This is an almost trivial application of special relativity. It was be absolutely shocking if the dozens of scientists involves in the neutrino experiment didn't take this into account.
I'd file this under "systematic measurement error", and the team specifically said that something like it was the most likely cause for the results. They also said that if neutrinos really were FTL, we'd have observed this effect much earlier (for example when we started measuring supernova radiation bursts). So, the article's hypothesis is a very good candidate for a real flaw in the experiment's design.
The scientists probably didn't take this into account because they assumed their setup already compensated for all kinds of clock drift... I wouldn't call this an epic failure just yet, because even if this turns out to be the root cause it's a pretty standard type of mistake as far as science experiments go. That's why we have independent reviews, and that's why they are necessary.
They also said that if neutrinos really were FTL, we'd have observed this effect much earlier (for example when we started measuring supernova radiation bursts).
I am seriously doubtful that these neutrinos are traveling faster than light, but I've also been skeptical of this argument since it was presented. It would be pretty hard to have observed this if they weren't looking for it because they would have to sift through old data. For example, for SN 1987A the FTL neutrino event would have preceded the visible light neutrino event by over four years.
They could go through all of the old data, to be sure, but they would have to specifically have had to be looking for something which they think fundamentally is impossible in order to find something like this. So, if these events were even recorded at all, it's certainly not clear to me that they would have done this (at the time of the FTL announcement, that is- of course, they should be doing it now).
it's a pretty standard type of mistake as far as science experiments go
Yes, but when one makes it this far it is big news. No matter what I give props to the scientists to publicly invite the scrutiny they did. That took balls.
"Almost trivial"? You're vastly exaggerating. I'm pretty sure most physics graduates would get problems of special relativity as applied to rotating (i.e. accelerating) systems completely wrong, as it's usually just not taught. Yep, someone doing the experiment should have ideally spotted it, but it's already an extremely complex system, so I'm not surprised they didn't.
They obviously did take all kinds of relativistic effects into account. It's not like they forgot about relativity. It's just that they may have overlooked a higher-order effect that is usually neglected because it is so small. Something like overlooking magnetism when looking at electricity (magnetism is a relativistic effect of moving electrical charge, but since the forces involved are so small, they are easy to miss and neglect)
Confusion, funny how you said weeks ago that "relativity cannot possibly be relevant in explaining the time difference" - http://news.ycombinator.com/item?id=3030735 - and you downvoted me who was suggesting a relativist effect could explain the 60ns difference (although I was wrong about which particular effect)... coughitoldyousocough ;)
Maybe the dude read a few articles or had time to think. Using one's posting history as a "gotcha" because we humans aren't allowed to change our minds for some reason, seems like a really, really odd thing to do.
What I meant, but I agree I didn't clearly say as much, was that completely forgetting about relativity could not possibly be the answer. At the time I was slightly annoyed at the large number of lay people who implied as much (which implies the team was being a bunch of idiots, which to seems typical of the less than respectful average attitude people have towards scientists). Those people certainly didn't have subtle effects like these in mind.
So I shouldn't post when I'm annoyed, because then I tend to bark at things that are not what they appear to be.
That's what I was thinking too- this may be destined to become a problem in a relativity class (perhaps a little above Modern Physics, though). But then maybe I don't fully understand the subtleties.
This is an almost trivial application of special relativity.
This is even less than a trivial application of special relativity, it's literally a third grade "distance = rate x time" problem:
Skipping over the relativistic stuff, which is quite frankly unnecessary (or rather, it's necessary, but the CERN authors apparently already included the corrections), the only two equations of import are (re-named vars for lack of LaTeX):
1) time_baseline = dist_baseline / c
2) time_observed = dist_baseline / (c+v)
where v is the speed of the satellite. In other words, if two things are moving towards each other, then you should use the combined velocity to compute the time. Duhhh...
Now, the fact that the difference in these formulas turns out to almost exactly explain away the problem is certainly suggestive, I'll be honest about that.
But if this was all there was to the story, it would be massively embarrassing for someone at CERN, this is the type of error I mentally ruled out immediately because these people should be way too careful to be making elementary screwups like this. This is the type of error that freshmen lose points for on a mechanics 101 test, not one that eludes dozens of physicists working around the clock for a month.
So I'm skeptical here; it's not that the author of this paper is wrong (though there are credibility red flags in the paper, even beyond the fact that he's not a physicist [he's a computer guy], like the fact that he defines gamma as the inverse of the commonly used relativistic quantity, something that indicates only a passing familiarity with the field), it's that I'm not sure that the CERN guys could reasonably be assumed to have made this mistake.
Then again, maybe everyone else looking over the work also assumed that they'd dotted their i's, and didn't bother checking the trivial stuff. It's certainly happened before...
if formula using (c+v) explains the situation while we may be sure that the CERN physicists calibrated their systems using various SR formulas with "gamma" (i.e. 1/(sqrt(1-v2/c2)) ), that would be an interesting comment on SR :) [especially considering that the Michelson-Morley experiment confirming the constant and isotropic "c" - the foundation of SR - wasn't calibrated using the SR's rules following from such properties of "c"].
my thoughts exactly - my guess is that the editor wanted to point out this potential source of an error, because his readers were likely to understand it. to me the error seems to be too trivial for an experiment of that magnitude.
How many of these guys are GPS satellite engineers? It sounds like they falsely assumed that the GPS system would take care of all relativistic effects and they can just use absolute time for measurement.
The GPS system was not remotely designed for this level of accuracy. The issue here could really be a misconception of how well GPS works and what it was designed to do. GPS, like all technology, has a distinct difference between theory and practice and is also engineered for certain use cases. It may be that no one really thought about this stuff until now because we're talking such tiny increments of time over such large distances.
Regardless, its early in the game to know whats going on, but I'd be really surprised if suddenly neutrinos were FTL and no one noticed until sometime this year. This is starting to look like another case of super-smart over-specialized eggheads making assumptions and not seeing the big picture, like when NASA/Lockheed lost the Mars Climate Orbitor over imperial to metric conversions.
If these guys were humble researchers unsure of their results, perhaps RUNNING TO THE MEDIA AND SCREAMING ABOUT BREAKING THE LIGHT BARRIER should have been agenda item #8484 not #1.
Seriously, if you're claiming you're doing FTL, asking for outside help isn't some noble act, its pretty much required. The idea that these guys are infallible and systemic errors never happen is incredibly naive.
Christ, remind me never to get between nerds and their starship Enterprise fantasies.
"RUNNING TO THE MEDIA AND SCREAMING ABOUT BREAKING THE LIGHT BARRIER" is an extremely unfair characterization of what they did. And the explanation being discussed has not been reviewed.
The gps receivers they are using are NOT $200 off the shelf components. I am pretty sure that when you buy such equipment you will have long discussions with the GPS engineers from the firm.
The GPS receivers they used are form Septentrio, and this guys know their shit. I can't find a reference right now, but if I remember correctly one of their claims to fame is detecting an error in GLONASS, the Russian gps system.
Note also that a $100 Trimble Thunderbolt available on eBay can get you reliable timing results to within about +/- 20 nanoseconds, given a good GPS antenna.
Compensating for special relativity in the timing calculations was a job that had to be done, and done perfectly, long before the first GPS satellite was launched.
My guess is that the bug will indeed turn out to be a relativity issue, but a consequence of GR rather than SR, arising from the fact that the detector cavern is under 1400 meters of rock.
I'm afraid that unless the Monolith is somewhere under Gran Sasso, those effects are completely negligible. The time scales of the experiment are very short indeed (1e-9 seconds), but the influence of General Relativity is even smaller (1e-15 seconds).
The point to remember that there are so many possible factors that could mess up their results, that the error estimates that were published by the OPERA team were way too low.
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?
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.
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.
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.
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.
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.
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 :
>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.
> 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.
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.
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.
But the GPS satellites and receivers already correct for these relativistic effects. Specifically:
"The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system. ... Further, each GPS receiver has built into it a microcomputer that (among other things) performs the necessary relativistic calculations when determining the user's location." [1]
Relativistic effects are only taken into account when determining the position of the satellite itself, and the rate of it's clock.
It can't compensate for the effect in the linked-to article (namely, the fact that the distance and flight time between the neutrino source and destination is shorter according to the satellite, versus an observer on the ground) because that effect depends on the specifics of the experiment.
Consider this: If you flipped the location of the neutrino source and destination, you'd actually get the reverse effect (neutrinos would appear to be going slower than light).
So it's up to observers on the ground to compensate for relativistic effects of this nature.
(As I mentioned in another comment, I would be shocked if they didn't already do that)
As I understand it, and I've only read the original OPERA experiment paper, they use the GPS signal to sync some caesium clocks (I'm assuming they're caesium based on their name CS-something) and that they've done a comparison by physically moving the clocks to check the synchronisation. The paper is pretty involved on the points of the GPS sync though so I could have misread that.
I was impressed that they allow for continental drift in their analysis and indeed that they were apparently able to detect the crusts movement by an Earthquake with the apparatus.
>Consider this: If you flipped the location of the neutrino source and destination, you'd actually get the reverse effect (neutrinos would appear to be going slower than light). //
Flipped WRT what? They've run the experiment at differing times of the day when the experiment is effectively flipped WRT the helios.
They also present a tentative energy relationship with the apparent superluminal speed which wouldn't, it seems, be accounted for by a simple relativistic [time-shift] systematic uncertainty.
>Flipped WRT what? They've run the experiment at differing times of the day when the experiment is effectively flipped WRT the helios.
It's "flipped" only with respect to the center of the earth. Since this isn't a point of measurement(the satellites are the ones effectively holding the stopwatch), it's not really worth taking into account.
If the neutrino stream was going west->east(i.e. with the satellites) rather than east->west, the receiving station would appear to be moving away from the starting point of the neutrino stream. That would effectively decrease the speed of neutrinos.
Neutrino's are hard to detect and even harder to generate in detectable quantites. So for now we have exactly one location and one path in the world where we can both generate and detect them at a reasonable distance.
Also, GPS satilites don't orbit in one direction you need 3 to quickly get an accurate posisiton so they use a wide range of orbits to minimize the number needed. http://www8.garmin.com/aboutGPS/ Which is something the article seems to miss.
1) Technicaly, there are 2 possible locations that the same distance from each of 3 satilites, but the other point is far off in space. The 4th is vary useful for increased accruacy when you have a shitty ground clock, but it's not 'needed' it's it's loss simply results in lower accracy which can be compensated for by more readings over time. (Which can be vary useful when want accuracy and have a ground station that only get's to see a small chunk of the sky.)
2) They all have polar orbits that reach the same location 4 minutes earlyer each day. However, there horizontal ground speed relative to a stationary observer changes over the course of their orbit. (It's zero at the pole and maxes out at the equator.) And is also diffrent form the other satilites you are comparing it with.
PS: Yea, that picture was fairly bad, I was looking for an easy to read article not a picture. The classic picture of a constilation with fixed polar obits is vary misleading once you take the earth's rotation into consideration. It's rare to find something that shows both the orbit's and their horisontal velocity fairly accuratly without making it look like they interweave. I once saw an animation showing the orbit of 4 satilites and the area they could cover area just those 4 satilites could give you coverage of but it's far harder with just a picture.
Suppose you have 3 points in 3d space.
P1 = (1,0,0),P2 = (0,1,0), P3 = (0,0,1)
You know point the distance from U to P1 is x, from U to P2 is x +1 and from U to P2 is x + 2)
You know know U is on a 1d curve (c1) though 3d space. (Or as you say you don't know time aka distance.)
Now suppose P1, P2, P3 velocity is more than 2x that of point U and you have you have new offsets from U to {P1,P2,P3} you are now going to have a new curve (c2) in 3d space, but you know U's vector must take it from c1 to c2.
Now add another time cycle, and you know it's vector must take it from C1 to C2 to C3. As you keep adding C's you constrain both the valid vectors(direction and velocity) as well as positions.
Now measurement accuracy as well as change in velocity limit the accuracy but GPS satellites are moving a lot faster than you are so you can get reasonably accurate information this way. Edit: Also you can basically ignore the sections of the curve that whose altitude is unreasonable so the solution space is fairly constrained to start with and for each subsequent curve. But you can also use an internal clock/oscillator, accelerometer, gyroscope to further constrain reasonable accelerations etc.
1) The intersection of three spheres results in two possible points. One of which is most likely somewhere in space or deep below ground. So 3 satellites are actually enough in theory. Altough you get a [much] higher precision with more satellites.
I agree on the other points. They all have an inclination of 55° in regard to the equator. See Wikipedia [1] for details and a more serious illustration
You would need three if you had an atomic clock: if you knew the precise time. But in practice you do not. You have a good clock that has an unknown shift with respect to the clocks in the satellites.
So you can measure differences in times, but not absolute times. I.e. you do not know the distance from the gps to the satellites, you know the difference of these distances. So you need a fourth satellite.
This was designed because it is easy to make accurate relative time measurements, but hard to have an absolute time reference.
I know for a fact that some aircraft are able to operate on three by using altimeter information to resolve the ambiguity between the two possible points. It's not as accurate as using four satellites, but it's still pretty damn accurate. In a boat you could get similar results by assuming that you are at MSL.
When you solve 3 simultaneous equations in 4 unknowns there are far more than 2 possible solutions. However, you are correct that if you have a priori information about one of the unknowns (usually the altitude, since it's easier than carrying your own atomic clock) you can solve for the remaining 3.
You can get around that by starting with a few reasonable amputations. aka speed less than 2,000 MPH Acceleration under 3g within 40miles of surface etc. And then refining your estimated local time based on the reasonable solutions and then repeating this a few times with several data points to get a better estimate for location, velocity, clock drift, and time. This tends to works quickly because your location and velocity are fairly constrained and the satellites are moving very quickly. As for a ground station, the velocity is vary constrained and which makes all of this a lot faster and more accurate.
Don’t forget we have a lot more CPU to throw at these problems than they did in 1980.
I think it's more subtle than that - it's due to the motion of the satellites relative to the experiment (i.e. the direction of the neutrino path), not to the individual ground stations
If true, this just goes to show how many effects you need to take into account when dealing with numbers that are 2 thousands of a percent. Effects that can normally be ignored because they're in the noise, turn out to be in the signal instead.
I think English isn't the author's first language:
The authors of the OPERA paper [5] seem to include a correction for the Lorentz transformations,
but they not correct for the change in scenario. And because they project back the time of
provided by the moving clock to the baseline they seem to incorrectly assume that the outcome of
their experiment should be equivalent to that using a clock in the baseline reference system
This comment will probably never be read, but nevertheless ...
I am a Frenchman living in the Netherlands. And you are both correct and incorrect ...
The Dutch are probably among the most fluent non-native English speakers in Europe, BUT, they speak for most of them a "good enough" English, and not at all a perfect English.
This usually materializes even more when they are writing.
There is even several books (usually written by Dutch authors themselves) making fun of "dutchisms".
That said, I don't necessarily consider myself better ... Simply, I do other kind of mistakes, so their mistakes usually strike me more than my own mistakes of course, but mistakes of other French speakers as well
While most of the Dutch people I've heard speak did so with perfectly fluent English (and American accents -- thank you, Hollywood), you're unwittingly assuming he's relatively young -- my understanding is that, not surprisingly, levels of English fluency drop off somewhat rapidly with age in the current Dutch population.
Until the faster than light result can be recreated in an independent experiment, I am treating this like cold fusion. Neat result and absolutely deserving of further investigation, but not definitive.
I don't really get why you're being downvoted to oblivion, that's a great stance to take on science in general. So much media buzz is made over n=1 things; you can cut out a lot from your information diet by ignoring things until they get replication. If special relativity is wrong, we'll find out in due course, and the current counter-evidence against special relativity is hardly a dent compared to the massive evidence in favor (both theoretical and experimental). Just a few days ago I discovered this paper: http://arxiv.org/abs/1005.4172 They assert Events as the only fundamental object, not space, not time. Then: "by asserting that some events have the potential to be influenced by other events, but that this potential is not reciprocal, we can describe the set of all events as a partially ordered set or poset, which is typically known as a causal set" and from there they derive Special Relativity.
Actually, while I fundamentally agree with the "ignoring things until they get replication" proposal, I think there's an impracticality there, due to the way information dissemination works.
There will be no flurry of HN links about this when someone replicates it (even assuming, for the sake of argument, that neutrinos really can be fired FTL, all of current physics is wrong, etc etc). Maybe a single link. It just won't have the network effect; too much of the collective audience's interest has already been consumed. And there'll definitely be no HN links when the third and fourth teams replicate it.
Even if that's a wrong claim for this hypothetical result about relativity, consider yesterday's "forced exercise and Parkinson's" link ( http://news.ycombinator.com/item?id=3106799 ). That result is _completely_ immature (the rat experiments tested something very different from the human experiments, there has only been one human experiment, the causal story is all conjecture, etc), and there's no _way_ we're gonna hear about it when it's usefully mature (i.e. after ten more studies). (Epistemologically, I think the current result is not far removed from alternative medicine - there's some evidence, but no elegant pattern of evidence across multiple contexts, and no rigorous-but-failed attempts at falsification.) It's an interesting subject, and an interesting research programme, and I want to know about things like this, but it's too early to take this into account when making lifestyle tradeoffs.
So it seems to me that my choices are kind of ugly: I can read a LOT of cutting-edge stuff, and read all the follow-ups, knowing that most of the ground-shakers won't actually pan out. Or I can wait 20 or 50 or more years until it starts showing up in undergraduate textbooks. Or... I don't know, there must be other options, but I don't know what they are. Another option is reading Malcolm Gladwell et al, which I think is generally viewed with a certain exasperation by the genuinely knowledgeable?
Is there a blog or magazine or whatever, that popularizes science, with this slightly delayed view? "Exciting science news from 10 years ago, complete with a decade of 20/20 hindsight!"
You're on to something here. One of my favorite subjects is 'what happened to 'x'' where 'x' is some discovery or bit of news some time down the line. Most people don't even remember 'x' when asked about it until you jog their memory a bit, I can't seem to help remembering all those things.
So, how did that story with the solar panels made from hair pan out? It was pretty solidly debunked here on HN (as it rightly should have been), but what interests me is what happened to the major players in that episode, if they're still making solar panels from hair or if they came to terms with their error and documented that and published it to negate some of the damage done.
This paper: http://tycho.usno.navy.mil/ptti/1996/Vol%2028_16.pdf
states that "the time rate is appropriate to observers on the surface of the rotating earth, that is, in the ECEF". I'm interpreting that to mean that the issue raised in the OP is not correct, but I am by no means an expert in relativity.
Interestingly, the paper also states ('Missing Relativity Terms?', pp. 195-197) that there has been confusion in the past caused by people thinking the time is measured in the ECI frame. It shows that the uncorrected-for relativistic effects have an error on the order of only 2-3mm for a stationary observer on the earth's surface (the same is not true for e.g. other satellites). 'In short, there are no "missing relativity terms."'
They do, and they used a mobile atomic clock to compare the times. The problem is that both locations are in different, accelerated frames of reference, so reasoning about time in those frames of reference can become non-trivial.
Apparently they didn't use a mobile atomic clock but a mobile gps clock to compare the times: http://operaweb.lngs.infn.it/Opera/publicnotes/note134.pdf
So it appears they synchronized both timing sources with an orbiting clock, and the critique from this dutch guy seemingly stands.
could someone please explain this, i wish i could say i get it, but i am so confused. i don't understand, are they not using gps just to synchronize the clocks on both ends? what does it matter if in orbit the distance seems shorter or longer if observed (viewed) from the satellites (is this what they are saying?)?
The simplest way I can (try to) understand it is to imagine a line drawn between CERN and Gran Sasso. From the GPS point of view(consider the GPS satellites as stationary), this line is moving approximately in a Gran Sasso->CERN direction, and is therefore very slightly shorter than what the researchers on the ground calculated
Let's suppose you're trying to time a 100 yard dash based on sound. Someone fires a gun, the race starts, and when the first runner crosses the finish line another gun is fired, you determine the elapsed time.
There are obvious things to correct for -- e.g. if you're standing at the finish line the sound from the finish line will take 1/3 of a second (roughly) to get to you, so you need to adjust your calculation.
Now suppose that you are standing off on a barge during the race. You know the distance to the start and finish lines but ignored the drift of the barge because you figured it was insignificant.
We're talking 60 nanoseconds. The satellites are moving at tens of thousands of miles an hour.
"Fools", he mutters under his breath, "Neutrinos flying faster than light... I pity your indolence." With wiry fingers he taps his pipe on his knuckles, flinging burnt tobacco beyond the edges of the cloud. "Ah well," he sighs, connecting his iPhone to his Macbook Air, "time to install iOS 5. I bet those servers are not running as red hot any longer".
