From: helbig@asclothestro.multivax.de
In article , Tom Roberts
writes:=20
Not a disagreement, just some comments:
> The observed neutrinos from SN1987A had energies up to 40 MeV [%]. The
> Particle Data Group gives the upper limit on the neutrino mass of 2 eV
> [$].=20
The upper limits on the mass depend on the neutrino type.
> For a mass of 2 eV, 40 MeV gives beta ~ 0.999999999999999 [#]; 1-beta ~
> 1E-15. After a trip of 160,000 years (5E12 seconds) [%], this implies an
> upper limit on the time difference between massless photons and
> neutrinos of a few milliseconds, which is completely unobservable.=20
>=20
> [%] See Mike Longo's papers, cited earlier in this thread.
> [$] Neutrino oscillations imply much smaller mass differences.
>=20
> Note that in 1987, neutrinos were thought to be massless; observations of
> neutrino oscillation were more than a decade in the future.
Right, but one can still use the observation---before or after other=20
things indicated that they are not massless---to put upper limits on the=20
mass based on the upper limit of the observed difference in arrival=20
times. This is probably still the best mass limit for the tau neutrino,=20
and maybe for the mu neutrino.
Such conclusions are probably limited by models of supernovae: when are=20
neutrinos emitted, when light, etc.
> [#] Excel is right at the limit of its accuracy here.
Then use Fortran. :-)
[[Mod. note -- As the author notes, modern Fortran offers excellent
support extended-precision floating-point arithmetic. Other common
software environments offering this include symbolic algebra systems
(Maple, Mathematica, Sage), Python, the gmp library (C API), and a
variety of C++ libraries such as 'doubledouble'.
-- jt]]
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