arXiv subjects
Publications and source records attributed to Jian-Miin Liu.
The Universe owns the electronic radiation of blackbody at temperature 2.725 K, which we call the cosmic electron background. We calculate its radiation spectrum. The energy distribution of number density of electrons in the cosmic electron background becomes zero as energy goes to both zero and infinity. It has one maximum peak near the energy level of 10**(-23) J.
In the framework of the solvable model of cosmology constructed in the Earth-related coordinate system, we derive the modified Hubble law. This law carries the slowly time-varying Hubble parameter. The modified Hubble law eliminates the need for dark energy.
As a note for paper [physics/0505035], this is to make it more clear how we can depend upon Einstein's theory of gravitation and two assumptions of the cosmological principle and perfect fluid, in the so-called Z-approximation, to construct a solvable model of cosmology in the Earth-related coordinate system. Hence, the cosmic acceleration becomes understandable.
In the Earth-related coordinate system, we reconstruct the standard model of cosmology based on the assumption of the cosmological principle and the perfect gas (or fluid). We exactly solve Einstein's field equation involved. The solution consists of three parts respectively on the line element for space-time of the Universe, the value for the cosmological constant and the equation of state for the matter of the Universe.
Relying on the obtained results in Rev.[1](physics/0505035), we derive the formula relating the red-shift of light signals coming from distant galaxies to the distance of these galaxies from us and the time of detecting of these light signals. The red-shift coefficient, instead of the Hubble parameter, is introduced. It varies with time and positive at all times. Its nowadays value equals the Hubble parameter. It increases forever as time is running from the past to the future. The derived formula enables us to estimate the nowadays increasing rate of the red-shift coefficient, which is nothing but the nowadays value of the "acceleration of the expansion of the Universe".
Based on Einstein's theory of gravitation, we discuss the influence of a spherically symmetric gravitational field on Maxwell's law of velocity distribution. We derive the equilibrium velocity distribution of low-energy particles in the spherically symmetric gravitational field and calculate the escape rate of low-energy particles in a container with a leak placed in the spherically symmetric gravitational field. They can serve as the tests of Einstein's theory of gravitation.
In my previous work, physics/0205011, I reported several observations on special relativity, its experimental facts and its relations to quantum mechanics and statistical mechanics. These observations made us conscious: Special relativity is not a ultimate theory; Some modification is needed; Any modification must not violate the principles of the constancy of the light speed and of the local Lorentz invariance; We probably have to change the assumption on local structures of gravity-free space and time in special relativity. Actually, such a kind of modification of special relativity has been already done. The generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system have been proposed. Here, in this lecture, I talk about these structures of gravity-free space and time and their recognized phenomena.
In solar interior, it is the equilibrium velocity distribution of few high-energy protons and nuclei that participates in determining nuclear fusion reaction rates. So, it is inappropriate to use the Maxwellian velocity distribution to calculate the rates of solar nuclear fusion reactions. We have to use the relativistic equilibrium velocity distribution for the purpose. The nuclear fusion reaction rate based on the relativistic equilibrium velocity distribution has a reduction factor with respect to that based on the Maxwellian distribution. The reduction factor depends on the temperature, reduced mass and atomic numbers of the studied nuclear fusion reactions, in other words, it varies with the sort of neutrinos. Substituting the relativistic equilibrium velocity distribution for the Maxwellian distribution is not important for the calculation of solar sound speeds. The relativistic equilibrium velocity distribution, if adopted in standard solar models, will lower solar neutrino fluxes and change solar neutrino energy spectra but maintain solar sound speeds. This velocity distribution is possibly a solution to the solar neutrino problem.
Introducing the primed inertial coordinate system, for each inertial frame of reference, in addition to the usual inertial coordinate system, we assume that gravity-free space and time possess the Euclidean structures in the primed inertial coordinate system and the generalized Finslerian structures in the usual inertial coordinate system. We combine these assumptions with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, to derive the localized Lorentz transformation as a linear transformation between any two usual inertial coordinate systems. Based on this, it is proposed that all laws of physics are locally Lorentz-invariant in the usual inertial coordinate system. As a Lorentz-invariant law of physics must be locally Lorentz-invariant while a locally Lorentz-invariant law is not necessarily Lorentz-invariant, the change from the requirement of Lorentz invariance to that of the local Lorentz invariance on laws of physics provides with a larger acceptable scope to explore these laws.
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.
The Coulomb barrier is in general much higher than thermal energy. Nuclear fusion reactions occur only among few protons and nuclei with higher relative energies than Coulomb barrier. It is the equilibrium velocity distribution of these high-energy protons and nuclei that participates in determining the rate of nuclear fusion reactions. In the circumstance it is inappropriate to use the Maxwellian velocity distribution for calculating the nuclear fusion reaction rate. We use the relativistic equilibrium velocity distribution for this purpose. The rate based on the relativistic equilibrium velocity distribution has a reduction factor with respect to that based on the Maxwellian distribution, which factor depends on the temperature, reduced mass and atomic numbers of the studied nuclear fusion reactions. This signifies much to the solar neutrino problem.
The generalized Finsler geometry, as well as Finsler geometry, is a generalization of Riemann geometry. The generalized Finsler geometry can be endowed with the Cartan connection. The generalized Finsler geometry and its Cartan connection are, as the necessary mathematical tools, involved in our modification of special relativity, which is made by assuming the generalized Finslerian structures of gravity-free space and time in the usual inertial coordinate system and combining this assumption with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference.
We propose a new test of Einstein's theory of gravitation. It concerns the velocity distribution of low-energy particles in a spherically symmetric gravitational field.
In the framework of special relativity, all particles are point-like or string-like. This nature of particles has caused the divergence difficulties in quantum field, string and superstring theories. In the framework of special relativity, due to the non-uniformity of the m-space and phase space in the usual inertial coordinate system, Boltzmann's hypothesis of the equality of the probability of equal volume element is no longer appropriate. That makes it very difficult to construct Lorentz-invariant statistical mechanics and thermodynamics for many-particle systems. Besides, some observations on special relativity itself and its experimental facts are also reported. The conclusions from these observations are: Special relativity is not an ultimate theory; Some modification is needed; Any modification must not violate the constancy of the light speed and the local Lorentz invariance; It seems that we have to change the assumption on local structures of gravity-free space and time in special relativity.
The current standard solar models can be improved by substituting the relativistic equilibrium velocity distribution for the Maxwellian velocity distribution. The relativistic equilibrium velocity distribution is close- fitting to the Maxwellian velocity distribution in the low-velocity part and substantially different from the Maxwellian velocity distribution in the high-velocity part, and vanishes at the velocity of light. If adopted in standard solar models, it will lower solar neutrino fluxes, change solar neutrino energy spectra but maintain solar sound speeds.
The relativistic equilibrium velocity distribution coincides with the Maxwellian distribution for small velocities and vanishes at c, the velocity of light. Based on the decay pattern of high-energy tail in the relativistic equilibrium velocity distribution, it is predicted for velocity and velocity rate distributions of astrophysical plasma particles that they fall off to zero, as velocity goes to c, slower than any exponential decay but faster than any power-law decay.
The relativistic corrections to the Maxwellian velocity distribution are needed for standard solar models. Relativistic equilibrium velocity distribution, if adopted in standard solar models, will lower solar neutrino fluxes and change solar neutrino energy spectra but keep solar sound speeds. It is possibly a solution to the solar neutrino problem.
High energy infers high velocity and high velocity is a concept of special relativity. The Maxwellian velocity distribution is corrected to be consistent with special relativity. The corrected velocity distribution reduces to the Maxwellian distribution for small velocities and vanishes at the velocity of light, and contains a relatively depleted high-energy tail.