arXiv subjects

Jukka Tulkki

Publications and source records attributed to Jukka Tulkki.

At least 19 recordsLinked to original sources

arXiv2025

Light deflection in unified gravity and measurable deviation from general relativity in the second post-Newtonian order

Light does not travel in a perfectly straight line when it passes near massive objects. In this work, we calculate the gravitational deflection of light using the gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)], formulated as an extension of the Standard Model. The nonlinear graviton-graviton interaction is accounted for in the lowest order. The dynamical equations of light in external gravitational field in unified gravity are essentially different from the dynamical equations obtained using the curved metric of general relativity. The goal of the present work is to compare the predictions of unified gravity and general relativity for the gravitational deflection of light. Since the calculation of the gravitational deflection of light in unified gravity is fundamentally different from the pertinent calculation in general relativity, we devote ample space for approximations used. The deflection angles obtained from unified gravity and general relativity are equal in the first post-Newtonian (PN) order, and agree with previous experiments available for the Sun. However, the second PN order terms of unified gravity reveal measurable relative differences of $7/30\approx23.3\%$ and $4/15\approx26.7\%$ for the out-of-plane and in-plane polarizations, respectively, in comparison with the polarization-independent value of general relativity. Therefore, we expect that experimentally differentiating between the two theories will become possible in the near future. For future experiments, we also make calculations for other astrophysical objects, such as for a neutron star, which is in the limit of the PN approximation. The application of unified gravity to black holes, for which the PN approximation is not valid, is left as a topic of further work.

gr-qc↗

arXiv2025

Extending unified gravity to account for graviton-graviton interaction

Recently, a gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)] has been developed to extend the Standard Model to include gravity. Here we present unified gravity using the ordinary four-vector and tensor field notation of the Standard Model. The main goal of the present work is to extend the original Minkowski spacetime formulation of the theory to account for graviton-graviton interaction. This is a necessary extension for problems involving interactions between gravitational fields, for example, in the propagation of gravitational waves in external gravitational potentials. The 4xU(1) gauge invariance of unified gravity is preserved in this extension.

gr-qc↗

arXiv2025

Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model

The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has been challenging due to incompatibilities of the underlying theories - general relativity and quantum field theory. While quantum field theory utilizes compact, finite-dimensional symmetries associated with the internal degrees of freedom of quantum fields, general relativity is based on noncompact, infinite-dimensional external space-time symmetries. The present work derives the gauge theory of gravity using compact, finite-dimensional symmetries in a way that resembles the formulation of the fundamental interactions of the Standard Model. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field. Four U(1) symmetries of the space-time dimension field are used to derive a gauge theory, called unified gravity. The teleparallel equivalent of general relativity in the Weitzenböck gauge is obtained from unified gravity by a gravity-gauge-field-dependent geometric condition. Unified gravity also enables a gravity-gauge-field-independent geometric condition that preserves the Minkowski metric. This differs from the use of metric in general relativity, where the metric depends on the gravitational field by definition. We study the renormalizability and radiative corrections of the theory at 1-loop order. The equivalence principle is formulated by requiring that the renormalized values of the inertial and gravitational masses are equal. In contrast to previous theories of gravity, all infinities that are encountered in the calculations of loop diagrams can be absorbed by the redefinition of the small number of parameters of the theory in the same way as in the gauge theories of the Standard Model.

gr-qc↗

arXiv2025

Atomic Dirac energy-level dynamics and redshift in the 4xU(1) gravity gauge field

Gravitational interaction unavoidably influences atoms and their electromagnetic radiation field in strong gravitational fields. Theoretical description of such effects using the curved metric of general relativity is limited due to the classical nature of the metric and the assumption of the local inertial frame, where gravitational interaction is absent. Here we apply unified gravity extension of the Standard Model [Rep. Prog. Phys. 88, 057802 (2025)] to solve the Dirac equation for hydrogen-like atoms in the 4xU(1) gravity gauge field, which appears alongside all other quantum fields. We show that the gravity gauge field shifts the atomic Dirac energy levels by an amount that agrees with the experimentally observable gravitational redshift. Our result for the redshift follows directly from quantum field theory and is strictly independent of the metric-based explanation of general relativity. Furthermore, we present how gravitational potential gradient breaks the symmetry of the electric potential of the atomic nucleus, thus leading to splitting of otherwise degenerate spectral lines in strong gravitational fields. Enabling detailed spectral line analysis, our work opens novel possibilities for future investigations of quantum photonics phenomena in strong gravitational fields.

quant-ph↗

arXiv2025

Perihelion precession of planetary orbits solved from quantum field theory

We derive the perihelion precession of planetary orbits using quantum field theory extending the Standard Model to include gravity. Modeling the gravitational bound state of an electron via the Dirac equation of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)], and taking the classical planetary state limit, we obtain orbital dynamics exhibiting a precession in agreement with general relativity. This demonstrates that key general relativistic effects in planetary motion can emerge directly from quantum field theory without invoking the geometric framework of general relativity.

gr-qc↗

arXiv2024

QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity

Quantum electrodynamics (QED) is the most accurate of all experimentally verified physical theories. How QED and other theories of fundamental interactions couple to gravity through special unitary symmetries, on which the standard model of particle physics is based, is, however, still unknown. Here we develop a coupling between the electromagnetic field, Dirac electron-positron field, and the gravitational field based on an eight-component spinorial representation of the electromagnetic field. Our spinorial representation is analogous to the well-known representation of particles in the Dirac theory but it is given in terms of 8x8 bosonic gamma matrices. In distinction from earlier works on the spinorial representations of the electromagnetic field, we reformulate QED using eight-component spinors. This enables us to introduce the generating Lagrangian density of gravity based on the special unitary symmetry of the eight-dimensional spinor space. The generating Lagrangian density of gravity plays, in the definition of the gauge theory of gravity and its symmetric stress-energy-momentum tensor source term, a similar role as the conventional Lagrangian density of the free Dirac field plays in the definition of the gauge theory of QED and its electric four-current density source term. The fundamental consequence, the Yang-Mills gauge theory of unified gravity, is studied in a separate work [arXiv:2310.01460], where the theory is also extended to cover the other fundamental interactions of the standard model. We devote ample space for details of the eight-spinor QED to provide solid mathematical basis for the present work and the related work on the Yang-Mills gauge theory of unified gravity.

physics.gen-ph↗

arXiv2024

Chiral-stress-energy-momentum tensor for covariant description of spin and torque densities of light

The measurement of the spin angular momentum of circularly polarized light by Beth [Phys. Rev. 50, 115 (1936)] can be explained by using a microscopic torque density. However, the experiment does not resolve the space- and time-dependent evolution of the spin density of light and the wave plate and the covariant form of the microscopic torque density. Here we focus on the covariant description of the helicity, spin, and torque densities of light in materials using the chiral-stress-energy-momentum tensor. We also perform simulations of Gaussian light pulses in quarter-wave-plate geometries made of birefringent and dielectric materials.

physics.optics↗

arXiv2023

Time-dependent theory of optical electro- and magnetostriction

Electrostriction, the deformation of dielectric materials under the influence of an electric field, is of continuous interest in optics. The classic experiment by Hakim and Higham [Proc. Phys. Soc. 80, 190 (1962)] for a stationary field supports a different formula of the electrostrictive force density than the recent experiment by Astrath et al. [Light Sci. Appl. 11, 103 (2022)] for an optical field. In this work, we study the origin of this difference by developing a time-dependent covariant theory of optical force densities in photonic materials. When a light pulse propagates in a bulk dielectric, the field-induced force density consists of two parts: (i) The optical wave momentum force density carries the wave momentum of light and drives forward a mass density wave of the covariant coupled field-material state of light. (ii) The optostrictive force density arises from the atomic density dependence of the electric and magnetic field energy densities. It represents an optical Lorentz-force-law-based generalization of the electro- and magnetostrictive force densities well known for static electromagnetic fields and derived from the principle of virtual work. Since the work done by the optostrictive force density is not equal to the change of the field energy density during the contraction of the material, we have to describe this difference by optostriction-related dissipation terms to fulfill the energy conservation. The detailed physical model of the dissipation is left for further works. The optostrictive force density can be understood in terms of field-induced pair interactions inside the material. Because of the related action and reaction effects, this force density cannot contribute to the net momentum transfer of the optical field. We also use the theory to simulate the propagation of a Gaussian light pulse through a dielectric material.

physics.optics↗

arXiv2022

Time-dependent optical force theory for optomechanics of dispersive 3D photonic materials and devices

We present a position- and time-dependent optical force theory for optomechanics of dispersive 3D photonic materials and devices. The theory applies to media including material interfaces, waveguides, and general photonic crystal structures. The theory enables calculation of the dynamical state of the coupled field-material system and the interference of this state with other excitations of the material, such as surface acoustic waves or phonons. As an example, we present computer simulations of energy and momentum flows through a silicon crystal with anti-reflective structured interfaces. Using commercially available simulation tools, the theory can be applied to analyze optical forces in complex photonic materials and devices.

physics.optics↗

arXiv2022

Negative radiation pressure in metamaterials explained by light-driven atomic mass density rarefication waves

The momentum and radiation pressure of light in negative-index metamaterials (NIMs) are commonly expected to reverse their direction from what is observed for normal materials. The negative refraction and inverse Doppler effect of light in NIMs have been experimentally observed, but the equally surprising phenomenon, the negative radiation pressure of light, still lacks experimental verification. We show by simulating the exact position- and time-dependent field-material dynamics in NIMs that the momentum and radiation pressure of light in NIMs can be either positive or negative depending on their subwavelength structure. In NIMs exhibiting negative radiation pressure, the negative total momentum of light is caused by the sum of the positive momentum of the electromagnetic field and the negative momentum of the material. The negative momentum of the material results from the optical force density, which drives atoms backward and reduces the local density of atoms at the site of the light field. In contrast to earlier works, light in NIMs exhibiting negative radiation pressure has both negative total momentum and energy. For the experimental discovery of the negative radiation pressure, one must carefully design the NIM structure and record the joint total pressure of the field and material momentum components.

physics.optics↗

arXiv2021

Covariant theory of light in a dispersive medium

The relativistic theory of the time- and position-dependent energy and momentum densities of light in glasses and other low-loss dispersive media, where different wavelengths of light propagate at different phase velocities, has remained a largely unsolved challenge until now. This is astonishing in view of the excellent theoretical understanding of Maxwell's equations and the abundant experimental measurements of optical phenomena in dispersive media. The challenge is related to the complexity of the interference patterns of partial waves and to the coupling of the field and medium dynamics by the optical force. In this work, we use the mass-polariton theory of light [Phys. Rev. A 96, 063834 (2017)] to derive the stress-energy-momentum (SEM) tensors of the field and the dispersive medium. Our starting point, the fundamental local conservation laws of energy and momentum, is close to that of a recent theoretical work on light in dispersive media by Philbin [Phys. Rev. A 83, 013823 (2011)], which however, excludes the power-conversion and force density source terms describing the coupling between the field and the medium. In the general inertial frame, we present the SEM tensors in terms of Lorentz scalars, four-vectors, and field tensors that reflect in a transparent way the Lorentz covariance of the theory. The SEM tensors of the field and the medium are symmetric, form-invariant, and in full accordance with the covariance principle of the special theory of relativity. The SEM tensor of the coupled field-medium state of light also has zero four-divergence. Therefore, light in a dispersive medium has well-defined four-momentum and rest frame. The volume integrals of the total energy and momentum densities of light agree with the model of mass-polariton quasiparticles having a nonzero rest mass. The predictions of our work are directly accessible to experiments.

physics.optics↗

arXiv2019

Lagrangian dynamics of the coupled field-medium state of light

In the recently introduced mass-polariton (MP) theory of light [Phys. Rev. A 95, 063850 (2017)], the optical force of light drives in a medium forward an atomic mass density wave. In this work, we present the Lagrangian formulation of the MP theory starting directly from the principle of least action and the well-known Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting Euler-Lagrange equations lead directly and without any further postulates to the unique expression of the optical Abraham force that dynamically couples the electromagnetic field and the medium in the MP theory of light. The field-medium coupling is symmetric and bi-directional and it fulfills the law of action and counteraction. The coupled dynamical equations also enable the exact description of the very small kinetic energy of the medium as a part of the total energy of the coupled state of light. Thus, the Lagrangian formulation of the present work is a complementary approach to Lorentz covariance properties of the MP theory discussed in our recent work [Phys. Rev. A 99, 033852 (2019)]. We show how the coupled dynamical equations of the field and the medium can be solved analytically for a Gaussian light pulse. It is astonishing how the simple analytic results for the dynamical equations, the optical force, and the stress-energy-momentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century.

physics.optics↗

arXiv2019

Comment on "Analysis of recent interpretations of the Abraham-Minkowski problem"

In a recent paper [I. Brevik, Phys. Rev. A 98, 043847 (2018)], Brevik analyzed the experiment by Kundu et al. [A. Kundu et al., Sci. Rep. 7, 42538 (2017)] reporting deformation of a graphene oxide (GO) film after it has been irradiated by a laser beam. The two-dimensional atomic force microscope (AFM) line scanning of the deformation of the GO film after switching off the laser beam takes by far too much time for any elastic changes to remain in the AFM scans. Thus, the changes in the GO film are irreversible and the optoelastic model used by Brevik is not applicable. The rough estimates of the kinetic energy and displacement of atoms by the optical force of a light pulse calculated by Brevik are correct, but in making a comparison with the corresponding high-precision results for the kinetic energy and displacement of atoms in our work [M. Partanen et al., Phys. Rev. A 95, 063850 (2017)], the kinetic energy of atoms is confused with their rest energy. The atoms and their masses are displaced forward by the field and their displaced rest energies give rise to an energy flux. The difference of arguments between ours and Brevik's culminates on the question whether the flux of rest energy caused by the displacement of the medium moving with light should be included in the total energy flux. We also show that the four-divergence of the stress-energy-momentum tensor of the mass polariton theory of light is zero.

physics.optics↗

arXiv2019

Lorentz covariance of the mass-polariton theory of light

In the mass-polariton (MP) theory of light formulated by us recently [Phys. Rev. A 95, 063850 (2017)], light in a medium is described as a coupled state of the field and matter. The key result of the MP theory is that the optical force of light propagating in a transparent material drives forward an atomic mass density wave (MDW). In previous theories, it has been well understood that the medium carries part of the momentum of light. The MP theory is fundamentally different since it shows that this momentum is associated with the MDW that carries a substantial atomic mass density and the related rest energy with light. In this work, we prove the Lorentz covariance of the MP theory and show how the stress-energy-momentum (SEM) tensor of the MP transforms between arbitrary inertial frames. We also compare the MP SEM tensor with the conventional Minkowski SEM tensor and show how the well-known fundamental problems of the Minkowski SEM tensor become solved by the SEM tensor based on the MP theory. We have particularly written our work for non-expert readers by pointing out how the Lorentz transformation and various conservation laws and symmetries of the special theory of relativity are fulfilled in the MP theory.

physics.optics↗

arXiv2018

Mass-polariton theory of sharing the total angular momentum of light between the field and matter

Light propagating in a nondispersive medium is accompanied by a mass density wave (MDW) of atoms set in motion by the optical force of the field itself [Phys. Rev. A 95, 063850 (2017)]. This recent result is in strong contrast with the approximation of fixed atoms, which assumes that atoms are fixed to their equilibrium positions when light propagates in a medium and which is deeply rooted in the conventional electrodynamics of continuous media. In many photonic materials, the atoms carry the majority of the total momentum of light and their motion also gives rise to net transfer of medium mass with a light pulse. In this work, we use optoelastic continuum dynamics combining the optical force field, elasticity theory, and Newtonian mechanics to analyze the angular momentum carried by the MDW. We show that accounting for the MDW in the analysis of the angular momentum gives for the field's share of the total angular momentum of light a quantized value that is generally a fraction of $\hbar$. In contrast, the total angular momentum of the mass-polariton (MP) quasiparticle, which is a coupled state of the field and the MDW, and also the elementary quantum of light in a medium, is an integer multiple of $\hbar$. The same coupling is found for orbital and spin angular momentum components. The physical picture of the angular momentum of light emerging from our theory is fundamentally more general than earlier theoretical models, in which the total angular momentum of light is assumed to be carried by the electromagnetic field only or by an electronic polariton state, which also involves dipolar electronic oscillations. These models cannot describe the MDW shift of atoms associated with light. We simulate the MDW of Laguerre-Gaussian pulses in silicon and present a schematic experimental setup for measuring the contribution of the atomic MDW to the total angular momentum of light.

quant-ph↗

arXiv2018

Light-driven mass density wave dynamics in optical fibers

We have recently developed the mass-polariton (MP) theory of light to describe the light propagation in transparent bulk materials [Phys. Rev. A 95, 063850 (2017)]. The MP theory is general as it is based on the covariance principle and the fundamental conservation laws of nature. Therefore, it can be applied also to nonhomogeneous and dispersive materials. In this work, we apply the MP theory of light to describe propagation of light in step-index circular waveguides. We study the eigenmodes of the electric and magnetic fields in a waveguide and use these modes to calculate the optical force density, which is used in the optoelastic continuum dynamics (OCD) to simulate the dynamics of medium atoms in the waveguide. We show that the total momentum and angular momentum in the waveguide are carried by a coupled state of the field and the medium. In particular, we focus in the dynamics of atoms, which has not been covered in previous theories that consider only field dynamics in waveguides. We also study the elastic waves generated in the waveguide during the relaxation following from atomic displacements in the waveguide.

physics.optics↗

arXiv2018

Measuring and engineering the atomic mass density wave of a Gaussian mass-polariton pulse in optical fibers

Conventional theories of electromagnetic waves in a medium assume that only the energy of the field propagates inside the medium. Consequently, they neglect the transport of mass density by the medium atoms. We have recently presented foundations of a covariant theory of light propagation in a nondispersive medium by considering a light wave simultaneously with the dynamics of the medium atoms driven by optoelastic forces [Phys. Rev. A 95, 063850 (2017)]. In particular, we have shown that the mass is transferred by an atomic mass density wave (MDW), which gives rise to mass-polariton (MP) quasiparticles, i.e., covariant coupled states of the field and matter having a nonzero rest mass. Another key observation of the mass-polariton theory of light is that, in common semiconductors, most of the momentum of light is transferred by moving atoms, e.g., 92% in the case of silicon. In this work, we generalize the MP theory of light for dispersive media and consider experimental measurement of the mass transferred by the MDW atoms when an intense light pulse propagates in a silicon fiber. In particular, we consider optimal intensity and time dependence of a Gaussian pulse and account for the breakdown threshold irradiance of the material. The optical shock wave property of the MDW, which propagates with the velocity of light instead of the velocity of sound, prompts for engineering of novel device concepts like very high frequency mechanical oscillators not limited by the acoustic cutoff frequency.

physics.optics↗

arXiv2017

Mass-polariton theory of light in dispersive media

We have recently shown that the electromagnetic field in a medium is made of mass-polariton (MP) quasiparticles, which are quantized coupled states of the field and an atomic mass density wave (MDW) [Phys. Rev. A 95, 063850 (2017)]. In this work, we generalize the MP theory of light for dispersive media assuming that absorption and scattering losses are very small. Following our previous work, we present two different approaches to the theory of light: (1) the MP quasiparticle theory, which is derived by only using the fundamental conservation laws and the Lorentz transformation; (2) the classical optoelastic continuum dynamics (OCD), which is a generalization of the electrodynamics of continuous media to include the dynamics of the medium under the influence of optical forces. For the coupled MP state of a single photon and the medium, we obtain the total MP momentum of the Minkowski form while the field's share of the momentum is equal to the Abraham momentum. We also show that the correspondence between the MP and OCD models and the conservation of momentum at interfaces gives an unambiguous formula for the optical force. The dynamics of the light pulse and the related MDW lead to nonequilibrium of the medium and to relaxation of the atomic density by sound waves in the same way as for nondispersive media. We also carry out simulations for optimal measurements of atomic displacements related to the MDW in silicon. In the simulations, we consider different waveguide cross-sections and optical pulse widths and account for the breakdown threshold irradiance of materials. We also compare the MP theory to previous theories of the momentum of light in a dispersive medium. We show that our generalized MP theory resolves all the problems related to the Abraham-Minkowski dilemma in a dispersive medium.

physics.optics↗