Bulletin of the American Physical Society
APS April Meeting 2020
Volume 65, Number 2
Saturday–Tuesday, April 18–21, 2020; Washington D.C.
Session C15: Quantum Theory of GravityLive
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Sponsoring Units: DGRAV Chair: David Craig, Oregon State University Room: Virginia B |
Saturday, April 18, 2020 1:30PM - 1:42PM Live |
C15.00001: Relational quantum dynamics: Quantum time dilation and temporal nonlocality Alexander R. H. Smith, Philipp A. Hoehn, Maximilian P. E. Lock, Mehdi Ahmadi The lesson of general relativity is background independence, which results in a Hamiltonian constraint. This presents a challenge for quantum gravity because the quantization of this constraint demands that physical states of geometry and matter are frozen, leading to the problem of time. We must then explain how the conventional notion of time evolution emerges, which motivates the need for relational quantum dynamics. Using covariant time observables, I will demonstrate the equivalence of two previously thought to be distinct approaches to relational quantum dynamics: the evolving constants of motion program and the Page-Wootters formalism. The equivalence between these approaches yields a temporal frame change map that transforms between the dynamics seen by different clocks. This map will be used to illustrate a temporal nonlocality effect that results in a superposition of time evolutions from the perspective of a clock indicating a superposition of different times. I will then demonstrate a novel quantum time dilation effect that occurs between two clocks when one moves in a superposition of different relativistic momenta. I will argue that this time dilation effect is observable with present-day technology and offers a new test of relativistic quantum mechanics. [Preview Abstract] |
Saturday, April 18, 2020 1:42PM - 1:54PM Live |
C15.00002: Gauge Independent Effective Field Equations Sanjib Katuwal, Richard Woodard Were it not for gauge dependence, the vacuum polarization could be used to quantum-correct Maxwell’s equations so that quantum gravitational corrections to electromagnetism could be studied the same way we understand classical electrodynamics. The received wisdom is that, no matter how small quantum corrections are, they can only be inferred using the gauge independent S-matrix. In this talk I demonstrate how gauge dependence can be removed by accounting for the quantum gravitational interactions of the source which disturbs the effective field and the observer who measures this field. The result is a set of gauge-independent effective field equations which can be studied in complete analogy to classical electrodynamics. [Preview Abstract] |
Saturday, April 18, 2020 1:54PM - 2:06PM Live |
C15.00003: Quantization of a causal diamond in 2+1 dimensional gravity Rodrigo Andrade e Silva, Ted Jacobson We develop the reduced phase space quantization of a ``causal diamond'' in pure 2+1 dimensional gravity with a negative cosmological constant. The system is defined as the domain of dependence of a spacelike topological disc with fixed boundary length. After removing all gauge redundancy, the phase space is found to be the cotangent bundle of $\text{Diff}^+\!(S^1)/\text{PSL}_2(\mathbb R)$, where $\text{Diff}^+\!(S^1)$ denotes the group of orientation-preserving diffeomorphisms of the circle. The physical degrees of freedom represent the possible shapes of causal diamonds that can have the topological disc as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical quantization is required -- in particular, since the configuration space is a homogeneous space for a Lie group, we apply the group-theoretic quantization scheme developed by Isham. There are strong indications that the Hilbert space of the associated quantum theory is given by wavefunctions on some coadjoint orbit of the Virasoro group, with labels in irreducible unitary representations of the corresponding little group. [Preview Abstract] |
Saturday, April 18, 2020 2:06PM - 2:18PM On Demand |
C15.00004: Some Implications of Invariant Boltzmann Statistical Mechanics to Quantum Gravity and Noncommutative Geometry of Physical Space and its Fractal Spectral Dimension. Siavash Sohrab According to invariant Boltzmann statistical mechanics [1], Kelvin absolute temperature T [K] is identified as Wien wavelength $\lambda _{\mathrm{w\beta -1}}$ [m] of thermal oscillations leading to \textit{internal} \textit{measures} of spacetime $(\lambda_{w\beta -1} ,\tau_{w\beta -1} )$ and \textit{external} \textit{measures} of space and time $(x_{\beta } =N_{x} \lambda_{w\beta -1} ,t_{\beta } =N_{t} \tau _{w\beta -1} )$. Therefore, temperature of space or Casimir vacuum fixes local measures of \textit{spacetime} $(\lambda_{w\beta -1} ,\tau_{w\beta -1} )$that are not \textit{independent} because $v_{ws} =\lambda_{ws} /\tau_{ws} $ must satisfy the vacuum temperature. Since Wien displacement law $\lambda_{w} T=0.29\mbox{\thinspace \thinspace cm-K\thinspace =\thinspace 0.0029\thinspace [m}^{2}]$ requires the change of units [m/cm] $=$ 100, the classical temperature conversion formula becomes $T[m]=^{o}\mbox{C[m]}\mbox{\thinspace +\thinspace 2.731}$ with 2.731 close to Penzias-Wilson [1965] cosmic microwave background radiation temperature $T_{CMB} \simeq 2.73\mbox{\thinspace [m}]$. The role of analytic functions, Cauchy-Riemann conditions, and possible imaginary nature of internal spacetime coordinates, due to connections to Riemann surfaces at lower scale $\beta \quad -$1, on path-independence of trajectories of quantum transitions and Heisenberg equation of motion are discussed. Finally, some implications of the hydrodynamic model to quantum gravity as a dissipative deterministic system [2] and fractal spectral dimension of noncommutative geometry of space [3] are examined. $^{\mathrm{1}}$ Sohrab, S. H.,\textit{ ASME J. Energy Resoures Technology} \textbf{138}, 1-12 (2016). $^{\mathrm{2}}$ `t Hooft, G., \textit{Quantum Grav}. \textbf{16}, 3263 (1999). $^{\mathrm{3\thinspace }}$Connes, A., \textit{Lett. Math. Phys}. \textbf{34}, 238 (1995). [Preview Abstract] |
Saturday, April 18, 2020 2:18PM - 2:30PM |
C15.00005: Poincare invariance of macroscopic observables in a lattice theory Bekir Baytas, Eugenio Bianchi, Pietro Dona In quantum field theory lattice discretization deforms the Poincar\'{e} algebra. In this paper we show how Poincar\'{e} invariance can be recovered by a set of generators in a definitive double-scaling limit. In particular, we introduce a set of smeared observables over mesoscopic regions as deformed Poincar\'{e} generators which form Poincar\'{e} algebra in the limit of infinite number of sites and infinite mesoscopic scale but fixed finite lattice spacing. We find that the lattice vacuum is Poincar\'{e}-smeared invariant under the transformation of the unitary operator from the deformed Poincar\'{e} generators in the double-scaling limit. The results presented demonstrate a new proposal that the Poincar\'{e} invariance is manifest on a lattice without taking the lattice spacing to zero. [Preview Abstract] |
Saturday, April 18, 2020 2:30PM - 2:42PM On Demand |
C15.00006: Memory and Infrared Divergences in Quantum Gravity Gautam Satishchandran, Robert Wald We investigate the implications of the close relationship between the memory effect and infrared divergences in quantum gravity. The memory effect implies that the ``out'' Hilbert space of any scattering process with nonvanishing memory is unitarily inequivalent to the ``in'' Hilbert space. Consequently, the memory effect implies that ``out'' scattering states live in an uncountably infinite set of unitarily inequivalent Hilbert spaces (one for each memory effect). It is, apriori, unclear if one can construct a Hilbert space for scattering that is (1) separable and (2) invariant under the action of the BMS group. In this talk I will present progress towards the construction of such a Hilbert space. [Preview Abstract] |
Saturday, April 18, 2020 2:42PM - 2:54PM On Demand |
C15.00007: Riemannian Geometry and General Relativity Reframed as a Generalized Lie Algebra Joseph Johnson Quantum Theory (QT) and the Standard Model (SM) are expressible in Lie algebra frameworks while General Relativity (GR) is framed in the non-linear differential equations of Riemannian Geometry (RG), a very different framework that makes their union difficult. We show that RG can be reframed as a NonCommutative Algebra (NCA) that is a generalization of a Lie algebra (LA) where ``structure functions'' of position (X) generalize the LA structure constants. Such a NCA becomes an (approximate) LA in small regions of space-time. We begin with an Abelian algebra of n Hermitian operators X$^{\mathrm{\mu }}$ ($\mu \quad =$ 0, 1, .. n-1) with representations on a Hilbert space whose eigenvalues represent independent variables such as space-time. We define operators D$^{\mathrm{\mu }}$ that by definition translate the corresponding eigenvalues of X$^{\mathrm{\mu }}$ each by a distance ds as dX$^{\mathrm{\lambda }}$(ds) $=$ exp(a ds $\eta _{\mathrm{\mu \thinspace }}$D$^{\mathrm{\mu }})$ X$^{\mathrm{\lambda \thinspace }}$exp(-a ds $\eta_{\mathrm{\nu \thinspace }}$D$^{\mathrm{\nu }}$ ) - X$^{\mathrm{\lambda }} \quad =$ ds $\eta_{\mathrm{\mu \thinspace }}$[ D$^{\mathrm{\mu }}$, X$^{\mathrm{\thinspace \lambda }}$]/a $+$ ho where a is a constant and $\eta_{\mathrm{\mu }}$ is a unit vector for the translation. We define the functions g$^{\mathrm{\mu \nu }}$(X) $=$ [D$^{\mathrm{\mu }}$, X$^{\mathrm{\nu }}$]/a and show that ds$^{\mathrm{2}}$ $=$ g$_{\mathrm{\mu \nu }}$(X) dX$^{\mathrm{\mu }}_{\mathrm{\thinspace }}$dX$^{\mathrm{\nu }}$ proving that g$_{\mathrm{\mu \nu }}$(X) is the metric for the space taken in the position diagonal representation where D$^{\mathrm{\thinspace \mu }} \quad =$ a g$^{\mathrm{\mu \upsilon }}$(y) ($\partial $/$\partial $y$^{\mathrm{\nu }}) \quad +$ A$^{\mathrm{\mu }}$ (y) thereby defining [D$^{\mathrm{\thinspace \mu }}$, D$^{\mathrm{\thinspace \nu }}$]. Integration with QT gives a $=$ iž. Details and predictions are discussed. [Preview Abstract] |
Saturday, April 18, 2020 2:54PM - 3:06PM Not Participating |
C15.00008: Breakdown of the Equivalence Principle for a composite quantum body. Andrei Lebed We investigate behavior of a quantum body with internal degrees of freedom in an external gravitational field. We show that all quantum states of such a body can be subdivided into two types: traditional states and exotic ones. For traditional quantum states, gravitational masses are shown to be equal to their inertial masses and, thus, the Equivalence Principle survives. On the other hand, for exotic quantum states -- coherent macroscopic ensembles of the superpositions of stationary quantum states -- gravitational masses are not anymore related to energies by the Einstein's equation, E $=$ mc$^{\mathrm{2}}$ . We discuss possibilities to create such exotic states, which break the Equivalence Principle, by lasers in the Earth's laboratories. [Preview Abstract] |
Saturday, April 18, 2020 3:06PM - 3:18PM Not Participating |
C15.00009: Rotating Gravastars Emil Mottola Gravitational Condensate Stars (gravastars) have been proposed as the non-singular end state of complete gravitational collapse consistent with quantum principles. Unlike black holes, gravastars have a finite density p$=$-$\rho $ condensate interior, and a boundary layer of finite surface tension replacing the classical black hole horizon. In the non-rotating spherically symmetric case, the gravastar solution actually follows from Schwarzschild's well-known interior solution, when its radius approaches the Schwarzschild radius. I will describe recent progress in finding solutions that describe rotating gravastars, and a new proposal for the interior of the Kerr geometry describing a spinning condensate, as well as the possibility of testing this proposal with gravitational wave and multi-messenger signatures. [Preview Abstract] |
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