- #1

mananvpanchal

- 215

- 0

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?