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Why is there an assumption that if neutrinos didn't have mass they would move at the speed of light? and how does the fact they oscillate prove they have mass?
Because of the [itex]E^2 -p^2 = m^2[/itex]Why is there an assumption that if neutrinos didn't have mass they would move at the speed of light
Because the oscillation pattern appears with the mass-squared difference between the neutrinos... if they are massless (or even mass-degenerate) there wouldn't be any oscillation visible.and how does the fact they oscillate prove they have mass?
Any massless particle is required to travel at c in a vacuum. Massless neutrinos would travel at c for the same reason massless photons do.Why is there an assumption that if neutrinos didn't have mass they would move at the speed of light? and how does the fact they oscillate prove they have mass?
Some small bit of nit-picking. The electron muon and tau states are not the neutrino mass states. In fact, it is crucial for oscillations that not only the masses of the mass eigenstates are different, but also that the flavour states, i.e., the electron muon and tau neutrino states, are not equivalent to the mass states but instead are linear combinations of the mass states.three mass states (electron, muon, and tau) are different
The mass eigenstates are the HamiltonIan eigenstates,but what about the flavour eigenstates,which operator's eigenstates they are?Some small bit of nit-picking. The electron muon and tau states are not the neutrino mass states. In fact, it is crucial for oscillations that not only the masses of the mass eigenstates are different, but also that the flavour states, i.e., the electron muon and tau neutrino states, are not equivalent to the mass states but instead are linear combinations of the mass states.
Some small bit of nit-picking. The electron muon and tau states are not the neutrino mass states. In fact, it is crucial for oscillations that not only the masses of the mass eigenstates are different, but also that the flavour states, i.e., the electron muon and tau neutrino states, are not equivalent to the mass states but instead are linear combinations of the mass states.
Quarks. The difference in the quark sector is that the masses are so different that any interference between the mass eigenstates quickly is subject to decoherence. This is why you have W interactions changing the quark generations.The above has confused me for a while, are there any other quantum phenomena in nature that have similar physics to the above?
Thanks!
Can I ask a question about the mass eigenstates and flavor eigenstates?Quarks. The difference in the quark sector is that the masses are so different that any interference between the mass eigenstates quickly is subject to decoherence. This is why you have W interactions changing the quark generations.
In terms of quantum oscillations, the mathematics is completely analogous to having a spin precessing in a magnetic field that is not parallel to the direction you are measuring the spin component in. For example, you can have a spin-1/2 particle and measure its x-component to be positive at t = 0. Applying a magnetic field in the z-direction, the probability to measure a positive x-component will oscillate between 0 and 1.
There is no such thing.like the mass of the electron neutrino or muon neutrinos
thanks for the reply but still I do not understand the quantum phenomena,so how the superposition is defined by PMNS matrix,and if we know the values of the matrix elements we can not find the definite masses, I mean by mathematics, can you help me to understand how a particle can not have a definite mass?There is no such thing.
The electron neutrino is a superposition of the three mass eigenstates. It doesn't have a well-defined mass. It only has an expectation value for the mass.
We can. Those are the masses of the mass eigenstates. General linear combinations of those do not have a definite mass.and if we know the values of the matrix elements we can not find the definite masses
We can. Those are the masses of the mass eigenstates. General linear combinations of those do not have a definite mass.
It is not a question of not knowing the masses of the flavour eigenstates, it is a matter of the flavour eigenstates not having definite masses.So we will never know the exact masses of neutrinos(flavor ones) , as they define by superposition of states?
That depends on what you put into the word "understand". Effectively, it is just the evolution of a three-state quantum system.What more, if anything, than the above is needed to understand neutrino oscillation physics?
Thanks for the reply.It is not a question of not knowing the masses of the flavour eigenstates, it is a matter of the flavour eigenstates not having definite masses.
See for example the oscillation equations on the Wikipedia page. They contain the masses only in the form ##\Delta m_{ij}^2## which means ##m_i^2 - m_j^2##.just the differences of mass squared?