Abstract

A unique hyperbolic geometry paradigm requires suspending the Relativistic principle that absolute velocity is unmeasurable. The idea that of two observers each sees the same constant velocity, therefore there is no absolute velocity, is true only because Relativity uses a particular Lorentz geometry. Our mathematical geometry constructs circle and hyperbola vectors with hyperbolic terms in an original formulation of complex numbers. We use a point on a hyperbola as a frame of reference. A theory of time is given. The physical laws of motion by Galileo, Newton and Einstein are forged using the absolute velocity and the precondition to electromagnetic velocity. The field of real and fictitious force accelerations is established. We utilize Galilean Invariance to measure absolute velocity. An experiment exemplifies the math from the Earth’s frame of reference. But Relativity is based on local Lorentz geometry. We discover a possible dark energy and gravitational accelerations and a geometry of gravitational collapse.

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