The Michelson-Morley experiment set out to determine the existence of the luminiferous ether, through which the speed of the earth was belived to be determined. Michelson and Morley attempted to determine the existence of the ether through its effects on the speed of light.
The reason both light beams reach the interferometer at the same time is due to the contraction of one of the device's arms. Lorentz supported this idea with the theory of the properties of electrons where electrons contract in the direction of motion. This led to the idea of relativity where the speed of an object is determined through the speed of the observer.
Time and distance are affected by motion.
The speed of light is the same for all observers. However, if light is in motion between two mirrors, the observer will see the light taking less time to complete one cycle. This is due to the increased diagonal distance.
The relativity of time is derived from the right triangle formed by the distances traveled.
The Pythagorean theorem shows that the path of the moving light is longer than the distance between the two mirrors.
delta(t) = 1/sqrt(1-(v^2/c^2))delta(t)'
delta(t) = gamma delta(t)'
Two observers can agree on the occurence of an event with respect to time using the Lorentz transformations
Galileo - x' = x - vt
Lorentz - x' = gamma( x - vt) the equation along the direction of motion.
y' = y the equation describing the perpendicular motion that is the same in both frames of observation.
z' = z
t' = gamma (t - vx/c^2)
The Lorentz transformations link time and space together.
Einstein developed two postulates:
1st - the laws of physics are the same for all inertial frames
2nd - the speed of light is the same for all observers.
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