Special relativity theory train and mosquito

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1. May 21, 2014

prehisto

1. The problem statement, all variables and given/known data
Train is moving along the x axis with speed v relative to platform, inside the train mosquito is flying with 3D speed v0.
1) Write mosquito s 4-speed components with respect to train coordinate system.
2) Using 4-vector component transformation write mosquito's 4-speed components with respect to platform,by transforming 4-vector speed components with respect to train.

2. Relevant equations

3. The attempt at a solution
1) This is quite easy,the speed components with respect to train coordinate system :
(icγ,v0xγ,v0yγ,v0zγ),where γ=1/$\sqrt{1-v_0^2/c^2}$
2) Here I Think i could use Lorenc transformation,but i have to use 4-vector component transformation which i think cant be used in Lorenc transform.
Some help here,please ?

Last edited by a moderator: May 21, 2014
2. May 21, 2014

TSny

Hello.

I'm not sure I'm following you here. The Lorentz transformation can be used for transforming the components of any 4-vector from one inertial frame to another.

3. May 21, 2014

prehisto

In that case im just not sure how to use transformation formulas.
Can i take the corresponding component and "plug it in" in the Lorentz formula?

4. May 21, 2014

TSny

Can you show explicitly what you are thinking?

5. May 21, 2014

prehisto

My first thought was just to plug in velocity (v0y and v0z..) in to Lorentz transform ,now i released that Lorentz transform is for coordinates and time only.

So maybe i can use vx=v'x+v/(1+v*v'x/c2) and plug velocity in there?

6. May 21, 2014

dauto

No, Lorentz transform is not for coordinates and time only. It applies for any 4-vector. Neat huh?

7. May 21, 2014

TSny

The Lorentz transformation is for any 4-vector. Here's a link that might help: http://physicspages.com/2011/04/18/four-vectors-basics/

See about a third of the way down where the transformation is given for a general 4-vector (A0, A1, A2, A3).

I think very few people any more use imaginary values for the zeroth component of a 4-vector. The link uses the more standard notation. You might need to make some adjustments in notation.

I don't think this is what the problem wants you to do.