Size of Atoms in RW Universe: a Correction to Dirac Equation for Curved Space-Time

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Referee this paper: viXra:1510.0138 by Sudesh Kumar Arora

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Dirac equation for curved space-time is solved in Cartesian coordinates giving a result which is contrary to the generally accepted notion in cosmology that space expansion does not impact size of atoms. The solution shows that size of atoms reduces in proportion to the square of scale factor in an expanding universe. Work of McVittie, who solved the same equation with a different result is reviewed, highlighting his mistake and why he got an incorrect result. As the result is completely counter-intuitive a correction to the Dirac equation for curved space-time is attempted, which is desired due to many other reasons as well. The corrected equation when solved, shows that size of atoms changes in proportion to square of scale factor. Same result has been reported earlier as well using Schrödinger equation indicating that correction proposed is in right direction. Gravitational redshift formula is derived using the new equation, which matches with general relativistic prediction. The new equation proposed in this paper is thus indeed correct Dirac equation for curved space-time. Validity of standard model of cosmology is questioned due to this discovery.