According to the theory of relativity, from the perspective of the high-energy muon itself, it would still experience a subjective passage of time of approximately 2.2 μs, despite the increased half-life as observed by a stationary observer.
Time dilation occurs due to the relative motion between two frames of reference. In this case, when the high-energy muon is traveling at a significant fraction of the speed of light, its internal clock appears to slow down as observed by an external observer. However, from the muon's perspective, its own internal processes, including its decay, would proceed at their normal rate.
To understand this, we can consider that the muon is at rest relative to itself, and therefore, its internal clock remains unaffected. However, when observed from a different reference frame, such as a stationary observer on Earth, the time dilation effect causes the muon's decay process to appear slower, leading to the longer observed half-life of 11 μs.
So, from the perspective of the high-energy muon, it would still experience its own decay process taking approximately 2.2 μs. This is consistent with the muon's reference frame, where time dilation effects are not noticeable.