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algebra of spacetime events
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algebra of spacetime events - 08-16-2005, 03:49 PM

Let U (the universe) denote a set of all possible spacetime events. An event E (whether a wave or a particle) is any subset of U. To say that the event E has occurred, is to say that a measurement done is a subset of two mutually exclusive disjointed sets of exact position in space S(\psi) and time interval of zero T(\phi) such that at the least the event E is associated with an element of S and an element of T.

E=\psi \cup \phi and \psi \cap \phi = 0

In classical mechanics, an event E is denoted by the union of more than one spacetime points, which are all mutually exclusive disjointed points.

E=\psi_1 \cup \phi_1 \cup \psi_2 \cup \phi_2 \cup \psi_3 \cup \phi _3 \cup …

and the intersections of all points in S and T is the empty set

\psi_1 \cap \phi_1 \cap \psi_2 \cap \phi_2 \cap \psi_3 \cap \phi _3 \cup…=0

However, for quantum mechanics and Einstein’s relativities (SR and GR), the intersections cannot be identically zero.
  
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