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Register a new userA nested sequence of comoving Rindler frames, the corresponding vacuum states, and the local nature of acceleration temperature
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The Bogoliubov transformation connecting the standard inertial frame mode functions to the standard mode functions defined in the Rindler frame $R_0$, leads to the result that the inertial vacuum appears as a thermal state with temperature $T_0=a_0/2pi$ where $a_0$ is the acceleration parameter of $R_0$. We construct an infinite family of nested Rindler-like coordinate systems $R_1, R_2, ...$ within the right Rindler wedge, with time coordinates $tau_1, tau_2, ...,$ and acceleration parameters $a_1, a_2, ...$ by shifting the origin along the inertial $x$-axis by amounts $ell_1, ell_2,cdots$. We show that, apart from the inertial vacuum, the Rindler vacuum of the frame $R_n$ also appears to be a thermal state in the frame $R_{n+1}$ with the temperature $a_{n+1}/2pi$. In fact, the Rindler frame $R_{n+1}$ attributes to all the Rindler vacuum states of $R_1, R_2, ... R_n$, as well as to the inertial vacuum state, the same temperature $a_{n+1}/2pi$. The frame with the shift $ell$ and the corresponding acceleration parameter $a(ell)$ can be thought of as a Rindler frame which is instantaneously comoving with the Einsteins elevator moving with a variable acceleration. Our result suggests that the quantum temperature associated with such an Einsteins elevator is the same as that defined in the comoving Rindler frame. The shift parameters $ell_j$ are crucial for the inequivalent character of these vacua and encode the fact that Rindler vacua are not invariant under spatial translation. We further show that our result is discontinuous in an essential way in the coordinate shift parameters. Similar structures can be introduced in the right wedge of any spacetime with bifurcate Killing horizon, like, for e.g., Schwarzschild spacetime. This has important implications for quantum gravity when flat spacetime is treated as the ground state of quantum gravity.
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This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the multiverse idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, is different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime and the cosmological geometry of mini-superspace (see Appendix B) will appear in later papers. In classical general relativity, extended Rindler space is equivalent to flat Minkowski space; it consists of the union of the four wedges in (u,v) light-cone coordinates as in Fig.(1). In quantum mechanics, the wavefunction is an analytic function of (u,v) that is sensitive to branch points at the horizons u=0 or v=0, with branch cuts attached to them. The wavefunction is uniquely defined by analyticity on an infinite number of sheets in the cut analytic (u,v) spacetime. This structure is naturally interpreted as an infinite stack of identical Minkowski geometries, or universes, connected to each other by analyticity across branch cuts, such that each sheet represents a different Minkowski universe when (u,v) are analytically continued to the real axis on any sheet. We show in this paper that, in the absence of interactions, information doesnt flow from one Rindler sheet to another. By contrast, for an eternal black hole spacetime, which may be viewed as a modification of Rindler that includes gravitational interactions, analyticity shows how information is lost due to a flow to other universes, enabled by an additional branch point and cut due to the black hole singularity.
Some of the most prominent theoretical predictions of modern times, e.g., the Unruh effect, Hawking radiation, and gravity-assisted particle creation, are supported by the fact that various quantum constructs like particle content and vacuum fluctuations of a quantum field are observer-dependent. Despite being fundamental in nature, these predictions have not yet been experimentally verified because one needs extremely strong gravity (or acceleration) to bring them within the existing experimental resolution. In this Letter, we demonstrate that a post-Newtonian rotating atom inside a far-detuned cavity experiences strongly modified quantum fluctuations in the inertial vacuum. As a result, the emission rate of an excited atom gets enhanced significantly along with a shift in the emission spectrum due to the change in the quantum correlation under rotation. We propose an optomechanical setup that is capable of realizing such acceleration-induced particle creation with current technology. This provides a novel and potentially feasible experimental proposal for the direct detection of noninertial quantum field theoretic effects.
Based on an examination of the solutions to the Killing Vector equations for the FLRW-metric in co moving coordinates , it is conjectured and proved that the components(in these coordinates) of Killing Vectors, when suitably scaled by functions, are emph{zero modes} of the corresponding emph{scalar} Laplacian. The complete such set of zero modes(infinitely many) are explicitly constructed for the two-sphere. They are parametrised by an integer n. For $n,ge,2$, all the solutions are emph{irregular} (in the sense that they are neither well defined everywhere nor are emph{square-integrable}). The associated 2-d vectors are also emph{not normalisable}. The $n=0$ solutions being constants (these correspond to the zero angular momentum solutions) are regular and normalizable. Not all of the $n=1$ solutions are regular but the associated vectors are normalizable. Of course, the action of scalar Laplacian coordinate independent significance only when acting on scalars. However, our conclusions have an unambiguous meaning as long as one works in this coordinate system. As an intermediate step, the covariant Laplacians(vector Laplacians) of Killing vectors are worked out for four-manifolds in two different ways, both of which have the novelty of not explicitly needing the connections. It is further shown that for certain maximally symmetric sub-manifolds(hypersurfaces of one or more constant comoving coordinates) of the FLRW-spaces also, the scaled Killing vector components are zero modes of their corresponding scalar Laplacians. The Killing vectors for the maximally symmetric four-manifolds are worked out using the elegant embedding formalism originally due to Schrodinger . Some consequences of our results are worked out. Relevance to some very recent works on zero modes in AdS/CFT correspondences , as well as on braneworld scenarios is briefly commented upon.
We give a quantum mechanical description of accelerated relativistic particles in the framework of Coherent States (CS) of the (3+1)-dimensional conformal group SU(2,2), with the role of accelerations played by special conformal transformations and with the role of (proper) time translations played by dilations. The accelerated ground state $tildephi_0$ of first quantization is a CS of the conformal group. We compute the distribution function giving the occupation number of each energy level in $tildephi_0$ and, with it, the partition function Z, mean energy E and entropy S, which resemble that of an Einstein Solid. An effective temperature T can be assigned to this accelerated ensemble through the thermodynamic expression dE/dS, which leads to a (non linear) relation between acceleration and temperature different from Unruhs (linear) formula. Then we construct the corresponding conformal-SU(2,2)-invariant second quantized theory and its spontaneous breakdown when selecting Poincare-invariant degenerated theta-vacua (namely, coherent states of conformal zero modes). Special conformal transformations (accelerations) destabilize the Poincare vacuum and make it to radiate.
We find exact formulas for the Extended Uncertainty Principle (EUP) for the Rindler and Friedmann horizons and show that they can be expanded to obtain asymptotic forms known from the previous literature. We calculate the corrections to Hawking temperature and Bekenstein entropy of a black hole in the universe due to Rindler and Friedmann horizons. The effect of the EUP is similar to the canonical corrections of thermal fluctuations and so it rises the entropy signalling further loss of information.
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