- #1
mananvpanchal
- 215
- 0
Hello, I have basic confusion about Time Dilation and Length Contraction. I have struggled much, but I haven't succeed. Please. help me to clear it.
In A frame I have [itex][t_{a1}, x_{a1}][/itex] and [itex][t_{a2}, x_{a2}][/itex]. If I assume c=1 and [itex]x_{a1}=x_{a2}[/itex], and if I transform it to B frame which is moving with v speed relative to A frame. I get this.
[itex]t_{b1}=\gamma (t_{a1}-vx_{a1})[/itex]
[itex]t_{b2}=\gamma (t_{a2}-vx_{a2})[/itex]
If I simply do [itex]t_{b2}-t_{b1}[/itex], I get
[itex]t_{b2}-t_{b1} = \gamma (t_{a2}-t_{a1})[/itex]
[itex]\Delta t_b = \gamma \Delta t_a[/itex]
[itex]\Delta t_b > \Delta t_a[/itex]
If As I understand [itex]\Delta t_a[/itex] is elapsed time in A frame and [itex]\Delta t_b[/itex] is elapsed time in B frame then it would be [itex]\Delta t_b < \Delta t_a[/itex], then why [itex]\Delta t_b > \Delta t_a[/itex]?
Now, If I have [itex][t_{a1}, x_{a1}][/itex] and [itex][t_{a2}, x_{a2}][/itex] where c=1 and [itex]t_{a1}=t_{a2}[/itex].
then,
[itex]x_{b1}=\gamma (x_{a1}-vt_{a1})[/itex]
[itex]x_{b2}=\gamma (x_{a2}-vt_{a2})[/itex]
If I simply do [itex]x_{b2}-x_{b1}[/itex], I get
[itex]x_{b2}-x_{b1} = \gamma (x_{a2}-x_{a1})[/itex]
[itex]\Delta x_b = \gamma \Delta x_a[/itex]
[itex]\Delta x_b > \Delta x_a[/itex]
If As I understand [itex]\Delta x_a[/itex] is length in A frame and [itex]\Delta x_b[/itex] is length in B frame then it would be [itex]\Delta x_b < \Delta x_a[/itex], then why [itex]\Delta x_b > \Delta x_a[/itex]?
What am I thinking wrong here?
In A frame I have [itex][t_{a1}, x_{a1}][/itex] and [itex][t_{a2}, x_{a2}][/itex]. If I assume c=1 and [itex]x_{a1}=x_{a2}[/itex], and if I transform it to B frame which is moving with v speed relative to A frame. I get this.
[itex]t_{b1}=\gamma (t_{a1}-vx_{a1})[/itex]
[itex]t_{b2}=\gamma (t_{a2}-vx_{a2})[/itex]
If I simply do [itex]t_{b2}-t_{b1}[/itex], I get
[itex]t_{b2}-t_{b1} = \gamma (t_{a2}-t_{a1})[/itex]
[itex]\Delta t_b = \gamma \Delta t_a[/itex]
[itex]\Delta t_b > \Delta t_a[/itex]
If As I understand [itex]\Delta t_a[/itex] is elapsed time in A frame and [itex]\Delta t_b[/itex] is elapsed time in B frame then it would be [itex]\Delta t_b < \Delta t_a[/itex], then why [itex]\Delta t_b > \Delta t_a[/itex]?
Now, If I have [itex][t_{a1}, x_{a1}][/itex] and [itex][t_{a2}, x_{a2}][/itex] where c=1 and [itex]t_{a1}=t_{a2}[/itex].
then,
[itex]x_{b1}=\gamma (x_{a1}-vt_{a1})[/itex]
[itex]x_{b2}=\gamma (x_{a2}-vt_{a2})[/itex]
If I simply do [itex]x_{b2}-x_{b1}[/itex], I get
[itex]x_{b2}-x_{b1} = \gamma (x_{a2}-x_{a1})[/itex]
[itex]\Delta x_b = \gamma \Delta x_a[/itex]
[itex]\Delta x_b > \Delta x_a[/itex]
If As I understand [itex]\Delta x_a[/itex] is length in A frame and [itex]\Delta x_b[/itex] is length in B frame then it would be [itex]\Delta x_b < \Delta x_a[/itex], then why [itex]\Delta x_b > \Delta x_a[/itex]?
What am I thinking wrong here?