Precision experiments reveal a discrepancy in the lifetime measurements of both beamed and bottled (stored) free neutrons on the order of approximately eight seconds. The origin is still unknown, but this discrepancy is seen in respective experiments persistently and worldwide. This discrepancy, with a high probability, excludes measurement problems and points to a previously unrecognized physical origin. In the following study, a novel, extended concept of special relativity on the grounds of a strictly symmetric Minkowski space is proposed; the concept predicts that the speed of transversal motion will increase with enduring observation time, and it fully explains the measured difference in the average lifetime of beamed and bottled neutrons. According to this novel notion of special... relativity, time and the measurement of translational motion are dependent on one-way or two-way measurement. Furthermore, the existence of an absolute rest frame of nature, indicated through the cosmic microwave background radiation (CMB), has been proposed to exist with the consequence that the true translational, nonaccelerative velocity between two rest frames must be referred to the CMB in the respective rest frame. Finally, the common relativistic origin of the beamed neutron measurement results and the recent measurements of neutrino speed at Fermilab are briefly discussed, as well as some astrophysical discrepancies.