At Pisa University, Physics and Mathematics Buidings are few meters apart.
When I eat in the neraby Cafeteria, a flux of complex and technical words from surrounding tables pounds my poor ears.
Neutrinos, light speed, GPS, CERN, GranSasso and Gelmini are the most easily recognized words.
What is all this of fuss about the superluminal neutrinos ?
Mathematicians are curious, so googling a litte I found this simple report about the findings of OPERA experiment (note: at some time between 2011 and 2015 this link did disappear...).
Wikipedia has a page about OPERA experiment and links to other sites about neurinos' detectors, that are very interesting.
A nice graph shows the trip that neutrinos have to do from CERN to Gran Sasso, 732Km througt the rocks of the earth crust, up to 11Km in depth.
There are some previous claims of faster than light speeds reported by Wikipedia:
Having something moving faster than light doesn't mean Relativity Principles are violated.
Several faster than ligth effects are well known and have simple explanations.
What about neutrinos ?
Detecting neutrinos is a difficul task, and neutrinos astronomy is young.
Some interesting findings have been done in 1987 from a Supenova, SN1987A,
168,000 light-years far from earth.
Neutrinos' burst were discovered 6 and 3 hours before the Supernova was visible.
Astrophicist thinks that burst 6 hours before was spurious, and that 3 hours was the time needed for the explosion to travel from inside
the star to where it could emit light.
Some eminent physicist, Rubbia between them, noted that if neutrino velocity is 20 part per million faster than light, in the 168,000
years of flight from SN1987A to us, neutrino should have gained more than 168,000 * 20 10-6 = 3.4 years, and this was not the case.
A lot of newspapers reported this fact.
Now, maybe there is an error somewhere in the very complex chain of difficult measures.
But I have great respect for the physicists that works at CERN.
I know how competitive is the world of high energy physics.
I am sure they double and triple checked everything before announcing the results.
And a similar previous experiment MINOS (and also the wikipedia page) in the US had similar results, on a similar distance, but with less precison, so that the discrepancy was accounted by the sperimental margins of error.
Now let us suppose that the measures of MINOS and OPERA are correct.
Let us ask why SN1987A neutrinos did not arrive 3 years before.
The main difference between the two cases is that we we have a little more matter between source and receiver here on the earth, than in interstellar space.
How much matter ?
Well, this is easy to compute if we are not too finicky to the details...
The earth mantel (more exacly the earth crust) has a density rougthy 2.7 g/cm3.
This means a cubic meter oth the rocks has a mass of 2.7 106 g.
Neuton or proton particles have a mass of 1.7 10-24 g.
In such a cubic meter we can count up 1.6 1030 particles.
Usually the share of neutrons versus protons is 50 to 50, so we will have
half of them neutrons, half protons, and a same number of electrons.
So in a a cubic meter of rocks we can count up 2.4 1030 between neutrons, protons and electrons.
Is it possible for a straigth line to go from CERN to Gran Sasso without "touching" any matter particle ?
Classical physics is not very good for athomic problems.
Anyway, in some sense, we can say that a proton or neutron or electron have
a "diameter", something of the order of 0.8 10-15m for neutron an proton,
and a some more for electron.
Obviously thinking of particles as rigid balls is not correct, and this "diameter" has a different meaning.
Anyway, as long as this can help the visualization of the problem, each particle has a
section of π x (radius)2 = 2 10-30.
In a parallelogram 1m x 1m x 732km we have a total section of 2 10-30 x 2.4 1030 x 7.32 105 =
3.5 106 m2
This covers up pretty well one square meter several times, so a straight line must pass
a lot of times inside a particle.
Very well, so now let us ask us how much road a neutrino will fare in open space between the particles, and how much road will be "inside the particles" (sigh!).
With 2.4 1030 in a cubic mater, supposing a regular lattice, we have
just to take the cubic root of the total number of particles, and we get 13.4 109
particles in each side.
Each particle has a diameter of roughty 2 10-15m, so in one meter we have
26.7 10-6 m "inside matter" and the rest in free space.
Particles are not uniformly spread but grouped in athoms, so the number will be
smaller than this.
Now this simple computation shows that roughtly 20 parts in a million of the road of
a neutrino from CERN to Gran Sasso are "inside" elementary particles, and
it is curious that exactly 20 parts in a million is the time discrepancy of
OPERA experiment, as if the path "inside" should not count in measuring distance.
I read some time ago a book on the mathematical wonders of Cheope's Phyramid....
May be it is the same kind of coincidence of that book.
Maybe not. Maybe there is some reason. Time will tell.
Pisa October 5th, 2011
Sergio Steffè
Unfortunately they said it was an error in the chain of measures needed for syncronizing the clocks ...
For SCI-FI fan like me it is a disappontment ... (2015)