# Special relativity theory train and mosquito

Tags:
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.

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.