameterdistance, we show how the small average density emerges from the largelocal spikes when integrating along the light ray. We find that therecan be a large correction to the angular diameter distance even forphoton energies much larger than the curvature. This may allow to seta strong upper limit on the mass of dark matter particles. We discussopen issues related to the validity of our approximations.

Axion as a fuzzy dark matter candidate: proofs in different gauges

Axion as a coherently oscillating massive scalar field is known to behave as a zero-pressure irrotational fluid with characteristic quantum stress on a small scale. In relativistic perturbation theory, the case was proved in the axion-comoving gauge up to fully nonlinear and exact order. Our basic assumption is that the field is oscillating with Compton frequency and the Compton wavelength is smaller than the horizon scale. Here, we revisit the relativistic proof to the linear order in the other gauge conditions. We show that the same equation for density perturbation known in the non-relativistic treatment can be derived in two additional gauge conditions: the zero-shear gauge and the uniform-curvature gauge. The uniform-expansion gauge fails to get the aimed equation, and the quantum stress term is missing in the synchronous gauge. For comparison, we present the relativistic density perturbation equations in the zero-pressure fluid in these gauge conditions. Except for the comoving and the synchronous gauge, the equations strikingly differ from the axion case. We clarify that the relativistic analysis based on time averaging is valid for scales larger than the Compton wavelength. Below the Compton wavelength, the field is not oscillating, and our oscillatory ansatz does not apply. We suggest an equation valid in all scales in the comoving gauge. For comparison, we review the non-relativistic quantum hydrodynamics and present the Schrödinger equation to first-order post-Newtonian expansion in the cosmological context.

Induced Vacuum Current and Magnetic Flux in Quantum Scalar Matter in the Background of a Vortex Defect with the Neumann Boundary Condition

A topological defect in the form of the Abrikosov–Nielsen–Olesen vortex in the space of an arbitrary dimension is considered as a gauge-flux-carrying tube that is impenetrable for quantum matter. The charged scalar matter field is quantized in the vortex background with the perfectly rigid (Neumann) boundary condition imposed at the side surface of the vortex. We show that a current circulating around the vortex is induced in the vacuum, if the Compton wavelength of the matter field exceeds the transverse size of the vortex considerably. The vacuum current is periodic in the value of the gauge flux of the vortex, providing a quantum-field-theoretical manifestation of the Aharonov–Bohm effect. The vacuum current leads to the appearance of an induced vacuum magnetic flux that, for some values of the tube thickness, exceeds the vacuum magnetic flux induced by a singular vortex filament. The results are compared to those obtained earlier in the case of the perfectly reflecting (Dirichlet) boundary condition imposed at the side surface of the vortex. It is shown that the absolute value of the induced vacuum current and the induced vacuum magnetic flux in the case of the Neumann boundary condition is greater than in the case of the Dirichlet boundary condition.

The cosmic microwave background and mass power spectrum profiles for a novel and efficient model of dark energy


 
 
 In a previous work [1] it was shown that by considering the quantum nature of the gravitational field mediator, it is possible to introduce the momentum energy of the graviton into the Einstein equations as an effective cosmological constant. The Compton Mass Dark Energy (CMaDE) model proposes that this momentum can be interpreted as dark energy, with a Compton wavelength given by the size of the observable universe RH, implying that the dark energy varies depending on this size. The main result of this previous work is the existence of an effective cosmological constant Λ = 2π2/λ2 that varies very slowly, being λ = (c/H0)RH the graviton Compton wavelength. In the present work we use that the dark energy density rate is given by ΩΛ = 2π2/3/RH2 , it only has the curvature Ωk as a free constant and depends exclusively on the radiation rate Ωr. Using Ωr = 9.54×10−5, the theoretical prediction for a flat universe of the dark energy rate is ΩΛ = 0.6922. We perform a general study for a non-flat universe, using the Planck data and a modified version of the CLASS code we find an excellent concordance with the Cosmic Microwave Background and Mass Power Spectrum profiles, provided that the Hubble parameter today is H0 = 72.6 km/s/Mpc for an universe with curvature Ωk = −0.003. We conclude that the CMaDE model provides a natural explanation for the accelerated expansion and the coincidence problem of the universe.
 
 

Graviton mass from X-COP galaxy clusters

The concept of massive graviton has long been the subject of extensive studies underlying most theories of modified gravity. When the graviton is given a mass, it is a generic feature that, in the weak-field limit, Newtonian potential gets modified by the Yukawa term. This opens up a possibility to constrain the graviton mass (or, equivalently, its Compton wavelength) based on dynamical properties of objects at different astrophysical scales, e.g. galaxy cluster scale. In this paper we address this question with X–COP galaxy cluster sample, where total masses up to certain radii were measured by using X-ray data from XMM-Newton telescope combined with Sunyaev-Zel'dovich data from Planck satellite. Our constraint for graviton mass of about mg<(4.99−6.79)×10−29eV (at 95% C.L.) is one of the most stringent available bounds. First assessments of mg<1.2×10−22eV made by LIGO/Virgo collaboration are complementary to ours since they are based on modified dispersion relation for gravitons. Synergy between gravitational wave domain and dynamical tests of the Yukawa term would be very promising in the nearest future.

The Heisenberg Limit at Cosmological Scales

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at $$m_\mathrm{H}=1.35 \times 10^{-69}$$ kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to $$m_\mathrm{H}$$ is , and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, is equated to the luminosity distance $$d_\mathrm{H}$$ which corresponds to a red shift $$z_\mathrm{H}$$ . When using the Concordance-Model parameters, we get $$d_\mathrm{H} = 8.4$$ Gpc and $$z_\mathrm{H}=1.3$$ . Remarkably, $$d_\mathrm{H}$$ falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond $$z_\mathrm{H}$$ . Finally, in terms of quantum quantities, the expansion constant $$H_0$$ reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant.

Non-linear density–velocity dynamics in f(R) gravity from spherical collapse

ABSTRACT We investigate the joint density–velocity evolution in f(R) gravity using smooth, compensated spherical top-hats as a proxy for the non-linear regime. Using the Hu-Sawicki model as a working example, we solve the coupled continuity, Euler, and Einstein equations using an iterative hybrid Lagrangian–Eulerian scheme. The novel aspect of this scheme is that the metric potentials are solved for analytically in the Eulerian frame. The evolution is assumed to follow GR at very early epochs and switches to f(R) at a pre-determined epoch. Choosing the ‘switching epoch’ too early is computationally expensive because of high frequency oscillations; choosing it too late potentially destroys consistency with ΛCDM. To make an informed choice, we perform an eigenvalue analysis of the background model which gives a ballpark estimate of the magnitude of oscillations. There are two length scales in the problem: the comoving Compton wavelength of the associated scalar field and the width of the top-hat. The evolution is determined by their ratio. When the ratio is large, the evolution is scale-independent and the density–velocity divergence relation (DVDR) is unique. When the ratio is small, the evolution is very close to GR, except for the formation of a spike near the top-hat edge, a feature which has been noted in earlier literature. We are able to qualitatively explain this feature in terms of the analytic solution for the metric potentials, in the absence of the chameleon mechanism. In the intermediate regime, the evolution is profile-dependent and no unique DVDR exists.

Electron Mass Is Specified by Five Fundamental Constants, &amp;lt;i&amp;gt;a&amp;lt;/i&amp;gt;, &amp;lt;i&amp;gt;&amp;amp;hstrok;&amp;lt;/i&amp;gt;, &amp;lt;i&amp;gt;G&amp;lt;/i&amp;gt;, &amp;amp;Lambda;, and &amp;amp;Omega;&amp;lt;sub&amp;gt;&amp;amp;Lambda;&amp;lt;/sub&amp;gt;, from Quantum Mechanics and General Relativity

Electron mass has been considered a fundamental constant of nature that cannot be calculated from other constants such as Planck’s constant &hstrok; and gravitational constant G. In contrast, holographic analysis takes account of the finite amount of information available to describe the universe and specifies electron mass to six significant figures in terms of five fundamental constants: fine structure constant a, &hstrok; , G, cosmological constant Λ, and vacuum fraction ΩΛ of critical density. A holographic analysis accounts for charge conservation, mass quantization, and baryon/antibaryon ratio. A holographic analysis relates electromagnetism and gravitation, specifies electron Compton wavelength in terms of Planck length and cosmological event horizon radius, and has implications for charged Standard Model fermion masses, minimum stellar mass at redshift z, and use of continuum mathematics in a discontinuous universe.

Quantum Mechanics and General Relativity Identify Standard Model Particles as Black Holes

The Standard Model of particle physics does not account for charged fermion mass values and neutrino mass, or explain why only three particles are in each charge state 0, -e/3, 2e/3, and -e. These issues are addressed by treating Standard Model particles with mass m as spheres with diameter equal to their Compton wavelength l =ħ/mc, where ħ is Planck’s constant and c the speed of light, and any charge in diametrically opposed pairs ±ne/6 with n = 1, 2, or 3 at the axis of rotation on the sphere surface. Particles are ground state solutions of quantized Friedmann equations from general relativity, with differing internal gravitational constants. Energy distribution within particles identifies Standard Model particles with spheres containing central black holes with mass m, and particle spin resulting from black hole angular momentum. In each charge state, energy distribution within particles satisfies a cubic equation in l, allowing only three particles in the charge state and requiring neutrino mass. Cosmic vacuum energy density is a lower limit on energy density of systems in the universe, and setting electron neutrino average energy density equal to cosmic vacuum energy density predicts neutrino masses consistent with experiment. Relations between charged fermion wavelength solutions to cubic equations in different charge states determine charged fermion masses relative to electron mass as a consequence of charge neutrality of the universe. An appendix shows assigning charge ±e/6 to bits of information on the event horizon available for holographic description of physics in the observable universe accounts for dominance of matter over anti-matter. The analysis explains why only three Standard Models are in each charge state and predicts neutrino masses based on cosmic vacuum energy density as a lower bound on neutrino energy density.

Newton Did Not Invent or Use the So-Called Newton’s Gravitational Constant; &amp;lt;i&amp;gt;G&amp;lt;/i&amp;gt;, It Has Mainly Caused Confusion

Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass; namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength.

Is the Higgs Field a Positive and Negative Mass Planckion Condensate, and Does the LHC Produce Extreme Dark Energy?

Assuming a two-component, positive and negative mass, superfluid/supersolid for space (the Winterberg model), we model the Higgs field as a condensate made up of a positive and a negative mass, planckion pair. The connection is shown to be consistent (compatible) with the underlying field equations for each field, and the continuity equation is satisfied for both species of planckions, as well as for the Higgs field. An inherent length scale for space (the vacuum) emerges, which we estimate from previous work to be of the order of, l+ (0) = l- (0) = 5.032E-19 meters, for an undisturbed (unperturbed) vacuum. Thus we assume a lattice structure for space, made up of overlapping positive and negative mass wave functions, ψ+, and, ψ-, which together bind to form the Higgs field, giving it its rest mass of 125.35 Gev/c2 with a coherence length equal to its Compton wavelength. If the vacuum experiences an extreme disturbance, such as in a LHC pp collision, it is conjectured that severe dark energy results, on a localized level, with a partial disintegration of the Higgs force field in the surrounding space. The Higgs boson as a quantum excitation in this field results when the vacuum reestablishes itself, within 10-22 seconds, with positive and negative planckion mass number densities equalizing in the disturbed region. Using our fundamental equation relating the Higgs field, φ, to the planckion ψ+ and ψ- wave functions, we calculate the overall vacuum pressure (equal to vacuum energy density), as well as typical ψ+ and ψ- displacements from equilibrium within the vacuum.

A New Theory of the Essence and Mass of Photon

Many properties of a single photon, such as density, rest mass, and orbital angular momentum, are still unknown. In a previous study, the photon was presented as a superfluid prolate spheroid structure, with a long-axis radius, short-axis radius, and volume, embodied with two spins—transversal and longitudinal—which are responsible for the three-dimensional helical trajectory of the electromagnetic wave. In this study, the rest mass, density, and energy of photon are mathematically derived, and the relationship between the radius of photon and its frequency is demonstrated. In addition, the difference between the Compton and de Broglie wavelengths is clarified. The calculated density, volume, and rest mass of photon agree with previous experimental results. The photon’s simultaneous longitudinal and transversal spins are moving forces of longitudinal and transversal trajectories, which are the origin of the three-dimensional helix shape of the electromagnetic field. A new mechanism for the photon movement is proposed, and the reason for the zero mass moving photon is revealed; a traveling photon in space exhibits zero mass because its boundaries demonstrate zero relative velocity with the surrounding vacuum. The orbital angular momentum of photon is described using similar macroscopic rotation concepts and applying hydrodynamics laws. A rotating photon is endowed with an angular velocity vector whose magnitude measures the speed with which the radius of the principal axis sweeps an angle, and whose direction indicates the principal axis of rotation and is given by the right-hand rule. The deviation angle is calculated using trigonometric functions, and the origin of the Lorenz factor is revealed.

Exceedingly Small Quantum of Time Kshana Explains the Structure of an Electron

In this study, an effort is made to find the attributes of an electron based on Maharishi Vyasa’s definition of kshana or moment. Kshana or moment is a very small quanta of time defined by Maharishi Vyasa. It is the time taken by an elementary particle to change the direction from east to north. It is found that the value of a kshana in the case of pair production is approximately 2 × 10-21 sec, and the radius of the spinning electron or positron is equal to the reduced Compton wavelength. The mass of the electron is equal to the codata recommended value of electron mass and time required in pair production is about four kshanas equal to spinning period of an electron. During validation, in case of the photoelectric effect, spectral series of hydrogen atoms, Compton scattering, and the statistical concept of motion of electron, the value of the number of kshanas in a second is the same as that found in pair production.

Universal semiclassical equations based on the quantum metric for a two-band system

We derive semiclassical equations of motion for an accelerated wavepacket in a two-band system. We show that these equations can be formulated in terms of the static band geometry described by the quantum metric. We consider the specific cases of the Rashba Hamiltonian with and without a Zeeman term. The semiclassical trajectories are in full agreement with the ones found by solving the Schr\"odinger equation. This formalism successfully describes the adiabatic limit and the anomalous Hall effect traditionally attributed to Berry curvature. It also describes the opposite limit of coherent band superposition giving rise to a spatially oscillating Zitterbewegung motion. At $k=0$, such wavepacket exhibits a circular trajectory in real space, with its radius given by the square root of the quantum metric. This quantity appears as a universal length scale, providing a geometrical origin of the Compton wavelength.

Acceleration in quantum mechanics and electric charge quantization

In this study, we have discussed the implications of acceleration in quantum mechanics by means of a generalized derivative operator (GDO). A new Schrödinger equation is obtained which depends on the reduced Compton wavelength of the particle. We have discussed its implications in quantum mechanics for different types of potentials mainly the infinite wall potential, the gravitational linear field potential, the Cornell potential and the Coulomb repulsive potential. The corresponding wave functions and discrete energies are modified and differ from the results obtained in the conventional formalism. The major results obtained concerned the large improvement of the ground energy of the electron subject to the gravitational acceleration in addition to Cornell potential and the emergence of quantized electric charge in the theory without including Dirac monopoles or using gauge theories.

Fifth-force screening around extremely compact sources

Many non-linear scalar field theories possess a screening mechanism that can suppress any associated fifth force in dense environments. As a result, these theories can evade local experimental tests of new forces. Chameleon-like screening, which occurs because of non-linearities in the scalar potential or the coupling to matter, is well understood around extended objects. However, many experimental tests of these theories involve objects with spatial extent much smaller than the scalar field's Compton wavelength, and which could therefore be considered point-like. In this work, we determine how the fifth forces are screened in the limit that the source objects become extremely compact.

Area Entropy and Quantized Mass of Black Holes from Information Theory

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.