- #1
umagongdi
- 19
- 0
Sorry if this qs been asked before, i couldn't find one similar.
JustinLevy said:The "proper time" argument and the other arguments seem incompatible with the following situation:
If one of the neutrino flavors is massless, and the other are massive... can there be oscillation between all the flavor pairs?
So which line of argument is correct? I assume the 'proper time' argument is the flawed one, but it is the most intuitive one. So is there something wrong with the proper time argument, and where is the implicit flaw? Is the issue that there is no inertial rest frame for massless objects and therefore proper-time (while well defined), is not an appropriate way to discuss their evolution?
genneth said:Massless things travel at the speed of light, and so in their rest frames, no proper time ever passes. If proper time does not proceed, then no oscillations are possible!
Meir Achuz said:Oscillation must go like sin[(E_1-E_2)t].
The only way that E_2 can differ from E_1 for the same momentum is if there is a mass.
PAllen said:Just curious, why must the two neutrino states differ in either energy, momentum, or mass? Suppose they are both massless, momentum and energy same, just some quantum number flips?
Parlyne said:Neutrino oscillation necessarily is a process that occurs during the free propagation between source and detector. As long as you're working in a basis where every state has a well defined mass (that is, the mass matrix is diagonal), there is nothing that can change any quantum numbers.
A little more technically, neutrinos are created in flavor states, which are generically superpositions of the mass eigenstates. This superposition, then, evolves under time evolution defined by the free Hamiltonian and is eventually detected. The detection method, of course, since it will involve charged leptons, is sensitive to flavor. So, the evolved state should be looked at in the flavor basis.
As an example, we can consider a toy model where there are only two states. Let's call the flavor states [itex]|a>[/itex] and [itex]|b>[/itex] and the mass states [itex]|1>[/itex] and [itex]|2>[/itex]. And, just to be really silly about it, let's assume that the flavor states are given by
[tex]|a> = \frac{1}{\sqrt{2}}\left(|1>+|2>\right)[/tex]
and
[tex]|b> = \frac{1}{\sqrt{2}}\left(|1>-|2>\right)[/tex]
This is, of course, horribly unphysical; but, it will illustrate my point nicely.
If we assume the particle is created in the a state and allowed to evolve freely for time T, we will find that, after the evolution, the state looks like
[tex]\begin{array}{rcl}
|a(T)> & = & e^{i\hat{H}T}\frac{1}{\sqrt{2}}\left(|1>+|2>\right)\\
& = & \frac{1}{\sqrt{2}}\left(e^{iE_1T}|1>+e^{iE_2T}|2>\right)\\
& = & \frac{1}{2}\left(\left(e^{iE_1T}+e^{iE_2T}\right)|a>+\left(e^{iE_1T}-e^{iE_2T}\right)|b>\right)
\end{array}[/tex]
If the two states have the same energy, the term proportional to [itex]|b>[/itex] vanishes, leaving the state changed only by an overall phase. And, of course, if they don't have the same energy, for most values of T, there's a non-zero probability of detecting the particle as a b, even though it was produced as an a.
The reason this is generally stated to require different masses is that the kinematics of production certainly won't allow two states in a superposition that have the same mass to have different energies.
PAllen said:Thanks, that's actually quite helpful. A university website I found had a nice calculation showing different neutrino masses lead to osciallation, but that only validates (mass different) -> oscillation; I was looking for (oscillation)->(mass <>0), for some very broad framework. I couldn't find that. What you've shown convinces me that within any reasonable quantum model, oscillation itself implies mass difference.
Neutrino oscillation is the phenomenon in which neutrinos change from one type to another as they travel through space. This is possible because neutrinos have mass, which allows them to interact and transform into different types.
According to the Standard Model of particle physics, neutrinos were initially thought to be massless particles. However, experiments have shown that neutrinos do indeed have mass, and this can be observed through their oscillation. The process of oscillation requires neutrinos to have mass in order to change from one type to another.
The mass of neutrinos determines the frequency and amplitude of their oscillation. Neutrinos with a higher mass will oscillate at a slower rate, while those with a lower mass will oscillate more quickly. The amplitude of the oscillation is also affected by the mass, with heavier neutrinos having a smaller amplitude compared to lighter ones.
There have been several experiments that have provided evidence for neutrino oscillation and mass. One of the most significant is the Super-Kamiokande experiment, which observed neutrinos from the sun changing from one type to another. Other experiments, such as the Sudbury Neutrino Observatory and the KamLAND experiment, have also provided strong evidence for neutrino oscillation and mass.
The discovery of neutrino oscillation and mass has significantly changed our understanding of the universe and the fundamental particles that make it up. It has challenged the Standard Model of particle physics and opened up new avenues for research into the nature of neutrinos and their role in the universe. It has also provided insights into the mysteries of dark matter and the balance of matter and antimatter in the early universe.