A novel perspective on relativistic transformation recently-proposed providesan insight into the very meaning of the principle of relativity. With thisnovel perspective and Bell's theorem, we argue that special relativity, insteadof quantum theory, should be radically reformulated to resolve inconsistenciesbetween the two theories. A new theory of relativistic quantum mechanics isformulated upon this novel perspective. This new relativistic quantum mechanicsis free from such anomalies as the negative probability density, thenegative-energy states, Zitterbewegung, and the Klein paradox deep-rooted inthe current relativistic quantum mechanics. Moreover, a remarkable result isfound that a particle can not be confined within an infinite square well ofwidth less than half of the Compton wavelength. As implications in nuclearphysics, there is a lower bound on the size of atomic nucleus. Neither anelectron, nor a positron, can be confined inside the nucleus by whateverinteraction. Furthermore, we argue that the postulates of non-relativistic quantumstatistics fulfill the principle of relativity, as extended to the relativisticrealm. A new theory of relativistic quantum statistics is formulated such thatthe probability distribution functions are the same as the three well-knownprobability distribution functions in non-relativistic quantum statistics. Arelativistic speed distribution of a dilute gas is then derived by the newrelativistic quantum statistics and the new relativistic quantum mechanics.This relativistic speed distribution reduces to Maxwell speed distribution inthe low temperature region. Yet, this relativistic speed distribution differsremarkably from J\"uttner speed distribution in the high temperature region.Also, thermal properties of a dilute gas are studied by the new relativisticquantum statistics.
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