4 ms·

I think this is the issue: The time is given by the GPS satellites sending out a signal. This signal is received by the two ground stations, who reset their tim

by lutorm 15y ago

I think this is the issue: The time is given by the GPS satellites sending out a signal. This signal is received by the two ground stations, who reset their time accordingly. This means that the two ground station clocks will define two events as simultaneous in the frame of the satellite. But the measurement is done in the ground frame. Two events that are simultaneous in the satellite frame are not simultaneous in the ground frame, due to the relative motion of the two frames. In the ground frame, there will be an offset between the two clocks, and that would, unless corrected for, result in a skewed measurement of the time of flight. In reality it's more complicated, since there is no one "satellite" frame. The GPS system determines position and receiver time from a global solution to all the satellites. Since GPS time is claimed to be accurate to something like 10ns, it seems the only way this would be possible is if the GPS solution has been constructed to specifically refer the frame of the observer, which would be a ground stationary frame. Is there someone with more intimate knowledge of the GPS algorithm that might be able to comment on this?

bermanoid 15y ago
I'm super-skeptical about this paper - I agree that more info on the GPS stuff is needed (this author seems to be making assumptions about how the correction procedures work that I couldn't find documentation for), but on its face, this just seems way like a way too obvious error to possibly be right. First off, I encourage everyone to read the actual paper at http://arxiv.org/pdf/1110.2685v1 http://arxiv.org/pdf/1110.2685v1 [PDF], I think many here are seriously overestimating the complexity of the author's claim. I've mostly said this already on this thread, but it's buried near the bottom of the page, so I'll summarize the paper here, it's extremely simple: 0) If you're measuring time in the reference frame of the moving clock, you've got to transform the length between the stations in accord with the Lorentz transformation. According to this author CERN already did this, so it's entirely irrelevant to the discussion - I couldn't verify this, because it's not mentioned in the CERN paper he referenced. 1) What they did not do (according to this paper) is account for the fact that in the satellite frame, during the neutrino's flight the receiver station was moving towards the source. 2) time = distance / rate 3) CERN used rate = c, but they should have used rate = c + v because the receiver station was moving towards the neutrino. That is quite literally the entire thing, check the math in the paper if you don't believe me. This is not a claim that CERN somehow misapplied special relativity, it's a claim that they simply forgot to include the motion of the receiver. IMO this is far too elementary a mistake to have been missed for this long, so I'm suspicious. The CERN paper that the author references (http://arxiv.org/pdf/1109.4897v1 http://arxiv.org/pdf/1109.4897v1) doesn't discuss relativistic corrections at all, so I don't know why the author assumes this mistake has been made, perhaps he's reading another paper that he didn't reference? From the OPERA one that he links (though I haven't read it in too much detail) I get the sense that if it was this simple, one of the many calibration tests that they've done would have easily caught the error (they talk about a lot of bidirectional synchronization stuff), so for now, at least, I would take this with a grain of salt.
- bermanoid 15y ago
  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.
  - lutorm 15y ago
    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.
    - DanielBMarkham 15y ago
      So the clocks were set incorrectly. 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?
      - bermanoid 15y ago
        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.
lucasjung 15y ago
I took a class on GPS in grad school. We built a GPS receiver in software (MATLAB, actually), and I remember that we had to account for relativistic effects. I do not remember exactly what the math was, though. I think that it was just a correction provided by each satellite, which was added/subtracted from the time/distance from that satellite to the receiver. If I can find the textbook, I'll try to look up exactly how it works.

by lutorm 15y ago

bermanoid 15y ago

I'm super-skeptical about this paper - I agree that more info on the GPS stuff is needed (this author seems to be making assumptions about how the correction procedures work that I couldn't find documentation for), but on its face, this just seems way like a way too obvious error to possibly be right. First off, I encourage everyone to read the actual paper at http://arxiv.org/pdf/1110.2685v1 http://arxiv.org/pdf/1110.2685v1 [PDF], I think many here are seriously overestimating the complexity of the author's claim. I've mostly said this already on this thread, but it's buried near the bottom of the page, so I'll summarize the paper here, it's extremely simple: 0) If you're measuring time in the reference frame of the moving clock, you've got to transform the length between the stations in accord with the Lorentz transformation. According to this author CERN already did this, so it's entirely irrelevant to the discussion - I couldn't verify this, because it's not mentioned in the CERN paper he referenced. 1) What they did not do (according to this paper) is account for the fact that in the satellite frame, during the neutrino's flight the receiver station was moving towards the source. 2) time = distance / rate 3) CERN used rate = c, but they should have used rate = c + v because the receiver station was moving towards the neutrino. That is quite literally the entire thing, check the math in the paper if you don't believe me. This is not a claim that CERN somehow misapplied special relativity, it's a claim that they simply forgot to include the motion of the receiver. IMO this is far too elementary a mistake to have been missed for this long, so I'm suspicious. The CERN paper that the author references (http://arxiv.org/pdf/1109.4897v1 http://arxiv.org/pdf/1109.4897v1) doesn't discuss relativistic corrections at all, so I don't know why the author assumes this mistake has been made, perhaps he's reading another paper that he didn't reference? From the OPERA one that he links (though I haven't read it in too much detail) I get the sense that if it was this simple, one of the many calibration tests that they've done would have easily caught the error (they talk about a lot of bidirectional synchronization stuff), so for now, at least, I would take this with a grain of salt.

bermanoid 15y ago
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.
- lutorm 15y ago
  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.
  - DanielBMarkham 15y ago
    So the clocks were set incorrectly. 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?
    - bermanoid 15y ago
      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.

lucasjung 15y ago

I took a class on GPS in grad school. We built a GPS receiver in software (MATLAB, actually), and I remember that we had to account for relativistic effects. I do not remember exactly what the math was, though. I think that it was just a correction provided by each satellite, which was added/subtracted from the time/distance from that satellite to the receiver. If I can find the textbook, I'll try to look up exactly how it works.