22 citations · 136 across the 26 of their papers we have counts for
18 papers · 1 filter
Causality and time order -- relativistic and probabilistic aspects
Michał Eckstein, Michael Heller
We investigate temporal and causal threads in the fabric of contemporary physical theories with an emphasis on empirical and operationalistic aspects. Building on the axiomatizatio…
Beyond the Space-Time Boundary
Michael Heller, Jerzy Król
In General Relativity a space-time is regarded singular if there is an obstacle that prevents an incomplete curve in to be continued. Usually, such a space-time is complete…
Gravity in the smallest
Michael Heller, Jerzy Król
Synthetic Differential Geometry (SDG) is a categorical version of differential geometry based on enriching the real line with infinitesimals and weakening of classical logic to int…
Synthetic Approach to the Singularity Problem
Michael Heller, Jerzy Król
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to wor…
Generalized derivations and general relativity
M. Heller, T. Miller, L. Pysiak +1
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra . Such a derivation, introduced by Bresar in 1991, is give…
General Relativity on Random Operators
Michael Heller, Leszek Pysiak, Wieslaw Sasin
We present a mathematical structure which unifies mathematical structures of general relativity and quantum mechanics. It consists of the noncommutative algebra of compactly suppor…
Anatomy of Malicious Singularities
Michael Heller, Zdzislaw Odrzygozdz, Leszek Pysiak +1
As well known, the b-boundaries of the closed Friedman world model and of Schwarzschild solution consist of a single point. We study this phenomenon in a broader context of differe…
Conceptual Unification of Gravity and Quanta
M. Heller, L. Pysiak, W. Sasin
We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{\cal A} on the groupoid Γ= E \times G where E is the…
Noncommutative Unification of General Relativity and Quantum Mechanics
Michael Heller, Leszek Pysiak, Wieslaw Sasin
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This…
Observables in a Noncommutative Unification of Quanta and Gravity. A Final Model
Leszek Pysiak, Michael Heller, Zdzislaw Odrzygozdz +1
We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in {\it Gen. Rel. Grav.} (2004) {\bf 36}, 111-126. Generalized symmetries of th…
Noncommutative Dynamics of Random Operators
Michael Heller, Leszek Pysiak, Wieslaw Sasin
We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra on a transformation groupoid where …
Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model
M. Heller, Z. Odrzygozdz, L. Pysiak +1
We 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 group…
Structure of Malicious Singularities
M. Heller, Z. Odrzygozdz, L. Pysiak +1
We investigate spacetimes with their singular boundaries as noncommutative spaces. Such a space is defined by a noncommutative algebra on a transformation groupoid ,…
Noncommutative regime of fundamental physics
M. Heller, W. Sasin, Z. Odrzygozdz
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 o…
Noncommutative Unification of General Relativity with Quantum Mechanics and Canonical Gravity Quantization
M. Heller, W. Sasin
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restrictin…
Nonlocal Phenomena from Noncommutative Pre-Planckian Regime
M. Heller, W. Sasin
A model unifying general relativity with quantum mechanics is further developed. It is based on a noncommutative geometry which supposedly modelled the universe in its pre-Planckia…
Origin of Classical Singularities
M. Heller, W Sasin
We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory…
Local and Global Properties of the World
Jacques Demaret, Michael Heller, Dominique Lambert
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss thi…