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Conservation of diagonal momentum in special relativity

 
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Mac



Joined: 15 May 2014
Posts: 1
Location: Bern

PostPosted: Thu May 15, 2014 11:14 am    Post subject: Conservation of diagonal momentum in special relativity Reply with quote

Hi,
I have a problem grasping one aspect of special relativity and I hope you can help. When looking at the calsic expanation of magntisim in special relativity, there is a wire with a current and then a charge moving parallel to the wire conducting the current. Im sure you are familiar with this scheme (the charges in relative motion space constricts etc.). My problem is this: There is obviously not supposed to be any space dilation in the direction diagonal to the movement i.e. in the direction the "magnetic" force acts. Independent of which viewpoint you look at it, momentum diagonal to the movement is converved right, so the charge is pulled towards the wire wiht the same force at which the wire is pulled towards the charge. But how does this fit in with time dilation? If local time differes, perceived force must differ. For example, the stationary object perceves time in the moving object to run slower but perceives a concervation in diagonal momentum meaning that the stationary object must perceive a stronger diagonal force acting on the moving object (per perceived time unit) than on itself. And if this is indeed the case, this will counteract time dilatin in dimentions diagonal to the motion... so time dilation can only happen in one dimention? I know the light clock shows it differently but this does not explain the problem in my thinking. I am just pointing out the part that does not make sense to me. How should I understand this in terms of momentum and force/time.

Kind regards
Mac
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