Related papers: Some Reflections on the Status of Conventional Qua…
One of the main challenges in theoretical physics over the last five decades has been to reconcile quantum mechanics with general relativity into a theory of quantum gravity. However, such a theory has been proved to be hard to attain due…
We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Section 1, we introduce these problems. In Section 2, we introduce topos theory,…
The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which…
In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
One of the major issues confronting theoretical physics is finding a quantum theory of gravity and a resolution to the cosmological constant problem. It is believed that a true quantum theory of gravity will lead to a solution to the this…
A brief synopsis of recent conceptions and results, the current status and future outlook of our research program of applying sheaf and topos-theoretic ideas to quantum gravity and quantum logic is presented.
The problem of time in quantum gravity occurs because `time' is taken to have a different meaning in each of general relativity and ordinary quantum theory. This incompatibility creates serious problems with trying to replace these two…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…
The incompatibility between GR and QM is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - QM gives a universally valid basis for the description of all natural…