Faster than Light Neutrinos at CERN

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Cern has reported they have measured neutrinos going faster than the speed of light. Did they send a light beam as a test case to see any variance in c of the light beam?

Also, were two clocks involved in the measurement? One in Switzerland and one in Italy? If so, wouldn’t it be impossible for these two clocks to tick at exactly the same rate or to be consistently synchronized at the nano second level? That is, this experiment was not conducted in pure, inertial space but within the gravitational curvature of space due to the Earth at the surface of the earth.

And the gravitational field intensity at the surface in Switzerland could not be precisely the same at the detector location in Italy. Hence, the two clocks could never tick at the same rate.

Because of instabilities of the earth’s crust- plate movements, changes in density of the Earth's crust, seismic dynamics, the changing distance between the center of mass of the Earth and a given point on the earth- all of these factors would fluctuate the gravitational field intensity at the earth’s surface for any given point on the earth’s surface.

And thus the difference in clock rates at the two points in the experiment would never be consistent.

Wouldn't these factors render it impossible to make a precise velocity measurement of the neutrinos or am I missing something?
 
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