Cosmological Singularities and Noncommutative Geometry

• Authors: Michał Heller

Title variants

PL

Osobliwości kosmologiczne i geometria nieprzemienna

EN

Cosmological Singularities and Noncommutative Geometry

• Languages of publication: PL

Abstracts

PL

In the previous paper (Filozofia Nauki No 3-4, 1994, pp. 7-17) we have shown how the initial and final singularities in the closed Friedman world model can be analysed in terms of the structured spaces in spite of the fact that these singularities constitute the single point in the b-boundary of space-time. In the present paper we generalize our approach by using methods of noncommutative geometry. We construct a noncommutative algebra in terms of which geometry of space-time with singularities can be developed. This algebra admits a representation in the space of operators on a Hilbert space, and the initial and final singularities in the closed Friedman model are given by its two distinct representations. The striking feature of this approach is its analogy with the mathematical formalism of quantum mechanics.

• Publisher: University of Warsaw, Institute of Philosophy
• Journal: Filozofia Nauki
• Year: 1997
• Volume: 5
• Issue: 3
• Pages: 5-14

Dates

published

1997-09-01

Contributors

author

Michał Heller