Special relativity theory train and mosquito

[prehisto]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

1) This is quite easy,the speed components with respect to train coordinate system :
(icγ,v_0xγ,v_0yγ,v_0zγ),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 can't be used in Lorenc transform.
Some help here,please ?

 

[TSny]

Hello.

2) Here I Think i could use Lorenc transformation,but i have to use 4-vector component transformation which i think can't be used in Lorenc transform.

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.

 

[prehisto]

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.

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

 

[TSny]

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

Can you show explicitly what you are thinking?

 

[prehisto]

Can you show explicitly what you are thinking?

My first thought was just to plug in velocity (v_0y and v_0z..) into Lorentz transform ,now i released that Lorentz transform is for coordinates and time only.

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

 

[dauto]

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

 

[TSny]

My first thought was just to plug in velocity (v_0y and v_0z..) into Lorentz transform ,now i released that Lorentz transform is for coordinates and time only.

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.

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

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