# Query about the Michelson interferometer

Say I am cycling past a Michelson interferometer set up. Someone at rest with the experiment will see both beams travelling a distance $$L_0$$ and hence conclude that $$T_{AB}=T_{AC}=\frac{2L_0}{c}$$.

However, according to me, the beam AB will not be travelling $$L_0$$, but a contracted distance $$\frac{L_0}{\gamma}$$, hence $$T_{AB}=\frac{2L_0}{\gamma c}$$. As AC is perpendicular to me and hence there is no relative motion along that axis, I don't observe AC to have any length contraction. However, I do still observe the whole light clock effect or time dilation. According to the observer at rest with the set up, the light beam travels along a horizontal line. According to me however, it travels diagonally, and the overall path $$ACA$$ describes a triangle. Hence, I see that $$T_{AC}=\frac{2L_0 \gamma}{c}$$.

This seems to imply I will observe interference while the observer at rest with the set up will not.

Note: $$T_{AB}$$ and $$T_{AC}$$ describe the time taken to travel the overall paths $$ABA$$ and $$ACA$$ respectively.