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2 - Definition of causality on a structureless set

Published online by Cambridge University Press:  04 August 2010

R. N. Sen
Affiliation:
Ben-Gurion University of the Negev, Israel
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Summary

In the following we shall assume that the space, time and space-time of physics are made up of ‘points’ in the sense of Euclidean geometry. This assumption has been questioned by Wigner since 1952, and his reservations will be the subject of Part II of this book.

We shall begin by defining the notion of causality (which we shall call Einstein–Weyl causality) on a set of points devoid of any mathematical structure. It will be defined as a partial order on the set. Our point of departure is the observation that the propagation of a light ray determines a total order (the past-future order) on its path. We shall try to build up the causal structure by abstraction from the intersection properties of these paths in Minkowski space, and in real life.

Light rays

The fundamental objects in our scheme will be:

  1. (i) A nonempty set of points M.

  2. (ii) A distinguished family of subsets of M, called light rays.

The fundamental relation in our scheme will be a total order defined on the light rays.

We shall use the term light ray as a shorthand for the space-time path of a light ray; more precisely, for a mathematical abstraction from the corresponding physical concept. Light rays will generally be denoted by the letter l. A light ray through the point x will be denoted by lx, one through the points x, y by lx, y.

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Publisher: Cambridge University Press
Print publication year: 2010

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  • Definition of causality on a structureless set
  • R. N. Sen, Ben-Gurion University of the Negev, Israel
  • Book: Causality, Measurement Theory and the Differentiable Structure of Space-Time
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511674761.006
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  • Definition of causality on a structureless set
  • R. N. Sen, Ben-Gurion University of the Negev, Israel
  • Book: Causality, Measurement Theory and the Differentiable Structure of Space-Time
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511674761.006
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Definition of causality on a structureless set
  • R. N. Sen, Ben-Gurion University of the Negev, Israel
  • Book: Causality, Measurement Theory and the Differentiable Structure of Space-Time
  • Online publication: 04 August 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511674761.006
Available formats
×