A theory of gravity reconciling Mach's Principle and General Relativity (GR) is proposed. At any location, total gravitational potential from the Universe's matter distribution is c². This Universal background potential constitutes unit rest energy of matter and provides its unit mass, which is the essence behind E=mc². The background gravity creates a local sidereal inertial frame at every location. A velocity increases gravitational potential through net blue-shift of Universe's background gravity, causing kinematic time dilation, which is a form of gravitational time dilation. Matter and energy follow different rules of motion, and speed of matter may exceed the speed of light. The theory is consistent with existing relativity experiments, and is falsifiable based on experiments whose predictions differ from GR. The theory also explains why all the ICARUS and corrected OPERA experiments still show mean neutrino velocities slightly above speed of light (early arrival of neutrinos by 0.1-6.5ns), even after correcting the issues that had led to the original OPERA experiments to erroneously report faster than light neutrinos (early arrival by ~60ns).