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Posted: Sun Nov 18, 2012 5:26 pm
suppose that a line is situated in a X-Y plane that the co ordinate of it's two end is (1,2) and (5,8).i am going just towards X axis in 0.5c.to me what will be the length of the line?
Posted: Mon Nov 26, 2012 3:36 pm
To you, there will be no length contraction of the line segment. It will appear to you the same long as it appears to an observer in the segment’s own (rest) frame of reference.
According to the special theory of relativity, length contraction happens ‘only’ in the direction of ‘relative motion. The motion (velocity) of the segment relative to you is 0.5c, but in the opposite, –X, direction. So, any contraction of the segment, if it is to happen, will appear (to you) in the –X direction only. But your one-dimensional segment has no length (space dimension) along that direction. Thus, you will see the segment ‘in length’ the same as it appears in its own rest frame of reference.
Now, if you consider a strip of parallelogram shape in place of the segment, while all other parameters remain as before, you would just see a thinner (i.e. less breadth along –X direction) strip, but of the same length as before.
Posted: Tue Nov 27, 2012 6:01 pm
i can't agree.if i divide the length in two axis the length which is in x axis must be reduced
Posted: Tue Nov 27, 2012 6:25 pm
Why don't you please elaborate your solution in light of the theory? A line/object from (1, 2) and (5, 8) is not the same thing as two separate lines/objects as in vector addition. If you please enlighten us on your logic in details, then perhaps we would be able to see where the mistake, if any, has occured.
Posted: Sat Dec 22, 2012 1:07 am
Rafe is right. The x-component of the length will decrease; the y-component will remain unchanged.