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## The logic of quantum mechanics derived from classical general relativity (1997)

Venue: | Foundations of Physics Letters |

Citations: | 9 - 4 self |

### Citations

312 |
The Quantum Theory of Motion
- Holland
- 1993
(Show Context)
Citation Context ... of the particle in a region. The particle-like axiom and the asymptotic flatness axiom assures us that the topologically non-trivial region can be confined but not split. We take the view of Holland =-=[11]-=- that most measurements can be reduced to position measurements. A sequence of shutters and collimators and filters (eg.such as used in a Stern-Gerlach apparatus) determines the state preparation, 4w... |

186 | Foundations of Quantum Mechanics - Jauch - 1968 |

89 |
Quantum Mechanics
- Ballentine
- 1990
(Show Context)
Citation Context ...bly to the familiar equations of non-relativistic and relativistic quantum mechanics respectively, together with commutation relations and a universal constant with the dimensions of Planck’s constant=-=[10]-=-. The conjectured 4-geon description of particles is speculative but this single assumption is able to unify the particle and field descriptions of nature, explain quantum logic and in doing so reconc... |

30 | Orthomodularity in infinite dimensions; a theorem of M
- Holland
- 1995
(Show Context)
Citation Context ... of the distributive law which is replaced with the weaker orthomodularity condition[4]. From this orthomodular lattice it is then possible to generate the Hilbert space structure of quantum mechanics=-=[5]-=-. That quantum systems satisfy a non-Boolean logic is an experimental fact that has never been satisfactorily explained. This paper suggests an origin for quantum logic and formally constructs an orth... |

28 |
A remarkable property of plane waves in general relativity
- Penrose
- 1965
(Show Context)
Citation Context ...f one existed, could not satisfy the logic of quantum mechanics. Gravitational waves are also described as evolving 3-manifolds and, although there may be some problems defining a global hypersurface =-=[16]-=-, they do not have the topological structure to exhibit the measurement-dependent effects characteristic of quantum mechanics. 3. It follows from the previous comment that there is no graviton. Potent... |

21 |
Indirect Evidence of Quantum Gravity
- Page, Geilker
- 1981
(Show Context)
Citation Context ...ach manifold consistent with the state preparation (M ∈ M) can 14have different asymptotic properties. This is an almost inevitable consequence of reconciling quantum mechanics and general relativity=-=[17]-=-. However, the present perspective on the origin of quantum mechanics accounts for the lack of a well-defined metric as being due to incompleteness of boundary conditions imposed by state preparation,... |

16 |
Classical physics as geometry
- Misner, Wheeler
- 1957
(Show Context)
Citation Context ...gests an origin for quantum logic and formally constructs an orthomodular lattice of propositions about manifolds in classical general relativity. Since the formulation of general relativity, attempts=-=[6, 7]-=- have been made to model elementary particles as topologically non-trivial structures in spacetime ∗ email: M.J.Hadley@warwick.ac.uk 1called geons. These models exhibited interesting particle-like pr... |

13 |
Closed Timelike Curves
- Thorne
- 1993
(Show Context)
Citation Context ...CTCs), their stability and the possibility of time travel with its associated inconsistencies [8]. Although CTCs appear unphysical, there is nothing in the theory of general relativity to exclude them=-=[9]-=-. General relativity treats spacetime as a manifold, which is locally diffeomorphic to ℜ 4 , but does not prescribe its topology[7]. Interacting classical objects (or fields) in a spacetime with CTCs ... |

12 |
Bell’s theorem: Does quantum mechanics contradict relativity
- Ballentine, Jarrett
- 1987
(Show Context)
Citation Context ...es from one arm of the experiment to the other. Quantum mechanics itself requires only a failure of weak-causality (statistical correlations of a non-local character between spacelike separated events=-=[18]-=-); with CTCs as an essential part of the structure of an elementary particle however, it is not clear why a failure of strong-causality (communication between spacelike separated events) is not appare... |

9 |
Half Integral Spin From Quantum Gravity
- Friedman, Sorkin
- 1982
(Show Context)
Citation Context ... By considering the measurements of the x and y components of spin of a 4-geon with spin-half it is possible to construct a modular lattice of propositions. It has been reported by Friedman and Sorkin=-=[13]-=- that manifolds with the transformation properties of a spinor can be constructed. For the construction which follows, we require the 4-geon to have more than one possible outcome from a Stern-Gerlach... |

6 |
The Logic of Quantum Mechanics, volume 15 of Encyclopedia of Mathematics and its Applications
- Beltrametti, Cassinelli
- 1981
(Show Context)
Citation Context ... is characterised by the propositions of an orthomodular lattice, the distinguishing feature of which is the failure of the distributive law which is replaced with the weaker orthomodularity condition=-=[4]-=-. From this orthomodular lattice it is then possible to generate the Hilbert space structure of quantum mechanics[5]. That quantum systems satisfy a non-Boolean logic is an experimental fact that has ... |

5 |
D Novikov, and Ulvi Yurtsever. Cauchy problem in spacetimes with closed timelike curves
- Friedman, Morris, et al.
- 1990
(Show Context)
Citation Context ...may not, be made. There has recently been much speculation about the existence of closed timelike curves (CTCs), their stability and the possibility of time travel with its associated inconsistencies =-=[8]-=-. Although CTCs appear unphysical, there is nothing in the theory of general relativity to exclude them[9]. General relativity treats spacetime as a manifold, which is locally diffeomorphic to ℜ 4 , b... |

4 |
A Gravitational Theory of Quantum Mechanics
- Hadley
- 1997
(Show Context)
Citation Context ... 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]. 2 INTRODUCTION Quantum logic is characterised by the propositions of an orthomodular lattice, the distinguishing feature ... |

3 |
Structural issues in quantum gravity - plenary session lecture given at the gr14 conference
- Isham
- 1995
(Show Context)
Citation Context ...offers a way to reconcile general relativity and quantum mechanics. Some of the implications and unresolved issues are: 1. Time is an asymptotic approximation as expected by workers in quantum gravity=-=[15]-=-. 2. The theory does not exclude classical objects. Measurements of a 3-geon, if one existed, could not satisfy the logic of quantum mechanics. Gravitational waves are also described as evolving 3-man... |

2 |
A gravitational explanation of quantum mechanics. Talk given at the
- Hadley
- 1996
(Show Context)
Citation Context ...omment 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]-=-. 2 INTRODUCTION Quantum logic is characterised by the propositions of an orthomodular lattice, the distinguishing feature of which is the failure of the distributive law which is replaced with the we... |