Mathematics Commons^™

Macrocausality Implies Lorenz Group: A Physics-Related Comment On Guts's Results, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in the space-time of Special Relativity, causality implies Lorenz group, i.e., if we know which events can causally influence each other, then, based on this information, we can uniquely reconstruct the affine structure of space-time. When the two events are very close, quantum effects, with their probabilistic nature, make it difficult to detect causality. So, the following question naturally arises: can we uniquely reconstruct the affine structure if we only know causality for events which are sufficiently far away from each other? Several positive answers to this question were provided in a recent paper by Alexander …

Discrete Causality Implies Lorenz Group: Case Of 2-D Space-Times, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that for Minkowski space-times of dimension larger than 2, any causality-preserving transformation is linear. It is also known that in a 2-D space-time, there are many nonlinear causality-preserving transformations. In this paper, we show that for 2-D space-times, if we restrict ourselves to discrete space-times, then linearity is retained: only linear transformation preserve causality.

Partial Orders For Representing Uncertainty, Causality And Decision Making: General Properties, Operations, And Algorithms, Francisco Adolfo Zapata

Open Access Theses & Dissertations

One of the main objectives of science and engineering is to help people select the most beneficial decisions. To make these decisions, we must know people's preferences, we must have the information about different possible consequences of different decisions. Since information is never absolutely accurate and precise, we must also have information about the degree of certainty of different parts on information. All these types of information naturally lead to partial orders:

- For preferences, a <= b means that b is preferable to a. This relation is used in decision theory.

- For events, a <= b means that a can influence b. This causality relation is one of the fundamental notions of physics, especially of physics of space-time.

* For uncertain statements, a <= b means that a is less certain than b. This relation is used in logics describing uncertainty, such as fuzzy logic.

In each of these areas, there is abundant research about studying the corresponding partial orders. …