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I give the problem and the solution. Can someone tell me if and where I am wrong? Thanks
Homework Statement
We have an observer O', who travels with constant speed U=0.8c, and another observer O with speed 0.
The Observer O' is traveling from point A to point B (1.2 \cdot 10^8m).
Since we know the speed of O', and the distance from A \rightarrow B, we can calculate the needed time (t') for the O' to arrive to the point B.The observer O counts the elapsed time, t_1 so the O' to arrive to the point B.
U=\frac{d}{t'} \Rightarrow t'= \frac{d}{U} \Rightarrow t' = \frac{1.2 \cdot 10^8}{0.8c}
t'=\frac{1.2 \cdot 10^8}{0.8 \cdot 3 \cdot 10^8} \Rightarrow t'=0.5s
The time t' is the dilated time for the Observer O'.Therefore, we can calculate the elapsed proper time t_0 for the Observer O'
t'= \frac{t_0}{\sqrt{1-(\frac{u}{c})^2}} \Rightarrow t_0 =t\sqrt{1-(\frac{u}{c})^2}
t_0=0.5 \sqrt{1-0.8^2} \Rightarrow t_0 = 0.3s
So when the Observer O' is at point B reads t_0=0.3s.
The first Observer who has zero speed is also counting the time needed for the Observer O' to be to the point B. This means two things
So when the Observer O' reads 0.3s the Observer O reads 0.75s, which is the time needed for the O' to get from point A to point B, plus the time needed for the information (light) to arrive to us.
I give the problem and the solution. Can someone tell me if and where I am wrong? Thanks
Homework Statement
We have an observer O', who travels with constant speed U=0.8c, and another observer O with speed 0.
The Observer O' is traveling from point A to point B (1.2 \cdot 10^8m).
Since we know the speed of O', and the distance from A \rightarrow B, we can calculate the needed time (t') for the O' to arrive to the point B.The observer O counts the elapsed time, t_1 so the O' to arrive to the point B.
U=\frac{d}{t'} \Rightarrow t'= \frac{d}{U} \Rightarrow t' = \frac{1.2 \cdot 10^8}{0.8c}
t'=\frac{1.2 \cdot 10^8}{0.8 \cdot 3 \cdot 10^8} \Rightarrow t'=0.5s
The time t' is the dilated time for the Observer O'.Therefore, we can calculate the elapsed proper time t_0 for the Observer O'
t'= \frac{t_0}{\sqrt{1-(\frac{u}{c})^2}} \Rightarrow t_0 =t\sqrt{1-(\frac{u}{c})^2}
t_0=0.5 \sqrt{1-0.8^2} \Rightarrow t_0 = 0.3s
So when the Observer O' is at point B reads t_0=0.3s.
The first Observer who has zero speed is also counting the time needed for the Observer O' to be to the point B. This means two things
- When O' is to the point B the proper time for O' is 0.3s
- The time needed to go from point A to point B is 0.5s. The Observer O, with a pocket calculator, calculated the time (later) because his reading was strange.
So when the Observer O' reads 0.3s the Observer O reads 0.75s, which is the time needed for the O' to get from point A to point B, plus the time needed for the information (light) to arrive to us.