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| Bulletin' Board for Physics II ::::::::::: ÀϹݹ°¸®ÇÐ 2 °Ô½ÃÆÇ |
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Here are some hints.
1.(a)
First of all, it is important to calculate the exact solution of your clock (and it is easy!)
In the case of your alien friend, lets think about the two different frame, one is your---therefore rest frame, and the other is your friends frame.
(Lets represent these two frames as (t,x,y,z) and (t,x,y,z))
Your friend thinks he does not change his position on his frame(it is obvious).
Hence, dx=dy=dz=0, but as we know dx =/= 0.
Also, because d¥ó^2 = dt^2 - dx^2 - dy^2 - dz^2 is same in both frames, we can calculate the relation between dt and dt.
Once we know the relation between two and the time on the rest frame, we can integrate dt and get the time on your friends frame.
1.(b)
If someone measure some object, then it is done in the condition that the time is fixed in his(or her) frame. So we can use the equation dt^2 - dx^2 = dt^2 - dx^2 again (in this case, we only consider t- and x- directions).
If we know about the direction of axes in each frame, then there is some condition between (dt, dx) and (dt, dx).
Also, if we add dt=0, then we can get the relation between dx and dx.
The rest of things are the same to the 1.(a).
2.
It is not difficult to calculate the equations directly.
The main question is to interpret these equations in Newtonian terms.
Newtonian dynamics can be represented as a special case of special/general relativity in the small velocity (v << 1).
If you want to interpret those equations in Newtonian terms, first you need to approximate the equations in the condition v << 1.
3.
You can calculate the negative/positive charge density in the particles frame.
It is different to the case of the wire-rest frame because of the length contraction.
Once negative charge is in the length contraction in the wire-rest frame but no longer in the particle frame, and vice versa.
If you calculate the negative/positive(therefore, net) charge density, then you can calculate the force as the force from the wire of uniform charge density (you need to know the relation between charge density and current).
This force is invariant in all frames, so it is same in the case of rest frame.
(I think there is something misspelt --- I guess F = -q v I / 2 ¥ð ¥å r. This answer is in the case v << 1)
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