Compton Wavelength Research Articles

The graviton Compton mass as Dark Energy

One of the greatest challenges of science is to understand the current accelerated expansion of the Universe. In this work we show that by considering the quantum nature of the gravitational field, its wavelength can be associated to an effective Compton mass. We propose that this mass can be interpreted as dark energy, with a Compton wavelength given by the size of the observable Universe, implying that the dark energy varies depending on this size. If we do so, we find that: 1.- Even without any free constant for dark energy, the evolution of the Hubble parameter is exactly the same as for the LCDM model, so this model has the same predictions as LCDM. 2.- The density rate of the dark energy is ΩΛ = 0.69 which is a very similar value as the one found by the Planck satellite ΩΛ = 0.684. 3.- The dark energy has this value because it corresponds to the actual size of the radius of the Universe, thus the coincidence problem has a very natural explanation. 4.- It is possible to find also a natural explanation to why observations inferred from the local distance ladder find the value H0 = 73 km/s/Mpc for the Hubble constant, we show that if we take the variability of the dark energy into account they should measure H0 = 67.3 km/s/Mpc as well. 5.- In this model the inflationary period contains a natural successful graceful exit.

An effective field theory of holographic dark energy

A general covariant local field theory of the holographic dark energy model is presented. It turns out the low energy effective theory of the holographic dark energy is the massive gravity theory whose graviton has 3 polarisations, including one scalar mode and two tensor modes. The Compton wavelength is the size of the future event horizon of the universe. The UV-IR correspondence in the holographic dark energy model stems from the scalar graviton's strong coupling at the energy scale that marks the breaking down of the effective field theory.

Quantum measurement of space-time events

The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is endowed with a natural positive-definite Riemannian metric that accommodates the underlying geometry of the indefinite Minkowski space metric, together with its symmetry group. A unitary representation of the 15-parameter group of conformal transformations can then be constructed that acts upon the Hilbert space of square-integrable holomorphic functions on the future tube. These structures are enough to allow one to put forward a quantum theory of phase-space events. In particular, a theory of quantum measurement can be formulated in a relativistic setting, based on the use of positive operator valued measures, for the detection of phase-space events, hence allowing one to assign probabilities to the outcomes of joint space-time and four-momentum measurements in a manifestly covariant framework. This leads to a localization theorem for phase-space events in relativistic quantum theory, determined by the associated Compton wavelength.

The graviton Compton mass as dark energy

One of the greatest challenges of science is to understand the current accelerated expansion of the Universe. In this work we show that by considering the quantum nature of the gravitational field, its wavelength can be associated to an effective Compton mass. We propose that this mass can be interpreted as dark energy, with a Compton wavelength given by the size of the observable Universe, implying that the dark energy varies depending on this size. If we do so, we find that: 1.- Even without any free constant for dark energy, the evolution of the Hubble parameter is exactly the same as for the LCDM model, so this model has the same predictions as LCDM. 2.- The density rate of the dark energy is ΩΛ = 0.69 which is a very similar value as the one found by the Planck satellite ΩΛ = 0.684. 3.- The dark energy has this value because it corresponds to the actual size of the radius of the Universe, thus the coincidence problem has a very natural explanation. 4.- It is possible to find also a natural explanation to why observations inferred from the local distance ladder find the value H0 = 73 km/s/Mpc for the Hubble constant, we show that if we take the variability of the dark energy into account they should measure H0 = 67.3 km/s/Mpc as well. 5.- In this model the inflationary period contains a natural successful graceful exit.

Constraining light dark photons from GW190517_055101 and GW190426_152155

Ultralight dark photons predicted in several Standard Model extensions can trigger the superradiant instability around rotating black holes (BHs) if their Compton wavelength is comparable to the BH radius. Consequently, the angular momentum of the BH is reduced to a value which depends upon the mass and spin of the BH as well as the mass of the dark photon. We use the mass and spin measurements of the primary BHs in two recently observed blackhole binary (BBH) systems, GW190517_055101 and GW190426_152155, to constrain dark photon mass in the ranges $1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{eV}<{m}_{{A}^{\ensuremath{'}}}<7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}$ and $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{eV}<{m}_{{A}^{\ensuremath{'}}}<4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{eV}$, respectively, assuming a timescale of a few million years from the time of formation of the BBH system to the time of their merger. We also discuss an interesting x-ray binary system, MAXI J1820_070, albeit with a relatively small value of the spin parameter.

Magnetic dominance of axion electrodynamics: photon capture effect and anisotropy of Coulomb potential

For magnetic fields larger than the characteristic scale linked to axion-electrodynamics, quantum vacuum fluctuations due to axion-like fields can dominate over those associated with the electron-positron fields. This conjecture is explored by investigating both the axion-modified photon capture by a strong magnetic field and the Coulomb potential of a static pointlike charge. We show that in magnetic fields characteristic of neutron stars sim 10^{13}–10^{15};mathrm{G}, the capture of gamma photons prior to the production of a pair can prevent the existence of an electron-positron plasma, essential for explaining the pulsar radiation mechanism. This incompatibility is used to limit the axion parameter space. Our bounds improve existing outcomes in the region of mass msim 10^{-10}–10^{-5};{mathrm{eV}}. The effect of capture, known in QED as relating to gamma-quanta, is extended in axion electrodynamics to include X-ray photons with the result that a specially polarized part of the heat radiation from the surface is canalized along the magnetic field. Besides, we find that in the regime in which the dominance takes place, the running QED coupling depends on the field strength and the modified Coulomb potential is of Yukawa-type in the direction perpendicular to the magnetic field at distances much smaller than the axion Compton wavelength, while along the field it follows approximately the Coulomb law at any length scale. Despite the Coulomb singularity manifested in the latter case, we argue that the ground-state energy of a non-relativistic hydrogen atom placed in a strong magnetic field turns out to be bounded due to the nonrenormalizable feature of axion-electrodynamics.

Searching for ultralight bosons within spin measurements of a population of binary black hole mergers

Ultralight bosons can form clouds around rotating black holes if their Compton wavelength is comparable to the black hole size. The boson cloud spins down the black hole through a process called superradiance, lowering the black hole spin to a characteristic value. It has been suggested that spin measurements of the black holes detected by ground-based gravitational-wave detectors can be used to constrain the mass of ultralight bosons. Unfortunately, a measurement of the individual black hole spins is often uncertain, resulting in inconclusive results. Instead, we use hierarchical Bayesian inference to combine information from multiple gravitational-wave sources and obtain stronger constraints. We show that hundreds of high signal-to-noise ratio gravitational-wave detections are enough to exclude (confirm) the existence of non-interacting bosons in the mass range $\left[10^{-13},3\times 10^{-12}\right]~\rm{eV}$ $\left([10^{-13},10^{-12}]~\rm{eV}\right)$. The precise number depends on the distribution of black hole spins at formation and the mass of the boson. From the few uninformative spin measurements of binary black hole mergers detected by LIGO and Virgo in their first two observing runs, we cannot draw statistically significant conclusions.

Ambiguities in the definition of local spatial densities in light hadrons

The relationship between the matrix element of a local operator and the Fourier transform of the associated form factor fails for systems such as the nucleon where its intrinsic size is of order its Compton wavelength. Although one can conceive of an intrinsic charge density distribution in the proton, there does not seem to be an unambiguous way to define, compute, or measure it precisely.

Unveiling the transverse formation length of nonlinear Compton scattering

The process of emission of electromagnetic radiation does not occur instantaneously but it is "formed" over a finite time known as radiation formation time. In the ultrarelativistic regime, the corresponding (longitudinal) formation length is given by the formation time times the speed of light and controls several features of radiation. Here, we elucidate the importance of the transverse formation length (TFL) by investigating nonlinear Compton scattering by an electron initially counterpropagating with respect to a \emph{flying focus} laser beam. The TFL is related to the transverse size of the radiation formation "volume" and, unlike the longitudinal formation length, has a quantum origin. Being the TFL typically of the order of the Compton wavelength, where any laser field can be assumed to be approximately uniform, related quantum interference effects have been ignored. However, we show analytically that if the focus in a flying focus beam with $n_L\gg 1$ cycles moves at the speed of light and backwards with respect to the beam propagation direction, the effects of the TFL undergo a large enhancement proportional to $n_L$ and may substantially alter the differential emission probability for feasible flying focus pulses.

Koide Lepton Relation Explained by Lepton Radius (Compton Wavelength)/4

The intriguing Koide relation between lepton masses, , involving electron mass me, muon mass mμ, and tau mass mt, was first presented in 1982. The reason why Q1 ≈ 2/3 has long been unclear. However, describing Standard Model fermions as spheres with radius (Compton wavelength)/4, allows only three fermions in each charge state and avoids the infinite energy density of point particles. Then the Koide parameter Q1 ≈ 2/3 because the electron Compton wavelength is more than 200 times the muon and tau Compton wavelengths. A tau mass equivalent of 1776.98 MeV, within experimental error bars, would result in Q1 = 2/3. The analysis is discussed in the context of efforts to extend the Standard Model of particle physics.

Standard Model Masses Explained

The Standard Model of particle physics requires nine lepton and quark masses as inputs, but does not incorporate neutrino masses required by neutrino oscillation observations. This analysis addresses these problems, explaining Standard Model particle masses by describing fundamental particles as solutions of Einstein’s equations, with radii 1/4 their Compton wavelength and half of any charge on rotating particles located on the surface at each end of the axis of rotation. The analysis relates quark and lepton masses to electron charge and mass, and identifies neutrino masses consistent with neutrino oscillation observations.

Various Empirical Equations for the Electromagnetic Force in Terms of the Cosmic Microwave Background Temperature

Previously, we proposed an empirical equation describing the relationship between the gravitational force and the temperature of the cosmic microwave background (CMB). After evaluating our equation, we discovered many empirical equations describing the electromagnetic force in terms of the CMB, including equations for the Rydberg constant, the Bohr radius, the Compton wavelength, the classical electron radius, the Hartree energy, the Coulomb’s law with distance, and the ratio between the gravitational force and electric force. The background theory is not yet complete. However, we can justify why the discovered empirical equations should not be coincidence.

The Size and Shape of a Single Photon

The size and shape of a single photon is a property of photon shown in the collision of the photon with charged particles. Applying scattering theory and classical electrodynamics is the most reliable way to solve this problem. The main intention of this paper is to reveal the electromagnetic structure of a single photon. It establishes the formulas for the Poynting vector (energy flow vector) and the energy density. Applying the new explanation of Compton wavelength creates the probability formula for the Compton effect when a photon collides with an electron. The research discovers that the electromagnetic field of a single linearly polarized photon confines to a membrane-like cuboid, while the electromagnetic field of a single circularly polarized photon confines to a membrane-like shell of a hollow cylinder.

Quenching mechanisms of photon superradiance

Rapidly rotating black holes are known to develop instabilities in the presence of a sufficiently light boson, a process which becomes efficient when the boson's Compton wavelength is roughly the size of the black hole. This phenomenon known as black hole superradiance generates an exponentially growing boson cloud at the expense of the rotational energy of the black hole. For astrophysical black holes with $M\ensuremath{\sim}\mathcal{O}(10){M}_{\ensuremath{\bigodot}}$, the superradiant condition is achieved for bosons with ${m}_{b}\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}11})\text{ }\text{ }\mathrm{eV}$; intriguingly, photons traversing the intergalactic medium acquire an effective mass (due to their interactions with the ambient plasma) which naturally resides in this range. The implications of photon superradiance, i.e., the evolution of the superradiant photon cloud and ambient plasma in the presence of scattering and particle production processes, have yet to be thoroughly investigated. Here, we enumerate and discuss a number of different processes capable of quenching the growth of the photon cloud, including particle interactions with the ambient electrons and backreactions on the effective mass (arising e.g., from thermal effects, pair production, ionization of the local background, and modifications to the dispersion relation from strong electric fields). This work naturally serves as a guide in understanding how interactions may allow light exotic bosons to evade superradiant constraints.

Galaxy morphology rules out astrophysically relevant Hu-Sawicki f(R) gravity

$f(R)$ is a paradigmatic modified gravity theory that typifies extensions to General Relativity with new light degrees of freedom and hence screened fifth forces between masses. These forces produce observable signatures in galaxy morphology, caused by a violation of the weak equivalence principle due to a differential impact of screening among galaxies' mass components. We compile statistical datasets of two morphological indicators -- offsets between stars and gas in galaxies and warping of stellar disks -- and use them to constrain the strength and range of a thin-shell-screened fifth force. This is achieved by applying a comprehensive set of upgrades to past work (Desmond et al 2018a,b): we construct a robust galaxy-by-galaxy Bayesian forward model for the morphological signals, including full propagation of uncertainties in the input quantities and marginalisation over an empirical model describing astrophysical noise. Employing more stringent data quality cuts than previously we find no evidence for a screened fifth force of any strength $\Delta G/G_\text{N}$ in the Compton wavelength range $0.3-8$ Mpc, setting a $1\sigma$ bound of $\Delta G/G_\text{N}<0.8$ at $\lambda_C=0.3$ Mpc that strengthens to $\Delta G/G_\text{N}<3\times10^{-5}$ at $\lambda_C=8$ Mpc. These are the tightest bounds to date beyond the Solar System by over an order of magnitude. For the Hu-Sawicki model of $f(R)$ with $n=1$ we require a background scalar field value $f_{R0} < 1.4 \times 10^{-8}$, forcing practically all astrophysical objects to be screened. We conclude that this model can have no relevance to astrophysics or cosmology.

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

Planck length: Lost + found

At mesoscopic scales, close to but somewhat larger than Planck length, one can describe the spacetime in terms of an effective geometry. The key feature of such an effective (quantum) geometry is the existence of a zero-point-length which, for example, modifies the propagator for a massive scalar field residing in that spacetime, in a specific manner. Such quantum gravitational effects arise, even in a globally flat spacetime, if one probes the spacetime at length scales close to Planck length. Principle of Equivalence demands that the effects of quantum spacetime observed in a freely-falling-frame (FFF) must be the same as those in a globally flat spacetime. But, in the FFF, gravity disappears and — along with it — the Newtonian gravitational constant G also disappears; therefore, operationally, the Planck length disappears in the FFF! So how can the quantum gravitational effects persist in the FFF, as they must? I show that the answer to this question is interesting and subtle. The Planck length reappears in FFF through the matter sector as the geometric mean LP=λcλg of the Compton wavelength λc=ħ/mic (where mi is the inertial mass) and the Schwarzschild radius λg=Gmg/c2 (where mg is the gravitational mass) when we invoke the Principle of Equivalence again, in the form mi=mg. So the Principle of Equivalence plays a crucial role in making the Planck length disappear and reappear to incorporate the effects of quantum spacetime in a FFF.

Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave

We consider the hydrodynamic quantum field theory proposed by Dagan and Bush, a model of quantum dynamics inspired by Louis de Broglie and informed by the hydrodynamic pilot-wave system discovered by Couder and Fort. According to this theory, a quantum particle has an internal vibration at twice the Compton frequency that generates disturbances in an ambient scalar field, the result being self-propulsion of the particle through a resonant interaction with its pilot-wave field. Particular attention is given here to providing theoretical rationale for the geometric form of the wave field generated by steady, rectilinear particle motion at a prescribed speed, where signatures of both the de Broglie and Compton wavelengths are generally evident. While focus is given to the one-dimensional geometry considered by Dagan and Bush, we also deduce the form of the pilot wave in two dimensions. We further consider the influence on the pilot-wave form of the details of the particle-induced wave generation, specifically the spatial extent and vibration frequency of the particle. Finally, guided by analogous theoretical descriptions of the hydrodynamic system, we recast the particle dynamics in terms of an integro-differential trajectory equation. Analysis of this equation in the non-relativistic limit reveals a critical wave-particle coupling parameter, above which the particle self-propels. Our results provide the foundation for subsequent theoretical investigations of hydrodynamic quantum field theory, including the stability analysis of various dynamical states.

New graviton mass bound from binary pulsars

In Einstein's general relativity, gravity is mediated by a massless metric field. The extension of general relativity to consistently include a mass for the graviton has profound implications for gravitation and cosmology. Salient features of various massive gravity theories can be captured by Galileon models, the simplest of which is the cubic Galileon. The presence of the Galileon field leads to additional gravitational radiation in binary pulsars where the Vainshtein mechanism is less suppressed than its fifth-force counterpart, which deserves a detailed confrontation with observations. We prudently choose fourteen well-timed binary pulsars, and from their intrinsic orbital decay rates we put a new bound on the graviton mass, $m_g \lesssim 2 \times 10^{-28}\,{\rm eV}/c^2$ at the 95% confidence level, assuming a flat prior on $\ln m_g$. It is equivalent to a bound on the graviton Compton wavelength $\lambda_g \gtrsim 7 \times 10^{21}\,{\rm m}$. Furthermore, we extensively simulate times of arrival for pulsars in orbit around stellar-mass black holes and the supermassive black hole at the Galactic center, and investigate their prospects in probing the cubic Galileon theory in the near future.

Constraint on the Yukawa suppression of the Newtonian potential from the planetary ephemeris INPOP19a

We use the latest solution of the ephemeris INPOP (19a) in order to improve our previous constraint on the existence of a Yukawa suppression to the Newtonian potential, generically associated to a graviton's mass. Unlike the ephemeris INPOP17a, several residuals are found to degrade significantly at roughly the same amplitudes of the Compton wavelength $\lambda_g$. As a consequence, we introduce a novel statistical criterion in order to derive the constraint with INPOP19a. After checking that it leads to a constraint consistent with our previous result when applied on INPOP17b, we apply the method to the new solution INPOP19a. We show that the residuals of Mars orbiters, Cassini, Messenger, and Juno, degrade significantly when $\lambda_g \leq$ $3.43 \times 10^{13}$ km with a 99,7% confidence level -- corresponding to a graviton mass bigger than $3.62 \times 10^{-23}$ eV$/c^2$. This is a stronger constraint on the Compton wavelength than the one obtained from the first gravitational-wave transient catalog by the LIGO-Virgo collaboration in the radiative regime, since our 90% C.L. limit reads $\lambda_g >3.93 \times 10^{13}$ km ($m_g <3.16 \times 10^{-23}$ eV$/c^2$).