'If we place x'=x-vt, it is clear that a point at rest in the system k must have a system of values x', y, z, independent of time. We first define tau as a function of x', y, z, and t. To do this we have to express in equations that tau is nothing else than the summary of the data of clocks at rest in system k, which have been synchronized according to the rule given in § 1.'
As the moving system is moving without acceleration, so with constant v, x'=x-vt is always the case. How can he say, it is clear that a point at rest in the moving system must have a system of coordinates in the stationary system, independent of time in the stationary system? It is always dependent.
Looks to me like you don't want a physicist so much as a native speaker of 1905-style German. But if I'm parsing this correctly, (x', y, z) are coordinates in the moving system; and a point at rest in the moving system obviously has constant (ie independent of time) moving-system coordinates. x, on the other hand, is its coordinate in the stationary system, and does change.
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quote:How can he say, it is clear that a point at rest in the moving system must have a system of coordinates in the stationary system, independent of time in the stationary system? It is always dependent.
I think by saying it is at rest he is narrowing the slice of local-frame-of-reference time to the specified conditions. While it's at rest, in other words, its coordinates in the local frame of reference do not change. This does have a time component but the time component doesn't affect the coordinates within the specified time period.
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