This question concerns with a problem encountered when doing a question on special relativity. A scenario in which the question is based will be described and the problem will be explained.
Scenario:
A spaceship travels by a planet at constant velocity $v=0.9c$ to the positive direction in the x-axis, both objects contain observers. After time interval $t_1$, planetary observer detects an explosion at distance $x_1$, at this time, the spaceship has not traveled past $x_1$.
Original question:
What is the time and place of the explosion as perceived by observer on spaceship?
Approach to question:
$t_1$ is proper time, $x_1$ is proper length, use spaceship's velocity to calculate Lorentz factor $γ$, then combine $γ$ and $t_1,x_1$ to find transformed distance and time.
The distance found by $$x_{1s}=\frac{x_1}{γ}$$ Is the distance between planet and the explosion as seen from the spaceship.
Problem:
The approach to the original question considers the planet to be the observer that can measure proper time and proper length, but this decision is arbitrarily made, only because the information was given from the planet's perspective.
This leads to two possible outcomes:
- Proper time and proper length involving two point in time and space is absolute and can only be measured by some observers, and the reason why the planet is the "proper observer" is unknown to me.
- Proper time and proper length can be measured by all observers and is relative. If the information was gathered by the spaceship, it can be treated by a method such that the outcomes are consistent with that of the planet, in which case I would like to know that method.
