Unruh Temperature Research Articles

Modified Unruh effect from generalized uncertainty principle

We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dependence on the cubic power of the acceleration of the reference frame. The dependence of the shifted temperature on the frequency is also pointed out and discussed.

Excitation of an Atom by a Uniformly Accelerated Mirror through Virtual Transitions.

We find that uniformly accelerated motion of a mirror yields excitation of a static two-level atom with simultaneous emission of a real photon. This occurs because of virtual transitions with probability governed by the Planck factor involving the photon frequency ν and the Unruh temperature. The result is different from the Unruh radiation of an accelerated atom, which is governed by the frequency of the atom, ω, rather than frequency of the emitted photon. We also find that the excitation probability oscillates as a function of the atomic position because of interference between contributions from the waves incident on and reflected from the mirror.

Implications of Maximum Acceleration on Dynamics

Considering the corrected Unruh temperature as well as the entropic force perspective of gravity, we are able to derive the modification of the Newton's law of gravity. In addition, we also investigate the effects of the highest achievable acceleration correction to the Unruh temperature on the Poisson equation. Moreover, we address modifications to the Newtonian cosmology as well as the Friedmann equations corresponding to the upper bound for acceleration.

Thermodynamic equilibrium with acceleration and the Unruh effect

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature T_U = A/2\pi where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.

NASA’s EM Drive Thrust from the Forces of the Quantum Vacuum of Spacetime

Building on the various manifestations of the forces latent in the quantum vacuum of spacetime such as Hawking’s radiation and Unruh temperature, we resolve a major paradox connected to an immensely important proposal by NASA scientists for constructing a practically fuelless spacecraft. In a nutshell, preliminary laboratory work shows that NASA’s electromagnetic drive project is viable and several experiments and measurements show it is real. Yet the proposal violates a fundamental principle of classical mechanics, namely Newton’s third law. The resolution of this paradox is quite straight forward in principle. It is simply the case that although the proposal seems to be based on classical mechanics and classical thinking it is only superficially so. Deep at the roots, the EM drive proposal of NASA is not classical physics but rather based on the vacuum forces of quantum cosmology and the theory of dark energy density of the universe. In fact the proposal is deeply linked to Hawking’s radiation and Unruh temperature, which is explained in some detail in the main body of the present short paper within the frame work of E-infinity Cantorian spacetime theory and D. Gross’ Heterotic superstring theory. In short the quintessence of our explanation is to regard the EM drive as a quasi electromagnetic cavity with an effective event horizon akin to that of a Hawking black hole emitting radiation causing ultimately the needed thrust to push the spacecraft forwards. In addition and by invoking fractal spacetime self similarity we show that a spacecraft will be subject to another cosmic thrust on the large scale of the entire cosmos.

Hawking effect and Unruh effect from the uncertainty principle

The exact expressions of the Hawking temperature and Unruh temperature are deduced using the uncertainty principle of Heisenberg and the vacuum fluctuations that cause the appearance of a particle-antiparticle pair close to an event horizon.

Rotation and spin dynamics in heavy-ion collisions

Statistical average of the axial current is evaluated on the basis of the covariantWigner function. In the zero-mass limit, the axial current is described by a smooth function only at temperatures higher than the Unruh temperature. At zero temperature, the axial current, as a function of the angular velocity and chemical potential, vanishes in a two-dimensional plane region.

Unruh effect in heavy ion collisions

We apply the idea of the Unruh effect to the description of particle production in relativistic heavy ion collisions. Because the full information about all particles is needed, we employ the spectra of hadrons generated by the UrQMD model for pp and Au+Au collisions at various energies. Particles are considered as generated straight at the Unruh horizon thus allowing estimation of the Unruh temperature of the source. The analysis is provided for different types of mesons and their charges.

Rainbow Rindler metric and Unruh effect

The energy of a particle moving on a space–time, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here, we find the explicit expressions for the coordinate transformations from rainbow Minkowski space–time to accelerated frame. The corresponding metric is also obtained which we call as rainbow Rindler metric. So far we are aware of that no body has done it in a concrete manner. Here, this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.

Anisotropic Unruh temperatures

The relative entropy between very high energy localized excitations and the vacuum, where both states are reduced to a spatial region, gives place to a precise definition of a local temperature produced by vacuum entanglement across the boundary. This generalizes the Unruh temperature of the Rindler wedge to arbitrary regions. The local temperatures can be read off from the short distance leading terms in the modular Hamiltonian. For free scalar and fermion fields they have a universal geometric expression that follows by solving a particular eikonal type equation in Euclidean space. This equation generalizes to any dimension the holomorphic property that holds in two dimensions. For regions of arbitrary shapes the local temperatures at a point are direction dependent. We compute their explicit expression for the geometry of a wall or strip.

Fast scrambling in holographic Einstein-Podolsky-Rosen pair

We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair exhibits fast scrambling. Strongly entangled quark and antiquark in mathcal{N} = 4 super Yang-Mills theory are considered. Their gravity dual is a fundamental string whose endpoints are uniformly accelerated in opposite direction. We slightly increase the acceleration of the endpoint and show that it quickly destroys the correlation between the quark and antiquark. The proper time scale of the destruction is τ∗ ∼ β ln S where β is the inverse Unruh temperature and S is the entropy of the accelerating quark. We also evaluate the Lyapunov exponent from correlation function as λL = 2π/β, which saturates the Lyapunov bound. Our results suggest that the fast scrambling or saturation of the Lyapunov bound do not directly imply the existence of an Einstein dual. When we slightly decrease the acceleration, the quark and antiquark are causally connected and an "one-way traversable wormhole" is created on the worldsheet. It causes the divergence of the correlation function between the quark and antiquark.

Comparing production cross-sections for QCD matter, Higgs boson, neutrino with dark energy in accelerating universe

In this research, the production cross-sections for quantum chromodynamics (QCD) matter, neutrino and dark energy due to acceleration of Universe are calculated. To obtain these cross-sections, the Universe production cross-section is multiplied by the particle or dark energy distribution in accelerating Universe. Also, missing cross-section for each matter and dark energy due to formation of event horizon is calculated. It is clear that the cross-section of particles produced near event horizon of Universe is much larger for higher acceleration of Universe. This is because as the acceleration of Universe becomes larger, the Unruh temperature becomes larger and the thermal radiations of particles are enhanced. There are different channels for producing Higgs boson in accelerating Universe. Universe may decay to quark and gluons, and then these particles interact with each other and Higgs boson is produced. Also, some Higgs bosons are emitted directly from event horizon of Universe. Comparing Higgs boson cross-sections via different channels, it is observed that at lower acceleration, [Formula: see text], the Universe will not be able to emit Higgs, but is still able to produce a quark and eventually for [Formula: see text] the Universe can only emit massless gluons. As the acceleration of Universe at the large hadron collider (LHC) increases, [Formula: see text], most of Higgs bosons production will be due to Unruh effect near event horizon of Universe. Finally comparing the production cross-section for dark energy with particle cross-sections, it is found that the cross-section for dark energy is dominated by QCD matter, Higgs boson and neutrino. This result is consistent with previous predictions for dark energy cross-section.

Unified first law and some general prescription: a redefinition of surface gravity

The paper contains an extensive study of the unified first law (UFL) in the Friedmann–Robertson–Walker spacetime model. By projecting the UFL along the Kodama vector the second Friedmann equation can be obtained. Also studying the UFL on the event horizon it is found that the Clausius relation cannot be obtained from the UFL by projecting it along the tangent to the event horizon as it can be for the trapping horizon. However, it is shown in the present work that Clausius relation can be obtained by projecting the UFL along the Kodama vector on the horizon and the result is found to be true for any horizon. Finally motivated by the Unruh temperature for the Rindler observer, surface gravity is redefined and a Clausius relation is obtained from the UFL by projecting it along a vector analogous to the Kodama vector.

Proper temperature of the Schwarzschild AdS black hole revisited

The Unruh temperature calculated by using the global embedding of the Schwarzschild AdS spacetime into the Minkowski spacetime was identified with the local proper temperature; however, it became imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of non-thermal radiation for that region. In this work, we revisit this issue in an exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem in terms of the Tolman's procedure. However, the process appears to be non-trivial in the sense that the original procedure assuming the traceless energy–momentum tensor should be extended in such a way that it should cover the non-vanishing case of the energy–momentum tensor in the presence of the trace anomaly. Consequently, we show that the proper temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes at both the horizon and the asymptotic infinity.

Van der Waals and resonance interactions between accelerated atoms in vacuum and the Unruh effect

We discuss different physical effects related to the uniform acceleration of atoms in vacuum, in the framework of quantum electrodynamics. We first investigate the van der Waals/Casimir-Polder dispersion and resonance interactions between two uniformly accelerated atoms in vacuum. We show that the atomic acceleration significantly affects the van der Waals force, yielding a different scaling of the interaction with the interatomic distance and an explicit time dependence of the interaction energy. We argue how these results could allow for an indirect detection of the Unruh effect through dispersion interactions between atoms. We then consider the resonance interaction between two accelerated atoms, prepared in a correlated Bell-type state, and interacting with the electromagnetic field in the vacuum state, separating vacuum fluctuations and radiation reaction contributions, both in the free-space and in the presence of a perfectly reflecting plate. We show that nonthermal effects of acceleration manifest in the resonance interaction, yielding a change of the distance dependence of the resonance interaction energy. This suggests that the equivalence between temperature and acceleration does not apply to all radiative properties of accelerated atoms. To further explore this aspect, we evaluate the resonance interaction between two atoms in non inertial motion in the coaccelerated (Rindler) frame and show that in this case the assumption of an Unruh temperature for the field is not required for a complete equivalence of locally inertial and coaccelerated points of views.

Matter equation of state in general relativity

We study how a strong gravity affects the equation of state of matters. For this purpose, we employ a canonical ensemble of classical monoatomic ideal gas inside a box in a Rindler spacetime. The total energy decreases monotonically with the increase of the external gravity representing its attractiveness. It is however bounded below, which is different from that of the Newtonian gravity case. As for the entropy, it decreases with the external gravity in the Newtonian regime. However, in the presence of strong gravity or ultra-relativistic high temperature, the entropy increases with the gravity. This result can be a resolution of the negative entropy problem of the ideal gas in the Newtonian gravity. In the presence of strong gravity, the bottom of the box is very close to the event horizon of the Rindler spacetime mimicking a blackhole and the gas behaves as if it is on an effective two dimensional surface located at the bottom of the box. Investigating the equation of state in the strong gravity regime, the temperature of the system is found to be not a free parameter but to approach a fixed value proportional to the external gravity, which is reminiscent of the Unruh temperature.

Local temperatures and local terms in modular Hamiltonians

We show there are analogues to the Unruh temperature that can be defined for any quantum field theory and region of the space. These local temperatures are defined using relative entropy with localized excitations. We show important restrictions arise from relative entropy inequalities and causal propagation between Cauchy surfaces. These suggest a large amount of universality for local temperatures, specially the ones affecting null directions. For regions with any number of intervals in two space-time dimensions the local temperatures might arise from a term in the modular Hamiltonian proportional to the stress tensor. We argue this term might be universal, with a coefficient that is the same for any theory, and check analytically and numerically this is the case for free massive scalar and Dirac fields. In dimensions $d\ge 3$ the local terms in the modular Hamiltonian producing these local temperatures cannot be formed exclusively from the stress tensor. For a free scalar field we classify the structure of the local terms.

Non-Markovian time evolution of an accelerated qubit

We present a new method for evaluating the response of a moving qubit detector interacting with a scalar field in Minkowski spacetime. We treat the detector as an open quantum system, but we do not invoke the Markov approximation. The evolution equations for the qubit density matrix are valid at all times, for all qubit trajectories and they incorporate non-Markovian effects. We analyze in detail the case of uniform acceleration, providing a detailed characterization of all regimes where non-Markovian effects are significant. We argue that the most stable characterization of acceleration temperature refers to the late time behavior of the detector, because interaction with the field vacuum brings the qubit to a thermal state at the Unruh temperature. In contrast, the early-time transition rate, that is invoked in most discussions of acceleration temperature, does not exhibit a thermal behavior when non-Markovian effects are taken into account. Finally, we note that the non-Markovian evolution derived here also applies to the mathematically equivalent problem of a static qubit interacting with a thermal field bath.

The Effect of Vacuum Fluctuations on Quantum Metrology for a Uniformly Accelerated Atom

We studied, in the framework of open quantum systems, the dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency for a uniformly accelerated polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields in Minkowski space-time. Our results show that the vacuum fluctuations in Minkowski space-time always make the quantum Fisher information decay, thus degrade the precision of the parameter estimation. The acceleration of the atom makes the quantum Fisher information of initial parameters of atomic state decay faster than those in case with static atom in Minkowski vacuum and even those in case with static atom in Minkowski thermal bath with corresponding Unruh temperature. The maxima of quantum Fisher information of atomic frequency and the optimal measurement time are shown to be smaller than those in the static atom in vacuum case as well as those in the corresponding thermal case.

Quantum gravity signatures in the Unruh effect

We study quantum gravity signatures emerging from phenomenologically motivated multiscale models, spectral actions, and Causal Set Theory within the detector approach to the Unruh effect. We show that while the Unruh temperature is unaffected, Lorentz-invariant corrections to the two-point function leave a characteristic fingerprint in the induced emission rate of the accelerated detector. Generically, quantum gravity models exhibiting dynamical dimensional reduction exhibit a suppression of the Unruh rate at high energy while the rate is enhanced in Kaluza-Klein theories with compact extra dimensions. We quantify this behavior by introducing the "Unruh dimension" as the effective spacetime dimension seen by the Unruh effect and show that it is related, though not identical, to the spectral dimension used to characterize spacetime in quantum gravity. We comment on the physical origins of these effects and their relevance for black hole evaporation.