Functions of State for Spinor Gas in General Relativity

The energy momentum tensor of perfect fluid is a simplified but successful model in astrophysics. In this paper, assuming the particles driven by gravity and moving along geodesics, we derived the functions of state in detail. The results show that, these functions have a little correction for the usual thermodynamics. The new functions naturally satisfy the causal condition and consist with relativity. For the self potentials of the particles we introduce an extra function $W$, which acts like negative pressure and can be used to describe dark matter. The results are helpful to understand the relation and interaction between space-time and matter.Comment: 13 pages, no figure. arXiv admin note: text overlap with arXiv:0708.296

Nonlinear Spinors as the Candidate of Dark Matter

In this paper, we discuss the equation of state for nonlinear spinor gases in the context of cosmology. The mean energy momentum tensor is similar to that of the prefect fluid, but an additional function of state $W$ is introduced to describe the nonlinear potential. The equation of state $w(a)\lesssim -1$ in the early universe is calculated, which provides a natural explanation for the negative pressure of dark matter and dark energy. $W$ may be also the main origin of the cosmological constant $\Lambda$. So the nonlinear spinor gases may be a candidate for dark matter and dark energy.Comment: 8 pages, no figure

Test of Einstein's Mass-Energy Relation

The Einstein's mass-energy relation $E=mc^2$ is one of the most fundamental formulae in physics, but it has not been seriously tested by an elaborated experiment, and only some indirect evidences in nuclear reaction suggested that it holds to high precision. Manifestly, for a particle, different self potential leads to different energy-speed relation, which can be used as the fingerprints of them. In this letter, we propose an experiment to test this relation. The experiment only involves low energy of particles and measurement of speed, which can be easily realized. The experiment may shed lights on a number of fundamental puzzles in physics.Comment: 6 pages, 1 figur