Moving muons should have a longer lifetime than resting ones. Relativity means relativity, i.e. actions are relative. Therefore something is at rest is also a relative concept.
A muon moving towards earth is moving relative to earth. But it is not moving from itself. A muon should have a surrounding environment. At least, this environment should be the space occupied by the muon. And a moving muon is not moving out of it's own environment. Therefore though a muon moving relative to earth increases decay time, it cannot increase decay time relative to its own environment. Therefore reduction of decay time due to time dilation leads to a contradiction.
There can be other reasons for the increase of decay time.
Particle decay is governed by the exponential decay — Pioson Distribution — where N is the quantity and λ is a positive rate called the exponential decay constant
Here N(t) is the quantity at time t, and N0 = N(0) is the initial quantity, i.e. the quantity at time t = 0.
Therefore decay probability or half life will depend on two things λ and t. Therefore either time dilation proposed by Special Relativity or changes in decay constant λ may be the reason for changes in decay time.
We assume λ is a constant but for some unknown reason it may depend on velocity relative to earth. Therefore there exists an alternative explanation other than Special Relativity for changes in muon decay time.
The same can be said about atomic clocks that show moving clocks runs slower. Atomic clocks are also related to atomic decay?????.
Also in particle accelerators if decay time reduction is observed it may be due to the same reason?????
t - time λ - τ γ N- P- Nₒ -
the
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