# Special relativity theory train and mosquito

## 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.

## 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.

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TSny
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Hello.

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.

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.

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

TSny
Homework Helper
Gold Member
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?

Can you show explicitly what you are thinking?

Can you show explicitly what you are thinking?

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?

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

TSny
Homework Helper
Gold Member
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.

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 vx=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.

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