[guest49538]

I've been reading recently about cosmic radiation and the creation of cosmic muons (- and +) due to the interaction of high energy cosmic protons with atoms at the higher layer of the atmosphere.

I've seen a chart from (Tueros and Sciutto, 2010) which validates the detection of muons with energy ranging from 10 MeV up to almost 700 GeV (700,000:1 ratio), but still the average time decay τ₀ = 2.2 μs is accepted for all of them, having each a "rest mass" of 106 MeV.

For the last 70 years, or more, the usual explanation at every serious academic source is that Lorentz's time dilation occurs from the perspective of an observer located at ground level. The expression τ_Earth=γτ₀ is applied at every case, with a high dispersion of  γ values.

Reciprocally, many documents persist in the use of length contraction ΔL_μ = ΔL_Earth/γ to accomodate every ΔL_Earth calculated (from 6 to 20 Km heigth).

Travelling at near "c" speed, cosmic muons allegedly decay in only 660 meters, so the explanations using time dilation or length contraction adjust the observed values of  τ₀', which is many times higher than 2.2μs.

I wonder if there isn't another explanation due to the cosmic origin of muons, whose decay process is affected by many other factors than those generated in laboratory tests (CERN, etc.).

After all, a muon is a super-heavy electron glued into "energy" that conforms more than 95% of its mass (specially the force carrier W Boson, with unknown decay time - as far as I could search).

I wonder if these widely used explanations (particularly length contraction) are still valid by today, and if there is any new finding that can explain the phenomena of the decay of cosmic muons (+ and -).
 

[guest49538]

I forgot to add a formula derived from Fermi's theory for nuclear elements decay, which is taught at the Zurich University, in the 2015 course:

Quantum Field Theory-I
Prof. G. Isidori

1  The muon decay in the Fermi theory


τ_μ = ħ192π³.G_F^-2m_μ^-5

where G_F is the Fermi's constant, with empirical value 0.0000116 GeV² and m_μ is the rest mass of the muon-.

[guest49538]

As far as I know, there is not any practical evidence of length contraction since 1905 STR.

The only "practical" evidence about time dilation (I don't agree with the use of GPS for this, as this is disproved by
several serious sources) is and has been the case of "cosmic muon's time dilation", since almost its reproduction at a lab, after its discovery in the '30s.

It's curious that, even using very expensive technology like "ring storage" at CERN and other labs, no time dilation has been observed at any of the 100's of thousands of experiments conducted.

I think that there are several factors beyond Lorentz, which modify and extend the life of cosmic muons, like:

-  Earth's variable magnetic and gravitational fields along the path.
-  Regeneration of muons (+, -) by collision of high energy muon+ with nucleii of atoms. Their mass is 1/9 that of a proton and they posesses very high energy levels all the way down. Even when cosmic muons seem to interact very little with atoms, I think that this is due to its energy level which, mostly, ionize atoms in the atmosphere. But I didn't read anything about the impossibility of a cosmic muon+ to act as a lighter proton.
-  The strange behavior of muon's density between 500 meters and 1,500 meters, where the density decay to increase above such heights.
-  Other unknown causes.


I understand that, even when cosmic radiation has been under study for more than a century, the origin of most of it has unknown origin outside the solar system and, maybe, different behavior than earthly reproduced components.

Of course, the above is my IMHO. I have no proofs but I think that I'm entitled to pose one or more doubts about the whole topic.

[chiralSPO]

It's curious that, even using very expensive technology like "ring storage" at CERN and other labs, no time dilation has been observed at any of the 100's of thousands of experiments conducted.

I don't believe that's true. There are many experiments using ring storage that have clearly demonstrated time dilation. Here's a good one: https://www.scientificamerican.com/article/einsteins-time-dilation-prediction-verified/?redirect=1

Also, I know from interpreting HR-TEM images that relativistic corrections must be made when predicting the wavelength of the accelerated electrons from the voltages used for acceleration--see here: http://www.materials.ac.uk/elearning/matter/IntroductionToElectronMicroscopes/Introduction/electrons.html

[guest49538]

I don't believe that's true. There are many experiments using ring storage that have clearly demonstrated time dilation. Here's a good one: scientificamerican.com/article/einsteins-time-dilation-prediction-verified

Also, I know from interpreting HR-TEM images that relativistic corrections must be made when predicting the wavelength of the accelerated electrons from the voltages used for acceleration--see here:
materials.ac.uk/elearning/matter/IntroductionToElectronMicroscopes/Introduction/electrons

You are correct in your post, but I made the mistake to not remark that I was talking about muons, exclusively.
Still, there are some experiments with storage rings for muons back in the 70's that proved relativistic time dilation
in almost perfect vacuum and with circular acceleration. You can just google it.

As I'm new here (my first post), the site forbids me to post any link. I don't know why.

I'm interested specifically on cosmic muons. I'm not a physicist, just an engineer messing with this science just
for curiosity. I'm interested in this particular topic after I read that a japanese company is developin a high resolution
muon's based microscopy. The company uses "slow motion muon+" at energies below 20 MeV (5 times or more less
energy than its "rest mass"), so I started to search about it.

Two big differences between cosmic muons and lab. generated muons is that the last ones are accelerated in circular motion and in almost perfect vacuum. Also, a third difference is that lab muons are slowly accelerated, while cosmic muons get an instantaneous acceleration (a Dirac impulse, to say so), which can't be reproduced at labs.

Finally, as I can't (or don't know) how to post links here, I write here details to find a link to a 1999 CERN document about the feasibility of constructing a muon accelerator.

I put the https link in this way: "inis.iaea.org/collection/NCLCollectionStore/_Public/30/054/30054265.pdf"
This is the partial link (https is missing) for the document "prospective study of storage rings at cern"
I hope you can get it.

I'd like to quote some parts which show the increasing interest and the problems behind the issue of creating muons
to be used for collisions. The technological and scientifical importance of applications with muons is being increasingly
appreciated.
I quote, from the CERN document (1999):

-----------------------------------------------------------------------------------------------

PROSPECTIVE STUDY OF MUON STORAGE RINGS AT CERN
Edited by Bruno Autin, Alain Blondel and John Ellis
Geneva, 1999


------------ Quote from FOREWORD --------------------------------------------

1  FOREWORD

The study  of muon  collider  design  hasbeen  under  way  in  the  USA  since  1992, 
and,  through  a  considerable  amount  of  ingenuity  andnovel ideas,  has  led to  a
plausible  design  philosophy  and  sets  of parameters  for  muon  colliders.
The  Muon  Collider  Collaboration  became  a formal  entity  in  May  1997. 

It  comprises  more  than 100 physicists  from  20 institutions  in the USA, with the
participation  of three  CERN  accelerator physicists.  The  goal  of the  collaboration
is to  complete  within  a  few  years  the  R&D  needed  to determine  whether  a  muon
collider  is technically  feasible,  and,  if it  is, to  design the  First  Muon Collider.

On  this  side  of  the  Atlantic,  the  European  community  is  blessed  with  the 
existence  ofa  solid  and  ambitious  project,  LHC,  able  to  explore  effectively 
parton-parton   centre-of-mass energies  up  to  1-2  TeV. 

Future  options  for  CERN beyond  the  LHC,  investigated  in  Ref.  [15], include  the  muon  collider  as  an 
interesting  possibility.  Because  the  muon  collider  is  so original, in both  its  accelerator  physics  aspects 
and  its physics capabilities,  it  seemed  necessary to study it  in  more  detail.

------------ Quote from Point 2.1.1 --------------------------------------------

2.1.1    Muon  lifetime
The muon lifetime at rest is 2.2  us  and its decay length (cTau) 660  m.   

High-energy  collisions may  nevertheless  be  contemplated  because of the dilation 
of  the  lifetime  in  the  laboratory  by the  Lorentz  factor. For an  average acceleration
of  1 MeV/m, the  acceleration of muons from 250  MeV up to  2.5 TeV takes 8 ms over 2500 km, 
and 25% of the  muons survive. It is at the beginning of the  acceleration that the losses are
the  most  severe.  This  makes  the  first  stages (momentum-spread reduction, cooling) 
particularly  critical.

----------------------------------------------------------------------------------

I hope this may clarify why I have some doubts about the replication of cosmic muons on Earth.

[evan_au]

a japanese company is developing a high resolution muon based microscopy.

Muons have a much higher rest-mass than electrons, and so a much shorter wavelength (for the same velocity).

High-power electron microscopes are only just able to image atoms - a muon microscope should be able to image atoms easily (provided the muons don't decay first...)

he average time decay τ0 = 2.2 μs

What do you think the average decay time should be, for muons?

If you could extend the decay time significantly, we could benefit from muon-catalysed hydrogen fusion - one form of "warm" fusion that has been reproduced in the lab...
See: https://en.wikipedia.org/wiki/Muon-catalyzed_fusion

[guest49538]

Quote from: rhertz

    a japanese company is developing a high resolution muon based microscopy.

Muons have a much higher rest-mass than electrons, and so a much shorter wavelength (for the same velocity).

High-power electron microscopes are only just able to image atoms - a muon microscope should be able to image atoms easily (provided the muons don't decay first...)

Quote

    he average time decay τ0 = 2.2 μs

What do you think the average decay time should be, for muons?

If you could extend the decay time significantly, we could benefit from muon-catalysed hydrogen fusion - one form of "warm" fusion that has been reproduced in the lab...
See: https://en.wikipedia.org/wiki/Muon-catalyzed_fusion

1) This is almost the complete URL of the japanese company: "slowmuon.kek.jp/aboutMuon_e".
     If you google it, you'll get the link and will access to interesting data.

    By the way, can you tell me why I'm not allowed to post external links? Thanks.

2) About the 2.2 microsec decay time: A I wrote, this is the universally accepted decay time for muon- (only -), as
    it is everywhere for more than 40 years, to the least. This is valid for a muon- at "rest", with a "rest mass" of
   105.66 MeV/c2.
 
    Also, if you google "muon decay", you'll find hundred of diagrams showing how a muon- decay into a muon neutrino (with
    0.17 MeV/c2 mass) and (due to the mediating force of a W- boson, 80.39 GeV/c2) into an electron and an electron
    neutrino (0.511 MeV/c2 and 2.2 eV/c2 mass, respectively).

    Well, this company is working in "slowing down" muons in this way:

        - They obtain slow muons (4MeV) to form "muonium atoms" which are ionized by a Lyman-alfa laser to get
          ultra-slow muon+, in the order of eV.
       -  This muon+ are later accelerated to get 10MeV muon+, which provide a resolution of 20 nm and an observable
           thickness of 14 micrometers. These parameters differs from electron microscopy (0.1-2.0 nm resolution and
           0.2 to 3 micrometer observable thickness).

As you can read, the target is the observable thickness using positive charged particles (muon+).

I wonder about these aspects:

1) Is the muon's decay time a function of its energy? Did japanese achieved long decay time by lowering muon's mass
    5 times or more respect to their "rest mass"?
2) What happens with the Feinnman's diagrams and the W boson? Do they "modulate" the W boson mass to be lower?

These are the questions that I have.

I hope that you can access to the link and, please, tell me how to post external links.

Thanks.

   
   

[Bored chemist]

The only "practical" evidence about time dilation (I don't agree with the use of GPS for this, as this is disproved by
several serious sources)

Cite one or two.

[guest49538]

Quote from: rhertz on Today at 02:57:06

    The only "practical" evidence about time dilation (I don't agree with the use of GPS for this, as this is disproved by
    several serious sources)


Cite one or two.

Hi, chemist.

The usual MSM numbers for relativistic effects on GPS give a 38 microsecond/day advance in time that should be corrected in almost real time: -45 us/day due to GTR and +7 us/day due to STR.

This simplicity ignores more than a dozen of complexities with GPS clocking, which affect its applications in the military field, not the civilian one. Relativistic effects are greatly exagerated by MSM.

This is a link for a paper from a relativity supporter, who base his entire development on GTR. You'll read that the impact
of GTR is the only one under study, but the results show that such effects can be dismissed for civil applications.
The paper also contains good references to the history of "relativistic" corrections, but ignores more than ten aditional
influences.

As I don't know how to post an external link here (my post keep being rejected when I do so), I give you references
so you can google and find it:

Relativity in the Global Positioning System
Neil Ashby, 2003

The link contain "ncbi.nlm.nih.gov/pmc/articles/PMC5253894/", so you
have to include the first part with ht**s and w3.

Good luck finding it.

By the way: do you know how can I post external links here? Thanks.

[Bored chemist]

I presume you mean this.

http://webs.ftmc.uam.es/juancarlos.cuevas/Teaching/GPS_relativity.pdf

You may have run aground on the limits for new posters which block posting links.

You'll read that the impact
of GTR is the only one under study, but the results show that such effects can be dismissed for civil applications.

OK, as you say the "famous" correction to GPS is 38 µs per day.
And fundamentally GPS works because we know the "right" time on all the satellites.
Now the issue of calculating what difference 38µs per day makes is complex.
But there's a useful simplification.
If you triangulate against where you think the transmitter is but, because its clock is wrong, you are actually making an error in position equivalent to the distance that the light travels in 38µs

Light travels amusingly close to 1 foot per nanosecond
So, 38000 ns would give an error of 38000 feet.
About 7 miles or 11 km.
So, after the 1st day, if you didn't correct for that 38 µs, you would be 7 miles adrift.
And that error would be cumulative. Your uncertainty would be 14 miles on the 2nd day and so on.
So, after a thousand days (about 3 years) the error would be 7000 miles- roughly the diameter of the Earth.

Now, I don't know what your view of "civil applications" is, but I think it would require a precision of better than "Probably somewhere on the planet Earth.".

And yet  much more than 3 years on, I can still find my way to the pub using gps.

I'm not saying relativity is the only, or even the biggest "correction" needed in GPS.
But it's a big enough factor that GPS is pointless if you don't include relativity.

[guest49538]

Thanks for your answer. I see that I have to wait in order to accumulate posts.

Could you access the document that I referenced? It's a serious study from a physicist that, I believe, work with NASA or at any of its agencies. He base the entire paper (long, by the way) on explanations using solutions of GTR Field Equations for Earth's surroundings.

He doesn't use explicitly STR. I think that this happened because he consider it embedded into GTR.

Anyways, at the document he tells at several parts how small the effects of GTR are for civil (or civilian) applications because, as you may known, the GPS network uses different frequencies for civilian and military applications.

Even when, "allegedly", use of GPS for civil applications was modified to transform uncertainties of +/- 100 meters (about 20 years ago) to be 100 more precise, military applications are a different matter.

To start with, the data is scrambled to prevent jamming (it's told at the document) and also, the accuracy is close to 100 times higher than the civilian counterpart (aboard the same satellite). This GPS on steroids is used for precision bombing, 3D  resolution of trajectories of long range cruise missiles, part of the trajectories of "ballistic" missiles, etc.

These properties of the military applications of the GPS network (funded by the Pentagon, by the way) are impossible to be accesed by any consumer or industrial GPS terminal, for security reasons.

It's like the Internet. DARPA throw it away (to the hands of MCI) by 1993 when US Congress allowed commercial applications to run on it, BUT they had a NEW perfected non-civilian Internet running up and debugged.

As an engineer, I've witnessed this behavior for no less than 50 years: military tech is years ahead of civilian one.

1) The world first microprocessor, 20 bit LSI MP944 built for the F-14 Tomcat, went operational by June 1970. Such level of integration was achieved only about 10 years later in the civilian field. You can google it. Is fascinating.
2) In the '70s and well into the '90s, commercial microprocessor's clock were well under 100 Mhz, starting with 2 Mhz with the first batch in the '70s. Meanwhile, DARPA funded the VHSIC and VHSIC-II projects by mid '70s to develop CPUs with 1 Ghz clocks and geometries below 0.5 micron. In the civilian field, this was achieve (or allowed) by the end of the '90s. Remember the 1Ghz Pentium III?
Of course, all of the above was classified, specially Point 1). After Reagan gained the US Presidency, and I remember it painfully, it was forbidden for ANY publication at any level (and it covered the whole Western market) to publish any paper (even a hint) that could provide information "to others".

The publishing industry never recovered from that XO, which is still vigent. And that's why ANYTHING that you can read at the Internet or buy as a publication contains important information. Only papers, articles and news with very little intrinsic value (and also plenty of disinformation).

I had subscriptions with several magazines and journals, and each month I received issues that were 1cm thick. By 1981, they had 1/3 to 1/4 the original thickness and any information of value (to develop things) was gone or was false.

GPS is a Pentagon initiative that is funded by the US Department of Defense (billions of USD). Do you think that ANY information publicly available about GPS is true? You have to know how counter-intelligence works.

If you search for information about the MP944, you'll be able to access to privileged information from one of its main architects. He had to respect a 30 years NDA pact, before talking about such project. The info is at the dedicated web site for this uP, which is easy to find by googling "MP944 F-14".

Then, after a while of rational thinking tell me, by heart, if you believe ANY information published about GPS.

I can cite many more examples if you want.

But going to my OP topic (muons and Lorentz Transforms). I don't believe that available information is certain, as most of the information about muons and their possible applications poses a HUGE value for military app., so the Reagan's XO Rule still applies today. Not a conspiracy theory, as I provided enough information about cases which were prevented to became public.

One thing more: If you google VHSIC (Very High Speed Integrated Circuits) you'll find incorrect info. Along with this, try to search about the history of the FIRST DSP (TMS320 Digital Signal Processor) from Texas Instrument, to see if the dates matches. They don't, because TMS320 was the commercial version, so the military one was at least 5 years behind (or more).

[Colin2B]

But going to my OP topic (muons and Lorentz Transforms). I don't believe that available information is certain, as most of the information about muons and their possible applications poses a HUGE value for military app., so the Reagan's XO Rule still applies today. Not a conspiracy theory, as I provided enough information about cases which were prevented to became public.

I think it important to try and keep the discussion on topic here. It’s very easy for discussions to wander off into all sorts of side issues and lose track of the question.
As has been pointed out earlier, experimental evidence of time dilation in accelerators has been demonstrated, so GPS is not really relevant to this discussion.
I believe the crux of the topic here is whether lab generated muons have a different decay rate to cosmic muons. In this area there is a lot of independent research not controlled by military that should give indications whether this might be the case.
By the way, it doesn’t matter how much information you provide they are still conspiracy theories -  even if proved correct. However, what you did provide is only conjecture.

[guest49538]

By the way, it doesn’t matter how much information you provide they are still conspiracy theories -  even if proved correct. However, what you did provide is only conjecture.

I didn't expect a comment like that.

I'm used to provide aboundant information to prove that a doubt exist, and the sources I select are always from academic sources (like the impact of GTR on GPS) or from certified institutions (slow motion muon's microscope).

But if you are telling me that what I provided are elements of conspiracy theories, being you a moderator here, sets the tone of future discussions here for me, at least.

I thought that this place could be a serious forum open to debate, if proper information is provided. But your assertion that it doesn't matter how much information I provide, because the muon's average decay time is settled for good, shows me that I was wrong. I'll have in mind your mindset on these matters if I keep posting here.

And, by the way, are you aware of US Custom's plans for inspecting cargo at borders by using "horizontally travelling muons"? Maybe there is a difference between laboratory experiments and applied technology. Google about it, if you want. I can't understand how such a technology can be developed using muons with 2.2 usec decay time. Nor I can understand how microscopy can be developed with such short lived particles (slow muon+).

Anyways, thanks for your answer.

[Colin2B]

But if you are telling me that what I provided are elements of conspiracy theories,

I wasn’t talking about muon microscopes etc, but quoted the very specific paragraph where you mentioned conspiracy theories:

But going to my OP topic (muons and Lorentz Transforms). I don't believe that available information is certain, as most of the information about muons and their possible applications poses a HUGE value for military app., so the Reagan's XO Rule still applies today. Not a conspiracy theory, as I provided enough information about cases which were prevented to became public.

It doesn’t matter how many cases you quote, it can’t prove a specific case. Also, a conspiracy theory is still one even if proven.

I agree that there is likely to be research held by military and not released, but there is also plenty of independent research that should show whether muon lifetime follows the calculated values from the standard model.

[TyroJack]

I find it interesting that you seem to be doubting Time Dilation, giving carefully thought out reasons, yet without looking in detail at, what exactly, time dilation is.
I feel that the behaviour of mouns provides insight into how time dilation works - what the mechanism is and why it happens at all.
It is true to say that the cosmic muons will be seen to be time dilated in the Earth's reference frame, but it is not just that they 'appear' to be time dilated: they physically are time dilated or they would not be found to have travelled so far. So the muon - considered as a clock has a half life of 2.2ms in its own frame but 90+ms in its journey to Earth - so how does that work? Yet it does! And that is why the muons explain why and how time dilation works...
as I understand it - but I am a mere beginner...

[guest49538]

I feel that the behaviour of mouns provides insight into how time dilation works - what the mechanism is and why it happens at all.

Hi, TyroJack.

I quoted your most relevant comment regarding the OP. I have to write the topic as a question, following the rules here.
But there is not a question in my mind. It's an objection concerning the poor flexibility that current physic theories have, due to the dogmatic adoption of Lorentz-Poincarè Transforms from STR and it's consequences, the adoption of GTR as the only valid explanation for gravitational effects and the widespread adoption of E=mc2 dogmatically, even when such expression has never been proved theoretically. Einstein's 1905 proposal for E=mc2 is just an approximation which is valid only for low ratios of v/c (less than 5%). For ratios higher than that, the original 1905 paper is invalid (it only takes a very short time to read the 2 and 1/2 pages of the original document to certify this).

Einstein himself couldn't find any analytical solution to this even when he tried four or six times along his life. None other scientist (to my knowledge) could, even when many gifted mathematicians tried in several opportunities between 1911 and 1919. After that, as far as I know, any attempt to prove it is
inexistent or not formally documented.

Muons are the only proof offered for STR time dilation (dropping the questionable GPS explanation). But the problem goes beyond time dilation. It's all around current physics, as this book can prove:

Handbook of Radioactivity Analysis
edited by Michael F. L'Annunziata

You can find it at Google Books and, if you go to "Chapter XII - Cosmic Radiation", you'll find that the ENERGY of any muon produced after nuclear reactions due to cosmic high energy protons (mainly extra-Solar System) colliding with nucleii at hight heights in the atmosphere (above 10 Km) and posterior pion's generations and decay, is related to muon's speed by the simple formula:

E= KE-mu.c^2, where mu is the rest mass-energy of muon- on Earth.

This expression is followed by this one: E = Gamma . mu.c^2 - mu.c^2 = mu.c^2 (Gamma -1).

And, in this simple way, you have a circular reference between speed and energy for any muon in the range from 0.1 GeV up to TeV. No matter how energetic a generated muon is, is always forced to verify Lorentz.

So, by accepting that KE increases almost Gamma times due to velocity, the speed of light can't be surpassed. With this, any other parameter from this phenomena is forced to verify STR (even when HUGE instantaneous acceleration is applied).

Time dilation in such scenario is just a collateral effect, and is used to explain why a muon with a 2.2 microsec decay time (at rest and on Earth) can reach Earth's surface. The fact that this keep going underground is related to nuclear physics and not to relativity.

So, there you have it: I don't accept that muon's decay time be independent of its energy NOR it enormous interaction with atoms in the downfall (consider that more than 10^16 atoms are in the pathway, and many of them are ionized by muons). It's accepted that muons are heavily de-accelerated in the downfall and that they lose an important amount of energy.

This is the opposite of what happens with muons produced at labs here on Earth:

1) They are created at almost a perfect vacuum inside accelerators.
2) Their generators (accelerated protons) collide other type of nucleii (not from O2 or N atoms present in atmosphere).
3) Muons are subjected to circular acceleration and they are stopped by the use of strong magnetic fields. Then, their trajectories spiral down until they decay into electrons and other particles, being registered doing that.

These three main differences betwen cosmic muons and lab muons is what is NOT taking into account. STR and Lorentz are applied in two completely different enviroments, and yet the earthly created muon with its decay time is used to explain the behavior outdoors.

I don't accept the explanation because, for me, data from one scenario is forced to fit into equations applied to a completely different scenario (Lorentz-Poincarè and Einstein STR mediating).

[evan_au]

I don't accept that muon's decay time be independent of its energy

I don't accept that, either.

The  energy of a muon includes its kinetic energy KE=½mv²
And the half-life of a muon can be calculated as 2.2us(1-v²/c²)^-½

This is entirely consistent with Einstein's work (the final version).

[guest49538]

Quote

    I don't accept that muon's decay time be independent of its energy

I don't accept that, either.

The  energy of a muon includes its kinetic energy KE=½mv2
And the half-life of a muon can be calculated as 2.2us(1-v2/c2)-½

This is entirely consistent with Einstein's work (the final version).

I made a horrible mistake when I wrote the expressions for KE: I forgot to add c^2 and I aditioned the rest energy, instead of substrancting it from the relativistic expression of KE for a particle at motion.

To validate what I wrote about how is used relativity for KE of a given particle (I wrote KE = m0.c^2.(Gamma-1), I want to refer to the CERN site, where this formula is explained (it's not my formula):

The link is "lhc-closer.es/taking_a_closer_look_at_lhc/0.relativity", which must be preceded by h***s and w3 to get the real one.

Incredibly, but using 1/2 m.v^2 gives HALF the KE if you simplify with v=c, instead of v=0.999c or closer.

Well, said that, I consider that my search for answers about muon's decay time differences is complete, as I wasn't able to create any doubt on this matter on you and the other members that replied. I respect that, so at least I've got that I agree that we disagree.

Thanks for your kind answers (everyone of you).

[Colin2B]

I find it interesting that you seem to be doubting Time Dilation, giving carefully thought out reasons, yet without looking in detail at, what exactly, time dilation is.

The reasons rhertz gives are not well thought out and are misleading. For example, in his reply to you he says  “Muons are the only proof offered for STR time dilation” and completely ignores the previous post by @chiralSPO

It's curious that, even using very expensive technology like "ring storage" at CERN and other labs, no time dilation has been observed at any of the 100's of thousands of experiments conducted.

I don't believe that's true. There are many experiments using ring storage that have clearly demonstrated time dilation. Here's a good one: https://www.scientificamerican.com/article/einsteins-time-dilation-prediction-verified/?redirect=1

Also, I know from interpreting HR-TEM images that relativistic corrections must be made when predicting the wavelength of the accelerated electrons from the voltages used for acceleration--see here: http://www.materials.ac.uk/elearning/matter/IntroductionToElectronMicroscopes/Introduction/electrons.html

Muons are quoted as an example of time dilation in all the textbook, not because they are the only proof of time dilation, but because they are part of an historic experiment to explain their apparently extended lifetime. Since that experiment there have been numerous experiments that confirm time dilation, to such an extent that such experiments are no longer of interest to the press and time dilation and length contraction (two sides of the same coin) are now common place occurrences at CERN etc.
Unfortunately, rhertz is somewhat economical with the truth in other assertions eg that Einstein’s famous E=mc² has never been demonstrated, whereas in truth it has been shown to be accurate many times eg https://www.nature.com/articles/4381096a

Despite this, it is valid to ask the question are cosmic muons different from lab created muons. If they are different then we would be looking at 2 different particles, however, the muons appear in all ways to be the same and no differences have been found. More importantly, the decay distribution of muons is predicted by the Standard Model of particle physics, and matches muons from both sources.

Time dilation (and length contraction) are facts, despite some people being unhappy about it. The why of these phenomena is far more interesting and is so much an essential part of real physics that much of our modern technology would not work if they did not exist.

[TyroJack]

I would have thought that comic muons travelling so far compared to static muons is a great example of how time dilation works.
The cosmic muon has a half life of 2.2ms which must be the same for both, the difference is the distance the cosmic muon will travel due to its speed.
But this is not Newtonian mechanics where the time it takes to travel is that same 2.2Ms. (Which considering the muon as a clock must be the proper time for the life of the muon.
No, the time it takes to travel is  Δt=γΔτ, for the time taken for the muon to travel must be added to the proper time...