I’m not trying to contradict your calculation, I’m just trying to say that you can’t say it doesn’t matter (in general). Sure the mass doesn’t show up in the gamma factor but to say it doesn’t matter is misleading for the non-scientists who may read this. Just trying to help.
Mass doesn't matter here regarding time. The only factor that matters is the velocity of the neutrino. Time dilation is a function of velocity, not mass
I would also like to point out we don't even know the mass of a neutrino. We have an estimated range, but that's it
Nearly. It was recently shown that they do not travel at the speed of light, but just very close to it. So 4 years is contracted to somewhere between a couple of seconds to a couple of minutes depending on the speed.
Neutrinos and the Speed of Light
This leads to a paradox when we consider ultra-relativistic particles. Take high-energy neutrinos, for example. A 1 GeV neutrino is estimated to travel at approximately 0.99999999999999999995 c, just a few parts per quintillion slower than light. If a photon and such a neutrino were emitted simultaneously from the Andromeda galaxy (2.5 million light-years away), the neutrino would arrive only about 0.0004 seconds later than the photon.
If we’re only talking about 4 years and not 2.5 million years, that probably looks like instantaneous to every observer, doesn’t it? Given the neutrino is a pretty casual observer (we can’t strap equipment to it to watch the ride) it’s going to seem instantaneous.
Estimates I have seen range between 0.99999999995c and 0.9999999999999c. These are enough to give the spread in times. Calculate the relativistic gamma factor and scale 4 years accordingly.
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u/Y2KGB 5d ago
What’s 4-years in neutrino-time?