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I am having a personal discussion with somebody elsewhere (not on Physics Forums) and we are stuck at the moment because of a disagreement that I narrowed down to the question whether, in the context of SR, two observers in different reference frames can choose the origin of their coordinate system independently of each other, or whether one observer is bound by the choice of the other. Let me explain in more detail:

assume you have two rulers with distance markings on them (assumed to be identical for the sake of the argument) but without any numerical (or other) labeling defining the origin. When the two rulers are moving past each other, all that the observer in each reference frame sees are the bare markings on his and the moving ruler. Analogously, assume the same applies to the clock ticks that each observers registers for his and the other system's clocks. One observer can now obviously arbitrarily assign the origins to a certain markings/ticks both on his as well as the moving ruler/clock and thus be able to numerically define the coordinate systems. The question is, can the other observer independently choose his own origins to describe the scenario, or is he bound by the choice of the first observer? If the latter, from which postulate is this constraint derived?

assume you have two rulers with distance markings on them (assumed to be identical for the sake of the argument) but without any numerical (or other) labeling defining the origin. When the two rulers are moving past each other, all that the observer in each reference frame sees are the bare markings on his and the moving ruler. Analogously, assume the same applies to the clock ticks that each observers registers for his and the other system's clocks. One observer can now obviously arbitrarily assign the origins to a certain markings/ticks both on his as well as the moving ruler/clock and thus be able to numerically define the coordinate systems. The question is, can the other observer independently choose his own origins to describe the scenario, or is he bound by the choice of the first observer? If the latter, from which postulate is this constraint derived?

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