
#1
Mar712, 03:06 AM

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When we dealing with questions like "S'frame moves with respect to Sframe at a velocity u in x direction" then we also assume that "Sframe also moves with respect to S'frame at a velocity u in x direction"
Why this assumption is correct? 



#2
Mar712, 04:30 AM

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Hi ENDLESSYOU! Welcome to PF!
We have to assume that the observers in S and S' are using units (of distance and time) which make their speeds equal … if S was using metres, and S' was using feet, it wouldn't work!(btw, this has nothing to do with einstein, it works for galileo also) 



#3
Mar712, 05:01 AM

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#4
Mar712, 05:02 AM

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about the principle of relativityBecause of symmetry? 



#5
Mar712, 05:06 AM

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#6
Mar712, 05:10 AM

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S's North is S''s North. 



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Mar712, 05:16 AM

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Mar712, 05:27 AM

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Mar712, 05:34 AM

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Mar712, 05:34 AM

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Mar712, 05:46 AM

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#12
Mar712, 05:47 AM

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#13
Mar712, 08:29 AM

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Let's suppose that u sees u' moving east at, say, 10 m/s. If they are next to one another at t= 0 then u will see u' move 100 m in 10 seconds. From u' point of view, u is moving west but he will still measure 100 m between them after 10 seconds. That's why u' sees u moving at 10m/s also but in the opposite direction: [itex]v_u= v_{u'}[/itex]




#14
Mar812, 09:20 AM

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#15
Mar812, 09:22 AM

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#16
Mar1112, 08:57 AM

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The relative velocity of the S' frame of reference with respect to the S frame of reference can generally be in any spatial direction (as reckoned from the S frame of reference), and the relative velocity of the S frame of reference with respect to the S ' frame of reference can be generally in any spatial direction (as reckoned from the S' frame of reference). The only constraint is that the magnitudes of these 3d velocity vectors must be equal to one another. Incidentally, there is a slight error in your description. You should replace the words "at a velocity u in x direction" with the words "at a velocity u in x' direction". The x and x' axes are not pointing in the same directions in 4D spacetime, even for Standard Configuration. Each has a component in the time direction of the other's frame of reference. Chet 


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