Re: Muon paradox

On 04/15/2025 02:48 AM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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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
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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.
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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....
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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.
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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.
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How about all the infinitely-many higher orders of acceleration,
and their units, how and where do they go?

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The system of all units of all physical quantities
must be a finite-dimensional algebra,
no matter what your unit system may be,
and how you choose to define relations between units,
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Jan
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I read that as "finite-dimensional spaces and infinite-dimensional
vector spaces are two different things".
There's no arbitrary highest order of acceleration, i.e.,
any highest order derivative of position with respect to time,
it's at least "unbounded", and greater than any "finite",
and not less than "infinite".
Perhaps you might look to Halmos about it.
When the physical interpretation rather demands it's
_not_ a finite dimensional space those quantities, each,
at any given instant or over a duration, then why do
you say "must" be finite-dimensional when the only
reasonable (in the wider, fuller dialectic) thing
is that "our methods are inadequate to address the
infinite-dimensional".
In my podcasts I sort of get into it with regards to
"Zeno's swath" and "the hypercube distance", and the
"stop derivative", then there's for reading Halmos who
talks about it.
https://www.youtube.com/watch?v=WT7yUJYtTz8&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=34&t=510
The physical description definitely admits there's
no highest-order derivative of acceleration.
The wider dimensional analysis has that _implicits_
are not _absent_.
The "partial" is _incomplete_.
So, what makes you think that reality is finite?
Because, relations among physical objects are physical
objects themselves as are those ad infinitum.