Well, this could change things (neutrinos)

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Re: Well, this could change things (neutrinos)

Postby Turtlewing » Tue Sep 27, 2011 9:07 pm UTC

Personally I'm excited because if it turns out neutrinos can travel faster than light this could be as big a deal for physics as the two light beam experiment to measure the luminiferous aether was.

While I understand that skepticism is important for the scientific process, and even if this is true it'll probably be a while before anything useful comes of it, so may as well make sure someone didn't just get their "SOH COH TOA" rhyme mixed up or similar before getting excited, it's still a little disappointing to hear a lot of "it's obviously a mistake" responses.

Personally I've wondered about the whole universal constant c thing. I know it's been well verified by experimentation (until now), but I'm generally wary of claims that something "always posses exactly property x". It makes me wonder if there's some crazy edge case where it turns out not to hold.

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Re: Well, this could change things (neutrinos)

Postby doogly » Tue Sep 27, 2011 9:25 pm UTC

Turtlewing wrote:While I understand that skepticism is important for the scientific process, and even if this is true it'll probably be a while before anything useful comes of it, so may as well make sure someone didn't just get their "SOH COH TOA" rhyme mixed up or similar before getting excited, it's still a little disappointing to hear a lot of "it's obviously a mistake" responses.

Surely people can check for systematic errors in the beam and detector design and so on without being insulting!
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Re: Well, this could change things

Postby OllieGarkey » Wed Sep 28, 2011 2:00 am UTC

Malconstant wrote:@Ollie, Argon, The thing is, relativity is correct, it really truly is. It's literally the most well-tested theory in physics, to many orders of magnitude greater than this measurement. It may be that we'll find evidence which will require a better theory in some regimes, but such a theory would have to yield the same results as relativity in the regimes we've already measured it to be correct in.


Oh yes, I know that. Relativity isn't going to be swept aside. It works. But perhaps we don't understand it fully, is all I'm saying. Perhaps our equations which explain a mostly correct theory are insufficient for a full understanding of the science involved. There are things out there that we haven't observed.

Like any major discovery in the modern era, this wont sweep away Einstein, it will only build on and perfect his work. I wonder about things like an inconstant c. It may not fit into the current mathematics, but it could fit into the current theory. Separate it from traditional mathematics, and turn it into a logic problem when you think about it.

Obviously, relativity exists. It's observable. Airline pilots have to periodically reset their watches. We've observed relativistic effects, and they're not hard to constantly reproduce.

The theory works, but perhaps we don't fully understand the why and how of it yet. That's what excites me.

The idea that the science we've been using, science that we know works, requires even greater testing.

The problem is that we're talking about relativity as if it's A or not A. We know that A exists, and has been proven.

What I'm suggesting is A and also B. Relativity, possibly corrected somewhat, and an inconstant or in certain conditions ignorable c. I'm saying there are circumstances where things might function differently, or that relativity theory might be incomplete, and we just don't know it.

There is an explanation for this, and I'm not going to enjoy waiting the year or years that it will take to verify this result, but it's obvious that no one will come to the conclusion that relativity is completely false.

Edit: And I can see why you would assume I was arguing that relativity might be false from my previous post. I should have been clearer. This discovery might see us rewrite or reinvestigate aspects of current theories.

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Re: Well, this could change things

Postby cpt » Wed Sep 28, 2011 2:51 am UTC

OllieGarkey wrote:What I'm suggesting is A and also B. Relativity, possibly corrected somewhat, and an inconstant or in certain conditions ignorable c. I'm saying there are circumstances where things might function differently, or that relativity theory might be incomplete, and we just don't know it.


I'm sure somebody will correct me if I'm wrong, but I believe that constant c is one of the starting assumptions of Relativity (at least the Special kind). If so, you can hardly have Relativity if c is inconstant.

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Wed Sep 28, 2011 3:08 am UTC

If you think the scientific community won't jump on this, won't put out hundreds of papers extrapolating on that result before it becomes tested and verified by other experiments, then you're evidently new to the ways of the discipline.

The current leading ideas that I've come across are:
-some flavors of neutrinos are tachyons while others aren't (tachyons, by the way, are something which came out of relativity theory and yet move faster than light, so it's wrong to say that relativity fundamentally cannot allow it, unless you can prove that this flavor of neutrino isn't a tachyon, and to current observational limits we can't say that)
-there's a small wormhole or other extra-dimensional curvature going on inside the earth, or at least between CERN and Italy. I'd imagine the Vatican would especially be okay with a wormhole theory centered on them.
-neutrinos are just fucking weird. This fits in well with the first option.

Of course the most plausible bet right now is still probably that it's just an uninteresting systematic error, but that's not going to keep theorists from extrapolating sexy things without realistic data to back them up. Such constraints as experimental verification are laughable to theorists.
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Re: Well, this could change things (neutrinos)

Postby doogly » Wed Sep 28, 2011 4:05 am UTC

Malconstant wrote:-there's a small wormhole or other extra-dimensional curvature going on inside the earth, or at least between CERN and Italy. I'd imagine the Vatican would especially be okay with a wormhole theory centered on them.

The wormhole option has the benefit of being completely consistent with known physics.
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Re: Well, this could change things (neutrinos)

Postby Tass » Wed Sep 28, 2011 8:26 am UTC

doogly wrote:
Malconstant wrote:-there's a small wormhole or other extra-dimensional curvature going on inside the earth, or at least between CERN and Italy. I'd imagine the Vatican would especially be okay with a wormhole theory centered on them.

The wormhole option has the benefit of being completely consistent with known physics.


Except for the missing explanation for a bunch of negative energy under the alps.

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Re: Well, this could change things (neutrinos)

Postby gorcee » Wed Sep 28, 2011 1:30 pm UTC

Tass wrote:
doogly wrote:
Malconstant wrote:-there's a small wormhole or other extra-dimensional curvature going on inside the earth, or at least between CERN and Italy. I'd imagine the Vatican would especially be okay with a wormhole theory centered on them.

The wormhole option has the benefit of being completely consistent with known physics.


Except for the missing explanation for a bunch of negative energy under the alps.


Have you never noticed that the alps are the perfect location for an evil lair?

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Re: Well, this could change things (neutrinos)

Postby Tass » Wed Sep 28, 2011 1:37 pm UTC

gorcee wrote:Have you never noticed that the alps are the perfect location for an evil lair?


Well 90km below the alps really. Its a quite hot place for an evil lair.

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Re: Well, this could change things (neutrinos)

Postby NotAllThere » Fri Sep 30, 2011 5:41 am UTC

Well, when I've been skiing down the alps, a few times I got to the bottom of the slope faster than I should have. But I suspect other factors - like having slipped on an icy bit - were at work then.

Could there be a fracture in spacetime, so that two adjacent parts are folded next to each other. Would a bit of cosmic string do this?

Is there anything that prevents massless particles going faster than light (why does light travel at light speed)? If not, then maybe the neutrinos encountered a higgs boson produced by the LHC, lost their mass, and got a bit of a kick, before the higgs-boson decayed and they got back their mass just before hitting the detector.

It'd be so brilliant if there was some new physics here. But my money's on an error.
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Re: Well, this could change things (neutrinos)

Postby Mr_Rose » Fri Sep 30, 2011 11:06 am UTC

It can't possibly be something as obvious and ridiculous as they took the GPS readings for the installation from the surface then forgot to account for them being underground and therefore slightl closer together, can it?
Also, I forget how the gravity well affects space-time but they accounted for that too, surely?
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Re: Well, this could change things (neutrinos)

Postby gmalivuk » Fri Sep 30, 2011 11:51 am UTC

NotAllThere wrote:Is there anything that prevents massless particles going faster than light (why does light travel at light speed)?
Yes: all of relativity.
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Re: Well, this could change things (neutrinos)

Postby Tass » Fri Sep 30, 2011 1:13 pm UTC

Mr_Rose wrote:It can't possibly be something as obvious and ridiculous as they took the GPS readings for the installation from the surface then forgot to account for them being underground and therefore slightl closer together, can it?
Also, I forget how the gravity well affects space-time but they accounted for that too, surely?


It is a discrepancy of twenty meters, I am pretty sure they used three dimensional coordinates. They have crustal movement due to an earthquake visible on their GPS data. They have been looking for the error for three years.

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Re: Well, this could change things (neutrinos)

Postby Angua » Fri Sep 30, 2011 2:29 pm UTC

Everyone's probably already heard this one by now:

Spoiler:
"The barman says, 'I'm sorry, we don't serve faster-than-light neutrinos in here.' A neutrino walks into a bar." New Scientist, putting the fun back into fundamental particles
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Re: Well, this could change things (neutrinos)

Postby mr-mitch » Fri Sep 30, 2011 2:30 pm UTC

What about the movement of the Earth, as a whole? Although a quick calculation of the orbit gives a max of only 3cm difference in the length traveled.

From a quick skim of the paper they didn't take it into account (unless the global geodesy reference frame takes this into account, although from a quick skim of that too it seems to only take into account the shape of the earth). Should you take into account the movement of the Earth?

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Fri Sep 30, 2011 2:51 pm UTC

As has been stated, this is a group of world class scientists who have been scouring over their data and experiment for three years trying to figure out what was wrong. If you can read their paper and realize that they didn't think of something then by all means say something and try to get some attention. But you really need to give these guys the benefit of the doubt when it comes to "I wonder if they accounted for this obvious thing that anybody thinking about the problem for 5 minutes might think of"

@Notallthere Tachyons are the closest thing to what you're thinking of (imaginary mass I think), as has been mentioned above. Cosmic strings don't work that way. Higgs doesn't work that way. And even if there is a wormhole going directly along the alps that caused this, there is absolutely no way that you would have been able to sense this in your ski trip.
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Re: Well, this could change things (neutrinos)

Postby gorcee » Fri Sep 30, 2011 2:56 pm UTC

Malconstant wrote:As has been stated, this is a group of world class scientists who have been scouring over their data and experiment for three years trying to figure out what was wrong. If you can read their paper and realize that they didn't think of something then by all means say something and try to get some attention. But you really need to give these guys the benefit of the doubt when it comes to "I wonder if they accounted for this obvious thing that anybody thinking about the problem for 5 minutes might think of"


It's also worth noting that while the scientists have thought of and accounted for many of those issues, the scale of the errors that things like that can make is an entire order of magnitude smaller than the observed error in the experiment.

So the researchers have accounted for continental drift, seasonal variations, day/night variations, tidal forces, earthquakes, rotation of the earth, etc. And all of those factors, added together, introduce less systematic error by about a factor of 10 than what was seen.

So if there is some effect along those lines that the scientists missed, it has to be ten times bigger. So, to find such a systematic error, it's not that productive to just say, "what might they have missed?" but rather ask, "they controlled for these things... what might they have missed that is ten times bigger than those things?"

And I myself ask, "is it really likely that they missed something ten times bigger than those other factors?"

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Re: Well, this could change things (neutrinos)

Postby gmalivuk » Fri Sep 30, 2011 3:00 pm UTC

mr-mitch wrote:What about the movement of the Earth, as a whole?
What about it?
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Re: Well, this could change things (neutrinos)

Postby gorcee » Fri Sep 30, 2011 3:23 pm UTC

gmalivuk wrote:
mr-mitch wrote:What about the movement of the Earth, as a whole?
What about it?


I think the rest of his post makes the context of his question clear.

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Re: Well, this could change things (neutrinos)

Postby PM 2Ring » Fri Sep 30, 2011 3:46 pm UTC

mr-mitch wrote:What about the movement of the Earth, as a whole? Although a quick calculation of the orbit gives a max of only 3cm difference in the length traveled.
[...]
Should you take into account the movement of the Earth?

They took the Earth's daily rotation about its axis into account, but they don't need to worry about its orbital motion around the Sun, or the solar system's orbital motion around the galactic centre, or the galaxy's orbital motion within the Local Group, or the Local Group's motion towards the Great Attractor, etc. All of those motions are irrelevant, since they are almost perfectly linear at the scale of this experiment, so they don't affect the relative velocity between the neutrino source & detector.

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Re: Well, this could change things (neutrinos)

Postby mr-mitch » Fri Sep 30, 2011 4:01 pm UTC

Thanks, that's what I wanted to know. I wasn't offering an explanation.
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Re: Well, this could change things (neutrinos)

Postby dockaon » Fri Sep 30, 2011 4:04 pm UTC

As a former experimental particle physicist, if I was to bet where the systematic error is I would say the measurement of the beam structure at CERN. For a couple of reasons:
1) Maintaining stability of the bunch shape over 3 years at the level they're requiring (60 nanoseconds out of 10.5 microseconds) seems tough. Remember they're not directly measuring the time of flight of individual neutrinos they're building the time distribution of neutrino arrivals and comparing that distribution to the time distribution of the protons in the beam at CERN to infere the time of flight.
2) Typically the efficiency of the measurement of the proton beam will go down as the number of protons increases. If the beam time structure isn't a perfect square wave (which it isn't) the efficiency of the measurement is changing during the bunch which could easily bias their time distribution.
3) They're assuming that the beam shape isn't changing between where they measure the time structure of the proton beam and where the secondary particle beam is decaying into neutrinos. It seems really easy to me for one of the magnets bending the proton beam into the target to change the time structure of the beam.
4) The OPERA physicists probably know their own detector better than they know the beam at CERN.

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Fri Sep 30, 2011 4:18 pm UTC

I don't quite follow. My understanding is that CERN records the shape of the beam pulse (not a square wave, but that's okay, the point is that they measure what it looks like), and then turn that beam into neutrinos via smashing, and the resulting neutrino beam pulse is then measured at OPERA to have the exact same shape as the initial CERN proton beam, except that it is shifted in time ahead. So it's not so much that they are assuming the beam doesn't change shape as they are measuring it and lo and behold it has the same shape.

A rogue magnet won't maintain the beam wave pattern but time shift it faster. Did I not understand what you were saying?

Edit:
Though actually I have a real question. I think I recall understanding that at Fermilab at least there was some preliminary neutrino detector positioned to get the signal right away after the neutrino beam was made in the Tevatron, so actually near or on the Fermilab campus. Is that accurate? Is that distance enough to test this measurement? Obviously our timing devices are good enough to measure the difference, but I don't know if the experimental design is good enough for that.
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Re: Well, this could change things (neutrinos)

Postby gorcee » Fri Sep 30, 2011 4:42 pm UTC

PM 2Ring wrote:
mr-mitch wrote:What about the movement of the Earth, as a whole? Although a quick calculation of the orbit gives a max of only 3cm difference in the length traveled.
[...]
Should you take into account the movement of the Earth?

They took the Earth's daily rotation about its axis into account, but they don't need to worry about its orbital motion around the Sun, or the solar system's orbital motion around the galactic centre, or the galaxy's orbital motion within the Local Group, or the Local Group's motion towards the Great Attractor, etc. All of those motions are irrelevant, since they are almost perfectly linear at the scale of this experiment, so they don't affect the relative velocity between the neutrino source & detector.


Actually, they did control for seasonal variations, ie, changes in tidal forces from the sun during apehelion/perihelion (which is different than orbital motion, but I wanted to point out that orbital location was considered).

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Re: Well, this could change things (neutrinos)

Postby dockaon » Fri Sep 30, 2011 5:50 pm UTC

Malconstant wrote:I don't quite follow. My understanding is that CERN records the shape of the beam pulse (not a square wave, but that's okay, the point is that they measure what it looks like), and then turn that beam into neutrinos via smashing, and the resulting neutrino beam pulse is then measured at OPERA to have the exact same shape as the initial CERN proton beam, except that it is shifted in time ahead. So it's not so much that they are assuming the beam doesn't change shape as they are measuring it and lo and behold it has the same shape.

A rogue magnet won't maintain the beam wave pattern but time shift it faster. Did I not understand what you were saying?



The beam shapes aren't identical, they're similar. They're making a fit between the two beam shapes and one of the parameters for that fit plays the role of the time of flight. If the shape of the beam at the relevant point is different than what they think it is, that fit isn't going to give you the true time of flight. Basically, anything that makes the secondary particle bunch time distritubtion shifted later in time relative to their measurement of the proton bunch distribution, would make them think the neutrinos arrived faster on average than they did.

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Fri Sep 30, 2011 7:04 pm UTC

Well sure, but then this is what their 6 sigma statistical argument is based on. They sent the beams in bunches, separated by microseconds so there's tons of downtime, and the signal bunch they received strongly recovers the emitted signal to high degrees of precision, only time shifted. The whole crazy shape of the beam is still there (not identically, as you point out, but plenty similar enough for statistical results), but time shifted.

so what are other ways which could time shift the beam? It doesn't matter what magnet configuration you set up, you can't get a burst to start sooner, that's what the microseconds of downtime are for.
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Re: Well, this could change things (neutrinos)

Postby gorcee » Fri Sep 30, 2011 7:29 pm UTC

dockaon wrote:
Malconstant wrote:I don't quite follow. My understanding is that CERN records the shape of the beam pulse (not a square wave, but that's okay, the point is that they measure what it looks like), and then turn that beam into neutrinos via smashing, and the resulting neutrino beam pulse is then measured at OPERA to have the exact same shape as the initial CERN proton beam, except that it is shifted in time ahead. So it's not so much that they are assuming the beam doesn't change shape as they are measuring it and lo and behold it has the same shape.

A rogue magnet won't maintain the beam wave pattern but time shift it faster. Did I not understand what you were saying?



The beam shapes aren't identical, they're similar. They're making a fit between the two beam shapes and one of the parameters for that fit plays the role of the time of flight. If the shape of the beam at the relevant point is different than what they think it is, that fit isn't going to give you the true time of flight. Basically, anything that makes the secondary particle bunch time distritubtion shifted later in time relative to their measurement of the proton bunch distribution, would make them think the neutrinos arrived faster on average than they did.


How would you account for such a statistical similarity in packet shape that still contains a time-shift? I understand the principle of your argument regarding the statistical inference, but it's diabolically hard to induce a substantial shape-preserving mean-shift in any kind of data.

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Re: Well, this could change things (neutrinos)

Postby SU3SU2U1 » Sat Oct 01, 2011 7:35 am UTC

The problem is that there is no neutrino mirror, so their speed measurement is one way. This requires a careful consideration of how to synchronize clocks for a one way measurement, which is a thorny relativity problem that often isn't looked at anymore. In this case, to get beyond the GPS accuracy, they had to use a "time transfer device" (a fancy way to say a movable clock), but there is no discussion of the classic moving clock synchronization problem. In the end, this seems likely to be the source of the error.

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Re: Well, this could change things (neutrinos)

Postby idobox » Sat Oct 01, 2011 2:51 pm UTC

Is the neutrino emission process well known? If for some reason we expect the proton to take a longer time than it really does to collide with the nucleus and cause it to release a neutrino, it could maybe explain the difference.
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Re: Well, this could change things (neutrinos)

Postby gmalivuk » Sat Oct 01, 2011 3:01 pm UTC

SU3SU2U1 wrote:The problem is that there is no neutrino mirror, so their speed measurement is one way. This requires a careful consideration of how to synchronize clocks for a one way measurement, which is a thorny relativity problem that often isn't looked at anymore. In this case, to get beyond the GPS accuracy, they had to use a "time transfer device" (a fancy way to say a movable clock), but there is no discussion of the classic moving clock synchronization problem. In the end, this seems likely to be the source of the error.
Except, couldn't they just compare neutrino arrival time to photon arrival time?
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Re: Well, this could change things (neutrinos)

Postby gorcee » Sat Oct 01, 2011 3:03 pm UTC

gmalivuk wrote:
SU3SU2U1 wrote:The problem is that there is no neutrino mirror, so their speed measurement is one way. This requires a careful consideration of how to synchronize clocks for a one way measurement, which is a thorny relativity problem that often isn't looked at anymore. In this case, to get beyond the GPS accuracy, they had to use a "time transfer device" (a fancy way to say a movable clock), but there is no discussion of the classic moving clock synchronization problem. In the end, this seems likely to be the source of the error.
Except, couldn't they just compare neutrino arrival time to photon arrival time?


No, because the photons aren't traveling to the detector at Gran Sasso. The timing issue still exists. However, I'm not sure sure that they didn't account for moving clock synchronization. They definitely did account for clock synchronization in general, and the total systematic error there was like 2 ns. I'm not sure if the moving clock problem was factored into that number.

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Sat Oct 01, 2011 3:12 pm UTC

gorcee wrote:No, because the photons aren't traveling to the detector at Gran Sasso.


Sure, but photons are emitted and detected inside the CERN detectors from the collisions quite plentifully, such that they should have a pretty good idea about when photons are emitted in the collisions. And presumably neutrinos are emitted at the same point.
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Re: Well, this could change things (neutrinos)

Postby gorcee » Sat Oct 01, 2011 3:17 pm UTC

Malconstant wrote:
gorcee wrote:No, because the photons aren't traveling to the detector at Gran Sasso.


Sure, but photons are emitted and detected inside the CERN detectors from the collisions quite plentifully, such that they should have a pretty good idea about when photons are emitted in the collisions. And presumably neutrinos are emitted at the same point.


That's... what they're doing. And the neutrinos are getting there faster.

No matter how accurate your timing of events at CERN is, the issue is that you have to synchronize that with the timing of the neutrino beam at OPERA. So you still have the same synchronization issues. You can't solve that by simply resolving timing to a better degree at CERN.

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Re: Well, this could change things (neutrinos)

Postby SU3SU2U1 » Sat Oct 01, 2011 5:21 pm UTC

gorcee wrote:I'm not sure sure that they didn't account for moving clock synchronization. They definitely did account for clock synchronization in general, and the total systematic error there was like 2 ns. I'm not sure if the moving clock problem was factored into that number.


If they did, they don't mention it in their report, and I'm sure they would have, its an extremely involved complication. In particular, how much time did the travelling clock spend at different gravitational potentials? In this case, the synchronization effects depend on the path of the "time transfer device", and the paper doesn't mention at all dealing with this detailed issue.

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Re: Well, this could change things (neutrinos)

Postby Technical Ben » Sat Oct 01, 2011 6:57 pm UTC

So could the neutrinos be emitted before the photons?
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Re: Well, this could change things (neutrinos)

Postby Malconstant » Sat Oct 01, 2011 8:20 pm UTC

Technical Ben wrote:So could the neutrinos be emitted before the photons?


I'm no expert on experimental particle physics, but they can track the proton beam throughout the collision, at which point it would be abundantly clear and inexplicable if the collision just sat there for 60 nano seconds before shooting out particles. This would be a thoroughly well known phenomenon, so I'm confident that it doesn't exist. Therefore no, the neutrinos couldn't have been emitted before the photons because the photons are emitted as soon as the collision occurs.
Technical Ben wrote:PS, doogly, way to miss the point.

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Re: Well, this could change things (neutrinos)

Postby Robert'); DROP TABLE *; » Sat Oct 01, 2011 8:39 pm UTC

Did they actually send photons there, or did they just calculate the distance travelled and divide by c?
...And that is how we know the Earth to be banana-shaped.

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Re: Well, this could change things (neutrinos)

Postby Malconstant » Sat Oct 01, 2011 8:45 pm UTC

Robert'); DROP TABLE *; wrote:Did they actually send photons there, or did they just calculate the distance travelled and divide by c?

To Italy? No, photons don't last very long when traveling through the Earth. That's a specialty of neutrinos. But we've got lots of other measurements to tell us exactly what the speed of photons are, so they're comparing neutrinos to that speed.
Technical Ben wrote:PS, doogly, way to miss the point.

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Re: Well, this could change things (neutrinos)

Postby Robert'); DROP TABLE *; » Sat Oct 01, 2011 9:44 pm UTC

Yes, but I meant it in the context of "Are they absolutely sure the nuetrinos appeared when they think they did?" I was just checking that racing the neutrino and a photon along the same path is impossible.
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Re: Well, this could change things (neutrinos)

Postby gorcee » Sat Oct 01, 2011 11:02 pm UTC

Robert'); DROP TABLE *; wrote:Yes, but I meant it in the context of "Are they absolutely sure the nuetrinos appeared when they think they did?" I was just checking that racing the neutrino and a photon along the same path is impossible.


The situation is more complicated. The neutrinos are a result of collisions of protons at LHC. The protons are not sent to Gran Sasso, so there's no racing going on.

So two things have to happen regarding timing. First, they need to know the time and duration of the proton beam collision. From within that, they also need to know the time of the neutrino generation from that collision.

The first time isn't that hard. Detectors at CERN can detect, with very small error, the timing of the proton collision. They can also (potentially) know the synchronization of that time with the time at Gran Sasso (the potentially is because SU3 brought up a legit question regarding this timing issue).

The second timing factor is tricky. Knowing when the neutrinos were formed during the collision is impossible to directly measure at CERN. But there are some very advanced statistical models that can be developed to understand that timing (known as maximum likelihood models). These models are based around uncertainty, but there are mathematical techniques that allow you to characterize that uncertainty and put limits on it. To that extent, the researchers have shown that their statistical model fits the data remarkably well. So it's pretty safe to say that they are inferring the timing of the neutrino beam generation very, very well.


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