The purpose of this paper is to present a model of a ‘quantum space‐time’ in which the global symmetries of space‐time are unified in a coherent manner with the internal symmetries associated with the state space of quantum‐mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space‐time imply that the pseudo‐Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space‐time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space‐time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen‐dimensional analogue of the Friedmann‐Robertson‐Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space‐time is an even perfect square, there exists a canonical way of breaking the global quantum space‐time symmetry so that a generic point of quantum space‐time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space‐time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space‐time description is an emergent feature arising as a consequence of a quantum averaging over the internal degrees of freedom. The familiar probabilistic features of the quantum state, represented by properties of the density matrix, can then be seen as a by‐product of the causal structure of quantum space‐time.
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25 April 2005
FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium
28 September-1 October 2004
Wroclaw (Poland)
Research Article|
April 25 2005
Twistor Cosmology and Quantum Space‐Time
D. C. Brody;
D. C. Brody
*Blackett Laboratory, Imperial College, London SW7 2BZ, UK
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L. P. Hughston
L. P. Hughston
†Department of Mathematics, King’s College London, The Strand, London WC2R 2LS, UK
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AIP Conf. Proc. 767, 57–95 (2005)
Citation
D. C. Brody, L. P. Hughston; Twistor Cosmology and Quantum Space‐Time. AIP Conf. Proc. 25 April 2005; 767 (1): 57–95. https://doi.org/10.1063/1.1923330
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