Quote:
Originally Posted by Kittens
That gets confusing as to when it's m and when it's im .. just use 'm' for the mass , which can have imaginary values
We have never observed any neutrinos that have speed much slower than light either .. doesn't mean there aren't any.
Also, how would you propose measuring the speed of neutrino that is moving at 141c or whatever? There could be such neutrinos coming from the sun, but we never realise because we don't know what order the received events were emitted.
It doesnt get confusing if one is familiar with the fact that for all real particles E^2=p^2+m^2 so a minus sign is easily the tachyon case as only there the total energy is less than momentum (if one wanted to always have equations with real numbers and used the measure of the mass).
Also (regarding speeds always close to c) it means that its hard to get them to small speeds because its hard to produce them in a way that their total energy is not many times over their assumed small rest mass (they think less than a few eV so far). This is a result of relativistic decay dynamics. Basically they always take away significant fraction of the excess available energy for the decay that is many hundred times a few eV. So they are in all natural processes produced at enormous gammas very close to c by two or more 9s (result of conservation of momentum and energy) . To produce them you need nuclear reactions or decays of mesons etc (weak force). You cannot have nuclear reactions that neutrinos are produced with say 2-3 eV total energy. And thats why we cant observe them at any smaller than 0.9..c type of speeds. If one could find a way to decelerate them maybe, but hard to design it.
And there have been other experiments like that in K2K that the neutrinos had energy only 1GeV (20 times less) and then the speed would have been 1.01c which is a lot easier to detect because within 250km they had in Japan that means easily 8340 nsec earlier arrivals that is 139 times larger than the G.Sasso time difference which means a lot easier to measure if they wanted beyond any experimental uncertainty nomatter how bad one messed up timing or distance. Look also at the energies of the MINOS experiment to see if they had small enough energy to correspond to proper speed under this tachyon idea.
Also you have supernova ones that in 1987 with less than 1Mev energy (ie my example initially) they would have had 141 c and they wouldn't have arrived just 3 hours earlier as observed but many thousands of years earlier ie we would get absolutely no signal nearby the optical one.
But of course they are not tachyons for this and other reasons and whatever causes this result if not 99.99% experimental screw up, may very well have such dependence with energy that it doesnt produce significantly over c speeds elsewhere in our experiments as a tachyon would but only in very high energies.
Always remember that its very hard to measure their speed since it has to be so close to that of light and their creation and detection can never be perfectly known for a single one unless one had a massive experiment that lasted years and had beams every few seconds with only a few protons significantly separated to each other timewise. In principle they sent ~10^20 and detected 16000 so basically if you were able to send 1 proton (tough enough as this is anyway) every 1 msec (time of flight near 2.5ms) for safety of identification, you still wouldnt get a single detection after many years with enough probability to be safe. So it gets extremely tough to measure them properly like that and you use beams of many with all the problems this introduces. Still i suppose future experiments can improve on proton beam intensity (luminosity) and reduce its duration to shrink even further the experimental errors or play with the duration as parameter to spot where the systematic error may be hiding.
Last edited by masque de Z; 10-04-2011 at 01:06 PM.