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NNTP-Posting-Date: Tue, 15 Apr 2025 18:36:22 +0000
Subject: Re: Muon paradox
Newsgroups: sci.physics.relativity
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 15 Apr 2025 11:36:27 -0700
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On 04/15/2025 11:06 AM, Ross Finlayson wrote:
> On 04/15/2025 02:48 AM, J. J. Lodder wrote:
>> Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
>>
>>> 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:
>>>>>
>>>>>> 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.
>>>>>>>
>>>>>>> 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.
>>>>>
>>>>> You are talking complete nonsense here.
>>>>> Natural units are just another well-defined unit system,
>>>>>
>>>>> Jan
>>>>>
>>>>>
>>>>>
>>>>
>>>> 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.
>>>>
>>>> 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".
>>>>
>>>>
>>>>
>>>> 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'?
>>>>
>>>>
>>>> A unit as "natural", i.e., to be replaceable with "1" its value,
>>>> can only be treated as a coefficient or a divisor.
>>>>
>>>>
>>>> What now you don't allow comprehension of algebra either?
>>>>
>>>>
>>>
>>> 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?
>>
>> 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,
>>
>> Jan
>>
>>
>
> 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.
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