Special relativity theory train and mosquito

In summary: I think you're supposed to use the Lorentz transformation, which I gave you a link to.In summary, the problem involves a train moving along the x-axis with a speed v relative to the platform. Inside the train, a mosquito is flying with 3D speed v0. The speed components of the mosquito with respect to the train coordinate system are (icγ, v0xγ, v0yγ, v0zγ), where γ=1/\sqrt{1-v_0^2/c^2}. To find the mosquito's 4-speed components with respect to the platform, the Lorentz transformation can be used, which applies to any 4-vector, not just coordinates and time. The
  • #1
prehisto
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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,v0xγ,v0yγ,v0zγ),where γ=1/[itex]\sqrt{1-v_0^2/c^2}[/itex]
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 ?
 
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  • #2
Hello.

prehisto said:
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.
 
  • #3
TSny said:
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?
 
  • #4
prehisto said:
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?
 
  • #5
TSny said:
Can you show explicitly what you are thinking?

My first thought was just to plug in velocity (v0y and v0z..) into 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
No, Lorentz transform is not for coordinates and time only. It applies for any 4-vector. Neat huh?
 
  • #7
prehisto said:
My first thought was just to plug in velocity (v0y and v0z..) 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 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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1. How does special relativity theory explain the observation of time dilation on a moving train?

Special relativity theory explains time dilation on a moving train by stating that time appears to pass slower for an observer on the train compared to an observer on the ground. This is due to the fact that motion affects the perception of time, and as the train moves at high speeds, time appears to slow down for the observer on the train.

2. Why is it difficult for a mosquito flying inside a moving train to reach the opposite wall?

According to special relativity theory, an object in motion experiences an increase in mass. As the train moves at high speeds, this increase in mass impacts the inertia of the mosquito, making it more difficult for the mosquito to reach the opposite wall.

3. Can special relativity theory explain the twin paradox on a moving train?

Yes, special relativity theory can explain the twin paradox on a moving train. This paradox states that if one twin travels in a high-speed rocket while the other twin stays on Earth, the traveling twin will age slower and the Earth-bound twin will age faster. This is due to the time dilation effect caused by the high speed of the rocket.

4. How does special relativity theory account for the concept of simultaneity on a moving train?

Special relativity theory states that the concept of simultaneity is relative and depends on the observer's frame of reference. On a moving train, two events that appear to happen simultaneously for an observer on the train may not appear simultaneous for an observer on the ground, due to the different frames of reference.

5. Can special relativity theory explain the phenomenon of length contraction on a moving train?

Yes, special relativity theory can explain length contraction on a moving train. This phenomenon states that objects in motion appear to contract in the direction of motion for an observer on the ground. This is due to the fact that the measurement of length is dependent on the relative motion of the observer and the object being measured.

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