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Comment by DanielBMarkham | Hacker News Reader

Okay. This should be an easy one but somehow I'm getting stumped.

I understand the difference in frames between the GPS satellites and the ground, but the sats themselves are fixed to each other, right? And the ground stations are also fixed to each other. Each pair is in a separate frame.

But the measurement was on the ground, and the ground stations are not accelerating relative to each other, not from the satellites. So is this saying that the ground stations set their clocks initially wrong because of their relative movement to the satellites? If so, wouldn't this be proven out by comparing the neutrinos time to the time of a photon?

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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?

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 [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) 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.

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.

That can not possibly have an effect. The clocks are synchronized before the experiment. Once the synchronization is done, the satellite could be swallowed by a black hole and it would not affect the measurement.

I believe the idea is that the clocks are synchronised in the frame of the satellite. Due to the relativity of simultaneity, it doesn't make sense to talk about the clocks being synchronised in an absolute sense.

Even if the satellite is swallowed by a black hole, that measurement frame still exists as an abstract concept.

I believe you're right, that's basically what this paper suggests.

Unfortunately I don't think it matches up with what CERN did in reality, which is synchronize clocks in the ground frame.

Is there even a single "ground frame" here? The two laboratories are in relative motion.

What you say is true, but that motion is small compared to the motion of the satellites in relation to either of the ground stations.

Oh, I think I misunderstood the statement. They original quote must mean receiver and source of neutrinos. Somehow I read it as being the GPS source and receiver, in which case it doesn't make sense.

What is synchronization? http://galileo.phys.virginia.edu/classes/109N/lectures/synch... Your sense of time ia very different from what relativity predicts.

Synchronization is ensuring that two events are simultaneous, which most definitely can be done. Relativity just says that you have to be careful to note in which frame the events are simultaneous.

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.

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?

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.

Aren't A and B traveling at slightly different velocities due to being at different latitudes?

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.

When using special relativity it is extremely important to understand which inertial frame you are using. So the in the formula

  Time = Distance / Velocity

you must explicitly say in which frame you are measuring the things. It could be

  Time_EarthCenterFrame = Distance_EarthCenterFrame / Velocity_EarthCenterFrame
  Time_LaboratoryFrame = Distance_LaboratoryFrame / Velocity_LaboratoryFrame
  Time_SateliteFrame = Distance_SateliteFrame / Velocity_SateliteFrame

and it is usualy not a good idea to mix the frames like

  Time_SateliteFrame ¿=? Distance_ LaboratoryFrame / Velocity_EarthCenter  :(

In the same way, it is not a good idea to add the velocities classically with

   v_tot = c + v

you should use the relativistic correction

  v_tot = (c + v)/(1+ cv/c^2) = (c + v)/(1+ v/c) = c* (c + v)/ (c+ v) = c

so in every inertial frame the speed of light is the same.

(Really, the SateliteFrame, LaboratoryFrame and EarthCenterFrame are not inertial frames, but this is another kind of problem.)

Actually, in this case the classical velocity addition formula is the correct one to use - the formula you mention applies to a moving reference frame, but the author's objection was that in the satellite frame the CERN folks mis-calculated the time it would take for a neutron moving to the right to meet up with a station moving to the left.

This is why to call this a relativistic objection is giving it far too much credit: the author is, quite literally, claiming that the physicists at CERN don't know how to solve a purely classical rate problem.

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.

>But the measurement was on the ground, and the ground stations are not accelerating relative to each other, not from the satellites. So is this saying that the ground stations set their clocks initially wrong because of their relative movement to the satellites? If so, wouldn't this be proven out by comparing the neutrinos time to the time of a photon? If so, wouldn't this be proven out by comparing the neutrinos time to the time of a photon?

Actually, the satellites and ground stations are accelerating relative to each other, since they're moving in(roughly) circular paths. Acceleration only means that the velocity vector is changing relative to the frame of reference. It doesn't mean that the absolute velocity is changing.

The problem is that the GPS satellites are the ones keeping time, not the ground. The ground stations are effectively "reading" the clocks on the satellites. So all of the relativistic time calculations should be done from the satellites' frame of reference, rather than from the ground stations' frame. The satellites are moving from west to east(with the Earth's rotation) with an orbital period of approximately 12 hours(http://en.wikipedia.org/wiki/Satellite_navigation#Comparison...). Their rotational velocity, relative to the center of the Earth, is twice that of the ground stations. In terms of absolute velocity, they're moving quite a bit faster. Since they are doing the timekeeping(and assuming that neutrinos move at c regardless of the frame of reference), the receiving ground station is moving towards the initial origin point of the neutrino stream. At that point, it's a doppler effect calculation taking into account the relative velocity of the ground stations to the satellite's frame of reference to find the offset.

Also, the photon time measurement isn't possible due to the curvature of the Earth and the fact that the receiving end is underground.

Disclaimer: It's been a few years since uni, and I haven't read the actual paper, just the linked article.

From what I can tell, the quoted passage, "From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter," is the core of the argument. I think this is what you need to consider/read into it:

- There is relative rotation involved, so the frames are accelerating with respect to each other.

- Since the times involved are very short with respect to the period of rotation, we can probably ignore the acceleration itself (?), BUT:

- LHC and GS have differing velocity vectors at any given time due to their difference in longitude. This means we have to treat them as separate frames of reference. ("From the perspective of the clock, the detector is moving towards the source")

- I think this is just about a single satellite (though since the satellites are in orbit, they too are accelerating wrt earth)

- I'm not sure if the effect will vary slightly depending on the satellite's position, but as it has to be "visible" from both locations, the range of possible positions is fairly constrained. I'd have to work it through/read the paper. :-P

And yeah, comparing to the time of a photon is going to be difficult through the earth. Even gamma radiation won't make it.

>And yeah, comparing to the time of a photon is going to be difficult through the earth. Even gamma radiation won't make it.

so instead of comparing to photon going through the fiber on the surface we're comparing against photon(s) going to the satellite and back. Even just using HAM radio bouncing from ionosphere would be less complicated and more straightforward than through GPS satellites here.

1. The distance traveled by a photon going through a fiber optic cable will be different from the distance through the ground.

2. The distance traveled by radio waves bouncing off the ionosphere would have much more uncertainty than the ~60 feet in question.

3. Radio waves in the air and photons in a fiber will move noticeably slower than c due to the fact that they are not traveling through a vacuum. Neutrinos, however, minimally interact with matter, so they would travel faster than the test photon(s).

>1. The distance traveled by a photon going through a fiber optic cable will be different from the distance through the ground.

it is still shorter than through the satellite. Also the fiber distance difference can be measured and accounted for - much simpler than to account for satellite position.

But they're not bouncing photons up to and down from a GPS satellite; they're only using GPS for clock synchronization and measuring the distance, which is accurate to a lot less than the distance light travels in 60ns.

>But they're not bouncing photons up to and down from a GPS satellite; they're only using GPS for clock synchronization

by noting photons coming from GPS when neutrinos start at CERN and when neutrinos reach Gran Sasso. 2 downward legs (actually 3 as the photons at the start of neutrino run need to be noted at both points) instead of 1 upward and 1 downward that would constitute proper "bouncing" - i don't see much difference to warrant specific term in this case than talking about general approach of racing the neutrinos against photons.

Compare to running through a fiber, which length (only 700km) and speed of light inside it can be easily accounted for, with GPS we have photons coming from the 12K miles distance (in the best case, ie. when the satellite is right overhead) which is measurable much less precisely than the fiber on the ground and these photons are coming through the atmosphere conditions of which (specifically speed of light in it) are much less precisely known than about the same fiber on the ground.

>and measuring the distance, which is accurate to a lot less than the distance light travels in 60ns.

until they used the military GPS they would have positioning error in the Earth surface tangential plane of a few feet at least (say 2 feet though it would be an extremely small error). Using 20000km/700km proportionality of that triangle, 2 feet on tangential plane would mean ~60 feet in GPS signal arrival precision, ie. 60ns+ of time of flight (it is of course oversimplification, only to demonstrate the scale of imprecision inherently present in the scheme with satellite flying over at 20K km)

Very interesting reading btw, especially on atmospheric and Stagnac effect errors :

http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_P...

> but the sats themselves are fixed to each other, right?

Whoa, why would you think that? GPS satellites are in 12-hr, medium-earth, circular orbits in six-orbital planes. How would satellites in different orbital planes maintain fixed distances from each other?

The neutrino is going through the earth - there's no tunnel - so there's no way to compare to a photon. Basically Gran Sasso is moving towards the neutrino as it travels, from the perspective of the GPS

I haven't read the article yet. However, the ground stations are deeper in the Earth's gravity well than the satellites. That is equivalent to acceleration in relativity.

Gravity is not accounted for in special relativity, only general relativity, and this argument is purely based on special relativity. I can't speculate quantitatively on the magnitude of gen. rel. effects, but given the short times, high neutrino speeds and low gravity I suspect they're dwarfed by the already minor effect discussed here.

And the ground stations have a different potential with respect to each other, so their reading of elapsed time could differ. That's what I understood from another article on that subject.

That's negligible.

When it comes to 60 nanoseconds, I'm not sure anything is negligible.

The GR effects here is on the scale of 1e-15s, i.e. several orders of magnitude less than observed 6e-8s. 7 orders of magnitude is "negligible" as GP correctly stated.

Actually gravitational time dilation on Earth's surface is on the order of 1e-9. But still negligible.

>Actually gravitational time dilation on Earth's surface is on the order of 1e-9. But still negligible.

it is compare to zero gravitation far from Earth. The effect i'm talking about is integral of gravitational dilation change along the path of neutrinos. This path is a chord under Earth surface - the 350 km down to 10km depth and the next 350km bringing back to surface. The dilation change is about 1e-16 per meter of depth.

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