quantum logic toposes
A quantum logic topos (QLT) is defined as an extension of the concept of a topos in which the Heyting algebra or subobject classifier of the standard elementary topos is replaced by a quantum logic that is axiomatically defined by a non-commutative lattice structure such as that of a many valued, -logic algebra, modified to a non-distributive lattice structure corresponding to that of the quantum physics events.
Quantum logics topoi are thus generalizations of the Birkhoff and von Neumann definition of quantum state spaces based on their definition of a quantum logic (lattice), as well as a non-Abelian, higher dimensional extension of the recently proposed concept of a ‘quantum’ topos which employs the (commutative) Heyting logic algebra as a subobject classifier.
Some specific examples are considered in the following two recent references.
- 1 Butterfield, J. and C. J. Isham: 2001, space-time and the philosophical challenges of quantum gravity., in C. Callender and N. Hugget (eds. ) Physics Meets Philosophy at the Planck scale., Cambridge University Press,pp.33–89.
- 2 Butterfield, J. and C. J. Isham: 1998, 1999, 2000–2002, A topos perspective on the Kochen–Specker theorem I - IV, Int. J. Theor. Phys, 37 No 11., 2669–2733 38 No 3., 827–859, 39 No 6., 1413–1436, 41 No 4., 613–639.
|Title||quantum logic toposes|
|Date of creation||2013-03-22 18:13:18|
|Last modified on||2013-03-22 18:13:18|
|Last modified by||bci1 (20947)|
|Synonym||extended quantum topos|
|Defines||quantum logics topoi|
|Defines||quantum logics toposes|
|Defines||toposes with quantum logics subobject classifiers|