Solution to the Muon Paradox

PSI Blog 20260126 Solution to the Muon Paradox

Do muons really travel 15 km through the atmosphere?

DVHM has left a new comment on the post "Time is Motion":

“Glenn, your perspective is very refreshing. I wonder if you would consider writing a post on muons? Specifically the claim that time dilation is proven by the detection of higher amounts of naturally-occurring muons at the earth's surface than should be detected according to muons' half-life in laboratories.”

[GB: Thanks for the compliment and for the interesting question. Here is some Gemini AI on the Muon Paradox:

“The Muon Paradox highlights how subatomic muons, created high in the atmosphere, reach Earth's surface despite their short lifespan, challenging classical physics but confirming Einstein's Special Relativity through time dilation (longer life for the muon) and length contraction (shorter atmosphere for the muon), showing both perspectives correctly explain why many survive to be detected.  

This video explains the basics of the muon paradox and how it provides evidence for relativity:

YouTube · Dec 17, 2021

 

The "Paradox" Explained

1.    The Setup: 

Muons are created in the upper atmosphere by cosmic rays and travel towards Earth at near light speed (around 99% c). 

2.    Classical Expectation: 

A muon's average lifespan is only about 2.2 microseconds (µs). At near light speed, they should only travel roughly 650 meters before decaying, meaning almost none should reach the ground from 10-15 km up. 

3.    The Observation: 

Muon detectors on Earth's surface consistently detect far more muons than expected, proving they live long enough to make the journey. 

The Relativistic Solutions

From Earth's Perspective (Time Dilation): 

 

Earth observers see the muon's internal clock ticking slower due to its high speed. Its 2.2 µs lifespan effectively stretches (dilates) to a longer time (e.g., 15 µs), giving it enough time to travel the 10-15 km distance. 

From the Muon's Perspective (Length Contraction): 

 

The muon experiences time normally. From its viewpoint, the atmosphere is rushing towards it at high speed, causing the 10-15 km distance to contract (shorten) significantly (e.g., to just 2 km), making the short trip possible within its natural lifespan. 

Both time dilation and length contraction are two sides of the same relativistic coin, resolving the apparent paradox and serving as strong experimental proof for Einstein's theory.”

 

[GB: False. Time is motion and motion cannot dilate. Length contraction is equally silly. While muon production occurs at the 15 km altitude, regressive physicists admit that it also occurs throughout the atmosphere. Gemini AI says:

“Muons are not created directly by the initial cosmic ray. Instead, they are the result of a two-step decay process that happens mid-flight:

Collision: A high-energy proton hits an atmospheric nucleus, creating pions and kaons.

Decay: These pions and kaons travel a short distance (meters to kilometers depending on energy) before decaying into muons and neutrinos. This decay happens continuously as the shower descends through the mid-atmosphere.”

 

In other words, plenty of muons are produced as protons and neutrons (erroneously called “cosmic rays”) from outer space collide with nitrogen and oxygen throughout the atmosphere. Those targets would increase in number as altitude decreases, making up for the decayed muons that were produced at the top of troposphere.

 

The false dilation and length contraction assumptions are a consequence of Einstein’s aether denial. By considering light to be a particle instead of a wave in a sea of aether particles, he falsely claimed that measurements of the velocity of light would be the same for all observers. In fact, the only way those calculations could result in c, was to use time dilation or length contraction. The correct frame actually was the aether medium itself.  Likewise, the correct frame for sound is the medium through which it travels. Physicists don’t speak of time dilation or length contraction with respect to sound. They simply calculate the distance to the source while taking into account their own motion and that of the source.

 

About the Muons that arrive at the Earth’s Surface According to Gemini AI:

 

“Cosmic Ray Interactions: Most natural muons are created approximately 15 km above the Earth when primary cosmic rays (mostly high-energy protons) collide with atmospheric nuclei. However, these high-energy interactions continue throughout the atmosphere; secondary cosmic rays can collide with matter directly at the Earth's surface to produce new muons.

 

Secondary Showers: These surface-level interactions typically produce pions, which almost instantly decay into muons.”

 

“The flux of muons arriving at sea level from the atmosphere is approximately 1 muon per square centimeter per minute.”

 

Here is a misleading use of the Lorentz Correction Factor for illustrating time dilation and length contraction:

 

https://www.youtube.com/watch?v=rVzDP8SMhPo&t=122

 

Back to reality…

 

Remember, I showed the proper derivation of the Lorentz Correction Factor in “Infinite Universe Theory.”[1] That simply takes into account the extra distance to be expected when an object is moving away from you. That takes longer, but it is not “time dilation.”

 

A particle traveling at c (300,000 km/s) 15 km from point A to point B is going to take 0.00005 s (50 µs) regardless of what anyone says about it. Muons with a lifespan of 2.2 µs obviously will decay during the early part of the trip. You can imagine the particle thinks it is experiencing “time dilation,” but that will be to no avail. Those muons produced at the top of the troposphere will never reach Earth. Only the ones produced during the last 15.2 µs (ten half-lives) over the last distance of 4.46 km will be observed on Earth.

 

As shown above, muons are produced from top to bottom of Earth’s atmosphere. Like the other “proofs of relativity,” that little bit of evidence can be misinterpreted to fit the preconceived notions of regressive physicists. This is akin to other misinterpretations such as Eddington’s claim starlight bending was caused by “perfectly empty curved space-time” instead of refraction in the plasma rim of the Sun.[2]]

 

  

PSI Blog 20260126

 

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[1] Borchardt, Glenn, 2017, Infinite Universe Theory: Berkeley, California, Progressive Science Institute, 337 p. [http://go.glennborchardt.com/IUTebook] p. 315.

[2] Ibid, p. 201.