What is x' for Moving Rocket from P?

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SUMMARY

The discussion centers on the application of Lorentz transformations in the context of a moving rocket and its relationship to events occurring at point P. When the rocket moves with velocity v, the coordinate x' can be expressed as x' = -vt' when considering the event from the rocket's frame of reference. The discussion emphasizes the importance of specifying the frame of reference for point P, particularly when x = 0 in the unprimed frame. A space-time diagram example illustrates that for a velocity of 0.6 and t = 4, the resulting x' for event B is -3, confirming that x' can indeed be negative.

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Lotto
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TL;DR
Observer S' is in a rocket that is moving relative to an observer S. Outside his rocket happened an event. How to construe the ##x'## of that event? Can be ##x'## negative?
I have a rocket and it is moving straight from a point P with a velocity ##v##. When I say that ##x'=0## is at the place we sit in the rocket, then when the event happened outside his rocket at the point P, can I say that the coordinate of the event is for him negative, so ##x'=-vt'##, although is it not in his stationary frame of reference?
 
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It depends what the ##x## coordinate of ##P## is which you have not specified, and which frame you are considering ##P## to be at rest in. If ##x=0## and the point is at rest in the unprimed frame then your answer is correct. Generally, you need to use the Lorentz transforms.
 
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Yes it can be negative

In the below space-time diagram enter .6 for velocity, 0 for x, 4 for t for event B.

You will see a negative x' for event B, x' = -3, t'=5

http://www.trell.org/div/minkowski.html
 

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