PX155 - G2 - galilean invariance and light

problem

maxwell unified electricity and magnetism, published in 1865, and showed that light is a wave with a unique speed:

c = \frac{1}{\sqrt{ϵ_{0} μ_{0}}}

galilean transformations: pulse of light moving along x-axis of $S^{'}$ with $v^{'} = c$ has $v = u + c$

maxwell's theory works in a special frame in which some light transmitting medium called the luminiferous aether is stationary
all other observers will measure speed of light as $v = c \pm δ$
- $δ$ depends on the direction of light compared to the direction of motion though aether

light from $S$ is split into two beans: $O \to A \to O$ and $O \to B \to O$
any difference in round trip time is due to the the difference in $L_{1}$ and $L_{2}$ , and the differences in the speed of light
so, interference fringes can be observed at $D$
rotate $90 °$ , expect to shift
zero shift to within $\pm 0.1$ of a fringe was, measured
therefore, it was proved that speed of light is the same in all directions, and galilean transformations don't apply