Life In 19x19

Cyclops: I dispute your argument. You are making the following oversight: it is extremely unreasonable to represent the earth's interior as a bunch of atoms on a cubical lattice. The earth's interior has - along a long path, and all the way from one side of the earth to the other is certainly a long path - no long-range lattice order.

Your calculation, in which you take "linear emptiness" as the third root of "spatial emptiness" looks fancy, but would only apply in the exceedingly unlikely case that a neutrino would pass through a nucleus at every possible lattice site. Since, as we noted, the earth interior has no long-range order, this does not happen. Thus, "linear emptiness"=="spatial emptiness"=="emptiness". So even if, somehow, the neutrino's would pass through a nucleus absolutely instantaneously, the speed excess would only be (1 + 1,39E-14) * c, using your numbers.

Gaius, thx for putting your finger at the rotten spot. ( sorry for using this dutch expression ). The third power root is indeed the weak point in my argument. I admit I am quite optimistic with my cubical lattice model as far as the time gained is concerned. But I think your model is definitely too pessimistic. The number 1,39E-14 is, apart from a form factor close to 1, the mean free path between nuclei as fraction of the nucleus size. Or equivalently the fraction inside nuclei of a random straight line segment through the earth, assuming them randomly distributed. At first sight it seems reasonable to take this number to calculate the time gained by my hypothesis of zero delay in nuclei. But, don't laugh, as in refraction, the path of least time is needed, and due to my hypothesis it is not going to be a straight line but a broken line zigzagging through nuclei. It needs a computer program or some good calculating to establish the amount of time saved in this model. To me it is not improbable that my third power root will be justified this way. Anyway the numerical coincidence I found will make me observe the tonight snooker match more intensely.

That is a somewhat interesting idea, but I don't really buy it. It would require somehow using the wave properties of a neutrino to the max to do this, and I don't think wave-particle duality really allows that without penalty! Besides, I have a very tough time imagining a zigzagging line that crosses most nuclei but does not make the total neutrino path length at least 0.0025% longer (which is what you need to explain the speed gain).

All of this seems exceedingly implausible to me, unless you would come up with a convincing explanation of: 1) how and why wave-particle allows you to do this and 2) why it allows you to do it so efficiently.

EDIT: mathematicians, please forgive me for using the term "zigzagging line". My shame knows no bounds.

gaius wrote:Besides, I have a very tough time imagining a zigzagging line that crosses most nuclei but does not make the total neutrino path length at least 0.0025% longer (which is what you need to explain the speed gain).

Forgive my ignorance, but when you calculate the time it takes light to travel from X to Y, you're already measuring the most direct path rather than the distance putatively transversed by the wave-function, right?

gaius wrote:That is a somewhat interesting idea, but I don't really buy it. It would require somehow using the wave properties of a neutrino to the max to do this, and I don't think wave-particle duality really allows that without penalty!

Photons behave this way, according to Feynman's book "QED". Is it its mass that you doubt neutrino's behave this way too?

gaius wrote:Besides, I have a very tough time imagining a zigzagging line that crosses most nuclei but does not make the total neutrino path length at least 0.0025% longer (which is what you need to explain the speed gain).

I did a rough calculation and alas I needed to confine my nuclei to quite close to their lattice positions in order not to loose what my zero delay hypothesis gained. 1% of the lattice distance was all freedom I could grant them. So indeed I need some ordering to survive. And I am not going to propose that gravitation and earth rotation might offer the needed ordening. My geological knowledge is not enough for that and besides Italy is not oriented North-South enough.

gaius wrote:All of this seems exceedingly implausible to me, unless you would come up with a convincing explanation of: 1) how and why wave-particle allows you to do this and 2) ....

Not that it relevant anymore but assuming my hypothesis I think it is a straightforward application of the QED book. Maybe apart from the fact that the neutrino is not supposed to be massless as photons are.

I don t think that mass affects the quoted behavior:
as far as i remember, Feynamnn says that classical trajectories corresponds to stationnary solutions of the path integral. i think this is also true for massive particules. But the point remains that its hard to imagine the extra distance by a zigzag path being compensated by quicker speed within nucleis

as to instant transportation within a nuclei, it reminds of the measurement paradox, ie the fact that after a measurment, the wave function is instantly projected to the measurment result. Thus the EPR paradox where measures on a an entangled photon affects the other one "faster than light".
I never really understood the specifics but this does not violates relativity because no information can be transmitted this way (you transfer the result of a random measurement).

but i am not sure it applies here: the arrival of a neutrino signal is a message and could be used to transmit information ?

I agree with gaius that the numerical coincidence you observe seems a bit far fetched. i dont see a reason to use the third root of the "emptyness" rather that the emptyness itself

...and the plausible explanations begin: http://www.technologyreview.com/blog/arxiv/27260/

daniel_the_smith wrote:...and the plausible explanations begin: http://www.technologyreview.com/blog/arxiv/27260/

That's the most plausible explanation I've heard yet. Neat. I'm far from qualified to review their work, though ...

Explanations would be premature which is why the team reporting this offered none.

First several other teams will attempt to replicate the result. ROFLOL last weekend a conference I was at (unrelated to physics) had a workshop about this (and other neutrino research)because one of the attendees is connected to one of the labs that will surely be doing that.

If you wonder at the extent of the work by the reporting team to show how they couldn't have a measureent error that's because the result being reported was so extraordinary that this was necessary before other labs would even try to replicate (there can't be an OBVIOUS error).

BTW -- what was being claimed wasn't that the neutrinos exceeded the speed of light in some medium but that they exceeded the speed of light in vacuum. Neutrinos regularly exceed the speed of light in various media.

Mike Novack wrote:BTW -- what was being claimed wasn't that the neutrinos exceeded the speed of light in some medium but that they exceeded the speed of light in vacuum. Neutrinos regularly exceed the speed of light in various media.

Thanks, that's what I thought.

daniel_the_smith wrote:...and the plausible explanations begin: http://www.technologyreview.com/blog/arxiv/27260/

The above mentioned article suggests that the clocks at either end are not properly synchronised.

The way to circumvent this problem is to have a transmitter and a reciever at both ends. Send neutrinos both ways at the same time. Then average the two results. Synchronization errors should cancel out.

Ok, it does require building some new hardware, but it is a theoretically elegant solution, IMHO.

Joaz Banbeck wrote:

daniel_the_smith wrote:...and the plausible explanations begin: http://www.technologyreview.com/blog/arxiv/27260/

The above mentioned article suggests that the clocks at either end are not properly synchronised.

The way to circumvent this problem is to have a transmitter and a reciever at both ends. Send neutrinos both ways at the same time. Then average the two results. Synchronization errors should cancel out.

Ok, it does require building some new hardware, but it is a theoretically elegant solution, IMHO.

Or, several billion dollars less expensively, record the flight path of the GPS satellite.

The explanation makes sense and the magnitude of the error correctly accounts for the effect, but if this is actually the problem with the paper, I'm unimpressed. Getting the special relativity wrong is not something I would expect them to do.

It's not that the clocks weren't synchronized, it's that they were synchronized to the orbiting GPS satellite, which means the frame of reference they were measuring from was that of the satellite. From the satellite's point of view, the distance the neutrinos traveled was slightly shorter, due to relativistic effects. It sounds pretty convincing, and I'm surprised that the original paper didn't consider that effect (if indeed it didn't). Einstein wins again...

daniel_the_smith wrote:It's not that the clocks weren't synchronized, it's that they were synchronized to the orbiting GPS satellite, which means the frame of reference they were measuring from was that of the satellite. From the satellite's point of view, the distance the neutrinos traveled was slightly shorter, due to relativistic effects. It sounds pretty convincing, and I'm surprised that the original paper didn't consider that effect (if indeed it didn't). Einstein wins again...

No, the arxiv paper you reference says the opera team accounted for the Lorentz transformation but forgot to account for the fact that from the perspective of the satellite the source and destination are moving, so the actual place (in the satellite's frame) of the destination moves (very slightly) closer or further from the source's original place (in the satellite's frame) during the travel time of the neutrinos. It claims satellites generally move West to East, roughly parallel to cern - gran sasso, so the destination moves closer (in the satellite's frame). You would be able to take a type of average over both directions to correct for this if you fired them in both directions.

prokofiev wrote:... but forgot to account for the fact that from the perspective of the satellite the source and destination are moving, so the actual place (in the satellite's frame) of the destination moves (very slightly) closer or further from the source's original place (in the satellite's frame) during the travel time of the neutrinos. ...

Er, I must be not understanding something because I thought that that (the relative motion) was what you needed to put into Lorentz transformation? Are you saying they didn't use the right data when they did the math? This isn't related to my field in any way so you're probably right, but now I'm confused...

For anyone else that needs to look up Lorentz (I didn't remember the name): http://en.wikipedia.org/wiki/Length_contraction