Constancy of the speed of light in the hypotenuse of the triangle in the Michelson and Morley experiment [closed]

In Michelson and Morley experiment, Michelson calculated that the total time traveled by light with respect to the stationary observer standing at ether field was $2L/c$.

Here, Michelson followed the Galilean Theory of relativity, i.e., since light was travelling not a vertical path but a longer hypotenuse path of a right triangle as seen by the stationary observer at the ether field, the relative speed of light with respect to the observer is $\sqrt{c^2+u^2}$, $u$ being the speed of whole apparatus assumed to be moving with respect to the observer on the ether field.

But, Alfred Potier and Lorentz corrected that light as seen by the observer should not be moving at $\sqrt{c^2+u^2}$ but at "$c$". My question is that how did Lorentz and Alfred know that light will be moving at "$c$" with respect to the Observer at the ether field when light is traveling perpendicular to the motion of the apparatus.

I am able to understand the longitudinal argument of the constancy of speed of light from the null result of the Michelson and Morley experiment. But not able to comprehend how can we say that light travels at constant speed perpendicular to the direction of uniform motion of the whole apparatus with respect to a stationary observer at the ether field.

closed as unclear what you're asking by knzhou, sammy gerbil, Gert, user36790, John RennieJul 22 '16 at 7:28

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• The speed $c$ of light comes from Maxwell's equations, and there is nothing special about that. You can find the speed of sound in a diffuse gas from kinetic theory or in an elastic solid from a first-order stress-strain analysis; similarly for surface waves on water. Having wave phenomena with with known speed was perfectly ordinary 19th century physics. It's just that they expected the speed to be relative a medium. Thus the "boat race on a river" metaphors that are sometimes used to explain the expected outcome: the fixed speed of the 'boat' is relative the 'water' (medium). – dmckee Aug 26 '16 at 3:29
• So, does that answer my question? – Jyotishraj Thoudam Aug 27 '16 at 11:17