# State vector reduction as a shadow of a noncommutative dynamics

@article{Heller2000StateVR, title={State vector reduction as a shadow of a noncommutative dynamics}, author={Michael Heller and Wiesław Sasin}, journal={Journal of Mathematical Physics}, year={2000}, volume={41}, pages={5168-5179} }

A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables…

## 10 Citations

Noncommutative unification of general relativity and quantum mechanics

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We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a…

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We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in Gen. Rel. Grav. (36, 111–126 (2004)). Generalized symmetries of the model are defined by a…

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- 2004

AbstractWe construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid Γ given…

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We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal…

Noncommutative Unification of General Relativity and Quantum Mechanics

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- 1999

We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct “limitingcases” of…

Noncommutative Unification of General Relativity with Quantum Mechanics and Canonical Gravity Quantization

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The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding…

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- Physics
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Basic ideas of noncommutative geometry are briefly presented. This mathematical theory, being global from the very beginning, can be used to model physics in which local concepts, such as those of…

Noncommutative regime of fundamental physics

- Mathematics
- 2001

We further develop a model unifying general relativity with quantum mechanics proposed in our earlier papers (J. Math. Phys. 38, 5840 (1998); 41, 5168 (2000)). The model is based on a noncommutative…

Time Flow in a Noncommutative Regime

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- 2007

We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal…

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