Some Remarks on the Logic of Quantum Gravity (original) (raw)
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Some reflections on the status of conventional quantum theory when applied to quantum gravity
The Future of Theoretical Physics and Cosmology: …
All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far as the use of these continuum quantities in standard quantum theory can be traced back to certain a priori assumptions about the nature of space and time: assumptions that may be incompatible with the view of space and time adopted by a quantum gravity theory. My conjecture is that in, some yet to be determined sense, to each type of space-time there is associated a corresponding type of quantum theory in which continuum quantities do not necessarily appear, being replaced with structures that are appropriate to the specific space-time. Topos theory then arises as a possible tool for 'gluing' together these different theories associated with the different space-times. As a concrete example of the use of topos ideas, I summarise recent work applying presheaf theory to the Kochen-Specher theorem and the assignment of values to physical quantities in a quantum theory.
Logic is to the quantum as geometry is to gravity
Foundations of Space and Time
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular.
The logic of quantum mechanics derived from classical general relativity
Foundations of Physics Letters, 1997
For the first time it is shown that the logic of quantum mechanics can be derived from Classical Physics. An orthomodular lattice of propositions, characteristic of quantum logic, is constructed for manifolds in Einstein's theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves-a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparation and measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic. 1 Comment This paper has been published in Foundations of Physics Letters [1]. The work forms the basis of my doctoral thesis [2]. A short, less formal talk about my work is archived in quant-ph/9609021 [3].
2009
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 to i) conceptual difficulties present in both the component theories (General Relativity (GR) and Quantum Theory); ii) lack of experimental evidence, since the regimes at which quantum gravity is expected to be applicable are far beyond the range of conceivable experiments. Despite these difficulties, various approaches for a theory of Quantum Gravity have been developed. In this thesis we focus on two such approaches: Loop Quantum Gravity and the Topos theoretic approach. The choice fell on these approaches because, although they both reject the Copenhagen interpretation of quantum theory, their underpinning philosophical approach to formulating a quantum theory of gravity are radically different. In particular LQG is a rather conservative scheme,...
Social Science Research Network, 2020
A case study of quantum mechanics is investigated in the framework of the philosophical opposition "mathematical model-reality". All classical science obeys the postulate about the fundamental difference of model and reality, and thus distinguishing epistemology from ontology fundamentally. The theorems about the absence of hidden variables in quantum mechanics imply for it to be "complete" (versus Einstein's opinion). That consistent completeness (unlike arithmetic to set theory in the foundations of mathematics in Gödel's opinion) can be interpreted furthermore as the coincidence of model and reality. The paper discusses the option and fact of that coincidence it its base: the fundamental postulate formulated by Niels Bohr about what quantum mechanics studies (unlike all classical science). Quantum mechanics involves and develops further both identification and disjunctive distinction of the global space of the apparatus and the local space of the investigated quantum entity as complementary to each other. This results into the analogical complementarity of model and reality in quantum mechanics. The apparatus turns out to be both absolutely "transparent" and identically coinciding simultaneously with the reflected quantum reality. Thus, the coincidence of model and reality is postulated as necessary condition for cognition in quantum mechanics by Bohr's postulate and further, embodied in its formalism of the separable complex Hilbert space, in turn, implying the theorems of the absence of hidden variables (or the equivalent to them "conservation of energy conservation" in quantum mechanics). What the apparatus and measured entity exchange cannot be energy (for the different exponents of energy), but quantum information (as a certain, unambiguously determined wave function) therefore a generalized law of conservation, from which the conservation of energy conservation is a corollary. Particularly, the local and global space (rigorously justified in the Standard model) share the complementarity isomorphic to that of model and reality in the foundation of quantum mechanics. On that background, one can think of the troubles of "quantum gravity" as fundamental, direct corollaries from the postulates of quantum mechanics. Gravity can be defined only as a relation or by a pair of non-orthogonal separable complex Hilbert space attachable whether to two "parts" or to a whole and its parts. On the contrary, all the three fundamental interactions in the Standard model are "flat" and only "properties": they need only a single separable complex Hilbert space to be defined.
Quantum Gravity:the axiomatic approach, a possible interpretation
Twenty years ago, by extending the Wightman axiom framework, it has been found possible to quantize only a conformal factor of the gravitational field. Gravitons being excluded from this quantum scalar field theory, numerous attempts were done to give a valuable description of what could be quantum gravity. In this talk we present a familly of Lorentz manifolds which can be foliated by isotropic hypersurfaces and pose severe restrictions on the form of the energy-momentum tensor in Einstein's equations. They can be associated to gravitational waves "without gravitons" in a vacuum described by two cosmological functions, but not to a massless particle flow. From this cross-checking with the previous remark, a "very" primordial quantum cosmological scenario is proposed.
A Gravitational Explanation for Quantum Mechanics
1996
It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat, particle-like and has a non-trivial causal structure. The usual Cauchy data are no longer sufficient to determine a unique evolution. The measurement apparatus itself can impose non-redundant boundary conditions. Measurements of such an object would fail to satisfy the distributive law of classical physics. This model reconciles General Relativity and Quantum Mechanics without the need for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it is not universal; classical particles and waves could exist and there is no graviton.
Foundations of quantum gravity: The role of principles grounded in empirical reality
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2014
When attempting to assess the strengths and weaknesses of various principles in their potential role of guiding the formulation of a theory of quantum gravity, it is crucial to distinguish between principles which are strongly supported by empirical data-either directly or indirectly-and principles which instead (merely) rely heavily on theoretical arguments for their justification. Principles in the latter category are not necessarily invalid, but their a priori foundational significance should be regarded with due caution. These remarks are illustrated in terms of the current standard models of cosmology and particle physics, as well as their respective underlying theories, i.e. essentially general relativity and quantum (field) theory. For instance, it is clear that both standard models are severely constrained by symmetry principles : an effective homogeneity and isotropy of the known universe on the largest scales in the case of cosmology and an underlying exact gauge symmetry of nuclear and electromagnetic interactions in the case of particle physics. However, in sharp contrast to the cosmological situation, where the relevant symmetry structure is more or less established directly on observational grounds, all known, nontrivial arguments for the "gauge principle" are purely theoretical (and far less conclusive than usually advocated). Similar remarks apply to the larger theoretical structures represented by general relativity and quantum (field) theory, where-actual or potential-empirical principles, such as the (Einstein) equivalence principle or EPR-type nonlocality, should be clearly differentiated from theoretical ones, such as general covariance or renormalizability. It is argued that if history is to be of any guidance, the best chance to obtain the key structural features of a putative quantum gravity theory is by deducing them, in some form, from the appropriate empirical principles (analogous to the manner in which, say, the idea that gravitation is a curved spacetime phenomenon is arguably implied by the equivalence principle). Theoretical principles may still be useful however in formulating a concrete theory (analogous to the manner in which, say, a suitable form of general covariance can still act as a sieve for separating theories of gravity from one another). It is subsequently argued that the appropriate empirical principles for deducing the key structural features of quantum gravity should at least include (i) quantum nonlocality, (ii) irreducible indeterminacy (or, essentially equivalently, given (i), relativistic causality), (iii) the thermodynamic arrow of time, (iv) homogeneity and isotropy of the observable universe on the largest scales. In each case, it is explained-when appropriate-how the principle in question could be implemented mathematically in a theory of quantum gravity, why it is considered to be of fundamental significance and also why contemporary accounts of it are insufficient. For instance, the high degree of uniformity observed in the Cosmic Microwave Background is usually regarded as theoretically problematic because of the existence of particle horizons, whereas the currently popular attempts to resolve this situation in terms of inflationary models are, for a number of reasons, less than satisfactory. However, rather than trying to account for the required empirical features dynamically, an arguably much more fruitful approach consists in attempting to account for these features directly, in the form of a lawlike initial condition within a theory of quantum gravity.
Quantum Physics Without Quantum Philosophy, 2012
We explore the possibility of a Bohmian approach to the problem of finding a quantum theory incorporating gravitational phenomena. The major conceptual problems of canonical quantum gravity are the problem of time and the problem of diffeomorphism invariant observables. We find that these problems are artifacts of the subjectivity and vagueness inherent in the framework of orthodox quantum theory. When we insist upon ontological clarity-the distinguishing characteristic of a Bohmian approach-these conceptual problems vanish. We shall also discuss the implications of a Bohmian perspective for the significance of the wave function, concluding with unbridled speculation as to why the universe should be governed by laws so apparently bizarre as those of quantum mechanics.