The special theory of relativity

Symmetry groups and the pseudo-Riemann spacetimes for mixed-hardening elastoplasticity

A modified group-preserving scheme for solving the initial value problems of stiff ordinary differential equations

The main purpose of this paper is to demonstrate that the analysis of the kinematical effects of special relativity holds the key to answering the question of the dimensionality of the world. It is shown that these effects and the experiments which confirmed them would be impossible if the world were three-dimensional. Section 2 shows that relativity of simultaneity, conventionality of simultaneity, and the existence of accelerated observers in special relativity would be impossible if the world were three-dimensional. Section 3 deals with the dimensionality of physical objects and demonstrates that the relativistic length contraction and the twin paradox would be impossible if the physical bodies involved in these relativistic effects were three-dimensional objects.

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Relativity, Dimensionality, and Existence

Even though there have been the various varying speed of light (VSL) cosmology models, they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable theory, it should inherit the success of special relativity including Maxwell equations and thermodynamics at least. Thus, we adopt that the speed of light, $\tilde c$ varies for the cosmic time not for the local time, i.e., $\tilde c[z]$ where $z$ is the cosmological redshift. When one describes the background FLRW universe, one can define the constant-time hypersurface by using physical quantities such as temperature, density, and $\tilde c$. It is because they evolve in time, and the homogeneity of the Universe demands that they must equal at the equal cosmic time. The variation of $\tilde c$ accompanies the joint variations of all related physical constants in order to satisfy the Lorentz invariance, thermodynamics, and Bianchi identity. We call this VSL model as a "minimally extended VSL (meVSL)". We derive cosmological observables of meVSL and obtain the constraints on the variation of $\tilde c$ by using the current observations. Interestingly, $z$ and all geometrical distances except the luminosity distance of meVSL are the same as those of general relativity. However, the Hubble parameter of meVSL is rescaled as $H = (1+z)^{-b/4} H^{(\rm GR)}$ which might be used as a solution for the tension of the Hubble parameter measurements. In this manuscript, we provide the main effects of meVSL on various cosmological observations including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and $\Delta \alpha$.

background

The minimally extended Varying Speed of Light (meVSL)

Projecting the linear equation X = AX , A ∈ so (n, 1) , yields a primitive model It is a prototype of several physical models, namely perfect elastoplasticity (on phase), spacetime of special relativity, special relativistic mechanics and so on, all of which may endow a Minkowskian spacetime and the Lorentz group left acts on it The mathematical structure of the perfect elastoplastic equations is then compared with those of the spacetime of special relativity and of the special relativistic equations of motion of a massive charged particle; their similarities in group properties and subtle differences in phase spaces are discussed It is remarkable that the evolutions from elastic constitutive equations to elastoplastic constitutive equations and from the Newtonian equations to the special relativistic equations are very similar in several facets, notably (a) from a linear theory to a non-linear theory, (b) the state space being enlarged from the usual Euclidean space to Minkowski spacetime, (c) from an n-space to a cone of (n+1)-space, (d) from a non-bounded state space to a bounded state space, (e) from a non-causal relation of states to a causal relation of augmented states

The special theory of relativity

Citations

Symmetry groups and the pseudo-Riemann spacetimes for mixed-hardening elastoplasticity

A modified group-preserving scheme for solving the initial value problems of stiff ordinary differential equations

Relativity, Dimensionality, and Existence

The minimally extended Varying Speed of Light (meVSL)

Some physical models with Minkowski spacetime structure and Lorentz group symmetry

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