Quantization of general relativity

Brill, Dieter R.; Gowdy, Robert H.

doi:10.1088/0034-4885/33/2/301

Cited by 43 publications

(16 citation statements)

References 60 publications

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“…Efforts to quantize Einstein gravity go back to the 1930s [58]; the field has repeatedly been reviewed [35,[59][60][61][62][63][64]. By 'conventional' quantum gravity we will mean here a theory that starts from a generating functional…”

Section: Quantizing Gravitymentioning

confidence: 99%

Rationale for a correlated worldline theory of quantum gravity

Stamp

2015

New J. Phys.

106

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It is argued that gravity should cause a breakdown of quantum mechanics, at low energies, accessible to table-top experiments. It is then shown that one can formulate a theory of quantum gravity in which gravitational correlations exist between worldline or worldsheet paths, for the particle or field of interest. Using a generalized equivalence principle, one can give a unique form for the correlators, yielding a theory with no adjustable parameters. A key feature of the theory is the 'bunching' of quantum trajectories caused by the gravitational correlations-this is not a decoherence or a 'collapse' mechanism. This bunching causes a breakdown of the superposition principle for large masses, with a very rapid crossover to classical behaviour at an energy scale which depends on the physical structure of the object. Formal details, and applications of the theory, are kept to a minimum in this paper; but we show how physical quantities can be calculated, and give a detailed discussion of the dynamics of a single particle. OPEN ACCESS RECEIVED

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Section: Quantizing Gravitymentioning

confidence: 99%

Rationale for a correlated worldline theory of quantum gravity

Stamp

2015

New J. Phys.

106

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“…According to Wheeler observable properties of matter and fields must be explained by geometrical and topological properties of space-time and the dynamics of matter and fields configuration are the result of the dynamics of space-time geometry and topology. This assumption and its motivations were discussed by many authors [2]- [17]. It was shown that the properties of matter and fields is indeed closely connected with the topology of space-time [18]- [20].…”

Section: Introductionmentioning

confidence: 99%

“…All existing attempts to describe topology change or topological fluctuation are phenomenological. It is often supposed that topology changes are pure quantum phenomena [2], [10], [9], [13], but there is no real progress in their quantum description also.…”

Section: Introductionmentioning

confidence: 99%

Some Problems of Topology Change Description in the Theory of Spacetime

Konstantinov

1998

Int. J. Mod. Phys. D

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The problem of topology change description in gravitation theory is analyzed in details. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of the boundary conditions (or constraints). Therefore to describe the changes of space or spacetime topology the number of the coordinate maps, the order of their junction and the junction conditions must be converted from the class of constraints or boundary data into the class of dynamical variables. In the framework of four-dimensional theory this problem cannot be solved in its general formulation, while it is possible to describe the changes of three-space topology on the given fourmanifold. In the framework of multidimensional theories the space (and spacetime) may be considered as the embedded manifolds. It gives the real possibilities both for the dynamical description of the topology of space or spacetime and for the description of the topology changes of general kind.

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“…All attempts at the quantisation of general relativity have met so far with considerable difficulties (see Anderson 1964, Brill and Gowdy 1970, Ashtekar and Geach 1974. The problems are of various types, from the conceptual to the technical ones.…”

Section: Introductionmentioning

confidence: 99%

On the quantisation of gravity by embedding spacetime in a higher dimensional space

Pavšič

1985

Class. Quantum Grav.

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Abstract. Certain difficulties of quantum gravity can be avoided if we embed the spacetime V 4 into a higher dimensional space V N ; then our spacetime is merely a 4-surface in V N . What remains is conceptually not so difficult: just to quantise this 4-surface. Our formal procedure generalises our version of Stueckelberg's proper time method of worldline quantisation. We write the equations of V 4 in the covariant canonical form starting from a model Lagrangian which contains the classical Einstein gravity as a particular case. Then we perform quantisation in the Schrödinger picture by using the concepts of a phase functional and wave functional. As a result we obtain the uncertainty relations which imply that an observer is 'aware' either of a particular spacetime surface and has no information about other spacetime surfaces (which represent alternative histories); or conversely, he loses information about a particular V 4 whilst he obtains some information about other spacetimes (and histories). Equivalently, one cannot measure to an arbitrary precision both the metric on V 4 and matter distribution on various alternative spacetime surfaces. We show how this special case in the 'coordinate' representations can be generalised to an arbitrary vector in an abstract Hilbert space.

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Quantization of general relativity

Cited by 43 publications

References 60 publications

Rationale for a correlated worldline theory of quantum gravity

Rationale for a correlated worldline theory of quantum gravity

Some Problems of Topology Change Description in the Theory of Spacetime

On the quantisation of gravity by embedding spacetime in a higher dimensional space

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