Twistor cosmology and quantum space-time
This project is concerned with a novel approach to the unification of space-time physics and quantum theory. We take the view that classical space-time itself is not to be regarded as a primary object which is then subjected to some form of quantisation procedure. Instead, the central object is a mathematical structure that we call a quantum space-time.
Quantum space-time structures
Intuitively, this structure can be regarded as the space of all space-time valued quantum operators. That is to say, each point in the infinite-dimensional quantum space-time corresponds to a quantum operator with the property that its expectation, in any quantum state, is a space-time point. The space of all such operators has a rich structure that appears to contain all the elements one needs both for a characterisation of the causal structure of relativistic space-time as well as a representation of the phenomena of quantum theory.
Extending four-dimensional space-time to higher dimensions
Many attempts to unify gravitational physics with other fundamental forces have pursued the idea of extending four-dimensional space-time to higher dimensions. Beginning with the introduction of the Kaluza-Klein theory of gauge potentials, such extensions have typically been carried out by increasing the spatial dimension of the space-time, while retaining the special role played by time.
In methodologies of this sort, however, it cannot be said that quantum mechanical characteristics of the fundamental forces are adequately incorporated into the structure of the higher dimensional space-time. Nor can it be said that the space-time itself is being treated in any useful sense as a quantum entity.
If we take the point of view that the universe is itself intrinsically quantum mechanical in an appropriate sense, then the most natural extension of space-time into higher dimensions has a completely different character from that suggested by the Kaluza-Klein theory and its generalisations.