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Register a new userQuantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity
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The mathematical apparatus of quantum--mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinational aspects. SU(2) recoupling theory, involving Wigners 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, play nowadays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory -and of its extension to other Lie and quantum group- by using the collective term of `spin networks. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey Scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper we list and discuss some aspects of these developments -such as for instance the hyperquantization algorithm- as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.
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Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.
We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies (particles) under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alices particle) and vacuum fluctuations of the electromagnetic field (which limits Bobs ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We correct an error in the analysis of Mari et al. and of Baym and Ozawa, who did not properly account for the conservation of center of mass of an isolated system. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.
This paper draws on a number of Roger Penroses ideas - including the non-Hamiltonian phase-space flow of the Hawking Box, Conformal Cyclic Cosmology, non-computability and gravitationally induced quantum state reduction - in order to propose a radically unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: quantum process are associated with fine-scale fractal geometry, gravitational process with larger-scale heterogeneous geometry. With this, it becomes possible to explain the experimental violation of Bell Inequalities without having to abandon key ingredients of general relativity: determinism and local causality. Ensembles in IST can be described by complex Hilbert states over a finite set $mathbb C_p$ of complex numbers, where $p$ is a large finite integer. The quantum mechanics of finite-dimensional Hilbert spaces is emergent as a singular limit when $p rightarrow infty$. A small modification to the field equations of general relativity is proposed to make it consistent with IST.
It has recently been reported [textit{PNAS} textbf{114}, 2303 (2017)] that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here we study an alternative scenario: the clocks have different masses and energy gaps, which would produce time difference via gravitational interaction. The proposal of quantum clock synchronization for the gravity-induced time difference is discussed. We illustrate how the stability of measurement probability in the quantum clock synchronization proposal is influenced by the gravitational interaction induced by the clock themselves. It is found that the precision of clock synchronization depends on the energy gaps of the clocks and the improvement of precision in quantum metrology is in fact an indicator of entanglement generation. We also present the quantum enhanced estimation of time difference and find that the quantum Fisher information is very sensitive to the distance between the clocks.
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.
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