special relativity - Has anyone ever measured the one way speed of light perpendicular to the Earth at the Earth's surface?

1 - Has anyone ever measured the one way speed of photons traveling perpendicular to the Earth at the Earth's surface?

2 - Given our current understanding of Physics is there any way both the upward and downward speed would not be $c$?

3 - If the measurement were made and the downward speed were found to be considerably faster than $c$, would there be any plausible explanation given our current understanding of Physics?

4 - If it hasn't been done in the past, how would one do so and how difficult would it be to make such a measurement in both the upward and downward directions with less than 1 km/s error bars?

EDIT: Someone helped me find my error on another thread. Thanks again for all help.

Answer

Everyone seems to be misunderstanding the question. The one-way speed of light cannot be measured even in principle. Einstein knew about this and even proclaimed that the one-way speed of light is not a feature of nature but rather a human preference. What we know as the speed of light c is actually 1/2 of the "Two-way speed of light." The one-way speed of light is simply DEFINED to be c for the sake of simplicity but this is not necessarily so. The one-way speed of light can be DEFINED to be ANY constant number within a range of values as long as the opposite direction of light compensates so that the Two-way speed of light is c. Many gets confused by this because this is not mentioned in basic relativity textbooks. This, I believe, for the sake of simplicity but at the expense of knowing a very peculiar and interesting part of Relativity.

To directly answer the questions:

1) No, the one-way of speed of light cannot be measured whether downward, upward, or any direction. (for a general reference see: http://en.wikipedia.org/wiki/One-way_speed_of_light)

2) Yes. Special Relativity allows you to DEFINE a constant, one-way speed of light as long as the two-way speed of light remains c. For instance, you can define the downward speed of light to be greater than c but you would then have the upward speed of light to be less than c such that you will still get c as the two-way speed of light.

3) Our current understanding of Physics (Special Relativity) allows you to define the downward speed of light to be greater than c. Infinity is also possible (this means it takes 0 time for distant light to arrive to an observer) and have the upward speed of light to be 1/2 c. (The total time of travel of light back and forth would be 2t corresponding to two-way speed of light to be c).

3) See answer 1.