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NNTP-Posting-Date: Wed, 16 Apr 2025 15:32:18 +0000
Subject: Re: Muon paradox
Newsgroups: sci.physics.relativity
References: <d74079263e98ec581c4ccbdab5c5fa65@www.novabbs.com>
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 16 Apr 2025 08:32:01 -0700
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On 04/16/2025 02:14 AM, J. J. Lodder wrote:
> Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
>
>> On 04/15/2025 12:34 PM, J. J. Lodder wrote:
>>> Ross Finlayson <ross.a.finlayson@gmail.com> 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".
>>>
>>> Your reading is irrelevant, and does not relate to what I wrote.
>>>
>>>> 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".
>>>
>>> Has it really escaped your notice that finite dimensional algebras
>>> have infinitely many elemens?
>>>
>>> Jan
>>>
>>> [snip irrelevancies]
>>>
>>>
>>
>> Not at all, neither that the classical units have infinitely-many
>> higher orders, of "the" their dimension, thusly infinite-dimensionally.
>
> So your problem is that you don't understand an elementary term
> such as 'finite dimensional algebra'.
>
> This is a structure that contains all elements of the form
> [A_1]^{n_1} . [A_2]^{n_2} . ..... [A_k]^{n_k}
> with a finite number of basic quantities [A_j]
>
> Systems of units are (by definition) finite-dimensional algebras.
> They can accomodate units for infinitely many physical quantities
> with a finite number of base units.
> (like all those time derivatives for example)
>
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