The spatial separation between the 2 events is 13.416 × 10⁸ m
In space time-interval, the invariance of line element explains that if there are two inertial reference frames S and S', the spatial separation is invariant in all inference frames.
i.e.
[tex]\mathbf{\Big [ [\Delta x]^2 -[c^2 \Delta t ^2] \Big]_{frame \ 1} = \Big [[\Delta x]^2 -[c^2 \Delta t ^2] \Big]_{frame\ 2} }[/tex]
[tex]\mathbf{[\Delta x_1]^2 -[c^2 \Delta t_1 ^2] = [\Delta x_2]^2 -[c^2 \Delta t_2 ^2] }[/tex]
where;
[tex]\mathbf{[0]^2 -[c^2 (4) ^2] = [\Delta x_2]^2 -[c^2 (6) ^2] }[/tex]
[tex]\mathbf{ [\Delta x_2]^2 =36(c^2) - 16(c^2)]}[/tex]
[tex]\mathbf{ [\Delta x_2]^2 =20(c^2)}[/tex]
[tex]\mathbf{ \Delta x_2 = \sqrt{20} \ c}[/tex]
here;
[tex]\mathbf{ \Delta x_2 = \sqrt{20} \times 3 \times 10^8}[/tex]
[tex]\mathbf{ \Delta x_2 =13.416 \times 10^8 \ m}[/tex]
Therefore, we can conclude that the spatial separation between the 2 events is 13.416 × 10⁸ m
Learn more about spatial separation here:
https://brainly.com/question/15694825?referrer=searchResults
