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On universal coordinate transform in kinematic changeable sets. (English) Zbl 1389.83001

From the text: “From an intuitive point of view, changeable sets are sets of objects which, unlike elements of ordinary (static) sets may be in the process of continuous transformations, and which may change properties depending on the point of view on them (that is depending on the reference frame)”.
“Universal coordinate transforms …are the coordinate transforms under which the geometrically-time provision of an arbitrary material object in any reference frame is determined by the geometrically-time position of this object in a certain, fixed frame, independently of any internal properties of the object”.
“In the present paper …we prove that, in the classical Galilean and the Lorentz-Poincaré kinematics, the universal coordinate transform always exists. Also we construct one class of kinematics in which every particle can have its own ‘velocity of light’ and prove that, in these kinematics, a universal coordinate transform does not exist in nontrivial cases”.

MSC:

83A05 Special relativity
03E75 Applications of set theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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