h8ter said:
Why is it that light goes faster with the rotation of earth, and light goes slower against the rotation of earth?
If you synchronize your clocks in the manner proposed by Einstein, the speed of light is independent of direction. So it's not really true that light goes faster or slower from east/west or from west/east.
But also note that is impossible to synchronize all clocks on a rotating planet or disk according to Einstein's "clock in the middle" method. See for instance
http://www.smcm.edu/nsm/physics/SMP03S/KeatingB.doc.pdf
This has been the source of a *lot* of confusion, as a brief websearch will reveal :-(.
There is a common synchronization method widely used, for instance in the definition of TAI time, that does allow all the clocks on a rotating object to be synchronized. This is not Einstein's method, of course, since we've already mentioned that it's impossible to do this via Einstein's method. One first thinks, perhaps, of emitting a signal from the center of the Earth and synchronizing outwards - when the obvious practical difficulties with this method raise their head, one thinks of synchronizing only along north-south lines to master clocks at one or both of the poles.
Before one gets too excited about the existence of such alternate synchronization methods, one should realize that Einstein's method, and only Einstein's method, allows one to keep Newtonian momentum p=mv or relativistic momentum p=mv/sqrt(1-(v/c)^2) as a conserved quantity.
So before one gets too excited by various commonly-found-on-the-web-but-ill-informed claims about the "one-way" speed of light being different from e-w or w-e, remember to check whether or not, by the definitions used, that a body of mass m moving east at a velocity v will come to a stop when colliding with a body moving west at a velocity v, according to the particular coordinate scheme used to measure velocity. It can, in fact, be shown that only an isotropic synchronization scheme such as Einstein's will conserve momentum. I'll mention that the isotropy requirement comes from Noether's theorem, but I think it would be getting to technical and wandering too far afield to go into any more detail at this point.