# Neutrino Oscillation and their gravitational implications

As I understand neutrinos, there are three different flavors, all with different masses. Although the masses of these neutrinos have not been directly measured, their mass differences have been. Current experiments, KATRIN and Project8 are going to measure neutrino masses and we shall know soon enough. Regardless, their mass states change as they travel through space. This leads to my question...

Since an object's gravitational field is related to its mass and neutrinos have different mass states while they are traveling, it must mean that every point in space must be constantly altering in gravity intensity!

Although every object alters the gravitational field intensity as it travels and passes a given point, neutrinos would do it differently because they keep changing mass states!

Let's assume a constant stream of neutrinos pass by a point in space versus neutrinos that don't oscillate (This is hypothetical) doing the same thing. Wouldn't these extremely weak gravitational waves be different given oscillations than not?

## 1 Answer

It doesn't quite work like that. Each of the three flavors is a quantum superposition of the three mass states. So if you make an electron neutrino, for example, you get a combination of the lightest neutrino state, the middle mass neutrino state, and the heaviest neutrino state. (You can look up the coefficients but they're not important here.) As the neutrino propagates through space, each of these three mass states goes on its way individually, just as a regular particle would. So there's nothing particularly strange about the way neutrinos interact with gravity.

• And they mix again when the re-interact (therefore being projected back into the flavor basis) the oscillations arise because the three states are all ultra-relativistic and are spread out by momentum uncertainty, so they overlap. – dmckee --- ex-moderator kitten Apr 28 '12 at 2:44
• Life can be funny. I had an extended interaction with Boris Kayser on these matters today and have consequently heavily re-written my previous answer. – dmckee --- ex-moderator kitten May 1 '12 at 0:22
• Read this just now and wondered if it would be proper to add that it can be confusing to mix the propagation of a quantum superposition of mass states with classical effects of gravity (as the question implies). There isn't a single well-defined gravitational field along the "classical" neutrino trajectory because of this (and it would require a good theory of quantum gravity to describe it eventually). But I might mix something up, I'm not a particle physicist :) – BjornW Nov 24 '14 at 16:07