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Register a new userGeneralized Principle of limiting 4-dimensional symmetry.Relativistic length expansion in accelerated system revisited
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In this article, Generalized Principle of limiting 4-dimensional symmetry: The laws of physics in non-inertial frames must display the 4-dimensional symmetry of the Generalized Lorentz-Poincare group in the limit of zero acceleration,is proposed.Classical solution of the relativistic length expansion in general accelerated system revisited.
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A Two-Spaceship Paradox in special relativity is resolved and discussed. We demonstrate a nonstandard resolution to the two-spaceship paradox by explicit calculation using Generalized Principle of limiting 4-dimensional symmetry proposed in previous paper [1].The physical and geometrical meaning of the nonholonomic transformations used in special relativity is determined.
The accelerated expansion of the universe has been established through observations of supernovae, the growth of structure, and the cosmic microwave background. The most popular explanation is Einsteins cosmological constant, or dynamic variations hereof. A recent paper demonstrated that if dark matter particles are endowed with a repulsive force proportional to the internal velocity dispersion of galaxies, then the corresponding acceleration of the universe may follow that of a cosmological constant fairly closely. However, no such long-range force is known to exist. A concrete example of such a force is derived here, by equipping the dark matter particles with two new dark charges. This result lends support to the possibility that the current acceleration of the universe may be explained without the need for a cosmological constant.
In this paper we aim to investigate a deformed relativistic dynamics well-known as Symmetrical Special Relativity (SSR) related to a cosmic background field that plays the role of a variable vacuum energy density associated to the temperature of the expanding universe with a cosmic inflation in its early time and an accelerated expansion for its very far future time. In this scenario, we show that the speed of light and an invariant minimum speed present an explicit dependence on the background temperature of the expanding universe. Although finding the speed of light in the early universe with very high temperature and also in the very old one with very low temperature, being respectively much larger and much smaller than its current value, our approach does not violate the postulate of Special Relativity (SR), which claims the speed of light is invariant in a kinematics point of view. Moreover, it is shown that the high value of the speed of light in the early universe was drastically decreased and increased respectively before the beginning of the inflationary period. So we are led to conclude that the theory of Varying Speed of Light (VSL) should be questioned as a possible solution of the horizon problem for the hot universe.
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the first order of the GUP parameter.
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $hat{A}$ and $hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension of the von Neumann model of measurement, in which two probes interact with the same system proper at two successive times, so we can exhibit how the disturbing effect of the first interaction affects the second measurement. Detecting the statistical properties of the second {em probe} variable $Q_2$ conditioned on the first {em probe} measurement yielding $Q_1$ we obtain information on the statistical distribution of the {em system} variable $b_m$ conditioned on having found the system variable $a_n$ in the interval $delta a$ around $a^{(n)}$. The width of this statistical distribution as function of $delta a$ constitutes an {em uncertainty relation}. We find a general connection of this uncertainty relation with the commutator of the two observables that have been measured successively. We illustrate this relation for the successive measurement of position and momentum in the discrete and in the continuous cases and, within a model, for the successive measurement of a more general class of observables.
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