User talk:Linsuain

As far as physics goes, I would like to provide this clarification: The world is understood in Classical Mechanics as a four-dimensional affine space. The points in this space are called world points or events. The set of all the translations (or parallel transports) of this space forms a four-dimensional vector space. Time is understood as a linear map from this four-dimensional vector space into a one-dimensional one. The kernel of this linear map is a three-dimensional vector subspace that consists of the parallel transports that map any event into a simultaneous one. The corresponding three-dimensional affine subspace of simultaneous events is the physical space. Finally, in this three-dimensional affine subspace there exists a metric (that provides the notions of distances and angles), defined through a scalar product in the corresponding vector space. So the three-dimensional space of simultaneous events is Euclidean. Note: Only the distance between simultaneous events has a precise meaning; the distance between non-simultaneous events depends on the reference system. In other words, we have a four-dimensional affine space and only in the three-dimensional subspaces formed by the set of all events simultaneous with a given one do we have a Euclidean metric. This structure is known in physics as a Galilean structure. Hope it helps.Linsuain 04:44, 1 August 2007 (UTC)