Time Variation of Photons' Velocity in a "Dark" Universe
We discuss the non-minimal interaction between gravitation and electromagnetism. It is shown that the velocity of photons varies with time in a Universe with zero matter density, zero cosmological constant but is filled only with “dark matter”. One of the great physical problems of this century is to unify general relativity and quantum mechanics. Together they can explain a vast storehouse of physical knowledge, from the subatomic realm to the large-scale structure of the universe. However, attempts to unify quantum mechanics with general relativity have all met with frustration. Ideally, we could like to see gravitational interactions and GUT theory emerge from a higher unified field theory from geometrical or group theoretical arguments, rather than being put in by hand. The search for a more sophisticated theory embracing both guage theory and general relativity has led to a re-examination of the old theory of Kaluza-Klein. Kaluza [1] originally proposed uniting both Maxwell’s theory of electromagnetism and Einstein’s theory of general relativity by embeding both theories into a generally covarient fivedimensional space-time. Kaluza assumed that the fifth dimension was curled up into a tiny ring so small that it could not be experimentally observed by any instrument. Klein [2] then assumed that quantum corrections caused the fifth dimension to curl up. In quantum gravity, there is only one dimensionful parameter, which is the Planck length, or 10 cm. Since this sets the scale for quantum gravity, it means that the fifth dimension might have curled up with approximately this radius, which is