If the total energy of all three types of neutrinos exceeded an
average of 50 eV per neutrino, there would be so much mass in the
universe that it would collapse. This limit can be circumvented by
assuming that the neutrino is unstable….These indicate that the summed
masses of the three neutrinos must be less than 0.3 eV source
Then, if I read this right, rest mass of a neutrino is, on average, $10^{14} h\nu$ and its speed is near (a few nanometres) the speed of light and recently there were also (false) allegations that its speed might exceed the speed of light.
I couldn't find data about the energies recorded at GranSasso on reception of the neutrinos from CERN or from other sources, but surely they are not exceedingly high, else they would have hit the headlines.
So, how come they do not have an almost infinite (or at least enormously huge) relativistic mass/energy which, according to SR, any body with restmass should have in order to approach $c$? Do you have any figures about their relativistic energy and relate it to SR formulas?
So if we plug in to find the total energy of the neutrino we find.
ev∼18keV∼0.03 $m_{electron} Which isn't that big.
Ia this answer correct? I posted this question because in my [previous question]
(How did Pauli and Fermi deduce the existence of the neutrino?) there was this comment:
What makes you think the energy carried away by the neutrino is tiny?
The mass of the neutrino is tiny, but its kinetic energy can be of the
same scale as that of the electron. – dmckee
Now, the energy of an electron is .5 Mega eV, what is then the correct maximum value of the energy of a neutrino?
Best Answer
So let's say these electrons go really really fast like 0.999999997 times the speed of light. We know the upper bound on the neutrino mass is less than 1 eV (the kinetic energy of taking one electron through a one volt potential difference) from experiments. So if we plug in to find the total energy of the neutrino we find.
$$E_{relativistic} = \gamma m_{neutrino}c^2 < \frac{1}{\sqrt{1-(0.999999997)^2}} \text{eV} \sim 13 \text{keV} \sim 0.03 m_{electron} $$
Which isn't that big. And as already stated the mass energy is on the order of at MOST 1eV. So what we find is that these things can travel extremely, extremely fast even though their kinetic energy is still mere percentage points of the next smallest particle, the electron.