A new theory is proposed in which the Galilean transformations hold and in which the experimental data that appear to support special relativity also support the new theory. We begin by constructing a new theory of light propagation in which the electric field around a source experiences an aerodynamic-like distortion when the source moves through a gravitational field. The Galilean transformations are maintained, the experimental evidence concerning the propagation of light is supported, and new experiments are suggested. It is then postulated that a body\'s inertial mass is related to this field distortion. The result is a new equation for mass in which motion relative to the gravitational fields with the locally dominant field energy densities is the critical factor in determining changes in mass. A field distortion dynamics is then derived according to which a body at the Earth\'s surface, moving at the velocity of light relative to the Earth\'s gravitational field, will have a large but finite energy that varies depending upon the time of day and time of year. At the Earth\'s surface this ?transition energy? has a minimum value of 1.2 ? 105 times the body\'s rest energy, corresponding to an energy of 60 GeV for an electron. Since 1989 the large electron positron (LEP) collider has been operating with a beam energy of 45 GeV. According to the new theory, LEP, operating with beams of 45 GeV, should experience a change in beam energy on the order of 1 MeV/hr throughout the year and, at times, a much larger change on the order of 20 MeV/min. These changes in beam energy may have been observed. According to the new theory, the minimum transition energy per revolution at LEP varies from 60 GeV to 97 GeV depending upon the time of day and time of year. If the minimum transition energy per revolution is exceeded, the electrons in LEP will exceed the velocity of light. LEP II, scheduled to begin operation in 1996, is expected to operate with beams of 90 GeV. With beams of 90 GeV it is predicted that LEP II will accelerate particles to a hyperlight velocity of c (1.000 06). Finally, the relationship between mass and time is examined. It is found that an increase in the mass of a system will result in a slowing of the time that system keeps, provided that the forces governing the system are not mass-dependent. Because motion relative to the gravitational fields with the locally dominant field energy densities is the critical factor in determining changes in mass, the twin paradox does not arise.