From Newsgroup: sci.math

Bertitaylor wrote:

When you bust a neutron you get positrons and muons.

A neutron is not "busted", but in theory it is possible that certain interactions with a neutron produces these particles.

That happens naturally in the Sun

No, solar positrons (erU|) are produced by stellar nuclear fusion instead, in the first step of the pp-I chain:

-|H + -|H raA -#H + erU| + ++rea.

This has been confirmed by detecting solar neutrinos (++rea) and their oscillations (++_++, ++_-a; cf. "Solar neutrino problem").

I doubt that muons are produced inside Sol. For a muon to be produced, the collision energy has to be *at least* the muon's rest energy; but the mass
of a muon is ca. 200 times that of an electron whose rest energy is 511 keV,
so for a muon you need at least 100 MeV.

A proton has a rest energy of 938 MeV, so in theory it is possible to
produce a muon from the collision of two solar protons. However, protons
have *positive* electric charge and muons have *negative* electric charge,
and the total electric charge must be conserved.

It would only be possible to produce an antimuon from a proton--proton collision directly, but that would be short-lived: it would decay to a
positron before it left Sol (its speed would be v = 0.9984 c, which is
pretty fast, but its mean life is only -a ree 2.2 ++s, and Sol is huge-|),
and like the positrons produced in the fusion reaction above, it would annihilate with one of the free electrons of the solar plasma to produce
two or more photons:

erU| + erU+ raA +| + +| (+ ...)

[as it happens in positron-emission tomography (PET) in hospitals on a daily basis -- just at much lower energies -- which confirms special relativity].

("Atmospheric") muons are produced instead when protons interact with
molecules of the terrestrial atmosphere:

<https://en.wikipedia.org/wiki/Cosmic_ray#Types>

ISTM that the phrase "solar muon" and "solar neutron" that can be found in
some papers (e.g. [1]) must not be misunderstood to mean that muons or
neutrons are emitted by Sol, but that they are _atmospheric_ muons and
neutrons that are produced by solar activity. For example, in the Abstract
of [1]:

| Ground Level Enhancement (GLE) events provide rare opportunities to study
| high-energy solar particle acceleration through direct detection of
| secondary radiation at ground level. On November 11, 2025, the Aragats
^^^^^^^^^^^^^^^^^^^
| Solar Neutron Telescope (ASNT) recorded a statistically significant
| increase in high-energy neutron and muon fluxes associated with an X5.1
| flare and the subsequent Solar Energetic Proton (SEP) event.

But the marked key word here is "secondary radiation" which is made clear by the "Introduction":

| Ground-Level Enhancements (GLEs) are rare episodes in which relativistic
| solar particles penetrate EarthrCOs atmosphere and produce significant
| secondary radiation detectable by groundbased detectors (Shea & Smart,
| 2012). GLEs are the highest-energy manifestation of solar energetic proton
^^^^^^^^^^^^^^^^^^^^^^
| (SEP) events, observed when relativistic ions accelerated in the vicinity
^^^^^ ^^^^^^^^^^^^^^^^^
| of the Sun enter the terrestrial atmosphere and generate secondary
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| radiation. More than 70 s have been observed since 1942, predominantly
^^^^^^^^^
| associated with major eruptive flares and CME-driven shocks (B|+tikofer &
| Fl|+ckiger, 2015). Energy spectra of muons and neutrons produced by solar
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| proton interactions in the atmosphere serve as direct indicators of the
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
| acceleration environment in the SEP and flare regions (Reames, 2021).

[I presume "70 s" is a typo and should be "70" (CMIIW).]

___
[1] Chilingarian, A. et al. (2025): "Solar neutron and muon detection on
November 11, 2025: First simultaneous recovery of energy spectra."
<https://arxiv.org/abs/2512.07859>

-| Suppose the rest energy of two protons would be entirely converted to
the total energy of a muon or antimuon (let us ignore conservation of
total electric charge here):

2 E_{p,0} = 2 m_p c^2 = +|(v_++) m_++ c^2 = E_++,

where +|(v_++) is the Lorentz factor. Then

+|(v_++) = 1/reU(1 - {v_++}^2/c^2) = 2 m_p/m_++
<==> 1/ (1 - {v_++}^2/c^2) = 4 {m_p}^2/{m_++}^2
<==> 1 - {v_++}^2/c^2 = {m_++}^2/[4 {m_p}^2]
<==> {v_++}^2/c^2 = 1 - {m_++}^2/[4 {m_p}^2]
<==> {v_++}^2 = c^2 (1 - {m_++}^2/[4 {m_p}^2])
<==> v_++ = c reU(1 - {m_++}^2/[4 {m_p}^2]).
ree 0.9984 c.

For calculating the distance that a potential solar muon or antimuon could travel before it decays to a positron/electron (which will be annihilated by/becomes part of the solar plasma), we have to consider that our proper distances are shorter in the muon's proper frame (where they are moving lengths); equivalently, that less proper time elapses in its proper frame (which is moving relative to us) than in ours in which we measure distance:

rear' = v_++ -a' = v_++ |u 2.2 ++s ree 658 m
==> rear = +|(v_++) rear' = 2 m_p/m_++ rear' ree 11.7 km.

rear = v_++ -a = v_++ +|(v_++) -a' ree v_++ |u 2 m_p/m_++ |u 2.2 ++s ree 11.7 km.

[That is also approximately the distance an atmospheric muon travels to the ground, once again confirming special relativity.]

But those (anti)muons would have to be produced in the solar core, and the solar radius is R_Sol ree 700 000 km. The (anti)muon would not even make it (much) outside the solar core (radius ree 0.25 R_Sol ree 175 000 km):

<https://en.wikipedia.org/wiki/Sun#Core>

and artificially on Earth.

Neither positrons nor muons are actually produced artificially by "busting
up neutrons"; see above.

Woof woof

You are literally barking up the wrong tree :-D

F'up2 sci.physics.relativity
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