Rindler Observer Research Articles

Symmetry restoration and uniformly accelerated observers in Minkowski spacetime

We reassess the problem of symmetry restoration induced by observers’ acceleration within the context of interacting quantum field theories in Minkowski spacetime. We argue that the imposition of a frame-independent renormalization condition negates any observed symmetry restoration by a Rindler observer. Technically, we compute the one-loop effective potential of a λφ4 theory for an accelerated observer, employing a distinct methodology from prior investigations. Emphasizing the intricacies of the model’s renormalization, the analysis offers novel insights into the interplay between acceleration and spontaneous symmetry breaking in quantum field theory.

Decoherence from horizons: General formulation and rotating black holes

Recent work by Danielson, Satishchandran, and Wald (DSW) has shown that black holes—and, in fact, Killing horizons more generally—impart a fundamental rate of decoherence on all nearby quantum superpositions. The effect can be understood from measurement and causality: An observer (Bob) in the black hole should be able to disturb outside quantum superpositions by measuring their superposed gravitational fields, but since his actions cannot (by causality) have this effect, the superpositions must automatically disturb themselves. DSW calculated the rate of decoherence up to an unknown numerical factor for distant observers in Schwarzschild spacetime, Rindler observers in flat spacetime, and static observers in de Sitter spacetime. Working in electromagnetic and Klein-Gordon analogs, we flesh out and generalize their calculation to derive a general formula for the precise decoherence rate for Killing observers near bifurcate Killing horizons. We evaluate the rate in closed form for an observer at an arbitrary location on the symmetry axis of a Kerr black hole. This fixes the numerical factor in the distant-observer Schwarzschild result, while allowing new exploration of near-horizon and/or near-extremal behavior. In the electromagnetic case we find that the decoherence vanishes entirely in the extremal limit, due to the “black hole Meissner effect” screening the Coulomb field from entering the black hole. This supports the causality picture: Since Bob is unable to measure the field of the outside superposition, no decoherence is necessary—and indeed none occurs. Published by the American Physical Society 2024

Computer-based Activity to Understand Proper Acceleration Using the Rindler Observer

Computer-based Activity to Understand Proper Acceleration Using the Rindler Observer

Schwinger effect and a uniformly accelerated observer

This article investigates the Schwinger effect for fermions with background electric and magnetic fields of constant strengths from the point of view of a uniformly accelerated or the Rindler observer. The Dirac equation is solved in a closed form, and the field quantisation in the (3+1)-dimensional Rindler spacetime is performed. The orthonormal local in and out modes for the causally disconnected right and left wedges and the Bogoliubov relations between them are obtained. Next, the global modes are constructed to cover the whole spacetime, and the Bogoliubov relationship between the local and global operators is found. Using them the squeezed state expansion of the global vacuum in terms of local states is acquired and accordingly, the spectra of created particles is found. Clearly, there are two sources of particle creation in this scenario – the Schwinger as well as the Unruh effects. Our chief aim is to investigate the role of the strength of the background electromagnetic fields on the spectra of created particles. We also discuss very briefly some possible implication of this result in the context of quantum entanglement.

Chaos in celestial CFT

Celestial holography proposes a duality between gravitational scattering in asymptotically flat space-time and a conformal field theory living on the celestial sphere. Its dictionary relates the infinite dimensional space-time symmetry group to Ward identities of the CFT. The spontaneous breaking of these asymptotic symmetries governs the dynamics of the soft sector in the CFT. Here we show that this sector encodes non-trivial backreaction effects that exhibit characteristics of maximal quantum chaos. A key element in the derivation is the identification of the Hilbert space of celestial CFT, defined through radial quantization, with that of a constantly accelerating Rindler observer. From the point of view of the bulk, Rindler particles exhibit Lyapunov behavior due to shockwave interactions that shift the observer horizon. From the point of view of the boundary, the superrotation Goldstone modes affect the relevant representations of the celestial Virasoro symmetry in a manner that induces Lyapunov behavior of out-of-time-ordered celestial correlators.

Light Propagating in a Born–Infeld Background as Seen by an Accelerated Observer

AbstractThe propagation of light in the Born–Infeld (BI) background as seen by an accelerated observer is examined. In a Born–Infeld electromagnetic field, light trajectories are governed by the null geodesics of the effective optical metric. The accelerated observer is in a Rindler frame, a situation that, according to the Einstein equivalence principle, is equivalent to being in a uniform gravitational field. The phase velocity of light propagating through a purely magnetic or electric BI background is determined as measured by the Rindler observer. The BI field and the acceleration of the frame have opposite effects on the propagating light; while the intense electric or magnetic BI background decreases the velocity of light, in the accelerated frame light may exceed its velocity in vacuum. Light propagating parallel or transversal to the acceleration direction of the Rindler frame is considered. The redshift of light pulses sent from one Rindler observer to another in the BI background is also calculated.

Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint

Abstract By using simplified 2D gravitational, non-Lorentz invariant actions constructed from the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a radial observer in Schwarzschild spacetime. We then fully characterize the remnant symmetries corresponding to this near-horizon 2D geometry by solving the motion equations adapted to 2D Milne space. This symmetries, which represent special or privileged diads, acquire the form of uniformly accelerated (Rindler) observers whose constant acceleration is proportional to the black hole mass M.

Correlation redistribution by causal horizons

The Minkowski vacuum |0rangle _M, which for an inertial observer is devoid of particles, is perceived as a thermal bath by Rindler observers living in a single Rindler wedge (Unruh in Phys Rev D 14:870, 1976) as a result of the discrepancy in the definition of positive frequency between the two classes of observers and a strong entanglement between degrees of freedom in the left and right Rindler wedges. We revisit the problem of quantification of the correlations in a two-mode state of a free neutral scalar field which is observed by an inertial observer Alice and left/right Rindler observers Rob/AntiRob, a problem that pertains to the field of relativistic quantum information and has been previously studied in Martin-Martinez et al. (Phys Rev D 82:064006, 2010) and Datta (Phys Rev A 80:052304, 2009). We focus on the analysis of informational quantities like the locally accessible and locally inaccessible information (Koashi and Winter in Phys Rev A 69:022309, 2004; Fanchini et al. in Phys Rev A 84:012313, 2011; Fanchini et al. in New J Phys 14:013027, 2012) and a closely associated entanglement measure, the entanglement of formation. We conclude that, with respect to the correlation structure probed by inertial observers alone, the introduction of a Rindler observer gives rise to a correlation redistribution which can be quantified by the entanglement of formation. Given the informational meaning of the derived correlations, we discuss on the capacity of a quantum channel to communicate classical information between accelerated parties.

Physical observers, T-vacuum and Unruh like effect in the radiation dominated early universe

We report the existence of an Unruh like effect, for physical observers (cosmo- logical and comoving observers) in the radiation dominated early universe, which is possible due to the discovery of a new vacuum state (referred here as the T−vacuum). Both the comoving and the cosmological observers, who are crucial in our understanding of cosmology, observe this T−vacuum as a particle excited state and are able to detect radiation due to particle creation. We draw a robust analogy with the Unruh effect, whereby — (i) the physical observers here are closely analogous to the accelerated (Rindler) observers in the flat spacetime, and (ii) the T−vacuum plays the role of the Minkowski vacuum state which contains particles when viewed from the physical observers frame. Our analogy is further supported by a proof of well-defined (hadamard) behavior of the T−vacuum in the entire spacetime. All our analysis of the particle creation process is done here within a two dimensional set up.

Simulating Indefinite Causal Order With Rindler Observers

Realization of indefinite causal order (ICO), a theoretical possibility that even causal relations between physical events can be subjected to quantum superposition, apart from its general significance for the fundamental physics research, would also enable quantum information processing that outperforms protocols in which the underlying causal structure is definite. In this paper, we start with a proposition that an observer in a state of quantum superposition of being at two different relative distances from the event horizon of a black hole, effectively resides in ICO space-time generated by the black hole. By invoking the fact that the near-horizon geometry of a Schwarzschild black hole is that of a Rindler space-time, we propose a way to simulate an observer in ICO space-time by a Rindler observer in a state of superposition of having two different proper accelerations. By extension, a pair of Rindler observers with entangled proper accelerations simulates a pair of entangled ICO observers. Moreover, these Rindler-systems might have a plausible experimental realization by means of optomechanical resonators.

Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame

The ongoing conjecture that the presence of horizon may induce chaos in an integrable system, is further investigated from the perspective of a uniformly accelerated frame. Particularly, we build up a model which consists of a particle (massless and chargeless) trapped in harmonic oscillator in a uniformly accelerated frame (namely Rindler observer). Here, the Rindler frame provides a Killing horizon without any intrinsic curvature to the system. This makes the present observations different from previous studies. We observe that for some particular values of parameters of the system (like acceleration, energy of the particle), the motion of the particle trapped in harmonic potential systematically goes from periodic state to the chaotic. This indicates that the existence of horizon alone, not the intrinsic curvature (i.e. the gravitational effect) in the background, is sufficient to induce the chaotic motion in the particle. We believe the present study further enlighten and balustrade the conjecture.

Quantum Fields as Deep Learning

In this essay we conjecture that quantum fields such as the Higgs field is related to a restricted Boltzmann machine for deep neural networks. An accelerating Rindler observer in a flat spacetime sees the quantum fields having a thermal distribution from the quantum entanglement, and a renormalization group process for the thermal fields on a lattice is similar to a deep learning algorithm. This correspondence can be generalized for the KMS states of quantum fields in a curved spacetime like a black hole.

Rindler Observer Sublimation

In this note, we propose that an object moving with proper constant acceleration, i.e., a Rindler observer experiences a sublimation (or evaporation) process. In this first proposal, we do not consider the backreaction due to the sublimation. We focus on charged matter particles for the discussion, but for simplicity, we present the quantization of the neutrally charged massive scalar field in Rindler space. The amplitude from the Minkowski observer perspective of detection of matter particles that have been emitted by a Rindler observer, or accelerated detector, is computed in a new fashion. We make a comparison between the Rindler observer sublimation and the black hole evaporation. We present three variants of a new experimental setup, and we show that in two of them, the Minkowski amplitude of detection of matter particles corresponds to that of a thermal process. There is one, however, where deviations from thermality can be found. It is numerically explored.

Embedding into flat spacetime and black hole thermodynamics

It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher-dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes á la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacetime, it is indeed possible to arrive at the area scaling law for black hole entropy. Thus, by using the flat spacetime field theory, one can indeed provide a thermodynamic description of black holes. Implications are also discussed.

Matter-as-constrained-gravity quanta on multiple Rindler observer grounds

By considering matter as a constraint on the availability of gravitational degrees of freedom and accounting for the statistical interpretation of Rindler horizons, the freedom to construct quantum gravity theories reproducing General Relativity and Quantum Field Theory (QFT) as special cases is considerably reduced. On one hand, the mathematical structure of quantum gravity is restricted by the properties of Quantum Mechanics. On the other hand, one can predict a value for the fundamental quantum constant of gravity which is related to the Planck area via the Planck constant. These findings are compatible with spin-less particles of matter. In the context of canonical ensemble statistics, the von Neumann entropy concept is found to extend from matter to gravity. An important motivation and pillar for this development is the concept of multiple observer statistics and the total entropy perceived by Rindler observers with a particular spacing, which has a one-to-one correspondence to the Gibbons-Hawking-York boundary term.

Emergent Lorentz symmetry and the Unruh effect in a Lorentzian fermionic tensor network

In this paper we attempt to understand Lorentzian tensor networks, as a preparation for constructing tensor networks that can describe more exotic backgrounds such as black holes. To define notions of reference frames and switching of reference frames on a tensor network, we will borrow ideas from the algebraic quantum field theory literature. With these definitions, we construct simple examples of Lorentzian tensor networks and solve the spectrum for a choice of ``inertial frame'' based on Gaussian models of fermions and integrable models. In particular, the tensor network can be viewed as a periodically driven Floquet system, that by-pass the ``doubling problem'' and gives rise to fermions with exactly linear dispersion relations. We will find that a boost operator connecting different inertial frames, and notions of ``Rindler observers'' can be defined, and that important physics in Lorentz invariant QFT, such as the Unruh effect, can be captured by such skeleton of spacetime. We find interesting subtleties when the same approach is directly applied to bosons -- the operator algebra contains commutators that take the wrong sign -- resembling bosons behind horizons.

Steady States, Thermal Physics, and Holography

It is well known that a Rindler observer measures a nontrivial energy flux, resulting in a thermal description in an otherwise Minkowski vacuum. For systems consisting of large number of degrees of freedom, it is natural to isolate a small subset of them and engineer a steady state configuration in which these degrees of freedom act as Rindler observers. In Holography, this idea has been explored in various contexts, specifically in exploring the strongly coupled dynamics of a fundamental matter sector, in the background of adjoint matters. In this article, we briefly review some features of this physics, ranging from the basic description of such configurations in terms of strings and branes, to observable effects of this effective thermal description.

New geometric and field theoretic aspects of a radiation dominated universe

The homogeneous and isotropic radiation dominated universe, following the inflationary stage, is expressed as a spherically symmetric and inhomogeneous spacetime upon a power-law-type conformal transformation of the null (cosmological) coordinates. This new spacetime metric has many interesting properties. While the static observers, at a fixed position in this new spacetime, do not see any horizon, some nonstatic observers encounter a horizon due to their motion which is analogous to the situation of Rindler observers in Minkowski spacetime. The symmetry of the new metric offers a unitarily inequivalent quantization of the massless scalar field and provides a new example of particle creation. We calculate the particle content of the cosmological vacuum state with respect to the static observer in this new spacetime who, with respect to cosmological time, is freely falling in the asymptotic past and future but accelerated in between.

Accelerated horizons and Planck-scale kinematics

We extend the concept of accelerated horizons to the framework of deformed relativistic kinematics at the Planck scale. We show that the non-trivial effects due to symmetry deformation manifest in a finite blueshift for field modes as measured by a Rindler observer approaching the horizon. We investigate whether, at a field theoretic level, this effect could manifest in the possibility of a finite horizon contribution to the entropy, a sort of covariant brick-wall. In the specific model of symmetry deformation considered it will turn out that a non-diverging density of modes close to the horizon can be achieved only by introducing a momentum space measure which violates Lorentz invariance.

Fluctuation-dissipation relation in accelerated frames

An uniformly accelerated (Rindler) observer will detect particles in the Minkowski vacuum, known as Unruh effect. The spectrum is thermal and the temperature is given by that of the Killing horizon, which is proportional to the acceleration. Considering these particles are kept in a thermal bath with this temperature, we find that the correlation function of the random force due to radiation acting on the particles as measured by the accelerated frame, shows the fluctuation-dissipation relation. It is observed that the correlations, in both ($1+1$) spacetime and ($1+3$) dimensional spacetimes, are of Brownian type. We discuss the implications of this new observation at the end.