Editing Lorentz factor (section)

==Applications in astronomy==
The standard model of long-duration gamma-ray bursts (GRBs) holds that these explosions are ultra-relativistic (initial {{mvar|γ}} greater than approximately 100), which is invoked to explain the so-called "compactness" problem: absent this ultra-relativistic expansion, the ejecta would be optically thick to pair production at typical peak spectral energies of a few 100&nbsp;keV, whereas the prompt emission is observed to be non-thermal.<ref>{{cite journal |last1=Cenko |first1=S. B. |display-authors=etal |title=iPTF14yb: The First Discovery of a Gamma-Ray Burst Afterglow Independent of a High-Energy Trigger |journal=Astrophysical Journal Letters |page=803 |date=2015 |volume=803 |issue=L24 |doi=10.1088/2041-8205/803/2/L24 |arxiv=1504.00673 |bibcode=2015ApJ...803L..24C }}</ref>

[[Muon]]s, a subatomic particle, travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme [[time dilation]]. Since muons have a mean lifetime of just 2.2&nbsp;[[Microsecond|μs]], muons generated from [[Cosmic ray|cosmic-ray]] collisions {{cvt|10|km|mi}} high in Earth's atmosphere should be nondetectable on the ground due to their decay rate. However, roughly 10% of muons from these collisions are still detectable on the surface, thereby demonstrating the effects of time dilation on their decay rate.<ref>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html |title=Muon Experiment in Relativity |website=HyperPhysics.Phy-Astr.GSU.edu |access-date=2024-01-06 }}</ref>