neutrinos faster than light?
i find the article poorly written, perhaps agent : Orange can chime in when he finds time.
i was put off at the beginning where it is stated that : mathematically an imaginary number is the square root of a negative number ,written bi where
i=−b^2, not the square. perhaps it works differently with mass equations (but i doubt it), or they mean
−b^2 . a negative number squared is always a positive number. EX: -22 (-2 multiplied by -2) is 4 (not -4) .
note i had to use the code tags to prevent autoformatting ,which made a huge mess of the post.
a month later i figure that the equation above is wrong. probably due to autoformatting.
-b^2 is -b squared which would be a postive number.
what was meant was i=SQROOT of -b
An imaginary number is written with i^2 = -1. So (i x m)^2 = -m^2
Or, if you like things in terms of square roots, sqrt( -m^2 ) = i x m, or just im if you prefer.
There are three kinds of paths particles can take through space-time in general relativity. These are defined in terms of path lengths or proper times, the time an observer travelling on that path would record on a watch they carried with them.
Time-like paths are the trajectories normal particles follow. These particles have positive mass like all of the matter we know. They move through time from the past to the future (though the rate at which they can be said to move from the past to the future is relative of course
) and they have speeds less than the speed of light. The proper time measured along this path is always positive, so causality is preserved for normal matter. As we would expect these particles all have positive mass that is real (which was good news for Einstein).
Null paths are the trajectories that light-rays follow. In fact, any particle with no mass (m=0) will follow one of these paths. The proper-time along these paths is 0, which means that light rays themselves don't experience time (which is infinitely fascinating to me). These kinds of paths are called null geodesics. Particles with no mass move at the speed of light always.
Space-like paths are the opposite to time-like paths, they are directed from the future to the past, and have proper times that are negative! Since energy must always be positive, the particles travelling along space-like paths are imaginary mass particles that must travel at speeds greater than the speed of light. In fact, the energy-velocity relationship is upside down for these kinds of particles. The slower they go, the more energy they have, which is weird and counter-intuitive. These kinds of particles are not widely considered realistic and when a tachyon shows up from a quantum field type of calculation then the theory is considered flawed and there's something wrong with the assumptions that have gone into developing it. These particles make all kinds of strange trouble for the universe and a lot of people have looked at what kind of paradoxes might exist if they were kicking around the universe.
So that article posted earlier is about trying to find such past-directed particles. But there are some big problems with this guys idea. The main one is that his claim hinges on the neutrino being a negative mass particle. Ehrlich claims the mass bound on neutrinos is -0.11 +- 0.016 electron Volts. (from his article here which i have not read http://arxiv.org/abs/1408.2804
). That may be, but the observations and experiments with neutrinos are still in their infancy and are not anywhere near precise enough to make the claim the neutrino really has a tiny and negative mass. So I would be suspicious of the whole thing and take it with a salt-shaker full of salt instead of just a few grains.
Still it would turn established physics on it's head so if there's still a possibility let's go do some small experiments first like the ones mentioned in the original article (ie using tritium beta decays and cosmic ray data) before we treat it any more seriously.
Blowing a kneecap off of an established idea is the dream of every theorist.
However, in closing, let me say this
Don't worry about it, the imaginary number isn't really there.