Muon
The muon is an unstable elementary particle carrying the same electric charge as the electron but about 207 times its mass (105.7 MeV/c2). It was found in cosmic radiation by Carl Anderson and Seth Neddermeyer in 1936–37, was for a decade mistaken for the meson predicted by Yukawa as the carrier of the nuclear force, and was eventually classified as a heavy relative of the electron — a second-generation lepton, in Standard Model terms, with no known internal structure. A muon at rest decays with a mean lifetime of about 2.2 microseconds into an electron and two neutrinos. Muons are produced in the upper atmosphere by cosmic-ray collisions and are the most abundant charged particles reaching sea level.
The muon carries an outsized burden of evidence in modern physics, for two reasons. First, its decay is the standard textbook demonstration of relativistic time dilation: at 2.2 microseconds and even at nearly the speed of light, a muon should on average travel only about 660 metres, yet muons created at 10–15 km altitude arrive at the ground in large numbers. The Rossi–Hall experiment of 1941, comparing muon flux on Mount Washington with flux at sea level, is the classic measurement; storage-ring experiments later measured the dilation of the lifetime directly at a known velocity. Second, because it is heavy, the muon orbits a nucleus about 200 times closer than an electron does, which makes muonic atoms a sensitive probe of nuclear size — the source of the proton radius puzzle.
One mainstream open question deserves mention. The muon's anomalous magnetic moment, g−2, was for two decades measured slightly away from the calculated value, and the gap was widely reported as a possible sign of physics beyond the Standard Model. The interpretation turns on a hadronic contribution that is difficult to compute, and as lattice calculations of that term have improved the theoretical prediction has moved toward the measurement. The case illustrates how much of "precision agreement" in particle physics is agreement between a measurement and a calculation whose hardest term is itself under revision.
On this wiki
Because the muon is the principal experimental support for time dilation, it is contested here mainly as a relativity question rather than as a structure question.
Carl A Zapffe confronts the standard reading directly in On Mass-Energy Equivalence, Mass Increase, Muon Decay and Time Dilation (1980), arguing that the muon result does not establish a dilation of time as such. Alexander L Kholmetskii and Tolga Yarman propose an alternative mechanism in Just Like the Gravitational Field, the Electric Field Too, Slows Downs a Clock, Interacting With It: A Whole New Appraoch to the Bound Muon Decay Retardation (2008): the retardation of bound muon decay is attributed to the electric field the muon sits in, so that a physical interaction with the environment, not the geometry of spacetime, slows the clock. James D Edmonds made a related proposal in The Muon Clock, Time Dilation and the Dynamic Vacuum (1978), locating the effect in the vacuum. This is the characteristic dissident move on the topic: accept the measured lifetime extension, deny that it licenses a claim about time itself. See Time Dilation and Category:Time for the wider argument, and Can Clocks Tell Time? (2008) by Al F Kracklauer for the conceptual objection in its sharpest form.
Neil E Munch argues from muon evidence among others that special relativity has restricted boundaries of applicability in Boundaries of Applicability of Special Relativity (1999), and Georg Galeczki's Dynamic Gamma Factor: Yes; Lorentz Transformation: No (1999) accepts the velocity-dependent factor that describes muon lifetimes while rejecting the Lorentz transformation that is usually said to explain it — a distinction that recurs throughout the relativity material here.
The muon also supplies positive evidence for an absolute frame in some of this work. Paul Wesley and Christian Monstein measured an anisotropy in the cosmic-ray muon flux and derived a solar-system velocity from it in Solar System Velocity from Muon Flux Anisotropy (1996), published in Apeiron; the result is treated here as detection of motion with respect to a preferred frame, which special relativity holds to be undetectable.
On the structural side, Carl R Littmann derives the muon-to-proton mass ratio from the volume ratios of close-packed spheres in Muon to Proton Mass Ratio, Geometric Volume Ratios, and an Overview of the Particle Zoo (2010), part of his programme of finding particle masses in geometry rather than in field theory. Ricardo L Carezani's Autodynamics predicts decay modes for the muon additional to the standard ones, and posits a related particle, the electromuon; the muon is accordingly one of the places where Autodynamics claims a testable difference from the standard account.