Time in a Quantum Sensitive Extension of Special Relativity

This paper proposes an extension of special relativity (SR) motivated by the properties of the mathematical continuum in nonstandard analysis of infinitesimals, with a direct impact on the fundamental aspects of quantum physics. The Planck length emerges spontaneously in Minkowski space as a halo around a lightlike point of the actual local present, induced by a hyperbolic metric. The halo generates an event horizon of the point, collapsing under observation/measurement. Unlike virtual black holes, the halo appears as a fundamental property of spacetime, regarded then as quantum foam that evaporates immediately by passing into the past. The extended SR (SRE) entails the following corollaries: (i) the relativity of extended simultaneity, (ii) Bell temporal non-separability, (iii) time vanishes at the cosmological horizon of the universe, (iv) the universe is closed from the inside. There is a complementarity in Bohr’s sense between classical SR and quantum-sensitive SRE by formally endowing the halo with the properties of a complex Hilbert space.