Question about derivation of lorentz transformation

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The discussion centers on the derivation of the Lorentz transformation, specifically addressing the use of t' instead of t in the equations. It clarifies that when the origin of the primed coordinate system moves at speed v relative to the unprimed system, the reverse holds true for the unprimed system, which moves at speed -v relative to the primed system. This symmetry is crucial, as it establishes that the transformation equations must be consistent regardless of the observer's frame of reference.

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Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register?

(The equation is uploades in the photo)
 

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Cozma Alex said:
Why does it use t' in that equation and not t? Isn't the equation relative to what an observer in the external frame of reference see? So if it is why not using the time he register?
If the origin of the primed coordinate system is moving at speed ##v## relative to the origin of the unprimed coordinate system, then the origin of the unprimed coordinate system is moving at speed ##-v## relative to the origin of the primed coordinate system. Because neither frame is prefered, the transformation from the primed coordinates to the unprimed coordinates must be the same as the transformation from the unprimed coordinates to the primed coordinates, except with ##v## replaced by ##-v##. That's where the circled equation comes from.
 
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