Re: Muon paradox

On 04/14/2025 08:31 AM, Ross Finlayson wrote:

On 04/13/2025 10:15 PM, Tom Roberts wrote:

On 4/10/25 3:02 PM, Aether Regained wrote:

There is one flaw I find in the SR explanation, can you confirm if it is
true:
What is really measured are these (the facts):
1. The mean proper lifetime of a muon is t₀ = 2.2 μs.
2. muons are created at a height ~15 km
3. The speed of the muons is ~c, so travel time is ~50.05 μs
4. muon flux measured on the Earth's surface is about 55.6% of what it
is at 15km.
 From 1, 2 and 3, the expected muon flux on the Earth's surface is:
N/N₀ = exp(-t/t₀) = exp(-50.05/2.2) = 1.32e-10 = 0.0000000132%
The important point (the flaw) is that the speed of the muon has not
actually been measured to be 0.999668⋅c, but instead is computed.
N/N₀ = exp(-t/γt₀) = .556 => γ = 38.8 => v = 0.999668⋅c
The SR explanation would have been more convincing, if the speed had
actually been measured to that many significant figures.

>
So consider other experiments that ARE "convincing" (in the sense you
mean). In particular, Bailey et al. They put muons into a storage ring
with a kinetic energy of 3.1 GeV. They measured the muons' kinetic
energy, their momentum, their speed around the ring, and their rate of
decay. All measurements are fully consistent with the predictions of SR.
(They also measured the muon g-2, which was the primary purpose of the
experiment; confirming SR was just a side issue.)
>
     Bailey et al, Phys. Lett. B 55 (1975) 420-424
>
There are literally hundreds of other experiments that confirm the
validity of SR. Some measure "time dilation", and some measure other
predictions of SR. To date, there is not a single reproducible
experiment within SR's domain that is not consistent with the
predictions of SR. There are so many such experiments that SR is one of
the most solidly confirmed theories/models that we have today.
>
BTW there are over 30,000 particle accelerators operating in the world
today. SR was essential in the design of each of them, and they simply
would not work if SR were not valid.
>
If you truly want to "regain aether" you will have to come up with an
aether theory that is indistinguishable from SR for EACH of those
experiments. And be sure to make it consistent with the quantum nature
of the universe we inhabit. To date, nobody has done so. AFAIK nobody
even has an inkling how to start....
>
Tom Roberts

>
It seems that the "convolutive" gets involved, which usually is with
regards to lower-bound and upper-bound, except as with regards to
that the lower-bound is zero and the upper-bound is infinity,
about where the "natural unit" is an upper-bound, instead of
being the usual multiplicative and divisive identity.
>
The natural units have overloaded their roles, with regards to their
products, and their differences.
>
Particle accelerators are pretty much all charged particles,
with regards to things like Z-Pinch or Aspect-type experiments,
variously not charged or in the kinetic and photonic,
that it's electrostatics and electrodynamics, and these
along with light have three different things that are, "c".
>
So, putting the Galilean back in for the differences between
linear accelerators and cyclotrons, and for modeling space-contraction
variously linear and rotational, then makes for tests of the equivalence
principle, which is about the kinetics and kinematics,
that there's aether the space-frames, then also about the "aether"
of the electrostatics and electrodynamics, frame-spaces.
>
>
>
So, "which aether", ....
>
>
Thanks for posting and helping introduce what requirements there
would be of any "aether" theory, about the Dirac/Einstein
positronic/white-hole sea, of space-frames and frame-spaces,
about the classical and super-classical mechanics of the linear and
rotational, and "the un-linear" and that "worlds turn", and for
helping explain differences "natural units" and "shoehorn bounds".
>
>

Since you last posted some other ideas that have been noted here
include that the Duhamel principle makes a free inner term about
the differintegro and integrodiffer and that it's not necessarily
merely a posterior method the Duhamel principle, yet also much
like the cosmological constant with regards to being the term of
the running constant, and being nominally non-zero in all differential
systems, that it fits within all sorts differential systems absent it,
then there's a certain centrality in the integral equations and
particularly the multiplicities about the singular integrals,
before even getting into quasi-invariant measure theory after
the quantization and normalization and the odd halving/doubling spaces,
that Duhamel principle is a rather usual aspect of the fulcrum
between the integrating and the differentiating.
The "worlds turn" bit though is a necessary deconstructive account
about mechanics and that it's a potentialistic theory and that
the potential fields are the real fields and the classical linear
is always only partial in any "open" system.
Which is an inertial-system.