Is the clock slowing real? YES!
Example of muons, sub-atomic particles that last about 1.5 ?sec = 1.5x10-6 sec when observed at rest.
Traveling near c, a muon would only go about 3x108 (m/s)x 1.5x10-6 sec = about 500 m. VERY few muons would make it to Earthš ¸‹ surface.
But about 70% actually do reach the earth.
How can this be? Because time appears to run slow by a factor of ? as measured by observer on earth.
muon shower created by cosmic rays in upper atmosphere