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Japan, Muon's Family, Str, Time Dilation, And History

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#1 rhertz



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Posted 21 May 2019 - 06:23 PM

I learnt about the slow motion muon's microscope built in Japan.







This news led me to think about muons and its use as one of the most published assertions about its fundamental

importance (cosmic muons) as an experimental proof of the certainty of the proposals of Einstein's STR: Time dilation.


In fact, this site: http://hyperphysics....ase/hframe.html

which is supported by the Department of Physics and Astronomy of Georgia State University (a serious site), offers

the cosmic muon effect as the only valid proof of STR time dilation.


From this site, I found a PDF which I attach here, which is a condensed version of STR time dilation proof, as conducted

by four scientists from such site: Movinka Bowie, Tom Hutchinson, Shivani Kanabar, and Shivakaran Sivanathan.


https://ph.qmul.ac.u... Relativity.pdf


Attached File  Muons and Special Relativity.pdf   282.7KB   6 downloads


This particular document has data (cosmic muon's density at ground level, velocity, etc.) which differs from the mainstream.

They assert that Special Relativity would be proved in two instances:

  1. If the rate of muons on ground level suggested a probable number of muons in the Earth’s atmosphere according to STR.
  2. If the number of muons was improbable when not considering the theory then this would be proof for Special Relativity.


I've read, at Wikipedia, the history of the discovery of the cosmic muon-


1) The first kind of muon- was discovered by Neddermeyer and Anderson at Caltech in 1936, while studying cosmic radiation.

2) The existence of the muon- was confirmed in 1937 by J. C. Street and E. C. Stevenson's cloud chamber experiment.

3) It was mistaken as the particle theoretically predicted by Hideki Yukawa, but it took another 10 years to find the Yukawa's

    particle within cosmic rays (the Pion- or Pi-, with 20 nsec half-time life). It resulted that the Pion-, a byproduct of collisions

    between energetic protons at high atmosphere and H, O or N atoms, is the father of the muon-.

4) In the following 15/20 years, different types of Mesons (muons, pions, etc.) were discovered at lab, using chambers and

    particle accelerators. This link contains a historical photograph of the first muon- as it was found in a bubble chamber

    (July 31, 1957).




5) History evolved since the '50s to the '70s, with the discovery of hundred elementary particles, until a communitary effort

    by particle's physicists created the basis for a simplified model in the mid '70s, which was enhanced and adopted as the

    Standard Model for Elementary Particles, after a big redefinition. The rest of particles, of mere existance, remain to be

    used as they are needed. Muon- and muon neutrinos are now labeled leptons.


6) Japanese applied physics consider muon-, muon+, pion- and pion+ of rock solid existence (see the link provided above,

    for the muon based microscope). They use muons and pions like in this pic:





By using muon+ (positive muons) they gain confidence when analyzing frozen organic matter, like in this pic:





7) Regarding to cosmic muons and STR's time dilation proofs, from Wikipedia



  • First experiment (Wikipedia): In 1940 at Echo Lake (3240 m) and Denver in Colorado (1616 m), Bruno Rossi and D. B. Hall measured the relativistic decay of muons (which they thought were mesons). Note: There were not available statistics by then.
  • A much more precise experiment of this kind was conducted by David H. Frisch and Smith (1963), who measured approximately 563 muons per hour in six runs on Mount Washington. By measuring their kinetic energy, mean muon velocities between 0.995 c and 0.9954 c were determined. Note: this data from 56 years ago is still used widely.
  • Since then, many measurements of the mean lifetime of muons in the atmosphere and time dilation have been conducted in undergraduate experiments. Note: Not oficial records since 1963.



There are several questions to clarify in order to validate the results, such as:

  • Are cosmic muons of the same nature as laboratory created muons, which are affected by strong magnetic fields and bubble's collisions? The average half-life of ground level generated muons- could be greater than the results at accelerators.
  • Is there consensus about the height at which cosmic muons- are generated? Results varies from 6 to 30 Km.
  •  How is measured the energy of muons- in outdoors experiments?. It's for when they are generated and when are detected.
  •  Is there a chance that a mix between muons- and muons+ changes the result?.
  •  Being the spread in time dilation factors at Frisch-Smith experiment above 40%, and that they averaged the results, has these values recalculated with precision, as well as the density of muons with height?
  •  How are considered the effects of magnetic and gravitational fields in outdoors experiments?.
  • May be possible that highly energetic muons- (GeV), which posesses mass 1/9 that of primary protons,  generate a chain cascade of regeneration of muons- until they reach ground level?. There is no way to mark which muon is which, specially by extrapolating a curve with just two points.
  • If the old concept of "relativistic mass" is used, the results should be discarded as invalid, as such a concept is not valid.

I'll try to find more reasons than the above mentioned, which I generated "on the fly" while writing this, without further research.


You are invited to post an opinion if you will, but please DEBATE and don't attack it with "ad-hominem" ways. This post only intend

to bring more topics to this forum.

Edited by rhertz, 22 May 2019 - 02:34 PM.

#2 rhertz



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Posted 23 May 2019 - 09:47 PM

I've been reading a lot about cosmic radiation (74% being free protons of extra-solar origin), its isotropy around Earth, the

generation of muon- and muon+ at high atmosphere (between 10 and 16 Km above ground level), the high energy that

cosmic proton posseses (from GeV to TeV), the wide dispersion of values of velocities of muon- and muon+ (which causes

a huge dispersion of Lorentz's Gamma  factor, between 5 and 1000+), the true average half life of muons, the density of

muons that reaches ground level or a given height, the behavior of the two favourite muon detectors and the huge dispersion

of muon's density that reach the designated targets. This is only a fraction of an important amount of information regarding

muons, cosmic rays and experiments to measure factors like density vs. height, density vs. energy, etc. Also, there is an

important contamination of background level radiation which requires that correct tests be conducted at no less than 700 m

above sea level.


To make the things more complex, cosmic muon-and muon+ have different half time life in laboratory tests (2.1 and 1.4 to 1.7

microsec avg) and, at the outer space, are created with a proportion 56% - 44% respectively. This imply an equation for

intensity decay that is a sum of TWO different exponential expressions of the type NK(t) = NK0.e-t/Tk plus a ground level factor.


Also, there is a concern with physicists IF the Lorentz's factor holds for high energy levels, which produces theoretical high values

of the Gamma factor, above 100 GeV and passing 100 TeV. This problem of energy dispersion, combined with the isotropy of the

distribution of the vectorial angle of incidence of radiation respect to the normal (90º above target) poses a very difficult scenario

to provide data with certainty respect to the density of muons over the target detector and the spread of travelling times to it.


I can keep going deeper on each aspect post after post but, after thinking it for a while, I've reached to some conclusions:


  1. The efforts to find relativistic explanations, since 1962, discard most of the complexities that I've described and settle with a very simple scenario, which uses only one value of half life time, an assumed heigth at which the muon (only one type) is generated and rudimentary techniques for detection that didn't change too much in 57 years (except microelectronics and computers).
  2. To prove Einstein's Restricted Relativity (STR), at most experiments two perspectives are applied: 1) What is PERCEIVED by an observer at the Earth's ground level reference frame and 2) What is PERCEIVED by an observer at the muon's reference frame.
  3. In this site:  https://en.wikipedia...cial_relativity , under the title " Lorentz transformations and its inverse", it is claimed that a perfect simmetry exists between PERCEPTIONS under the basic reference frame and its primed counterpart.
  4. However, most of the experiments published (many by undergraduates), use "time dilation" for observations from Earth's ground level and use "length contraction" for observations at the muon's reference frame. As both results are coincident, researchers are satisfied and claim that Einstein's STR is verified.

As far as I know, there is no evidence that a real observed had measured "length contraction" at any time, anywhere.


Also, if STR is to be true, the simmetry has to be verified experimentally. And this would be highly appreciated IF time dilation is proven from any of the TWO reference frames. Otherwise, an unilateral "pseudo-verification" should be discarded as invalid for several reasons:


  • The extreme simplification of the real context at which the experiments take place, without any justifications for the dissmisal of an important amount of parameters which, if they were considered, would NOT proof STR (complexity vs. simplicity).
  • Being that experiments are conducted with thousands of runs, each one accumulating hundred or thousands values there is a flaw: statistics are applied for the value of frequency of hits on measurement target versus time, providing a normal distribution of values. BUT, in no case this method is used for the distribution of velocities of muons within the path, which poses doubts about IF some values are supraluminal.
  • Even when it is assumed as certain that a given muon (+ or -) suffer millions of collisions in the trajectory towards ground level, only ionization is considered as the single collateral effect of its trajectory down to Earth and only a loss of about 20% of its energy is considered to be lost. There is not a single conjecture about the TIME INVESTED in such processes of ionization, as if they are considered INSTANTANEOUS.
  • IF, for instance, a tiny time of 10 picoseconds (10-12 sec) would be used at each ionization's process, then the ALLEGED time dilation could be explained simply by delays in a complex trajectory while any given muon bounces back from every O or N molecule along its path down to Earth.
  • More yet, being muons (specially muon+) such a massive particle created with energies ranging from 10's of GeV to TeV+, and having a mass that is 1/9 that of a free proton, that REGENERATIONS OF MUONS in the downpath be discarded is unproven and such dismissal (as the above one) seems to be an aditional argument to enforce STR (which, by the way, is hammered heavily to fit ubersimplified data).


I'll follow this particular topic, which gained my attention in the few past days, as I never focused on this particular issue.


I want to remark that my interest was gained by an article of a japanese enterprise to develop a "slow motion muon microscope", with details in my OP. No intentions to refute Einstein's STR are driving me, except to challenge this particular proof of time dilation. I have no intention to compite with 110 years of discussion about STR rationality or validity, which consumed hundred of millions of man-hour in futile disputes (and keep happening at every physics forum, until some sensitive moderator bans the author, because he/she looks like is challenging what is called "stablished science").


At any case, the disputes had ended with a "herd mentality's consensus" on one side and a "cranck mentality's consensus" on the other side. It's a dogmatic fight, which is futil and has no rational basis but only a dogmatic one, like religious, social or political dissidences. Always a binary polarization is present, like a karma upon humanity, as if to think about to three or more possibilities to exist simultaneously is too much for our brainpower and emotional stability.

Edited by rhertz, 23 May 2019 - 11:34 PM.

#3 Flummoxed



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Posted 24 May 2019 - 04:07 AM

You might find this link interesting, there are different ways of viewing the Michelson Morley experiment conclusions.


#4 rhertz



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Posted 24 May 2019 - 07:12 AM

You might find this link interesting, there are different ways of viewing the Michelson Morley experiment conclusions.



Flummoxed, thanks for the references. I've read that one of the two answers is signed by Pentcho Valev, a known antirelativist that have been posting at almost every physics forum created for more than 20 years.


For me, special relativity is a result of a collective effort that spans from 1887 to 1905 aand that hasn't a patent number awarded to Einstein. Names like Maxwell, Michelson, Morley, Voigt, FitzGerald, Heaviside, Lorentz, Poincarè, Einstein and many others working in the darkness of what an electron, atom or molecule was is more than remarkable.


My concern is connected with applications for Muons derivated from Cosmic Radiation near the Earth, which are more than 50% of the radiation from space at Earth's surface. Cosmic Radiation poses an enormous value to space science (human activities and artifacts in the outer space, astrophysics, etc.) as well as in Earth's science (technology, enviromental sciences, particle physics, medicine and many others).


I've learned that many goverments around the globe spend an important amount of money researching about cosmic radiation, and scientists try to figure out its origin, which is unkown, except for the fact that most of it is generated outside the Solar System. Cosmic radiation impacts on human life at high altitude (airline pilots) and at the outer space. Also affects the reliability of electronics as it can produce software and hardware malfuctioning , for which a lot of money has been invested in the last 60 years, to counteract its effects.


I'm interested in knowing how the decay time of subatomic particles is measured and finally stablished, in order to believe (or not) current techniques for geological dating using half life time of radioactive residuals of samples. My doubts increases with the figure of calculated age, that now can be stablished as old as as 500 million years, using increasingly complex techniques and radioactive elements in samples.


It's increasingly difficult to preserve samples from contaminations, af measured age increases. I wonder if there is not some kind of fudging or falsification of data, in order to present a connected order of evolution for the last 4.5 billion years and, yet more, with the big bang theory.


In the case of muons, even when NIST has data about muon's rest energy and half life time, with astonishing accuracy, I'm interested in critics about how mass and decay time are measured using  super strong magnetic fields, different types of chambers and statistics. I seems that the basis for the calculations have been the same for the last 80 years, more or less.


What if a natural decay of unstable particles, without external magnetic forces, is many times much larger than at a laboratory?




Edited by rhertz, 27 May 2019 - 08:32 AM.

#5 Flummoxed



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Posted 24 May 2019 - 07:29 AM

You may have seen this, but if you haven't you will enjoy it https://arxiv.org/pd...ics/0205065.pdf Michelson Morley experiment revisited. It is by Reg Cahill of the Quantum Foam inflow gravity theory. He reckons the conclusions drawn from experiment were wrong. With appropriate corrections the MM experiments agree with the COBE 


"The re-analysis here of the Michelson-Morley experimental data, correcting for the refractive index effect of the air, reveals an absolute speed of the Earth of v = 359±54 km/s, which is in excellent agreement with the speed of v = 365±18 km/s determined from the dipole fit, in 1991, to the NASA COBE satellite Cosmic Background Radiation (CBR) observations. Other experiments where the interferometers operated in air (Miller 1925,1933) or helium (Illingworth 1927) give similar results when re-analysed."



#6 rhertz



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Posted 24 May 2019 - 08:06 AM

Flummoxed, thanks for the link. I correspond with this one: https://www.research...rley_Experiment


I don't know if you was aware that the great James Clerk Maxwell was behind Michelson's conception of the experiment, as they exchanged correspondence.

Maxwell suggested that Michelson should use Jupiter's moons for his experiment but, as Michelson was in the US Navy and had money to expend, he did so.

Not only that, but for the 1887 experiment with Morley and with private funds, he contracted a german company to develop his interferometer. German technology dominated the scientific world for almost a century, till 1945. Just read my post about black body radiation and the timelapse between 1859 and 1900, and the rol of the PTR Institute at Berlin.


But, keeping on topic of my OP, when you may contribute with some comments, I'll appreciate.


P.S.: I forgot that the original target of the Michelson experiment was to prove that Earth moved around the Sun at a given speed. Maxwell, the forefather of relativity, was convinced that such experiment was going to be negative, and he was right. That was the original goal of MM experiment, not to disprove the ether.

A pity that Maxwell died being 48 y.o. in 1879. I'm convinced that he would have been the King of Modern Physics (not Einstein) if he only would have lived more.

#7 rhertz



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Posted 24 May 2019 - 10:03 PM

After a wide research about muon decay time, I found several papers related to nuclear physics, where the Fermi's Golden Rule

for decays of particles is used to find an approximate theoretical value. The formula for decay apply for muon-, as observed in tests

at a laboratory. Muons generated by cosmic radiation are called "secondary muons", but still they are assigned the same mass as

primary muons. Muons are considered elementary particles because it's believed that they don't have any other elementary parts

like quarks, and are a kind of heavy electron (or anti-electron in the case of muon+).


Muons are unstable and decay into an electron plus two neutrinos or a positron plus two neutrinos. Only muon+ can be produced as

surface leptons (to be used as slow muons by the microscope), because pion- (which generates muon-) at surface, are captured by

nuclei. Slow motion muon+ have 25 times less energy than muon- at rest (about 4 MeV) and are slowered even more by using a laser

to cool them off, which are later accelerated at the desire rate within the microscope.


These formulae are used in almost all the papers related to muon- decay time and have a significant dispersion of values, which is a proof that the parameters are fit into the equations to get the desired value of 2.2 microsec for 106 MeV muon-. The sum of the components of

the decay (electron or positron plus two neutrinos) don't explain in what more than 100 MeV remaining are transformed into. If cosmic muons

have less mass-energy that laboratory's muons, then the decay time would increase, as is observed at the theoretical formula for decay.


The Fermi's Coupling Factor GF is derived empirically and has not an analytical expression, and was originally proposed by Fermi in 1933 to explain the weak interaction (radioactive) of elements at the nucleii of atoms. The same thing happens with the muon- decay time Taumu, which is derived from different experiments around the globe and averaged per consensus since early 80's.


The whole formula for the muon's decay time is derived from approximations, which include the use of h-bar to comply with units.


CONCLUSION: Theory and practice around this particular topic (muon's decay time) gives consistently the same results since the

early works 70 years ago, in order to satisfy Einstein's STR and its derivate E=mc2.

With more than 20 academic papers revisited (period 1984 - 2015), there is a generalized consensus to use 2.2 microsec as the

muon-  decay time and its energy, expressed as 106 MeV. Also, the use of time-dilation along with length-contraction in the same

document for explanations about the muon's phenomena are commonplace. What varies, in more than 50 years of "controlled"

experiments is the height at which most of the cosmic protons produce muons. Only a few documents contemplate the almost equal

existance of muon+ and muon- in the cosmic shower, being that each one has a different decay time and a complex expression is

needed to explain the mean decay.


I've observed that have a circular reference in order to express theoretical formulae, as two or three parameters are empirical, and the

original 1933 Fermi's Constant for Weak Interaction (Weak Forces) hasn't yet a definite mathematical formulation. The empirical value of

muon's decay time is generally the one derived from laboratories (some very expensive), and then applied to outdoor experiments to

validate the data and STR over the so called "secondary muons".


So, for me, at Quantum and Nuclear Physics, everything that is accepted today (as published for open download at the internet) is built

around the goal to verify STR. For instance, if some value is missing it's calculated using STR and extensions of E=mc2.



The following document, from the Zurich University




is the most detailed one that I've found and uses the empirical mean value of Taumu  to extract a theoretical value of the Fermi's Factor GF.

This document is from a lecture about QFT


Quantum Field Theory-I

Prof. G. Isidori

Assistants: K. Ferreira, A. Greljo, D. Marzocca, A. Pattori, M. Soni


The muon decay in the Fermi theory





The following values are used at the end of the document:


hbar = 6,5821 10-25 GeV.Sec

G= 1.166 10-4 GeV-2  (current best empirical value)

mmu = 105.66 MeV/c2 (only for muon-, as muon+ has a positive charge and less mass, with decay time of 1.7 microsec)

Tau = 2.189 10-06 sec (Here as a result for muon-. In the paper at the link, as a value introduced to find GF).

The formulae for the theoretical approximation to the muon's decay time are:


[math] \Gamma_\mu = \large\frac {G_F^2{m_\mu}^5}{192\pi^3} [/math]


[math] \tau_\mu = \large\frac {\hbar}{\Gamma_\mu} [/math]

Edited by rhertz, 25 May 2019 - 01:18 PM.

#8 Flummoxed



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Posted 25 May 2019 - 01:49 AM




But, keeping on topic of my OP, when you may contribute with some comments, I'll appreciate.




I am going sailing for a few weeks so wont be posting for a while. 


Enjoyed your threads, 

#9 rhertz



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Posted 27 May 2019 - 08:41 AM

I am going sailing for a few weeks so wont be posting for a while. 


Enjoyed your threads, 


Have a good and safe trip, Flummoxed.


I'll start a different thread on this topic, but evaluating how Lorentz Transforms are applied to explain muon's decay time.


I've read a lot of documents that use direct LT to justify the phenomena using time dilation with an observer at the muon's reference frame, and inverse LT for length contraction perceived by an observer at rest on Earth's surface.


Here is a link that explain how it's applied to explain cosmic muon's behavior:



#10 rhertz



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Posted 01 June 2019 - 10:42 PM

Have a good and safe trip, Flummoxed.


I'll start a different thread on this topic, but evaluating how Lorentz Transforms are applied to explain muon's decay time.


I've read a lot of documents that use direct LT to justify the phenomena using time dilation with an observer at the muon's reference frame, and inverse LT for length contraction perceived by an observer at rest on Earth's surface.


Here is a link that explain how it's applied to explain cosmic muon's behavior:




I changed my mind. I'll do it right here, as it's simple math.


Following Einstein's 1905 STR, assume the existence of two reference frames K(x,y,z,t) and K'(x',y',z',t') which verify sinchronization by

verifying K(0,0,0) = K'(0,0,0) when their times verify t = t' = 0 (sync by electromagnetic means). Assume that K' is travelling at "v" speed

towards positive values of x', being "v" a constant velocity measured as relative to any of both inertial reference frames.


Then, Lorentz Transforms for the horizontal axis at both frames apply, as well as for their local times.


The perception of K values of x,t are the following at the frame K':


x' = Y (x-vt)

t' = Y (t-v.x/c2)


where Y is the Gamma factor [1-(v/c)2]-1/2


A difference between two consecutive values 1 and 2, either for distances or for times, can be

expressed as differences Delta:d, as follows:


dx' = Y (dx-v.dt)

dt' = Y (dt-dx.v/c2)


As per consensus (see Hyperphysics and any other "serious" source), it is considered that:


For measurements of length at K', these measurements are done simultaneously at K, what gives " OBSERVED length variation" at K for K' values:


dx' = Y dx   (from instantaneous observations in K' from K). This is "length expansion upon K' as being observed from K in an interval dt=0)


As there IS NOT a privileged reference frame, Inverse Lorentz Transforms stablish that if K' is adopted at a relative rest from K, it happens that:


dx = dx'/Y   (this is the famous "observed" length contraction).




For measurements of time intervals at K', these measurements are done AT THE SAME PLACE at K, what gives " OBSERVED time variation" at K for K' values:


dt' = Y dt   (from observations in K' from the same place at K). This is "time dilation upon K' as being observed from K at the same place, for what dx=0)


As there IS NOT a privileged reference frame, Inverse Lorentz Transforms stablish that if K' is adopted at a relative rest from K, it happens that:


dt = dt'/Y   (this is the "observed" time dilation).



To justify that muons can be detected at Earth's surface with an average decay's time SEVERAL times higher than laboratory measurements of 2.2 microseconds, being that cosmic muons are believed to be generated at the high heights in the atmosphere (from 10 to 16 Km) at velocities almost close to "c" (between 0.994.c and 0.99995.c) and only COULD travel an average of c.2.2usec (660 meters), from the four formulae ONLY two are used:


1) To explain time dilation, K': Earth's surface  and K: Muon's reference frame.


     In this case, time dilation is observed: dt' = Y dt (which explains that muons can travel between 10 and 16 Km without decaying).

     In this case, dt = 2.2 usec ALWAYS, without any interference of height or muon's energy (which gives v).


2) To reinforce time dilation from 1), the formula for length contraction from the perspective of the muon's reference frame.


     Then, dx = dx'/Y is used, with dx being ALWAYS about 660 meters. To verify this, dx' varies between 10 and 16 Km and Y do so, accordingly.





These have been the tricky explanations used in the last 70 years to explain why there are aboundant cosmic muons at Earth's surface.

These particles, that are detected even 100 meters underground, are about 50% of the radiation detected on the surface of the Earth.

With a small contribution of the Sun, most of them are from unknown sources at galactic level (or beyond).


Lately, and due to controversies about Length Contraction as a real phenomena, this second explanation is not used.


So, only one out of four Lorentz equations (time dilation) are being used in the last decade or so.


I have to add that the fact that muons are created by instantaneous acceleration (impossible to obtain at a laboratory) is ignored.

This acceleration appears when highly energetic COSMIC protons collide with O2 or N atoms at high atmosphere, producing pions (+ and -)

which decay in 20 nanosec (allegedly) into muons (+ and -) and byproducts.




So, this is the history of time dilation and muons, along with its history.


I have to add that slow motion and ultra slow motion muon+ are being used at Japan to develop muon's based microscopy, as i wrote in my OP.


This imply muon+ with energies 10 to 100 times slower than its rest mass (in MeV), but not a word about their decay time is known.

Edited by rhertz, 01 June 2019 - 10:43 PM.