Euclidean and Lorentzian quantum gravity—lessons from two dimensions

Ambjørn, J.; Loll, R.; Nielsen, Jakob Lindberg; Rolf, Juri

doi:10.1016/s0960-0779(98)00197-0

Cited by 47 publications

(78 citation statements)

References 22 publications

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“…A similar approach was successful in 2D Lorentzian gravity, where the regularized transfer matrix could be calculated, and its continuum limit taken in a straightforward way. 7 The resulting Hamiltonian agreed with the one obtained by continuum formal manipulations in the proper-time gauge ͓30͔, showing that the educated guesses made in this paper were justified. This calculation can be generalized to our 3D Lorentzian gravity model, but the matrix-model methods will probably only work in the case of a spherical spatial topology.…”

Section: Summary and Discussionsupporting

confidence: 68%

Nonperturbative 3D Lorentzian quantum gravity

Ambjørn¹,

2001

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We have recently introduced a discrete model of Lorentzian quantum gravity, given as a regularized nonperturbative state sum over simplicial Lorentzian space-times, each possessing a unique Wick rotation to the Euclidean signature. We investigate here the phase structure of the Wick-rotated path integral in three dimensions with the aid of computer simulations. After fine tuning the cosmological constant to its critical value, we find a whole range of the gravitational coupling constant k 0 for which the functional integral is dominated by nondegenerate three-dimensional space-times. We therefore have a situation in which a well-defined ground state of extended geometry is generated dynamically from a nonperturbative state sum of fluctuating geometries. Remarkably, its macroscopic scaling properties resemble those of a semiclassical spherical universe. Measurements so far indicate that k 0 defines an overall scale in this extended phase, without affecting the physics of the continuum limit. These findings provide further evidence that discrete Lorentzian gravity is a promising candidate for a nontrivial theory of quantum gravity.

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Section: Summary and Discussionsupporting

confidence: 68%

Nonperturbative 3D Lorentzian quantum gravity

Ambjørn¹,

2001

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“…Unlike previous approaches, we use a space of piecewise linear Lorentzian space-times as our starting point. That this procedure is in general inequivalent to path integrals over bona fide Euclidean geometries has already been demonstrated in two dimensions [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…We will again characterize simplices in terms of their vertex labels. The first two types of moves, (2,8) and (4,6), reproduce a set of ergodic moves in three dimensions when restricted to spatial slices. We will describe each of the moves in turn.…”

Section: Moves In Four Dimensionsmentioning

confidence: 99%

Dynamically triangulating Lorentzian quantum gravity

Ambjørn¹,

2001

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Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated extensively in d < 4, with promising results. It is based on a simplicial regularization of Lorentzian space-times and, most importantly, possesses a well-defined, non-perturbative Wick rotation. We present a detailed analysis of the geometric and mathematical properties of the discretized model in d = 3, 4. This includes a derivation of Lorentzian simplicial manifold constraints, the gravitational actions and their Wick rotation. We define a transfer matrix for the system and show that it leads to a well-defined self-adjoint Hamiltonian. In view of numerical simulations, we also suggest sets of Lorentzian Monte Carlo moves. We demonstrate that certain pathological phases found previously in Euclidean models of dynamical triangulations cannot be realized in the Lorentzian case.

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“…Fortunately, there are now non-trivial proposals [31,32,33,34,35,36,37] and results [38,39] concerning formulations of quantum gravity in terms of causal,lorentzian path integrals. In such a causal histories formulation, each history in the sum over histories comes with its own causal structure.…”

Section: Second Problem: Measurabilitymentioning

confidence: 99%

The strong and weak holographic principles

Smolin

2001

Nuclear Physics B

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We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious problems, which give rise to counterexamples already at the semiclassical level. The null form, proposed by Fischler, Susskind, Bousso and others, in which the bound is on the entropy of certain null surfaces, appears adequate at the level of a bound on the entropy of matter in a single background spacetime, but attempts to include the gravitational degrees of freedom encounter serious difficulties. Only the weak form seems capable of holding in the full quantum theory.The conclusion is that the holographic principle is not a relationship between two independent sets of concepts: bulk theories and measures of geometry vrs boundary theories and measures of information. Instead, it is the assertion that in a fundamental theory the first set of concepts must be completely reduced to the second. * smolin@phys.psu.edu 1

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Euclidean and Lorentzian quantum gravity—lessons from two dimensions

Cited by 47 publications

References 22 publications

Nonperturbative 3D Lorentzian quantum gravity

Nonperturbative 3D Lorentzian quantum gravity

Dynamically triangulating Lorentzian quantum gravity

The strong and weak holographic principles

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