If you want to measure neutrinos transforming, then knowing the distance to source lets to calculate rate of transformation.

Why can't you sample at one point on the earth's surface and sample again at that point's antipode? You would know the distance that was travelled, and have measurements at both points.

How would you know the two different neutrinos interactions came from the same source/distance without producing them yourself?

Well that's not the problem. The problem is natural sources are too big. The distance difference between you and the top of the sun and the middle is like 100x the length of the equator. Neutrino sources in the sun have very irregular shapes, so that too changes the distance. And you have zero control over it all. All you'd ever see is the equivalent of a soft shadow, you'd never get a point source.

The second thing you might want to do: "filter" neutrinos ... well that just doesn't work at all. Nothing stops (a decent amount of) neutrinos. So you can't filter them and create a known point with, say, only electron neutrinos like you can with light. There are also no known astronomical objects that filter neutrinos. They fly right through a star, so that's no good either.

Third you could filter observations. But again you hit the filter problem. You can focus neutrinos measurements (even if you can't focus the neutrinos themselves), but that lowers the amount of neutrinos you measure further. And you're only measuring like maybe 50 per cubic meter of water, so you don't have much to work with.

I guess you could wait for things to get especially good for your measurement but you'll be waiting a long time.

I wouldn’t need to. By sampling hundreds of thousands of events, I would know the odds of getting a particular neutrino from a particular source is the same.

That’s part of the problem, they had 500 detection “events” over 15 years of operation.

Neutrinos mainly come from the sun, and the sun is massively larger than the earth. You can't draw any conclusions from measurements at two points at a distance that is much smaller than the size of the source itself.

From TFA:

> the three types of neutrino-flavors mix into each other. That means, if you start with, say, only electron-neutrinos, they’ll convert into muon-neutrinos as they travel. And then they’ll convert back into electron neutrinos. So, depending on what distance from a source you make a measurement, you’ll get more electron neutrinos or more muon neutrinos.