Re: Muon paradox

On 04/14/2025 04:01 PM, Ross Finlayson wrote:

On 04/14/2025 12:01 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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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 t? = 2.2 ?s.
2. muons are created at a height ~15 km
3. The speed of the muons is ~c, so travel time is ~50.05 ?s
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/N? = exp(-t/t?) = 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/N? = exp(-t/?t?) = .556 => ? = 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.
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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

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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.
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The natural units have overloaded their roles, with regards to their
products, and their differences.

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You are talking complete nonsense here.
Natural units are just another well-defined unit system,
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Jan
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Au contraire, classical velocities near zero are related
approximately linearly to light's speed c, yet those near
c have approximately infinite resistance to acceleration,
thus that in otherwise simple translations where acceleration's
drawn out an invariant, what "running constants" vanish or
diverge, obliterate the arithmetic and analytic character
of the expression of the quantity or its implicit placeholder
in the algebraic manipulations and derivations.
>
Natural units for the normalizing and standardizing don't
have this feature, as it were, according to algebra,
the arithmetic and analysis.
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You can leave it in and observe this, since otherwise
there's a neat simple reasoning why mass-energy equivalency
makes as much a block to any change at all as Zeno,
having the features of both "1" and "infinity".
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Do you even acknowledge that there are three ways to
arrive at "c" vis-a-vis the electrodynamics, electromagnetism
and the statics, and as with light's velocity, as for example
O.W. Richardson demonstrates in his 1916 'The Electron Theory
of Matter'?
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A unit as "natural", i.e., to be replaceable with "1" its value,
can only be treated as a coefficient or a divisor.
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What now you don't allow comprehension of algebra either?
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>

It's in a, "system of units", see, all the units.
How about all the infinitely-many higher orders of acceleration,
and their units, how and where do they go?
You know, 0 meters/second is infinity seconds/meter, ....
I guess I have to agree that setting c = 1 is _calling_ it
a natural unit, yet that in the wider surrounds of the units
and the conditions it _behaves_ as infinity and not unity,
sees that reason can arrive at that furthermore the wider
system of units that sees _derived_ "the three c's",
and all the series that converge to them variously,
in their units, and that after the _derivation_ of
mass-energy equivalency the initial-term-of-the-series
way that _all the following terms after the initial
term have their own, less compatible units_,
has that as a contrivance in the hyper-geometric,
whose regular singular points are 0, 1, and infinity,
that it's more of a, "hyper-unit".
So, you keep lazy-minding your units in your theory away,
all sorts practical and empirically evident fields keep
their own, and may look askance at calling c "a natural
unit", when it's a natural bound, as the bit naive.