Re: Muon paradox

On 04/15/2025 12:34 PM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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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.

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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.)
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        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".

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Your reading is irrelevant, and does not relate to what I wrote.
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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".

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Has it really escaped your notice that finite dimensional algebras
have infinitely many elemens?
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Jan
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[snip irrelevancies]
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Not at all, neither that the classical units have infinitely-many
higher orders, of "the" their dimension, thusly infinite-dimensionally.
Consider for explain flipping a coin, or tiddly-winks if that's still
a word, at once arbitrarily unobservable, yet ultimately deterministic,
where the heuristic no longer applies, yet must be there is one.
No one denies that the heuristic as it were of classical mechanics
is simple and so, yet it results merely a heuristic, then that
the introduction of any dynamics results breaking the classical
heuristic, there must be some super-classical heuristic as what
explains there are no fictitious or virtual, yet real, forces in
the result.
Then, it is not so that "physics the open system" is merely
finite-dimensional, any more so than to say that the universe
is closed, or that's like AP's big dot theory, and other
severe, to the point of insensate, reductions.
Classical mechanics is great and a great heuristic,
yet while it's simple that the kinetic adds up,
it is not so that the kinematic breaks down,
and this can be read off from mass-energy equivalency
in at least two ways: first that the term in energy
of the usual _derivation_, and not definition like some
SR'ian's make instead the _derivation_, is merely the
first term in the Taylor series and all the following
terms have higher order, to infinity, units. Then,
another way is about Einstein's "second mass-energy
equivalency" formulation that results the nominally
and formally, "un-linear", i.e. rotational. This
gives two different bases for the linear and rotational,
and furthermore has infinitely-many nominally non-zero
and yet higher-order terms from the heuristic of
the character of the first term, or the heuristic
of assuming a perfect balance, in these at least
two different examples, from very fundamental theorems.
So, if you've, for example, defined instead of derived
K.E. then what results all derived the rest of mechanics,
it's underdefined there are nominally (and formally)
non-zero other terms, and similarly, the linear and
kinetic and rotational and kinematic are _not_ the same.
Then, force "as a function of time", as it were,
reflects these what must be deterministic inputs
and as are nominally non-zero and what via mathematics
are actually in the mathematics, infinite-dimensional,
makes for "Zeno's new arguments", then besides of course
that formal mathematics _owes_ physics more and better.
Muons are arbitrarily extended bodies, and then
things like SR's relativity of simultaneity,
has that they're non-local, or as Einstein put
it in "Out of My Later Years", in paraphrase, say,
"relativity of simultaneity is non-local".
Here though there are greater issues in the
actual assumptions and heuristics of classical
mechanics, evident in a few orders of magnitude
in dynamics, that don't require a billion dollar
super-collider, yet do require super-classical
and infinitary reasoning, to arrive at reasons
for what result the heuristics.