Consider the relative position of the inertial reference frames I and I’ as detected from I when the standard synchronized clocks of that frame read t. The reference frames I and I’ are in the arrangement which leads to the Lorentz transformations of the space-time coordinates of the same event. The distance between of the origins O and O’ is at that very moment V(t-0). Let M(x) and M’(x’) be two points located on the permanently overlapped OX(O’X’) axes, located ate the same point in space, when detected from I and I’ respectively. The length (x’-0) is a proper length in I. Measured from I it is the Lorentz contracted length (x’-0)/g where g is the Lorentz factor. Adding only lengths measured by observers from I the result is(adsbygoogle = window.adsbygoogle || []).push({});

(x’-0)/g=(x-0)-V(t-0). (1)

We obtain the “inverse” of (1) by changing the sign of V and interchanging the corresponding primed physical quantities with unprimed ones i.e.

(x-0)/g=(x’-0)+V(t-0) . (2)

Solving the simultaneous equations (1) and (2) for t and t’ respectively we obtain

(t-0)/g=(t’-0)+V(x’-0)/cc (3)

(t’-0)/g=(t-0)-V(x’-0)/cc (4)

Confronted with the “four line” derivation of the Lorentz transformations presented above would Einstein object?

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# Would Einstein object?

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