Measuring Neutrino Mass from a Supernova

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I tried and I got a ridiculous large number for the neutrino mass. I basically used E=\gamma m c and then, for 10 MeV neutrinos, time taken is t + 10 seconds to reach Earth, for 50 MeV neutrinos, time taken is t seconds.
Speed = \frac{100 000}{(t+10)} for 10 MeV and Speed = \frac{100 000}{t} for 50 MeV. Here's the question:

Neutrinos were detected from a supernova (distance ~ 100 000 light years) over a time period of ~ 10 seconds. The neutrinos have an energy range from 10 MeV to 50 MeV.
What's the mass of the neutrino, assuming all neutrinos were produced at the same time and their mass is small compared to their energy.
 
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Your speed is in LY/sec. Did you convert units?
Speed in LY/Y is so close to one that you have to use a Taylor expansion.
 
Meir Achuz said:
Your speed is in LY/sec. Did you convert units?
Speed in LY/Y is so close to one that you have to use a Taylor expansion.

Yes, I did unit conversions. A light year = 9.46 \times 10^{15} meters

Here's what I did:

for 10 MeV neutrinos, 10\;Me = \frac{m\;c}{\sqrt{1 - (\frac{d}{t+10})^2/c^2}}

and hence, t+10 = \frac{10\;M\;e\;d}{10\;M\;e\;c}(1-\frac{m^2\;c^2}{10^2\;M^2\;e^2})^{-1/2}

Binomial expansion, keep only first two terms yield:
t+10 = \frac{d}{c}(1+\frac{m^2\;c^2}{2\times10^2\;\M^2\;e^2})

do the same for 50 Mev neutrinos,

for 50 MeV neutrinos, 50\;Me = \frac{m\;c}{\sqrt{1 - (\frac{d}{t})^2/c^2} }

simultaneous equations, cancelling t, yield:

10 = \frac{d\;m^2\;c}{2\;M^2\;e^2}(\frac{1}{10^2}-\frac{1}{50^2})

Solving for m (neutrino mass), I got 7.7 GeV !?
 
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I get: 10 sec=(10^5 yr X m^2/2)(1/100-1/2500), with m in MeV.
I don't see where your e^2 came from, why your c is i the numerator.
What is your M?
Use 1LY/c=1 year, keep all masses in MeV.
Use t=(L/c)\sqrt{m^+p^2}/p~L/c-(m^2/2E)(L/c).
 
You also must take into account how long the neutrino sees itself moving as compared to what the Earth sees as how long the neurtino is moving from a to b
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?

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