Worldline Research Articles

Universal quantum modifications to general relativistic time dilation in delocalised clocks

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we demonstrate that, in the weak-field, low-velocity limit, all ``good'' quantum clocks experience time dilation as dictated by general relativity when their state of motion is classical (i.e. Gaussian). For nonclassical states of motion, on the other hand, we find that quantum interference effects may give rise to a significant discrepancy between the proper time and the time measured by the clock. The universality of this discrepancy implies that it is not simply a systematic error, but rather a quantum modification to the proper time itself. We also show how the clock's delocalisation leads to a larger uncertainty in the time it measures – a consequence of the unavoidable entanglement between the clock time and its center-of-mass degrees of freedom. We demonstrate how this lost precision can be recovered by performing a measurement of the clock's state of motion alongside its time reading.

Statistical Physics and Thermodynamics of Processes in General Relativity

A model of a relativistic process as a finite set of elementary events is considered. General properties of statistics of elementary events are considered. The model has the following properties. Any macroscopic property of any process is a consequence of this statistics. The least action principle means that a macroscopic process chooses a variant with maximum probability. A massive particle is a repetitive process. One cycle is a subset of elementary events. A sequence of these subsets forms a world line. The proper time on an interval of a world line is proportional to the number of cycles in this interval. The mass of a particle is the number of elementary events in this process per unit time. The gravitational field is a manifestation of information generated by the processes. Empty space-time doesn’t exist.

Derivation of a new multiscale model: I. Derivation of the model for the atomic, molecular and nano material scales

In the present work, a generalized form for the energy equation is derived following the concepts of a new theory called the time of events theory. This theory assumes a dynamic space-time in addition to the static space-time assumed explicitly in the special theory of relativity and implicitly in quantum mechanics. Assuming two spacetimes necessitates the complex space-time. Therefore, the energy equations are rederived assuming a real space-time, represented by the dynamic space-time, and an imaginary space-time represented by the static space-time. An angle θ is assumed between the particle’s world line and the real axis. The θ value depends on the particle’s mass and directly proportional to it. The heavy particles have larger θ, therefore have larger imaginary component, and the reverse is true for the light particles. The energy equations in the complex space-time were written in terms of complex velocities’ squares, each equation is written independently for each particle. Then, the equations are combined to give the final equation for the assembly that is composed of atoms, ions, or molecules. Applying this procedure for the hydrogen atom led to an equation similar to the Schrodinger equation. Based on the above procedure, a general equation for more complicated systems (atoms or molecules) is derived. We find that there is a difference in the leading factors for the electron-electron term from the traditional forms of quantum mechanics. For the case of ions and non-neutral molecules, a different equation is predicted by the current work, due to differences between electrons and protons numbers.

Classical defocussing of world lines—Cosmological Implications

We have extended our result on defocussing of world lines (Parthasarathy et al., 2018) by modifying gravity in the early epoch by a 5-d theory with scalar ψ(r). The acceleration term in the Raychaudhuri equation has been shown to be positive for flat FRW metric. The scalar ψ(r) satisfies a non-linear differential equation which is solved. Though singular, the acceleration term turns out to be finite. With this, the equations for the Hubble parameter H(t) and the scale factor a(t) are obtained. These are analyzed using ‘fixed point analysis’. Without the scalar field, the age of the universe is finite showing a beginning of the universe and with out bounce. With the contribution of the scalar field included, the age of the universe is shown to be infinite, thereby resolving the singularity. The scale factor a(t) exhibits classical bounce, the bounce being proportional to the effect of the scalar field. The effect of the 5-d gravity in the early universe is to cause defocussing of the world lines, give infinite age of the universe thereby resolving the big bang singularity and classical bounce for the FRW scale factor.

Time-resolved electrical detection of chiral edge vortex braiding

A 2\pi2π phase shift across a Josephson junction in a topological superconductor injects vortices into the chiral edge modes at opposite ends of the junction. When two vortices are fused they transfer charge into a metal contact. We calculate the time dependent current profile for the fusion process, which consists of {\pm e/2}±e/2 charge pulses that flip sign if the world lines of the vortices are braided prior to the fusion. This is an electrical signature of the non-Abelian exchange of Majorana zero-modes.

Braiding Majorana fermions and creating quantum logic gates with vortices on a periodic pinning structure

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a cnot gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.

Oscillatory convection of a colloidal suspension in a horizontal cell

The finite difference numerical simulations performed are for convection of a non-uniformly heated colloidal suspension (Hyflon MFA) filling a horizontal cell of finite length. The cell has solid and impermeable boundaries and is heated from below. A linear temperature distribution is maintained at the side walls. Due to the negative effect of thermodiffusion (Soret) and gravity sedimentation, a heavy impurity is collected at the hot lower boundary, and convection transfers it inside the cell. The stable and transient oscillatory convection modes observed experimentally are analyzed. If the initial distribution of the concentration is uniform, then stationary convection occurs in the cell. As the concentration inhomogeneities accumulate, oscillatory perturbations begin to increase. A modulated traveling wave may form in the layer. Stable traveling waves are observed when the Rayleigh number exceeds a certain critical value, which depends on the cell length. There is a good agreement between the experimental data [1] and the results of numerical research. The spatial structure of the concentration field and the time evolution of the convective characteristics of the colloid suspension are determined. The behavior of the colloidal suspension in the regimes of modulated traveling waves and transient flows near the threshold of convection, including localized traveling waves and waves that change their direction, is simulated and elucidated. By analyzing the behavior of the world lines of the vortices and the concentration field, the mechanism of formation of defects in the form of vortex coalescence is clarified. In the process of defect formation, two vortices with the opposite direction of rotation are involved.

Singular Terms, Identity, and the Creation of Fictional Characters

Abstract How to interpret singular terms in fiction? In this paper, we address this semantic question from the perspective of the Artifactual Theory of Fiction (ATF). According to the ATF, fictional characters exist as abstract artifacts created by their author, and preserved through the existence of copies of an original work and a competent readership. We pretend that a well-suited semantics for the ATF can be defined with respect to a modal framework by means of Hintikka’s world lines semantics. The question of the interpretation of proper names is asked in relation to two inference rules, problematic when applied in intensional contexts: the Substitution of Identicals and Existential Generalization. The former fails because identity is contingent. The latter because proper names are not necessarily linked to well-identified individuals. This motivates a non-rigid interpretation of proper names in fiction, although cross-fictional reference (e.g. to real entities) is made possible by the interpretative efforts of the reader.

Lattice Unruh Effect and World-line Entanglement for the XXZ Chain

For the XXZ chain, we discuss the relation between a lattice version of Unruh effect and the ground-state entanglement on the basis of the corner Hamiltonian. We find that the lattice Unruh temperature is interpreted as $\beta_\lambda = 2\pi/a$ with an effective acceleration $a=\pi/\lambda$, where $\lambda$ denotes the anisotropy parameter of the XXZ chain. Using quantum Monte Carlo simulation for the corner Hamiltonian at $\beta_\lambda$, we demonstrate that world lines of spins surrounding the entangle point provides an intuitive understanding the quantum entanglement. We also propose an XXZ-chain analogue of the detector for the thermalized entanglement spectrum with use of the angular time evolution defined by the corner Hamiltonian.

Descriptions of Relativistic Dynamics with World Line Condition

In this paper, a generalized form of relativistic dynamics is presented. A realization of the Poincaré algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in R 4 . The construction of this realization is explicitly shown to clarify the role of the commutation relations of the Poincaré algebra versus their description in terms of Poisson brackets in the no-interaction theorem. Moreover, a geometrical analysis of the “eleventh generator” formalism introduced by Sudarshan and Mukunda is outlined, this formalism being at the basis of many proposals which evaded the no-interaction theorem.

Conservative Relativistic Algebrodynamics Induced on an Implicitly Defined World Line

In the framework of the Stueckelberg-Wheeler-Feynman concept of a ``one-electron Universe'' we consider a worldline implicitly defined by a system of algebraic (precisely, polynomial) equations. Collection of pointlike ``particles'' of two kinds on the worldline (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and detected then by an external inertial observer through the light cone connections. Then the observed collective dynamics of the particles' ensemble is, generally, subject to a number of Lorentz invariant conservation laws. Remarkably, this poperty follows from the Vieta's formulas for the roots of the generating polynomial system. At some discrete moments of the observer's proper time, mergings and subsequent transmutations of a pair of particles-roots take place simulating thus the processes of annihilation/creation of a particle/antiparticle pair

Non-reversible evolution of tilted Szekeres spacetimes with f(R) gravity

This paper is devoted to understanding the effects of modification of gravity on some dynamical features of the Szekeres model (SM). The physical characteristics of matter content and kinematical quantities with respect to tilted and non-tilted reference frames are discussed. In the presence of f (R) gravity corrections, the non-radiative and radiative nature of SM have been observed for the observers moving with non-tilted and tilted congruences, respectively. The importance of congruences of matter world lines in the appearance of vorticity factor has also been studied.

Quantum harmonic oscillator, entanglement in the vacuum and its geometric interpretation

Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive definite scalar product. Adopting several simple postulates we show that a quantum harmonic oscillator can be constructed as a positive definite sector in that space. We discuss the two-dimensional oscillator constructed in such a way that the ground state is maximally entangled. Being a vector in the Hilbert space, it has also a non-trivial expansion in a bigger extended space. On one hand, the space is not free of negative norm states. On the other hand, it allows one to interpret the ground state geometrically in terms of AdS3. The interpretation is based solely on the form of the expansion, revealing certain structures at the boundary and in the bulk of AdS3. The former corresponds to world lines of massless particles at the boundary. The latter resembles interacting closed strings.

Models of lightlike charges with nongeodesic worldlines

Massless particles in General Relativity move with the speed of light, their trajectories in spacetime are described by null geodesics. This is independent of the electrical charge of the particle being considered, however, the charged light-like case is less well understood. Starting with the Maxwell field of a charged particle having a light-like geodesic world line in Minkowskian space-time we construct the Maxwell field of such a particle having a non-geodesic, light-like world line. The necessary geometry in the neighbourhood of an arbitrary null world line in Minkowskian space-time is described and properties of the resulting electromagnetic field are discussed. The electromagnetic field obtained represents a light-like analogue of the Lienard-Wiechert field, which generalises the Coulomb field of a charge having a time-like geodesic world line to the field of a charge having an accelerated world line.

Consistent Coordinate Transformation for Relativistic Circular Motion and Speeds of Light

A world system is composed of the world lines of the rest observers in the system. We present a relativistic coordinate transformation, termed the transformation under constant light speed with the same angle (TCL-SA), between a rotating world system and the isotropic system. In TCL-SA, the constancy of the two-way speed of light holds, and the angles of rotation before and after the transformation are the same. Additionally a transformation for inertial world systems is derived from it through the limit operation of circular motion to linear motion. The generalized Sagnac effect involves linear motion, as well as circular motion. We deal with the generalized effect via TCL-SA and via the framework of Mansouri and Sexl (MS), analyzing the speeds of light. Their analysis results correspond to each other and are in agreement with the experimental results. Within the framework of special and general relativity (SGR), traditionally the Sagnac effect has been dealt with by using the Galilean transformation (GT) in cylindrical coordinates together with the invariant line element. Applying the same traditional methods to an inertial frame in place of the rotating one, we show that the speed of light with respect to proper time is anisotropic in the inertial frame, even if the Lorentz transformation, instead of GT, is employed. The local speeds of light obtained via the traditional methods within SGR correspond to those derived from TCL-SA and from the MS framework.

The Motions of Dark Matter

Abstract The absence of dark matter (DM) in stars is interpreted as an important constraint on its allowable kinematics rather than implying extremely small cross sections. A model for the motions of DM particles in the vicinity of stars and spiral galaxies is developed assuming internal motions in a DM particle can couple to its translational motion. A DM particle having rapid “spin” must move in a tight helix around its guiding center world line, in a manner similar to an ion moving in a magnetic field. Compared to ordinary matter particles, DM particles cannot enter deep gravitational wells because their total angular momentum is too high. Numerical examples seem reasonable. It is very doubtful that this DM can be found in the solar system, or be present in stars or protostars, or be found in the interior regions of galaxies.

A Frenet–Serret interpretation of particle dynamics in high-intensity laser fields

In this paper we discuss the dynamics of charged particles in high-intensity laser fields in the context of the Frenet–Serret formalism, which describes the intrinsic geometry of particle world lines. We find approximate relations for the Frenet–Serret scalars and basis vectors relevant for high-intensity laser particle interactions. The onset of quantum effects relates to the curvature radius of classical trajectories being on the order of the Compton wavelength. The effects of classical radiation reaction are discussed, as well as the classical precession of the spin-polarization vector according to the Thomas–Bargman–Michel–Telegdi equation. We comment on the derivation of the photon emission rate in strong-field QED beyond the locally constant field approximation, which is used in Monte Carlo simulations of quantum radiation reaction. Such a numerical simulation is presented for a possible experiment to distinguish between classical and quantum mechanical models of radiation reaction.

Black hole geodesic parallel transport and the Marck reduction procedure

The Wigner rotations arising from the combination of boosts along two different directions are rederived from a relative boost point of view and applied to gyroscope spin precession along timelike geodesics in a Kerr spacetime, clarifying the geometrical properties of Marck's recipe for describing parallel transport along such world lines expressed in terms of the constants of the motion. His final angular velocity isolates the cumulative spin precession angular velocity independent of the spacetime tilting required to keep the spin 4-vector orthogonal to the gyro 4-velocity. As an explicit example the cumulative precession effects are computed for a test gyroscope moving along both bound and unbound equatorial plane geodesic orbits.

Anti-Newtonian Expansions and the Functional Renormalization Group

Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory.

The holographic non-abelian vortex

We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find, in the classical approximation in the bulk, a gapless ℂℙ1 excitation on the vortex world line.