Three Roads to Quaternion Gravity

Three roads merge to create a different approach to gravity. Our deepest insights into nature use symmetries because symmetries remain unchanged. Using quaternion algebra instead of tensor calculus, the conservation of space-times-time is the symmetry underlying the quaternion gravity proposal for non-inertial observers in a gravitational field. Where there is a symmetry, there need also be a transformation law to detail how change is permitted to happen. The notion of relaxed relativity holds that in a gravitational field, one observer looking at another observer measuring the speed of light will find the product of wavelength and frequency differs from the speed of light c in a precise way (c'=cγ²_esc). Lorentz invariance remains for inertial observers, but non-inertial observers are governed by different symmetries. Gravity is different everywhere, so a field theory is also necessary using gravitational escape velocities. With some reasonable guesses constrained by observations, one can form a quaternion gravity proposal that is consistent with weak field gravity tests to first order Parameterize Post Newtonian accuracy. No gravitons are required for this technical variant of special relativity. Pre-print available on line: http://bit.ly/vp-three-roads