The Meaning of Relativity
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 "Reparametrization invariance is an essential ingredient of many fundamental theories of physics, including particle models, general relativity, supergravity and string theory [1] [2] [3] [4] [5] [6]. An important consequence of this large local symmetry is the imposition of constraints, especially the hamiltonian constraint restricting the dynamics to a fixed hypersurface in phase space, characterized by the vanishing of the hamiltonian [7] [8] [9]. "
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ABSTRACT: The construction of physical models with local timereparametrization invariance is reviewed. Negativeenergy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant HamiltonJacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the FriedmannLemaitreRobertsonWalker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a $\sg$model on some scalar manifold. An explicit gaugeinvariant solution is constructed for the nonlinear O(N)models.Fortschritte der Physik 07/2014; 62(7). DOI:10.1002/prop.201400008 · 1.23 Impact Factor 
 "However, there are different viewpoints on how physical laws should be formulated in order to fulfill the principle of relativity [43] [44] [45] [46]. The most accepted viewpoint is the Lorentz covariance criterion – to fulfill the principle of relativity, the mathematical formula of a physical law must be Lorentz covariant under the LT of spacetime coordinates [42] [47] [48]. Nonetheless, as mentioned previously in Sec. "
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ABSTRACT: A novel perspective on relativistic transformation recentlyproposed provides an insight into the very meaning of the principle of relativity. With this novel perspective and Bell's theorem, we argue that special relativity, instead of quantum theory, should be radically reformulated to resolve inconsistencies between those two theories. A new theory of relativistic quantum mechanics is formulated upon this novel perspective. This new relativistic quantum mechanics is free from such anomalies as the negative probability density, the negativeenergy states, Zitterbewegung, and the Klein paradox deeprooted in the current relativistic quantum mechanics. Moreover, a remarkable result is found that a particle can not be confined within an infinite square well of width less than half of the Compton wavelength. As implications in nuclear physics, there is a lower bound on the size of atomic nucleus. Neither an electron, nor a positron, can be confined inside the nucleus by whatever interaction. Furthermore, with this novel perspective, we argue that the postulates of nonrelativistic quantum statistics fulfill the principle of relativity, as extended to the relativistic realm. A new theory of relativistic quantum statistics is formulated such that the probability distribution functions are the same as the wellknown MaxwellBoltzmann, FermiDirac and BoseEinstein distribution functions in nonrelativistic quantum statistics. A relativistic speed distribution of a dilute gas is then derived by the new relativistic quantum statistics and the new relativistic quantum mechanics. This relativistic speed distribution reduces to Maxwell speed distribution in the low temperature region. Yet, this relativistic speed distribution differs remarkably from Jüttner speed distribution in the high temperature region. Also, thermal properties of a dilute gas are studied by the new relativistic quantum statistics. PACS numbers: Quantum mechanics, 03.65.w; Special relativity, 03.30.+p; Entanglement and quantum nonlocality, 03.65.Ud; Foundations of quantum mechanics, 03.65.Ta; Philosophy of science, 01.70.+w, *43.10.Mq; Nuclear models, 21.60.n; theory of quantized field, 03.70; 05.30d quantum statistical mechanics; 05.20y classical statistical mechanics. Keywords: conflict between quantum theory and special relativity, quantum theory, special relativity, the principle of relativity, Lorentz covariance, nonlocality, indeterminacy, Bell inequality, entanglement, realism, completeness, quantum mechanics, relativistic quantum theory, Klein paradox, Zitterbewegung, relativistic quantum field theory, KleinGordon theory, Dirac theory, Atomic nucleus, relativistic quantum statistics, relativistic statistical physics, relativistic kinetic theory. 
 "We see that the source contains elements of metric tensor. This is in accord with the conclusion of Mach's principle [3] [5] which says that the inert mass of a mass body depends on the magnitude and mutual distance of the neighbouring mass distribution. Thus, from the point of view of Mach's principle, Rastall's field equations seem to be more " Machian " than those of the Einstein general relativity. "
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