system
Given the following post, respond as if you're commenting on Reddit:
human
How do we know neutrinos have mass?

My own answer is: since the Super Kamiokande and SNOLAB we know that neutrinos can change flavours. My reasoning is: solar neutrinos are all electron neutrinos originally. To change flavour an infinitesimal (but non-zero) amount of time needs to pass (simply to have the 'room' to switch). Particles moving at c don't experience time. All particles with mass have to move slower than c. Hence, neutrinos have mass. Is that the gist of it?
gpt
Your understanding is more or less correct. 

The key piece is that neutrino oscillation implies that the flavor states are not the same as the mass states. This means that flavor states are mixtures of the mass states, and vice versa. 

The existence of flavor oscillations (observed as a deficit of solar electron neutrinos... because some of them turned into muon neutrinos and tau neutrinos) indicate that this is the case. So the evidence for neutrino oscillation is that we see a third of the expected electron neutrino flux from the sun, because they've turned into other flavors of neutrinos, and neutrino oscillation is the evidence for neutrino masses.