where I described the equation del_tau = (del_x)^2 – (del_t)^2 = 0, for photons.
I change this by multiplying -1.
del_tau = (del_t)^2 – (del_x)^2 = 0, for photons, positive for material particles such as neutrinos.
Also check the diagrams here: “The diagrams for Relativity”
One of the biggest puzzle we are seeing in time is the neutrino anomaly from OPERA experiment. It is suggesting that the propertime of neutrinos is -ve, about 60 nanosecs for the distance the neutrino traveled in the experimental apparatus where it was expected to be positive as per the equation above.
This brings in not a puzzle but a far more deal of consternation because it throws many physical insight, intuition and results of a great many number of observations on which modern physics is rested, to be not completely true, that is partially untrue. This therefore isn’t accepted to be true by itself, atleast in the tradition of sceptism from mainstream physics community.
One way to go about this problem would be to go for constructing a propertime for photons and material particles such that it is a function of energy. A very slim function of energy. SO thin and so slow that it grows to a negative value for energies in teh order of GeV. Even shows up very very small negative excess even at the order of MeVs. and grows like that at higher and higher energy to make this excess prominent, even if negative, this had never happened so clearly in Physics.
One thing to note is this function is not only zero for a somewhat finite mass of 2 eV, but keeps it zero for masses as small as 10^-18 eV. But even for that small mass of 10^-18 eV this function gives a propertime which grows +ve at very very high energy lets say 10 GeV, so that for 2 eV it is -ve at that energy. A propertime which is going the reverse way and was escaping our attention for a century. This could come from the detailed geometry, the structure of Universe and the geometry that we know or do not know so far, or from inconsistencies of the theory we have so graciously and soo meticulously constructed and tested everyday, for a century.
The internet keeps playing hide and seek, which is a pretty common affair I don’t know how, SO I lost a small paragraph. Here is what I wanted add.
Note that this propertime as a function of energy (rest energy and total energy) is such that it again keeps the higher masses such as electrons and muons +ve in their propertime like it does to photon but keeps the 2 eV neutrinos -ve. Then you can shift your zerolevel and make the neutrinos zero propertime and the other particles with masses above and below the neutrino +ve, by a slight shift, to make the neutrino “0” propertime. Such radical Physics has always been studied but not exactly with this purpose.
Once we can have that function constructed and it fits consistently with everything we know whoever does this is at par with Einstein, for all time to come, and the underlying physics is at par with all that we know, for all time to come. It would be a revolutionary idea, ofcourse rested on the correctness of all that we observe not just the neutrino excess. Once it sufficiently fits with neutrinos though, you can bet your boxer or whatever that it will be so for everything else we observe, till in decades or a century we again hit such shocking surprises that changes world course of physics everynow and then, but very slowly.