How much energy could the various types of neutrinos be converted into per E = MC[sup]2[/sup] at 100% efficiency?
Then, how many neutrinos would need to be captured (in say a reasonably small = power plant-sized generator) to produce at 1% efficiency (i.e., not total conversion of mass into energy; I think I read that solar fusion is about 4% efficient, so let’s go with 1% to be conservative) to produce enough energy to power New York City?
And is that feasible (mathematically, not necessarily technologically)? I.e., could the flow of neutrinos through the generator sustain that level of power at 1% conversion?
Well if you could convert a mole of these heavy neutrinos into energy each second, you could power 290 100 watt light bulbs.
To get that mole per second from the solar neutrino flux (about 5 X 10[sup]6[/sup] neutrinos (of all types) per cm[sup]2[/sup] per second), you’d need a perfectly efficient neutrino trap about 3.5km square.
No one’s going to be lighting up NYC with neutrino-energy converters any time in the foreseeable future.
Almost nobody has questioned the existence of neutrino oscillations since SNO (the Sudbury Neutrino Observatory) “found” the “missing” solar neutrinos in 2001. And the easiest way to make neutrinos oscillate, given what we know about particles physics, is for them to have mass. However, nobody has been able to come up with an experiment to directly measure the masses of the neutrinos; we can (so far) only measure the differences in the masses (roughly speaking.)
The rest mass of the neutrino is still, for most purposes, irrelevant. All off the neutrinos so far detected have been very highly relativistic, and thus have kinetic energies much higher than their rest masses. And the kinetic energy is easier to harness than the rest mass, anyway.
All that said, the primary natural source of neutrinos is the Sun, and the Sun radiates a lot more energy in other forms (i.e., light) that are a lot easier to harness than neutrinos.
If you’re capturing solar neutrinos, the energy from the mass isn’t what you’d be after. The energy due to the rest mass is peanuts compared to the typical kinetic energy of millions of eV.
The solar flux of energy at earth due to neutrinos is not way different from the radiation flux:
neutrinos: ~100 W/m[sup]2[/sup]
radiation: ~1000 W/m[sup]2[/sup]
This is because the energy from fusion goes to neutrinos and radiation, and that’s pretty much it. (I actually would have expected these numbers to be a little closer, but my by-eye integration of multiple log-scale flux plots could certainly be off by 5x or so.)
You’ll never get even a kajillionth of that neutrino energy, though. About 99.9999999999998% of the neutrino energy passes right on through the earth due to the tiny interaction probability of neutrinos. (Interesting: I calculate that solar neutrinos are depositing about 20 watts in the bulk volume of the earth. This is definitely peanuts compared to the 2 quadrillion watts impacting the earth in the form of solar radiation.)