3 - 6 June 2024  ♦  Aalto University

Abstracts

Relativistic Transformations of Thermodynamics, Relativistic Statistical Mechanics and Einstein's Dual Theory
Gonzalo Ares de Parga, Instituto Politecnico Nacional

A brief description of the Redefined Relativistic Thermodynamics is exposed relating it with the Relativistic Statistical Mechanics and showing that Einstein-Planck, Ott and Rohrlich proposals represent particular choices of a reference frame where the instantaneity is considered. The Einstein’s dual theory is described arriving to the conclusion that for a system of particles a universal time exists called the proper time. The instantaneity can be considered in the frame where the observer is at rest in the canonical dual Hamiltonian center of mass. This will relate the different proposals to the Proper Time of the system.

Progress in evaluating a possible electromagnetic interaction energy in a gravitational field
Mayeul Arminjon, CNRS, Grenoble-Alpes University

The Lorentz-Poincaré interpretation of special relativity (SR) keeps the clas- sical concepts of separated space and time, at the cost of postulating an indetectable preferred inertial frame or “ether”. But SR does not contain gravity. The presence of gravity could make the ether detectable. This is one idea behind the “scalar ether theory of gravitation” (SET), which co- incides with SR if the gravity field vanishes, and passes a number of tests. However, the coupling of SET with the Maxwell electromagnetic (EM) field needs to use the theory’s dynamical equation for the energy tensor in a non- trivial way. It cannot be assumed that the energy tensors of the charged matter and the EM field add to give the total energy tensor, source of the gravitational field. Thus, an additional, “interaction” energy tensor \(T_{inter}\) has to be postulated. Asking that \(T_{inter}\) is Lorentz-invariant in the situation of SR, fixes its form. It depends only on a scalar field \(p\). \(T_{inter}\) is an exotic kind of matter and is distributed in the whole space, hence it could con- tribute to dark matter. For a weak gravitational field, \(p\) obeys a first-order PDE involving the EM field and the Newtonian potential. However, the EM field varies on the scale of the wavelength, which is extremely small. To get the field \(p\) in a galaxy, some averaging has to be done. After several attempts based on the homogenization theory, a simpler way has been found recently: If the macro-averages of \(p\) and the EM field vary smoothly, it can be shown that the PDE for \(p\) remains valid in the same form with spacetime-averaged fields. The current stage of calculations will also been shown.

The Dirac Equation in Cantorian Hyperspace
Ashley Asa Western Kentucky University

Though Einstein's mass-energy equation is derived under the assumption of absolute smooth spacetime, in reality, discontinuity is intrinsic at quantum scales. In recent years, it has also been shown that fractional and fractal differential equations can describe discontinuous media. Given such, this paper presents a formulation of the Dirac equation in Cantorian-fractal hyperspace. Herein, we present a derivation via conformal differential geometry in Weyl space, find bound state solutions for various potentials using the Generalized Fractional Nikiforov-Uvarov method, and discuss the effect of fractional order on curvature and particle dynamics. Finally, through the lens of E-infinity theory, the implications of this result are explored with groundbreaking applications in microphysics and the development of analytical systems for dark energy.

Time dispersion in bound states
John Ashmead, University of Pennsylvania

In standard quantum electrodynamics (QED) the path integrals used to compute Feynman diagrams are limited to sums over paths that are on-shell. In earlier work, we asked: what happens if we include off-shell paths as well? We recovered standard QED in the long time limit. And we predicted effects at attosecond and shorter times, timescales that are now becoming accessible. We here extend this work to include bound states. The predicted bound state wave functions extend in time as well as space; the energy levels match the existing; but there are subtle differences at attosecond time scales in the emission, absorption, and scattering processes. Further the Lamb shift calculations are finite: the additional dispersion in time/energy regularizes the loop integrals. The previous work was limited by the need to estimate the initial wave functions, making the predictions subject to errors associated with those estimates. But with the extension to bound states we can now give precise values for the initial wave functions, so we can make correspondingly precise predictions. And there are a wide variety of experimental targets: in general any time-dependent processes should show effects. Falsification will be technically challenging (due to the short time scales) but immediate and unambiguous. Confirmation would have significant implications for attosecond physics, quantum computing and communications, quantum gravity, and our understanding of the measurement problem.

Are Tachyons Responsible for Cosmic Inflation?
John Fanchi, Texas Christian University

The manifestly covariant quantum theory with invariant evolution parameter called parametrized Relativistic Quantum Theory (pRQT) can be used to consider the question that is the subject of this talk: are tachyons responsible for cosmic inflation? The creation and annihilation of real mass tachyons is a possibility within pRQT. Here we show that tachyon kinematics associated with pRQT can be combined with general relativity to quantify a mechanism for achieving cosmic inflation.

Quantum fields in cosmological spacetime and the early Universe
Antonio Ferreiro de Aguiar, Utrecht University

Understanding the behaviour of quantum fields propagating and interacting in gravitational backgrounds is essential to understand the physics of the early Universe. In this talk I will present two interesting quantum phenomena: Gravitational Baryogenesis model and the gravitational wave generation due to reheating particle production. I will show how recent developed techniques of quantum field theory in curved spacetime are able to account for these phenomena in a consistent way.

Mathematical Equivalence is not Physical Equivalence
Tepper Gill, Howard University

This talk is devoted to the relationship between physics and mathematics. I plan to show that, in general, mathematical equivalence cannot be equated to physical equivalence. I will discuss and provide proofs of the following: 1. The Dirac equation is not physically equivalent to the square root equation but is related by a unitary transformation. 2. The Hilbert space for Feynman’s path integral formulation of quantum theory \(KS^2[R_n]\), is not physically equivalent to \(L2[R_n]\), the Hilbert space for the Schödinger formulation, but is related by a unitary transformation.

Fluctuations of Quantum Fields and Thermodynamics of Spacetime
Bei-Lok Hu, University of Maryland

My research in the past 40 years can summarily be represented in a 2D phase space with Quantum-Classical on the horizontal axis, and micro-Macro on the vertical. You can tell from the title of my talk that the intention is to connect the micro features of quantum matter to the macro- structures of spacetime: matter via quantum field theory, spacetime via general relativity, and micro/macro interface via nonequilibrium statistical mechanics. This stretch may sound wild on surface, but not so surprising if you knew that in my view, general relativity is in the nature of a hydrodynamic theory [arXiv:gr-qc/9607070, arXiv:gr-qc/9511077], valid only in the long wavelength, low energy domain. GR is a beautiful theory, yet only an effective theory, emergent from quantum gravity -- theories describing the microscopic structures of spacetime at the Planck length (\(10^{-35} m\)), not unlike thermo- and hydro- to molecular-dynamics. To me, hydrodynamics and thermodynamics not only serve as a set of useful tools, but provide the correct perspective to ask meaningful questions about the nature and behavior of spacetime as we know it. My recent work with H. T. Cho and J. T. Hsiang attempts to link up the stress energy fluctuations of quantum fields in spacetimes (with nontrivial topology or curvature) with their thermodynamic properties. The former is represented by the noise kernel, the stress energy tensor correlator of quantum matter fields, while the latter by the heat capacity and the (adiabatic and isothermal) compressibility. Noise kernel is the centerpiece of stochastic gravity, a theory for the dynamics of curved spacetimes based on the Einstein-Langevin equation [arXiv:0802.0658] which incorporates fully and self-consistently the backreaction effects from the mean values and the fluctuations of quantum field stress tensors. Examining the noise kernel from a thermodynamic perspective can add a new dimension to our understanding of its physical properties. E.g., heat capacity gives a measure of the fluctuations of the energy density to the mean, acting as a criterion for the validity of the canonical distribution. An intriguing fact coming from the past 3 decades of work is that the fluctuations of energy density to the mean is close to unity for quantum fields in many different spacetimes. From a thermodynamic perspective we conjecture that this feature, even for quantum fields in ordinary Minkowski spacetime, is an indication that the balance between spacetime and quantum matter fields has some built-in thermodynamic instability, that their co-existence meets with a saturation criterion in the “capacity of spacetime” to “hold" the quantum field, a theme we view as worthy of deeper thoughts.

The nuclear electron's mass and Heisenberg uncertainty
Andras Kovacs, BroadBit Energy Technologies

This presentation further investigates the nuclear electron's properties, which were introduced by the author at the IARD-2022 conference. Under certain conditions, a short-lived nuclear electron is released from the nucleus. Prior to its decay into an electron, it may be re-captured by an other nucleus, consequently emitting single-frequency gamma radiation. The precise measurement of the nuclear electron mass is based on comparing this gamma peak energy against the electron capture energy of the given nucleus. Two such measurements were introduced at IARD-2022: the nuclear electron capture by the 58Ni and 1H isotopes. A third experiment was recently carried out, which demonstrates nuclear electron capture by the 14N isotope. All three experiment yield exactly the same result: the nuclear electron mass is 1554 keV. In the context of the nuclear electron hypothesis, the question of Heisenberg uncertainty comes up: how the reconcile the nuclear electron's relatively low mass with its low position uncertainty in the nuclear bound state? Instead of working with the \(\Delta(x)\Delta(p)\) formulation, it is more fundamental to work with the \(\Delta(x)\Delta(hk)\) uncertainty formulation, where \(k\) is the quantum mechanical wavenumber. I show that \(k\) is the Lorentz-transformed component of the particle's Zitterbewegung frequency. Normally, a particle's Zitterbewegung frequency is proportional to its relativistic mass, and is determined by its internal magnetic field configuration. However, in case of a proton-bound nuclear electron, its Zitterbewegung frequency becomes determined by the proton's magnetic field.

Dynamics of a two-state system under measurement
Alexey Kryukov, University of Wisconsin-Milwaukee Spontaneous collapse models use non-linear stochastic modifications of the Schr{\"o}dinger equation to suppress superpositions of eigenstates of the measured observable and drive the state to an eigenstate. It was recently demonstrated that the collapse of the wave function under observation can be modeled by the linear Schr{\"o}dinger equation with a Hamiltonian represented by a random matrix from the Gaussian unitary ensemble. The matrices representing the Hamiltonian at different time points throughout the observation period are assumed to be independent. Instead of suppressing superpositions, such Schr{\"o}dinger evolution makes the state perform an isotropic random walk on the projective space of states. The probability of reaching a particular final state is then given by the Born rule. Here, we apply this method to study the dynamics of a two-state system undergoing measurement. It is shown that in this basic case, the state undergoes the gambler's ruin walk that satisfies the Born rule, providing a suitable representation of the transition from the initial state to an eigenstate of the measured observable.

Perturbative decoherence of relativistic entanglement
Martin Land, Hadassah College

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, defined at the same time. A covariant theory of relativistic spin and entanglement has been given by Horwitz and Arshansky, in which representations of O(3,1) are induced with respect to an arbitrary timelike unit vector \(n_\mu\). In this paper, we construct an induced relativistic representation of spin on an extended phase space \({(x_\mu , p_\mu ), (\pi_\mu , \pi_\mu )}\), in which we associate the unit vector \(n_\mu\) with the momentum \(\pi_\mu\) , thus providing a dynamical interpretation for this new quantity. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states. As in non-relativistic quantum theory the magnetic field couples to the rotation generators of SU(2), however the electric field couples to the non-compact and anti-Hermitian boost generators. We show that to first order in perturbation theory, a constant external magnetic field will produce a perturbative contribution to the total mass (the eigenvalue of the Lorentz scalar Hamiltonian) or a transition between states in the same representation of SL(2,C), and so will not disrupt a singlet state. However, an electric field normal to \(\pi_\mu\) can produce a transition between states in inequivalent representations of SL(2,C), and potentially cause decoherence of the relativistic entanglement.

Unruh effect on relativistic single-electron wavepacket in quantum electromagnetic fields
Shih-Yuin Lin, National Changhua University of Education

We present a linearized effective theory using a Gaussian wavepacket description of a charged relativistic particle coupled to quantum electromagnetic fields to study the interplay between single electrons and quantum fields in free space, at a scale well below the Schwinger limit. The proper values of the regulators in our effective theory are determined from the data of individual experiments, and will be time-dependent in the laboratory frame if the single electrons are accelerated. Using this theoretical tool, we address the issues of decoherence of flying electrons in free space and the impact of Unruh effect on the electrons.

Lorentz force law as a geodesic equation and electric charge as divergence of the electromagnetic four-potential
Jussi Lindgren, Aalto University

The Lorentz force law of electromagnetism can be understood as a geodesic equation, if the electromagnetic four-potential is included into the metric structure of the spacetime and we consider a Weyl geometry. The Lorentz force law is just the geodesic equation in disguise. Semimetricity condition then provides that the covariant divergence of the electromagnetic four- potential is exactly the charge density in the spacetime. Random vacuum fluctuations at Planck scales are then argued to lead to random accelerations of charged particles producing random electromagnetic radiation. The random fluctuations of the metric give rise to a random electromagnetic field, which fluctuates at Planck scales. The random fluctuation of the spacetime fabric is argued to be the reason for the instrumental validity of quantum mechanics. Moreover, the random covariant divergence of the electromagnetic four-potential seems to create and annihilate charges at Planck scales. The present results indicate that the correct spacetime geometry for electromagnetism is the Weyl geometry, where the non-zero connection coefficients correspond to Weyl curvature. With such an approach, electric charge seems to be directly related to the divergence of the (singular) metric tensor. This provides some aesthetic features into the model, as electromagnetism seems to be orthogonal to gravity in the sense that current theory of gravity is a theory based on metric compatible connections. Furthermore, assuming spacetime fluctuations in the metric tensor at Planck scales leads to randomly fluctuating electromagnetic field in vacuum.

Quantum mechanics in real space using Slater-Condon rules
Ophelliam Loiselet

Atomic spectral line computation has been one of the most successful proofs of quantum mechanics relevance to describe the physical world at small scale. The Schrodinger equation, which is a wave equation based on Hamiltonian mechanics, has allowed to compute the hydrogen principal spectral lines in 1927. Then Hartree in 1928 proposed the Hartree equation to describe atoms with more than one electron, including electrostatic electron-electron repulsion. However the Hartree model does not describe the electron correlation revealed by the electron-electron exchange interaction that appeared in Hartree-Fock theory, due to the multi-electronic wave function expressed as a Slater determinant. Nevertheless, the so-called Slater-Condon rules already allow to express Hartree-Fock theory in a set of 3D equations of individual electronic wave functions. In this talk, we will describe quantum mechanics in real space using Slater-Condon rules, taking the Hartree-Fock and relativistic Dirac-Hartree-Fock equations in 3D for multi-electronic systems. We will provide a physical meaning to the electronic exchange potential, extended to a relativistic 4-exchange potential, linked to the so-called Dirac transition current with, as an example, a derivation of Einstein's spontaneous emission coefficient.

Calculating electromagnetic properties of the vacuum using electrodynamics to describe the interaction of photons with vacuum fluctuations
Bruce Mainland, Ohio State

A fundamental postulate of physics is that the properties of a physical system are determined by its structure. The physical system being considered here is photons traveling through the quantum vacuum. The appearance of vacuum fluctuations is the mechanism by which the quantum vacuum is manifest. Since the speed \(c\) of light in the quantum vacuum is an electromagnetic property of the quantum vacuum, it is possible to calculate \(c\) using Maxwell’s equations and quantum electrodynamics to describe the interaction of a photon with vacuum fluctuations. The value of \(c\) that is calculated satisfies the second postulate of special relativity, obviating the need for the postulate. Values for the permittivity \(\epsilon_0\) of the vacuum and the fine-structure constant \(\alpha\) are also obtained. An experiment is discussed that would use an intense laser beam to study a second-order interaction of photons with vac- uum fluctuations that could provide additional experimental confirmation of the theoretical ideas used to calculate \(\epsilon_0\) , \(c\), and \(\alpha\).

Proposals for laser experiments on vacuum fluctuations
Theophilos Maltezopoulos, European X-ray Free Electron Laser facility

Usually the number density of photons in light beams is many orders of magnitude less than the number density of vacuum fluctuations. Therefore, if a vacuum fluctuation interacts with a photon, it almost never interacts with a second photon before the single-photon-excited vacuum fluctuation decays and emits a photon. With developing laser technology, short, intense laser pulses have photon number densities in the focus approaching the high number density required to create a sufficient number density of two-photon-excited vacuum fluctuations that the vacuum permittivity will be increased and the speed of light will be measurably decreased. Particle colliders create high energies and these laser experiments create high photon number densities as they appeared at the beginning of the big bang. In my presentation I will present ideas for laser experiments on vacuum fluctuations: If some photons in the focus interact with single-photon-excited vacuum fluctuations, they will be delayed, and this could be measured with a diode. Additionally, in a pump-probe geometry this intense laser focus (pump) could be measured with a second laser pulse (probe) in transmission or reflection. After passing the intense focus, perhaps even the wavefront, spectrum, and duration of the laser pulse could be influenced, all of which can be measured by standard optical techniques.

Spin-charge-family theory offers a new understanding of elementary fermion and boson fields and cosmological phenomena
Norma Mankoc, University of Ljubljana

A long series of works demonstrate that the spin-charge-family theory offers the explanation for all in the standard model assumed properties of quarks and leptons, as well as for many of the so far observed cosmological phenomena. The internal spaces of fermion and boson fields are described by the Clifford algebra elements with the same number of odd (for fermions) and even (for bosons) Clifford algebra elements, arranged as seen from \(d= (3+1)\), leading to the creation and annihilation operators, which anti-commute (for the Clifford odd objects), and commute (for the Clifford even objects), explaining the second quantization postulates for fermion and boson fields. The theory assumes a simple starting action in \(d= (13+1)\), with massless fermion and boson fields, with nonzero momentum only in \(d=(3+1)\), manifesting the observed boson fields, with graviton and the Higgs scalars included, predicting the fourth family to the observed three, explaining the existence of the dark matter and the matter-antimatter asymmetry in the universe, and predicting new scalar fields carrying the triplet colour charge. In odd-dimensional spaces, the theory explains the appearance of the Fadeev-Popov ghosts.

Dirac Like Quantum Equation for Free Particles of Any Spin in a Global Space-time
Amnon Moalem, Ben Gurion University

We demonstrate that free particles of any spin in a global curved space-time satisfy a Dirac like equation, , where are vierbein fields , the gammas are block matrices defined as where are the Pauli matrices, is the determinant of the metric and is components spinor wave function. For spin particle . For the Minkowski, Schwarzschild, FWR and stationary rotating Kerr black holes, the wave function factorizes into three factors: (1) An overall normalization function which can be calculated analytically, (2) A common reduced angular wave function identically the same as in a Minkowski space-time, and, (3) Radial wave functions and which satisfy second order non-homogeneous equations with non-homogeneous terms depending on the ratio of time to space curvatures. In keeping with the correspondence principle, in the limit of zero mass and angular momentum of a black hole the non-homogeneous terms vanish and the expressions above reduces to those of a flat Minkowski space-time.

Holographic Quantum Foam
Jack Ng, UNC

Quantum fluctuations endow spacetime with a foamy structure which John Wheeler dubbed quantum foam, aka spacetime foam. We show (in several ways) that the degree of foaminess is dictated by black hole physics to be of the holographic type such that the uncertainty in length measurements is given by the product of the cube-root of the length itself and the 2/3-power of Planck length. There are also corresponding uncertainties in energy-momentum measurements. Applied to cosmology, the holographic quantum foam model predicts the existence of dark energy (and dark matter) in the current universe, the quanta of which obey infinite statistics (with an algebra intermediate between Bose and Fermi statistics). Furthermore, we use the deep similarities between turbulence and the spacetime foam phase of strong gravity to argue that the early universe was in a turbulent regime when it underwent a brief cosmic inflation with a graceful transition to a laminar regime. Finally we briefly discuss some possible (but conceivably difficult) ways to test holographic quantum foam, including the use of laser-based interferometers, and detection of blurring in the observation of high-energy gamma rays from extragalactic sources.

The Milky Way as a test for gravity theories
James O'Brien, Springfield College

Recently published data about the rotation curve of the Milky Way galaxy could provide enough evidence to serve as a testing ground for alternative theories of gravity. Unlike most large spiral galaxies, the rotation curve of the Milky Way seems to be declined Which is a testable outcome of gravitational theories. Analysis of the data as well as comparisons of the leading gravitational theories will be applied to this latest data set.

Lagrange's and Hamilton's equations from Hamilton's characteristic function
Paul O'Hara, Istituto Universitario Sophia

Synge and Griffith in their classical text “Principles of Mechanics” when referring to Hamilton’s characteristic (or principal) function, \(S\), note that it characterizes the dynamical system much as the Hamiltonian \(H(q, p, t)\) characterizes it, but better.”(S&G, p. 450). Using the principle of least action, this function, \(S\), can be used to derive both Lagrange’s and Hamilton’s equations of motion, which have become the corner stones of modern physics. In practise, most physicists begin with a Hamiltonian and not \(S\). In this presentation, it will be shown that for any characteristic function \(S = S(q_\mu , t)\) with associated Lagrangian \(L\) that

\(\frac{d}{dt} \frac{\partial S}{\partial q_\mu} = \frac{\partial }{\partial q_\mu} \frac{dS}{dt} \Leftrightarrow \frac{d}{dt} \frac{\partial L}{\partial \dot q_\mu} - \frac{\partial L}{\partial q_\mu} = 0 \)

The equation associated with \(S\) can be rewritten in commutator form as

\(\frac{d}{dt} \frac{\partial S}{\partial q_\mu} = \frac{\partial }{\partial q_\mu} \frac{dS}{dt} \Leftrightarrow \left[\frac{d}{dt} , \frac{\partial }{\partial q_\mu}\right]\)

We investigate its implications for quantum physics and also note that the quantum wave function is in reality an action function restricted to \(L^2\) spaces. This in turn has consequences for the probability interpretation associated with quantum mechanics. We also give a necessary and sufficient condition for these equations to be covariant.

Instantons in finite volume, quantum tunnelling and cosmic bounce
Silvia Pla Garcia, King's College London

Tunnelling between two degenerate vacua is allowed in finite-volume Quantum Field Theory. This effect induces a non-trivial vacuum energy, which result from the competition of different saddle point configurations in the partition function. In this talk, I will describe this mechanism and discuss its relevance to induce a cosmological bounce.

A Charged Hadronic String Model Within The R. Feynman Proper Time Paradygm And Vacuum Field Theory Approach
Anatolij Prykarpatski, Cracow University of Technology

The classical least action principle is considered in modern physics as a fundamental tool for deriving true and physically sound equations governing the dynamics of the corresponding physical objects. By means of this principle there has been described many physical models including those of classical mechanics, electrodynamics and Einsteinian gravity theory. As it was mentioned in many classical manuals, a suitable and physically motivated method of choosing the corresponding Lagrangian functions appears nowadays to be open for studying. Application of the least action principle is strongly complicated by inconsistencies often accompanying the derived physical statements which are considered to be well understood and checked by means of other physical theories. In particular, in modern electrodynamics of a charged point particle moving under influence of an external electromagnetic field, there is well known misreading related to the charged point particle energy expression. Namely, the latter being obtained by means of the classical least action principle, gives rise to the charged particle ”dynamical" mass expression not depending on the external potential energy. This fact was also discussed in the literature, for instance in, where there are also described other physically reasonable examples. Taking this into account and being motivated by R. Feynman’s considerations of the problem in and a recently devised vacuum field theory approach to a physically reasonable formulation of the corresponding least action principle for describing the charged point particle electrodynamics, we have revisited in the approach, based on the Feynman proper time paradygm and applied it to describing the dynamics of a charged point particle and stated its complete physical adequacy. Based on this experience we apply in the present work the devised vacuum field theory approach to describing space-time dynamics of a charged hadronic string model

\(S^{(\tau)}=-\int^{\tau_2}_{\tau_1} d\tau \int^{\sigma_2(\tau)}_{\sigma_1(\tau)} q \bar W (\vert r^\prime\vert^2 (1 + \vert \dot r\vert^2) - \langle \dot r \vert r^\prime \rangle^2_{E^3} )^{1/2} d\sigma\)

under influence of an extrnal vacuum field potential. We analyze in detail the related Lagrangian and Hamiltonian string model description, in particular, we state that with respect to some conformal local coordinates the resulting space-time dynamics is described by means of the linear second order elliptic equation under the corresponding Dirac type constraints, well fitting for its quantization. The Hamiltonian functional of the charged string model can be equivalently represented in the symbolic form as

\( H= \int^{\sigma_2}_{\sigma_1} \vert \bar W r^\prime \pm ip \vert_{C^3} d\sigma\)

where \(i := \sqrt{-1}\) and \(\vert \cdot \vert_{C^3}\) denotes the norm on the complex space \(C^3\). Moreover, concerning the result obtained above, we need to mention here that one can not construct the suitable Hamiltonian function expression and relationship with respect to the laboratory reference frame \(K\). Thereby, one can formulate the following proposition.

Observations of Holographic Quantum-Foam Blurring
Eric Steinbring, Canadian Gemini Office

The "foamy" nature of spacetime at the Planck scale was an idea first introduced by John Wheeler in the 1950s. And for the last twenty years or so it has been debated whether those inherent uncertainties in time and path-length might also accumulate in transiting electromagnetic wavefronts, resulting in measurable blurring of images of distant galaxies and quasars. Observationally, a confusing aspect is that "pointlike" objects will always be blurred out somewhat by the optics of a telescope, especially in the optical. But it turns out that Gamma-Ray Bursts (GRBs) are more useful to test this, and have been observed by a host of ground-based and space-based telescopes, including by the Fermi observatory for well over a decade. And a recent one was unprecedented: GRB 221009A was extremely bright, allowing follow-up from the infrared through the ultraviolet to X-rays and gamma-rays, including a first association with photons at high TeV energies. I will discuss how that observation is in direct tension with the calculus of how spacetime "foaminess" can add up in an image of a pointsource at cosmological distances, which at high-enough energy could spread these out over the whole sky without resulting in photon loss. A simple multiwavelength average of foam-induced blurring consistent with holographic quantum gravity is described, analogous to atmospheric seeing from the ground. This fits with measured instrumental point-spread functions and with the highest-energy localization of GRB 221009A, resolving observational issues and pointing to a key physical implication: spacetime does not look smooth.

TBA
Matthew Trump, IARD Secretary

Gravity through the prism of condensed matter physics
Grigory Volovik, Aalto University

The condensed matter experience suggests that gravity and Standard Model can be the phenomena, which emerge in the low energy corner of quantum vacuum. Condensed matter demonstrates how analogs of gravity, gauge fields and chiral fermions emerge in the many-body systems on a macroscopic level. The advantage of condensed matter system is that we know its physics both on macro-level, and on the micro-level - the interatomic analog of Planck length. The known IR-UV connections allow us to look for possible solutions of problems in quantum gravity, including the cosmological constant problem. In the equilibrium state of condensed matter (analog of quantum vacuum) the diverging contribution of zero-point energy of quantum fields is cancelled by atomic (trans-Planckian) degrees of freedom. This cancellation follows from thermodynamics, valid both for condensed matter and relativistic vacua. The emergent macroscopic phenomenon can be generated by different microscopic backgrounds. Superfluid phases of liquid 3He suggest at least six different scenarios of emergent gravity. In all scenarios, tetrads (vielbein) are the primary emergent objects. Metric is the secondary object -- the bilinear combination of tetrads. In 3He-A scenario, gravity emerges together with Weyl fermions near Weyl points in quasiparticle spectrum. Tetrads have the form of contravariant vectors. In 3He-B scenario, the covariant tetrads emerge -- bilinear combinations of fermionic fields (analog of Akama-Diakonov-Wetterich quantum gravity). Different scenarios of emergent physics suggest various possible directions in study of the deep vacuum. Whatever scenario is preferred by Nature, gravity is not described by Einstein metric and requires the theory in terms of vielbein.

The Relativistic Virial Theorem
Asher Yahalom, Ariel University

A Possible Resolution of the "Dark Matter" Problem up to the Galactic Cluster Scale Weak Field General Relativity and in fact any physical theory applicable to an arbitrary inertial observer must be symmetrical under the Lorentz group. Equations which are invariant under the Lorentz transformation do not allow "action at a distance" solutions of the Newtonian gravity type, but rather require retarded solutions. Galaxies and even more so clusters of galaxies are huge physical systems having dimensions of many tens of thousands of light years in the first case and millions of light years in the later. Thus, any change at the center of the system will be noticed at the rim only tens of thousands or millions of years later. Those retardation effects seem to be neglected in present day modeling used to calculate rotational velocities of matter in the rims of the galaxy, or velocities of galaxies within a galaxy cluster. The significant differences between the predictions of Newtonian theory and observed velocities are usually explained by either assuming dark matter or by modifying the laws of gravity (MOND as a typical example). In this presentation, we will show that taking retardation effects into account one can explain the azimuthal velocities of galactic matter and the well-known Tully-Fisher relations of galaxies. Moreover, gravitational lensing phenomena which is attributed to "dark matter" can also be explained by retardation. It is shown that due to retardation "dark matter" mass must be the same for both lensing and galactic rotation curves. Finally, we demonstrate that the virial theorem must be corrected and thus the "dark matter" of galaxy clusters can be interpreted in terms of retardation.

Particle as a Proper Time Oscillator
Hou-Ying Yau, FDN Research

By restoring the symmetry between time and space, we demonstrate that a matter field with proper time oscillations can mimic the properties of a bosonic field. The particles observed are proper time oscillators. If we neglect all quantum effects, a proper time oscillator can be treated as a ’stationary’ classical object, equivalent to a point mass at rest in general relativity. Under this assumption, we demonstrate that the proper time oscillator can curve the surrounding spacetime and generate a gravitational field; its solution is the Schwarzschild metric. To test the theory, we propose to study the uncertainty of the neutrinos/photons arrival time and the decaying rate of a muon. Proper time oscillation in a Higgs field is also investigated.