There's something about the lorentz transformations which is somewhat confusing to me, and that is how to treat the "x" coordinate. Supposing I have some spaceship which is moving from earth to some other planet located at a distance "D" (from earth) with a velocity v. Now, the spacetime coordinates of the events "1. leaving earth" and "2. reaching the planet" are (the spaceship frame is {S'} and that of earth is {S} ) :(adsbygoogle = window.adsbygoogle || []).push({});

Leaving earth:

[tex] (x_{1},t_{1})=(x'_{1},t'_{1})=(0,0) [/tex]

Reaching the planet:

[tex] (x_{2},t_{2})=(D, \frac{D}{v} ) [/tex]

[tex] (x'_{2},t'_{2})=(0 , \gamma (t_{2} - (v/c^{2})x_{2})=(0 , \gamma (t_{2} - (v/c^{2})D) [/tex]

Now comes the confusing point which is how to treat [tex] x_{3} [/tex] which corresponds to the event of returning back to earth in the earth's frame. (in the spaceship frame it is [tex] x'_{3} = 0 [/tex] )

The Lorentz transformations relates coordinates and not distances so [tex] x_{3} = 0 [/tex] because the spaceship returns to the origin of earth and [tex] t_{3} = \frac{2D}{v} [/tex]. However, as I have seen in my notes:

[tex] x_{3} = 2D [/tex]

, that is, the distance that this spaceship travels is what is accounted for and not its coordinate.

Can anyone clear this point for me?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The lorentz transformations usage

**Physics Forums | Science Articles, Homework Help, Discussion**