Energy Conservation in Neutrino Propagation

In summary, during the journey from the sun to the earth, an electron neutrino changes its flavor to a muon neutrino, which has a different mass and momentum. This leads to a violation of conservation of four vector momentum, as the mass of the muon neutrino is greater than the initial electron neutrino. This is due to the uncertainty of energy and mass in a superposition state, similar to the phenomenon of dispersion in optics. A precise measurement of energy and momentum can prevent coherence and oscillations. The question of whether charged leptons oscillate or not is process dependent and can be yes or no.
  • #1
thoms2543
52
0
when an electron neutrino is produced in the sun, it have the total energy of E. the total energy E have the relation with mass and momentum as E2=p2+m2. during the journey of its propagation from sun to earth, the electron neutrino change their flavor to muon neutrino which have mass m', momentum p', and energy E'.

E2-p2=m2 (initial)

E'2-p'2=m'2 where m'>m (final)

then the four vector momentum is not conserved ie m'>m.

if we say the energy and momentum is conserved, E=E', p=p', then m'=m. but in reality we know than m'>m

I am confusing...can anybody helps?
 
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  • #2


The neutrino is in the state which is a SUPERPOSITION of neutrinos with two different masses and energies. Thus the energy and the mass are uncertain, but the average energy is conserved with time. What changes (oscillates) with time is the probability that the neutrino will have this or that mass. When you do a measurement, you "collapse" the state into a state with a definite mass.
 
  • #3


I made this mistake (both here and in my own research, I'm sad to say!) more than once.

I've recently come to the conclusion that it's easiest (although by no means necessary!) to think of it in terms of wave mechanics. In particular, compare it to CLASSICAL E&M (light):

Let's say you have a beam of (polychromatic) light traveling through a (nonlinear) medium. Then you know that the different frequencies of light that make up the beam will be traveling at different speeds, since the index of refraction depends on the frequency of the light. This is the phenomenon of "dispersion" from optics.

Now the frequency of the light is its energy. But energy is ALWAYS conserved! It's not that energy is not conserved here, but that the components of the light that make the beam all have different energies.

Now return to the neutrino problem: think of an "electron neutrino" as a beam of "polychromatic light" (since the electron neutrino is composed of various mass eigenstates, it's like the light being composed of various wavelengths). Now the analogy is virtually exact.

Hope that helps!
 
  • #4


If you have access, questions such as "how a precise measurement of energy and momentum prevents coherence and thus oscillations" are dealt with in details in PRD vol 48 n 9 (1993)

See also Paradoxes of neutrino oscillations
 
  • #5


humanino said:

I found this reference you recommended to be very useful. In that article, I found the reference [7] to be even more useful. It deals with the question of whether charged leptons oscillate or not. In these forums I have seen answers saying yes and no both. I learned that the answer is process dependent. It can be yes, and it can be no. The explanation is very clear, despite the fact that the problem is just as tricky as the EPR paradox. I highly recommend it. You can reach it with this link: Do Charged Leptons Oscillate?
 

1. What is energy conservation in neutrino propagation?

Energy conservation in neutrino propagation refers to the conservation of energy as neutrinos travel through space. This means that the total energy of the neutrino remains constant throughout its journey, even as it interacts with other particles and changes its energy state.

2. How does energy conservation affect neutrinos?

Energy conservation has a significant impact on neutrinos because it dictates how they interact with other particles and how they change energy states. Without energy conservation, neutrinos would not be able to maintain their energy levels and would not be able to travel long distances through space.

3. What is the role of energy conservation in neutrino oscillations?

Energy conservation plays a crucial role in neutrino oscillations, which is the phenomenon where neutrinos change between different types (or "flavors"). This is because the conservation of energy ensures that the total energy of the neutrino remains the same, even as it changes its flavor.

4. How does energy conservation impact our understanding of neutrinos?

Energy conservation is a fundamental principle in physics and plays a vital role in our understanding of neutrinos. It allows us to make predictions about how neutrinos will interact with matter and how they will change over time, helping us to better understand their properties and behavior.

5. Are there any exceptions to energy conservation in neutrino propagation?

While energy conservation is a fundamental principle in physics, there are some scenarios where it may not apply to neutrinos. For example, in extremely high-energy environments such as supernovae, the conservation of energy may not hold true due to the complex interactions between particles. However, in most cases, energy conservation is a crucial factor in understanding neutrinos and their propagation.

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