Also worth noting, DanielBMarkham's comment is spot on, from what I read in the OPERA paper, the clocks in question are indeed not on the satellites, they're just synchronized using the satellites, and then that synchronization is tested extensively on the ground. So the time measurements should not depend on the satellite frame at all, by my understanding.
then that synchronization is tested extensively on the ground
Not possible. There is no way to test whether the clocks are synchronized. If they could "check" the synchronization by any other, more accurate, source then that should have been the reference.
Then I'm left with just being confused about frames. How is it that the satellites slow one result and not the other? Assuming for simplicity you are using one satellite, it would have to be directly between the test sites in order for this to happen, right? If the satellite is approaching both sites, or if it is leaving both sites, the changes would affect both sites equally.
I'm not following how the general east-west orbits of the satellites have anything to do with anything. The only thing that's important is the relative motion between the satellites and each station. Both should be affected the same way I would think. No?
First off, let me reiterate that I don't believe that the objection in this paper is likely valid, because I don't think the CERN scientists were actually measuring anything from the satellite frame. Buuuuut...
Assuming for simplicity you are using one satellite, it would have to be directly between the test sites in order for this to happen, right? If the satellite is approaching both sites, or if it is leaving both sites, the changes would affect both sites equally.
I think I can explain this - first, the position of the satellite is not important to this argument, it's only the velocity that matters.
Here's what we need to assume, for the purposes of pretending that the paper has a valid objection: we figure out what the clock on the satellite says at the moment that the neutrino leaves station A (this requires some computation, because it takes time for light to travel, etc. - don't sweat that, we assume we're calculating this after the fact, and can pinpoint the exact moment it leaves). Then we figure out what the clock on the satellite says when the neutrino hits station B. From the point of view of the satellite, here's a picture of the way everything is moving:
<-A neutrino-----> <-B
A and B are moving to the left with velocity v, and the neutrino is (we assume) moving to the right with velocity c. The distance from A to B is L, as observed by the satellite (ignore whatever length contraction stuff you're tempted to think of - we're in the satellite frame, now and forever).
Now, the author here is arguing that CERN calculated the theoretical time of transit for this situation as delta_t_wrong = L / c and then expressed surprise when the measured value was less than that. But that's clearly a wrong formula - station B is moving to the left as the neutrino moves to the right, so the true time that they meet is delta_t_correct = L / (v + c).
Notice that it doesn't matter where the satellite is, we're just looking at the relative velocities from the perspective of the satellite. If it was orbiting the other direction, then the error would be that it looked like it took too long.
[If it bothers you that no matter what the speed of the satellite the speed of the neutrino is always c, then hello relativity!, that's another story for another day]
I should point out that this would be a completely valid complaint if CERN actually was calculating things this way and getting measurements from the satellite's inertial frame. But I don't think they are, I'm pretty sure all of their time measurements come from the ground clocks, in which case there's no time-of-transit shenanigans to be monkeyed with.
Yes, but as far as the argument in the paper goes, A's velocity doesn't even matter, all that matters is the time on the satellite clock when the neutrino was emitted from A, the distance between the stations, and the velocity of B relative to the satellite. The difference in latitude would change the exact result somewhat because the neutrino is not travelling exactly along the velocity, but to be fair, I'm pretty sure the author mentioned that this was not an exact calculation, just a suggestion of where to look for an error.
